Finite Group Databasebeta

← #17197862

Subgroups — #17197862

Order 4352.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763394C211yesmaximal, characteristic
2#14531971C211yesmaximal, characteristic, complemented
3#14531953C211yesmaximal, characteristic, complemented
4#14531936C211yesmaximal, characteristic, complemented
5#14531934C211yesmaximal, characteristic, complemented
6#14531901C211yesmaximal, characteristic, complemented
7#14531862C211yesmaximal, characteristic, complemented
8#14531850C211yesmaximal, characteristic, complemented
9#14531829C211yesmaximal, characteristic, complemented
10#14531805C211yesmaximal, characteristic, complemented
11#14531795C211yesmaximal, characteristic, complemented
12#14531784C211yesmaximal, characteristic, complemented
13#14531782C211yesmaximal, characteristic, complemented
14#14531718C211yesmaximal, characteristic, complemented
15#14531711C211yesmaximal, characteristic, complemented
16#14531689C211yesmaximal, characteristic, complemented
17#14