Finite Group Databasebeta

← #17200124

Subgroups — #17200124

Order 4352.

2544 conjugacy classes of subgroups.

The subgroup lattice has 1656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763548C211yesmaximal, characteristic
2#14531923C211yesmaximal, characteristic, complemented
3#14531923C211yesmaximal, characteristic, complemented
4#14531912C211yesmaximal, characteristic, complemented
5#14531911C211yesmaximal, characteristic, complemented
6#14531902C211yesmaximal, characteristic, complemented
7#14531845C211yesmaximal, characteristic, complemented
8#14531833C211yesmaximal, characteristic, complemented
9#14531832C211yesmaximal, characteristic, complemented
10#14531819C211yesmaximal, characteristic, complemented
11#14531817C211yesmaximal, characteristic, complemented
12#14531805C211yesmaximal, characteristic, complemented
13#14531797C211yesmaximal, characteristic, complemented
14#14531782C211yesmaximal, characteristic, complemented
15#14531773C211yesmaximal, characteristic, complemented
16#14531581C211yesmaximal, characteristic, complemented
17#14531571C211yesmaximal, characteristic, complemented
18#14531557C211yesmaximal, characteristic, complemented
19#14531556C211yesmaximal, characteristic, complemented
20#14531547C211yesmaximal, characteristic, complemented
21#14531545C211yesmaximal, characteristic, complemented
22#14531505C211yesmaximal, characteristic, complemented
23#14531488C211yesmaximal, characteristic, complemented
24#14531485C211yesmaximal, characteristic, complemented
25#14531480C211yesmaximal, characteristic, complemented
26#14531470C211yesmaximal, characteristic, complemented
27#14531454C211yesmaximal, characteristic, complemented
28#120×Dic17C211yesmaximal, characteristic, complemented
29#14531283C211yesmaximal, characteristic, complemented
30#14531283C211yesmaximal, characteristic, complemented
31C17×#2375C211yesmaximal, characteristic, complemented
32C24×Dic17C2211yescharacteristic
33#11763548C4116yescomplemented
34C2×#10587626C2211yescharacteristic
35C2×#10587565C2211yescharacteristic
36C2×#10587565C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587621C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587625C2211yescharacteristic
44C2×#10587624C2211yescharacteristic
45C2×#10587624C2211yescharacteristic
46C2×#10587639C2211yescharacteristic
47C2×#10587639C2211yescharacteristic
48C2×C4×D68C2211yescharacteristic, complemented
49C2×D4×Dic17C2211yescharacteristic
50C2×D4×Dic17C2211yescharacteristic
51C2×D4×Dic17C2211yescharacteristic
52C2×C4×C22⋊D17C2211yescharacteristic, complemented
53C2×#10587567C2211yescharacteristic
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic
56C2×#10587567C2211yescharacteristic
57C2×#10587567C2211yescharacteristic
58C2×#10587567C2211yescharacteristic
59C2×#10587567C2211yescharacteristic, complemented
60C2×#10587558C2211yescharacteristic, complemented
61C2×#10587563C2211yescharacteristic, complemented
62C2×C4⋊C4×D17C2211yescharacteristic, complemented
63#11762710C2211yescharacteristic, complemented
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic
68#11762709C2211yescharacteristic
69#11762709C2211yescharacteristic
70#11762709C2211yescharacteristic, complemented
71#11762709C2211yescharacteristic, complemented
72#11762707C2211yescharacteristic, complemented
73#11762706C2211yescharacteristic, complemented
74#11762705C2211yescharacteristic, complemented
75#11762704C2211yescharacteristic, complemented
76#11762704C2211yescharacteristic, complemented
77#11762704C2211yescharacteristic, complemented
78#11762703C2211yescharacteristic
79#11762703C2211yescharacteristic
80#11762703C2211yescharacteristic
81#11762703C2211yescharacteristic
82#11762703C2211yescharacteristic
83#11762703C2211yescharacteristic
84#11762701C2211yescharacteristic, complemented
85#11762700C2211yescharacteristic, complemented
86#11762699C2211yescharacteristic, complemented
87#11762698C2211yescharacteristic, complemented
88#11762697C2211yescharacteristic
89#11762697C2211yescharacteristic
90#11762697C2211yescharacteristic
91#11762697C2211yescharacteristic
92#11762697C2211yescharacteristic
93#11762697C2211yescharacteristic
94#11762697C2211yescharacteristic, complemented
95#11762697C2211yescharacteristic, complemented
96#11762696C2211yescharacteristic, complemented
97#11762696C2211yescharacteristic, complemented
98#11762696C2211yescharacteristic, complemented
99#11762694C2211yescharacteristic, complemented
100#11762694C2211yescharacteristic, complemented
101#11762693C2211yescharacteristic, complemented
102#11762692C2211yescharacteristic, complemented
103#11762692C2211yescharacteristic, complemented
104#11762691C2211yescharacteristic, complemented
105#11762691C2211yescharacteristic, complemented
106#11762691C2211yescharacteristic, complemented
107#11762690C2211yescharacteristic, complemented
108#11762689C2211yescharacteristic
109#11762689C2211yescharacteristic
110#11762689C2211yescharacteristic
111#11762688C2211yescharacteristic, complemented
112#11762687C2211yescharacteristic, complemented
113#11762687C2211yescharacteristic, complemented
114#11762686C2211yescharacteristic
115#11762686C2211yescharacteristic
116#11762686C2211yescharacteristic
117#11762686C2211yescharacteristic
118#11762686C2211yescharacteristic
119#11762686C2211yescharacteristic
120#11762686C2211yescharacteristic, complemented
121#11762685C2211yescharacteristic
122#11762685C2211yescharacteristic
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic
125#11762685C2211yescharacteristic
126#11762685C2211yescharacteristic
127#11762685C2211yescharacteristic, complemented
128#11762685C2211yescharacteristic, complemented
129#11762684C2211yescharacteristic
130#11762684C2211yescharacteristic
131#11762684C2211yescharacteristic
132#11762683C2211yescharacteristic, complemented
133#11762681C2211yescharacteristic
134#11762681C2211yescharacteristic
135#11762681C2211yescharacteristic
136#11762681C2211yescharacteristic
137#11762681C2211yescharacteristic
138#11762681C2211yescharacteristic
139#11762681C2211yescharacteristic, complemented
140#11762680C2211yescharacteristic, complemented
141#11762673C2211yescharacteristic, complemented
142#11762671C2211yescharacteristic, complemented
143#11762667C2211yescharacteristic, complemented
144#11762666C2211yescharacteristic, complemented
145#11762665C2211yescharacteristic
146C4⋊C4×Dic17C2211yescharacteristic, complemented
147C4⋊C4×Dic17C2211yescharacteristic, complemented
148C4×#63225C2211yescharacteristic, complemented
149C4×#63225C2211yescharacteristic, complemented
150C4×#63225C2211yescharacteristic, complemented
151C4×#63225C2211yescharacteristic, complemented
152C4×C4⋊Dic17C2211yescharacteristic, complemented
153#11762660C2211yescharacteristic, complemented
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C22⋊C4×Dic17C2211yescharacteristic
162C22⋊C4×Dic17C2211yescharacteristic
163C22⋊C4×Dic17C2211yescharacteristic, complemented
164C4×#63227C2211yescharacteristic, complemented
165C4×#63227C2211yescharacteristic, complemented
166C4×C22⋊Dic17C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic, complemented
170#11762654C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#120C2211yescharacteristic
174C17×#390C2211yescharacteristic
175C17×#390C2211yescharacteristic
176C17×#390C2211yescharacteristic
177C17×#388C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#388C2211yescharacteristic
181C17×#388C2211yescharacteristic
182C17×#388C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#379C2211yescharacteristic
187C17×#379C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C23×Dic17—42no—
202C23×Dic17—42no—
203C23×Dic17—42no—
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C22×D68C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C17×#120C2×C418yescomplemented
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C42×C17C2311yescharacteristic
242C2×C42×C17C2311yescharacteristic
243C2×C42×C17C2311yescharacteristic
244#10587639C2×C418yescomplemented
245#10587639C2×C418yescomplemented
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262#10587626C2×C418yescomplemented
263#10587625C2×C418yescomplemented
264#10587625C2×C418yescomplemented
265#10587624C2×C418yescomplemented
266#10587624C2×C418yescomplemented
267#10587621C2×C418yescomplemented
268D4×Dic17—42no—
269D4×Dic17—42no—
270D4×Dic17—42no—
271C4×C22⋊D17—42no—
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C4⋊C4×D17—42no—
324#10587570C2×C418yescomplemented
325#10587570C2×C418yescomplemented
326#10587569C2×C418yescomplemented
327#10587569C2×C418yescomplemented
328#10587567—42no—
329#10587567—42no—
330#10587567—42no—
331#10587567—42no—
332#10587567—42no—
333#10587567—42no—
334#10587567—42no—
335#10587565C2×C418yescomplemented
336#10587565C2×C418yescomplemented
337#10587563—42no—
338C4×D68—42no—
339#10587558—42no—
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376C24×C17—41no—
377C24×C17—41no—
378C24×C17—41no—
379C24×C17—41no—
380C24×C17—41no—
381C24×C17—41no—
382C24×C17C22×C414yes—
383C24×C17C2411yescharacteristic
384C24×C17C2411yescharacteristic
385C24×C17C2411yescharacteristic
386C24×C17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C23×D17C2411yescharacteristic
389C2×D4×C17—41no—
390C2×D4×C17—41no—
391C2×D4×C17—41no—
392C2×D4×C17—41no—
393C2×D4×C17—41no—
394C2×D4×C17—41no—
395C2×D4×C17C22×C414yes—
396C2×D4×C17C22×C414yes—
397C2×D4×C17C22×C414yes—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C2×C22⋊D17—41no—
413C2×C22⋊D17—41no—
414C2×C22⋊D17—41no—
415C2×C22⋊D17—41no—
416C2×C22⋊D17—41no—
417C2×C22⋊D17—41no—
418C2×C22⋊D17—41no—
419C2×C22⋊D17—41no—
420C2×C22⋊D17—41no—
421C2×C22⋊D17—41no—
422C2×C22⋊D17—41no—
423C2×C22⋊D17—41no—
424C2×C22⋊D17—41no—
425C2×C22⋊D17—41no—
426C2×C22⋊D17—41no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17C22×C414yes—
429C2×C22⋊D17C22×C414yes—
430C2×C22⋊D17C22×C414yes—
431C2×C22⋊D17C22×C414yes—
432C2×C22⋊D17C22×C414yes—
433C2×C22⋊D17C22×C414yes—
434C2×C22⋊D17C22×C414yescomplemented
435C2×C22⋊D17C22×C414yescomplemented
436C22×Dic17—22no—
437C22×Dic17—22no—
438C22×Dic17—22no—
439C22×Dic17—22no—
440C22×Dic17—22no—
441C22×Dic17—22no—
442C22×Dic17—22no—
443C22×Dic17—22no—
444C22×Dic17—22no—
445C22×Dic17—22no—
446C22×Dic17—41no—
447C22×Dic17—41no—
448C22×Dic17—41no—
449C22×Dic17—41no—
450C22×Dic17—41no—
451C22×Dic17—41no—
452C22×Dic17—41no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17—41no—
459C22×Dic17—416no—
460C22×Dic17C22×C414yescomplemented
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C2×D68—41no—
476C2×D68—41no—
477C2×D68C22×C414yescomplemented
478C2×C4×D17—22no—
479C2×C4×D17—22no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17—41no—
485C2×C4×D17—41no—
486C2×C4×D17—41no—
487C2×C4×D17—41no—
488C2×C4×D17—41no—
489C2×C4×D17—41no—
490C2×C4×D17—41no—
491C2×C4×D17—41no—
492C2×C4×D17—41no—
493C2×C4×D17—41no—
494C2×C4×D17C22×C414yescomplemented
495C2×C4×D17C22×C414yescomplemented
496C4⋊C4×C17—41no—
497C4⋊C4×C17—41no—
498C4⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17—41no—
501C22⋊C4×C17—41no—
502C22⋊C4×C17—41no—
503C22⋊C4×C17—41no—
504C22⋊C4×C17—41no—
505C22⋊C4×C17—41no—
506C22⋊C4×C17—41no—
507C22⋊C4×C17—41no—
508C22⋊C4×C17—41no—
509C22⋊C4×C17—41no—
510C22⋊C4×C17—41no—
511C22⋊C4×C17—41no—
512C22⋊C4×C17—41no—
513C22⋊C4×C17—41no—
514C22⋊C4×C17C22×C414yes—
515C22⋊C4×C17C22×C414yes—
516C22⋊C4×C17C22×C414yes—
517C42×C17—41no—
518C42×C17—41no—
519C42×C17—41no—
520C22⋊Dic17—22no—
521C22⋊Dic17—22no—
522C22⋊Dic17—41no—
523C22⋊Dic17—41no—
524C22⋊Dic17—41no—
525C22⋊Dic17—41no—
526C22⋊Dic17—41no—
527C22⋊Dic17—41no—
528C22⋊Dic17—41no—
529C22⋊Dic17C22×C414yes—
530C22⋊Dic17C22×C414yes—
531C22⋊Dic17C22×C414yes—
532C22⋊Dic17C22×C414yes—
533C22⋊Dic17C22×C414yes—
534C22⋊Dic17C22×C414yes—
535C22⋊Dic17C22×C414yescomplemented
536#63227—22no—
537#63227—22no—
538#63227—22no—
539#63227—22no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545#63227—41no—
546#63227—41no—
547#63227—41no—
548#63227C22×C414yescomplemented
549#63227C22×C414yescomplemented
550C4⋊Dic17—22no—
551C4⋊Dic17—22no—
552C4⋊Dic17—41no—
553C4⋊Dic17C22×C414yescomplemented
554C4⋊Dic17C22×C414yescomplemented
555#63225—22no—
556#63225—22no—
557#63225—22no—
558#63225—22no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225C22×C414yescomplemented
568#63225C22×C414yescomplemented
569#63225C22×C414yescomplemented
570#63225C22×C414yescomplemented
571C4×Dic17—22no—
572C4×Dic17—22no—
573C4×Dic17—22no—
574C4×Dic17—41no—
575C4×Dic17—41no—
576C4×Dic17—41no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17—41no—
581C4×Dic17—41no—
582C4×Dic17—41no—
583C4×Dic17—41no—
584C4×Dic17—41no—
585C4×Dic17—41no—
586C4×Dic17C22×C414yescomplemented
587#34511—171nomaximal, Sylow
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—21no—
612C23×C17—44no—
613C23×C17—44no—
614C23×C17—44no—
615C23×C17—44no—
616C23×C17—44no—
617C23×C17—44no—
618C23×C17—44no—
619C23×C17C23×C412yes—
620C23×C17C23×C412yes—
621C23×C17C23×C412yes—
622C23×C17C23×C412yes—
623C23×C17C2511yescharacteristic
624C22×D17—21no—
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
628C22×D17—21no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17C23×C412yes—
637C22×D17C23×C412yes—
638D4×C17—44no—
639D4×C17—44no—
640D4×C17—44no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—82no—
672C2×C4×C17C23×C412yes—
673C2×C4×C17C23×C412yes—
674C2×C4×C17C23×C412yes—
675C22⋊D17—44no—
676C22⋊D17—44no—
677C22⋊D17—44no—
678C22⋊D17—44no—
679C22⋊D17—44no—
680C22⋊D17—44no—
681C22⋊D17—44no—
682C22⋊D17—44no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—44no—
717C2×Dic17—44no—
718C2×Dic17—44no—
719C2×Dic17—44no—
720C2×Dic17—44no—
721C2×Dic17—44no—
722C2×Dic17—44no—
723C2×Dic17—82no—
724C2×Dic17C23×C412yes—
725C2×Dic17C23×C412yes—
726C2×Dic17C23×C412yes—
727C2×Dic17C23×C412yes—
728C2×Dic17C23×C412yes—
729C2×Dic17C23×C412yes—
730C2×Dic17H(5,𝔽2)12yes—
731C2×Dic17H(5,𝔽2)12yes—
732C2×Dic17H(5,𝔽2)12yes—
733D68—44no—
734C4×D17—44no—
735C4×D17—44no—
736C4×D17—82no—
737C4×D17—82no—
738C4×D17—82no—
739C4×D17—82no—
740C2×#560—171no—
741#2375—171no—
742#2375—171no—
743#2375D1711yescharacteristic, complemented
744#2374—171no—
745#2373—171no—
746#2373—171no—
747#2366—171no—
748#2364—171no—
749#2364—171no—
750#2363—171no—
751#2363—171no—
752#2361—171no—
753#2361—171no—
754#2359—171no—
755#2359—171no—
756#2335—171no—
757#2335—171no—
758#2334—171no—
759#2334—171no—
760#2333—171no—
761#2333—171no—
762#2328—171no—
763#2325—171no—
764#2325—171no—
765#2324—171no—
766#2324—171no—
767#2322—171no—
768C4×#120—171no—
769C4×#120—171no—
770C4×#120—171no—
771C22×C17—22no—
772C22×C17—22no—
773C22×C17—22no—
774C22×C17—22no—
775C22×C17—22no—
776C22×C17—22no—
777C22×C17—22no—
778C22×C17—22no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—416no—
784C22×C17—41no—
785C22×C17—41no—
786C22×C17—41no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17—41no—
792C22×C17—41no—
793C22×C17—41no—
794C22×C17—41no—
795C22×C17—41no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17C24×C411yescharacteristic
801C22×C17C2×H(5,𝔽2)11yescharacteristic
802C22×C17C2×H(5,𝔽2)11yescharacteristic
803C22×C17C2×H(5,𝔽2)11yescharacteristic
804C22×C17#58511yescharacteristic
805C22×C17#58511yescharacteristic
806C22×C17#58511yescharacteristic
807C2×D17—22no—
808C2×D17—22no—
809C2×D17—22no—
810C2×D17—22no—
811C2×D17—22no—
812C2×D17—22no—
813C2×D17—41no—
814C2×D17—41no—
815C2×D17—41no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—41no—
820C2×D17—41no—
821C4×C17—22no—
822C4×C17—22no—
823C4×C17—22no—
824C4×C17—41no—
825C4×C17—41no—
826C4×C17—41no—
827C4×C17—41no—
828C4×C17—41no—
829C4×C17—41no—
830C4×C17—41no—
831C4×C17—41no—
832Dic17—22no—
833Dic17—22no—
834Dic17—22no—
835Dic17—22no—
836Dic17—22no—
837Dic17—22no—
838Dic17—22no—
839Dic17—22no—
840Dic17—22no—
841Dic17—41no—
842Dic17—41no—
843Dic17—41no—
844Dic17—41no—
845Dic17—41no—
846C24×C4—171no—
847#560—1716no—
848C2×#127—171no—
849C2×#126—171no—
850C2×#126—171no—
851C2×#123—171no—
852C2×#123—171no—
853C2×#123—171no—
854C2×#121—171no—
855C2×#121—171no—
856C2×#121—171no—
857C2×#121—171no—
858C2×#121—171no—
859C2×#121—171no—
860C2×#120—171no—
861C2×#120—171no—
862C2×#120C2×D1711yescharacteristic
863C2×C4×D4—171no—
864C2×C4×D4—171no—
865C2×C4×D4—171no—
866C2×C4×D4—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×C4×D4—171no—
870C2×C4×D4—171no—
871C2×C4×D4—171no—
872C2×C4×D4—171no—
873C2×C4×D4—171no—
874C2×C4×D4—171no—
875C2×#117—171no—
876C2×#117—171no—
877C22×C4⋊C4—171no—
878#390—171no—
879#390—171no—
880#390—171no—
881#390—171no—
882#390—171no—
883#390—171no—
884#390—171no—
885#390—171no—
886#390—171no—
887#390C2×D1711yescharacteristic
888#390C2×D1711yescharacteristic
889#390C2×D1711yescharacteristic
890#389—171no—
891#389—171no—
892#389—171no—
893#389—171no—
894#389—171no—
895#389—171no—
896#388—171no—
897#388—171no—
898#388—171no—
899#388—171no—
900#388—171no—
901#388—171no—
902#388—171no—
903#388—171no—
904#388—171no—
905#388—171no—
906#388—171no—
907#388—171no—
908#388—171no—
909#388—171no—
910#388—171no—
911#388—171no—
912#388—171no—
913#388—171no—
914#388C2×D1711yescharacteristic
915#388C2×D1711yescharacteristic
916#388C2×D1711yescharacteristic
917#388C2×D1711yescharacteristic
918#388C2×D1711yescharacteristic
919#388C2×D1711yescharacteristic
920#387—171no—
921#387—171no—
922#387—171no—
923#387—171no—
924#387—171no—
925#387—171no—
926#387—171no—
927#387—171no—
928#387—171no—
929#387—171no—
930#387—171no—
931#387—171no—
932#386—171no—
933#386—171no—
934#386—171no—
935#386—171no—
936#386—171no—
937#386—171no—
938#386—171no—
939#386—171no—
940#386—171no—
941#386—171no—
942#386—171no—
943#386—171no—
944#386—171no—
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386—171no—
953#386C2×D1711yescharacteristic
954#386C2×D1711yescharacteristic
955#386C2×D1711yescharacteristic
956#385—171no—
957#385—171no—
958#385—171no—
959#385—171no—
960#385—171no—
961#385—171no—
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385—171no—
968#382—171no—
969#381—171no—
970#380—171no—
971#380—171no—
972#379—171no—
973#379C2×D1711yescharacteristic
974#379C2×D1711yescharacteristic
975C4×C4⋊C4—171no—
976C4×C4⋊C4—171no—
977C4×C4⋊C4—171no—
978C4×C4⋊C4—171no—
979C4×C4⋊C4—171no—
980C4×C4⋊C4—171no—
981C4×C4⋊C4—171no—
982C4×C4⋊C4—171no—
983C4×C22⋊C4—171no—
984C4×C22⋊C4—171no—
985C4×C22⋊C4—171no—
986C4×C22⋊C4—171no—
987C4×C22⋊C4—171no—
988C4×C22⋊C4—171no—
989C4×C22⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992C4×C22⋊C4—171no—
993C4×C22⋊C4—171no—
994C4×C22⋊C4—171no—
995C4×C22⋊C4—171no—
996C4×C22⋊C4—171no—
997C4×C22⋊C4—171no—
998C4×C22⋊C4—171no—
999#376—171no—
1000C2×#95—171no—
1001C2×#95—171no—
1002C2×C17—42no—
1003C2×C17—42no—
1004C2×C17—42no—
1005C2×C17—42no—
1006C2×C17C4×H(5,𝔽2)11yescharacteristic
1007C2×C17C4×H(5,𝔽2)11yescharacteristic
1008C2×C17C4×H(5,𝔽2)11yescharacteristic
1009C2×C17#353211yescharacteristic
1010C2×C17#353911yescharacteristic
1011C2×C17#353911yescharacteristic
1012C2×C17#354011yescharacteristic
1013D17—42no—
1014D17—42no—
1015C25C22×D1711yescharacteristic
1016C22×D4—171no—
1017C22×D4—171no—
1018C22×D4—171no—
1019C22×D4—171no—
1020C22×D4—171no—
1021C22×D4—171no—
1022C22×D4—171no—
1023C22×D4—171no—
1024C22×D4—171no—
1025C22×D4C22×D1711yescharacteristic
1026C22×D4C22×D1711yescharacteristic
1027C22×D4C22×D1711yescharacteristic
1028C23×C4—171no—
1029C23×C4—171no—
1030C23×C4—171no—
1031C23×C4—171no—
1032C23×C4—171no—
1033C23×C4—171no—
1034C23×C4—171no—
1035C23×C4—171no—
1036C23×C4—171no—
1037C23×C4—171no—
1038C23×C4—171no—
1039C23×C4—171no—
1040C23×C4—171no—
1041C23×C4—171no—
1042C23×C4—682no—
1043C23×C4—682no—
1044C23×C4—682no—
1045C23×C4C22×D1711yescharacteristic
1046#127—178no—
1047#126—178no—
1048#126—178no—
1049#123—178no—
1050#123—178no—
1051#123—178no—
1052#121—178no—
1053#121—178no—
1054#121—178no—
1055#121—178no—
1056#121—178no—
1057#121—178no—
1058#120—178no—
1059#120—178no—
1060#120C4×D1718yescomplemented
1061C4×D4—682no—
1062C4×D4—682no—
1063C4×D4—682no—
1064C4×D4—682no—
1065C4×D4—682no—
1066C4×D4—682no—
1067C4×D4—682no—
1068C4×D4—682no—
1069C4×D4—682no—
1070C4×D4—682no—
1071C4×D4—682no—
1072C4×D4—682no—
1073#117—682no—
1074#117—682no—
1075C2×C4⋊C4—171no—
1076C2×C4⋊C4—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4—171no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—171no—
1093C2×C4⋊C4—171no—
1094C2×C4⋊C4—171no—
1095C2×C4⋊C4—171no—
1096C2×C4⋊C4—682no—
1097C2×C4⋊C4C22×D1711yescharacteristic
1098C2×C4⋊C4C22×D1711yescharacteristic
1099C2×C4⋊C4C22×D1711yescharacteristic
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4C22×D1711yescharacteristic
1131C2×C22⋊C4C22×D1711yescharacteristic
1132C2×C22⋊C4C22×D1711yescharacteristic
1133C2×C22⋊C4C22×D1711yescharacteristic
1134C2×C22⋊C4C22×D1711yescharacteristic
1135C2×C22⋊C4C22×D1711yescharacteristic
1136C2×C22⋊C4C22×D1711yescharacteristic
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C22⋊C4C22×D1711yescharacteristic
1139C2×C22⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4C22×D1711yescharacteristic
1141C2×C22⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C22⋊C4C22×D1711yescharacteristic
1145C2×C22⋊C4C22×D1711yescharacteristic
1146C2×C22⋊C4C22×D1711yescharacteristic
1147C2×C22⋊C4C22×D1711yescharacteristic
1148C2×C42—171no—
1149C2×C42—171no—
1150C2×C42—171no—
1151C2×C42—171no—
1152C2×C42—171no—
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42—171no—
1158C2×C42—171no—
1159C2×C42—171no—
1160C2×C42—171no—
1161C2×C42—171no—
1162C2×C42—171no—
1163C2×C42—171no—
1164C2×C42C22×D1711yescharacteristic
1165C2×C42C22×D1711yescharacteristic
1166C2×C42C22×D1711yescharacteristic
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95C22×D1711yescharacteristic
1198#95C22×D1711yescharacteristic
1199#95C22×D1711yescharacteristic
1200#95C22×D1711yescharacteristic
1201#95C22×D1711yescharacteristic
1202#95C22×D1711yescharacteristic
1203C17#3451111yescharacteristic, complemented, Sylow
1204C24—41no—
1205C24—41no—
1206C24—41no—
1207C24—41no—
1208C24—41no—
1209C24—41no—
1210C24—171no—
1211C24—171no—
1212C24C2×C4×D1714yes—
1213C24C23×D1711yescharacteristic
1214C24C23×D1711yescharacteristic
1215C24C23×D1711yescharacteristic
1216C24C23×D1711yescharacteristic
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—174no—
1224C2×D4—174no—
1225C2×D4—174no—
1226C2×D4—174no—
1227C2×D4—174no—
1228C2×D4—174no—
1229C2×D4—174no—
1230C2×D4—174no—
1231C2×D4—174no—
1232C2×D4—681no—
1233C2×D4—681no—
1234C2×D4—681no—
1235C2×D4—681no—
1236C2×D4—681no—
1237C2×D4—681no—
1238C2×D4—681no—
1239C2×D4—681no—
1240C2×D4—681no—
1241C2×D4—681no—
1242C2×D4—681no—
1243C2×D4—681no—
1244C2×D4—681no—
1245C2×D4—681no—
1246C2×D4—681no—
1247C2×D4—681no—
1248C2×D4—681no—
1249C2×D4—681no—
1250C2×D4C2×C4×D1714yes—
1251C2×D4C2×C4×D1714yes—
1252C2×D4C2×C4×D1714yes—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—171no—
1257C22×C4—171no—
1258C22×C4—171no—
1259C22×C4—171no—
1260C22×C4—171no—
1261C22×C4—171no—
1262C22×C4—171no—
1263C22×C4—171no—
1264C22×C4—171no—
1265C22×C4—174no—
1266C22×C4—174no—
1267C22×C4—174no—
1268C22×C4—171no—
1269C22×C4—171no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—171no—
1273C22×C4—342no—
1274C22×C4—342no—
1275C22×C4—342no—
1276C22×C4—342no—
1277C22×C4—342no—
1278C22×C4—342no—
1279C22×C4—342no—
1280C22×C4—342no—
1281C22×C4—342no—
1282C22×C4—342no—
1283C22×C4—342no—
1284C22×C4—342no—
1285C22×C4—681no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4—681no—
1293C22×C4—681no—
1294C22×C4—681no—
1295C22×C4—681no—
1296C22×C4—681no—
1297C22×C4—681no—
1298C22×C4—681no—
1299C22×C4—681no—
1300C22×C4—681no—
1301C22×C4—681no—
1302C22×C4—681no—
1303C22×C4—681no—
1304C22×C4—681no—
1305C22×C4—681no—
1306C22×C4—681no—
1307C22×C4—681no—
1308C22×C4—681no—
1309C22×C4—681no—
1310C22×C4—681no—
1311C22×C4—681no—
1312C22×C4—6816no—
1313C22×C4C23×D1711yescharacteristic
1314C22×C4C23×D1711yescharacteristic
1315C22×C4C23×D1711yescharacteristic
1316C22×C4C23×D1711yescharacteristic
1317C22×C4C23×D1711yescharacteristic
1318C22×C4C23×D1711yescharacteristic
1319C22×C4C23×D1711yescharacteristic
1320C22×C4C23×D1711yescharacteristic
1321C22×C4C23×D1711yescharacteristic
1322C22×C4C23×D1711yescharacteristic
1323C22×C4C23×D1711yescharacteristic
1324C4⋊C4—41no—
1325C4⋊C4—41no—
1326C4⋊C4—41no—
1327C4⋊C4—174no—
1328C4⋊C4—174no—
1329C4⋊C4—174no—
1330C4⋊C4—174no—
1331C4⋊C4—174no—
1332C4⋊C4—174no—
1333C4⋊C4—342no—
1334C4⋊C4—342no—
1335C4⋊C4—342no—
1336C4⋊C4—342no—
1337C4⋊C4—342no—
1338C4⋊C4—342no—
1339C4⋊C4—681no—
1340C4⋊C4—681no—
1341C4⋊C4—681no—
1342C4⋊C4—681no—
1343C4⋊C4—681no—
1344C4⋊C4—681no—
1345C4⋊C4—681no—
1346C4⋊C4—681no—
1347C4⋊C4—681no—
1348C22⋊C4—41no—
1349C22⋊C4—41no—
1350C22⋊C4—41no—
1351C22⋊C4—41no—
1352C22⋊C4—41no—
1353C22⋊C4—41no—
1354C22⋊C4—41no—
1355C22⋊C4—41no—
1356C22⋊C4—41no—
1357C22⋊C4—41no—
1358C22⋊C4—41no—
1359C22⋊C4—41no—
1360C22⋊C4—41no—
1361C22⋊C4—41no—
1362C22⋊C4—41no—
1363C22⋊C4—174no—
1364C22⋊C4—174no—
1365C22⋊C4—174no—
1366C22⋊C4—174no—
1367C22⋊C4—174no—
1368C22⋊C4—174no—
1369C22⋊C4—174no—
1370C22⋊C4—174no—
1371C22⋊C4—174no—
1372C22⋊C4—342no—
1373C22⋊C4—342no—
1374C22⋊C4—342no—
1375C22⋊C4—342no—
1376C22⋊C4—342no—
1377C22⋊C4—342no—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C22⋊C4—681no—
1383C22⋊C4—681no—
1384C22⋊C4—681no—
1385C22⋊C4—681no—
1386C22⋊C4—681no—
1387C22⋊C4—681no—
1388C22⋊C4—681no—
1389C22⋊C4—681no—
1390C22⋊C4—681no—
1391C22⋊C4—681no—
1392C22⋊C4—681no—
1393C22⋊C4C2×C4×D1714yes—
1394C22⋊C4C2×C4×D1714yes—
1395C22⋊C4C2×C4×D1714yes—
1396C42—41no—
1397C42—41no—
1398C42—41no—
1399C42—174no—
1400C42—342no—
1401C42—342no—
1402C42—342no—
1403C42—681no—
1404C42—681no—
1405C42—681no—
1406C42—681no—
1407C42—681no—
1408C42—681no—
1409C42—681no—
1410C42—681no—
1411C42—681no—
1412C42—681no—
1413C42—681no—
1414C42—681no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—44no—
1440C23—44no—
1441C23—44no—
1442C23—44no—
1443C23—44no—
1444C23—44no—
1445C23—44no—
1446C23—172no—
1447C23—172no—
1448C23—341no—
1449C23—341no—
1450C23—341no—
1451C23—341no—
1452C23—341no—
1453C23—341no—
1454C23—341no—
1455C23—341no—
1456C23—341no—
1457C23—341no—
1458C23—341no—
1459C23—341no—
1460C23C22×C4×D1712yes—
1461C23C22×C4×D1712yes—
1462C23C22×C4×D1712yes—
1463C23C22×C4×D1712yes—
1464C23C24×D1711yescharacteristic
1465D4—44no—
1466D4—44no—
1467D4—44no—
1468D4—684no—
1469D4—684no—
1470D4—684no—
1471D4—684no—
1472D4—684no—
1473D4—684no—
1474D4—684no—
1475D4—684no—
1476D4—684no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—82no—
1508C2×C4—172no—
1509C2×C4—172no—
1510C2×C4—172no—
1511C2×C4—172no—
1512C2×C4—172no—
1513C2×C4—172no—
1514C2×C4—172no—
1515C2×C4—172no—
1516C2×C4—172no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—684no—
1551C2×C4—684no—
1552C2×C4—684no—
1553C2×C4—684no—
1554C2×C4—684no—
1555C2×C4—684no—
1556C2×C4—684no—
1557C2×C4—684no—
1558C2×C4—684no—
1559C2×C4—1362no—
1560C2×C4—1362no—
1561C2×C4—1362no—
1562C2×C4—1362no—
1563C2×C4—1362no—
1564C2×C4C22×C4×D1712yes—
1565C2×C4C22×C4×D1712yes—
1566C2×C4C22×C4×D1712yes—
1567C22—22no—
1568C22—22no—
1569C22—22no—
1570C22—22no—
1571C22—22no—
1572C22—22no—
1573C22—22no—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—416no—
1580C22—41no—
1581C22—41no—
1582C22—41no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—342no—
1597C22—342no—
1598C22—342no—
1599C22—342no—
1600C22—342no—
1601C22—342no—
1602C22—681no—
1603C22—681no—
1604C22—681no—
1605C22—681no—
1606C22—681no—
1607C22—681no—
1608C22—681no—
1609C22—681no—
1610C22C23×C4×D1711yescharacteristic
1611C22H(5,𝔽2)×D1711yescharacteristic
1612C22H(5,𝔽2)×D1711yescharacteristic
1613C22H(5,𝔽2)×D1711yescharacteristic
1614C22#1176364411yescharacteristic
1615C22#1176364411yescharacteristic
1616C22#1176364411yescharacteristic
1617C4—22no—
1618C4—22no—
1619C4—22no—
1620C4—41no—
1621C4—41no—
1622C4—41no—
1623C4—41no—
1624C4—41no—
1625C4—41no—
1626C4—41no—
1627C4—41no—
1628C4—342no—
1629C4—342no—
1630C4—342no—
1631C4—342no—
1632C4—342no—
1633C4—342no—
1634C4—342no—
1635C4—342no—
1636C4—342no—
1637C4—681no—
1638C4—681no—
1639C4—681no—
1640C4—681no—
1641C4—681no—
1642C2—42no—
1643C2—42no—
1644C2—42no—
1645C2—42no—
1646C2—682no—
1647C2—682no—
1648C2#1454198811yescharacteristic
1649C2#1454198811yescharacteristic
1650C2#1454198811yescharacteristic
1651C2#1454293711yescharacteristic
1652C2#1454303811yescharacteristic
1653C2#1454303811yescharacteristic
1654C2#1454305711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2375C2
socle, cosocleC23×C17C25
prime radicalC2×#11763548C2
hypercenter#2375D17
hypocenterC17#34511
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2375

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14531923C2semidirect
3. #14531923C2semidirect
4. #14531912C2semidirect
5. #14531911C2semidirect
6. #14531902C2semidirect
7. #14531845C2semidirect
8. #14531833C2semidirect
9. #14531832C2semidirect
10. #14531819C2semidirect
11. #14531817C2semidirect
12. #14531805C2semidirect
13. #14531797C2semidirect
14. #14531782C2semidirect
15. #14531773C2semidirect
16. #14531581C2semidirect
17. #14531571C2semidirect
18. #14531557C2semidirect
19. #14531556C2semidirect
20. #14531547C2semidirect
21. #14531545C2semidirect
22. #14531505C2semidirect
23. #14531488C2semidirect
24. #14531485C2semidirect
25. #14531480C2semidirect
26. #14531470C2semidirect
27. #14531454C2semidirect
28. #120×Dic17C2semidirect
29. #14531283C2semidirect
30. #14531283C2semidirect
31. C17×#2375C2semidirect
33. #11763548C4semidirect
48. C2×C4×D68C22semidirect
52. C2×C4×C22⋊D17C22semidirect
59. C2×#10587567C22semidirect
60. C2×#10587558C22semidirect
61. C2×#10587563C22semidirect
62. C2×C4⋊C4×D17C22semidirect
63. #11762710C22semidirect
70. #11762709C22semidirect
71. #11762709C22semidirect
72. #11762707C22semidirect
73. #11762706C22semidirect
74. #11762705C22semidirect
75. #11762704C22semidirect
76. #11762704C22semidirect
77. #11762704C22semidirect
84. #11762701C22semidirect
85. #11762700C22semidirect
86. #11762699C22semidirect
87. #11762698C22semidirect
94. #11762697C22semidirect
95. #11762697C22semidirect
96. #11762696C22semidirect
97. #11762696C22semidirect
98. #11762696C22semidirect
99. #11762694C22semidirect
100. #11762694C22semidirect
101. #11762693C22semidirect
102. #11762692C22semidirect
103. #11762692C22semidirect
104. #11762691C22semidirect
105. #11762691C22semidirect
106. #11762691C22semidirect
107. #11762690C22semidirect
111. #11762688C22semidirect
112. #11762687C22semidirect
113. #11762687C22semidirect
120. #11762686C22semidirect
127. #11762685C22semidirect
128. #11762685C22semidirect
132. #11762683C22semidirect
139. #11762681C22semidirect
140. #11762680C22semidirect
141. #11762673C22semidirect
142. #11762671C22semidirect
143. #11762667C22semidirect
144. #11762666C22semidirect
146. C4⋊C4×Dic17C22semidirect
147. C4⋊C4×Dic17C22semidirect
148. C4×#63225C22semidirect
149. C4×#63225C22semidirect
150. C4×#63225C22semidirect
151. C4×#63225C22semidirect
152. C4×C4⋊Dic17C22semidirect
153. #11762660C22semidirect
163. C22⋊C4×Dic17C22semidirect
164. C4×#63227C22semidirect
165. C4×#63227C22semidirect
166. C4×C22⋊Dic17C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762656C22semidirect
170. #11762654C22semidirect
171. C2×#10587502C22semidirect
172. #95×D17C22semidirect
219. C17×#120C2×C4semidirect
244. #10587639C2×C4semidirect
245. #10587639C2×C4semidirect
262. #10587626C2×C4semidirect
263. #10587625C2×C4semidirect
264. #10587625C2×C4semidirect
265. #10587624C2×C4semidirect
266. #10587624C2×C4semidirect
267. #10587621C2×C4semidirect
324. #10587570C2×C4semidirect
325. #10587570C2×C4semidirect
326. #10587569C2×C4semidirect
327. #10587569C2×C4semidirect
335. #10587565C2×C4semidirect
336. #10587565C2×C4semidirect
434. C2×C22⋊D17C22×C4semidirect
435. C2×C22⋊D17C22×C4semidirect
460. C22×Dic17C22×C4semidirect
477. C2×D68C22×C4semidirect
494. C2×C4×D17C22×C4semidirect
495. C2×C4×D17C22×C4semidirect
535. C22⋊Dic17C22×C4semidirect
548. #63227C22×C4semidirect
549. #63227C22×C4semidirect
553. C4⋊Dic17C22×C4semidirect
554. C4⋊Dic17C22×C4semidirect
567. #63225C22×C4semidirect
568. #63225C22×C4semidirect
569. #63225C22×C4semidirect
570. #63225C22×C4semidirect
586. C4×Dic17C22×C4semidirect
743. #2375D17semidirect
1060. #120C4×D17semidirect
1203. C17#34511semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117635482
#145319232
#145319122
#145319112
#145319022
#145318452
#145318332
#145318322
#145318192
#145318172
#145318052
#145317972
#145317822
#145317732
#145315812
#145315712
#145315572
#145315562
#145315472
#145315452
#145315052
#145314882
#145314852
#145314802
#145314702
#145314542
#120×Dic172
#145312832
C17×#23752
#3451117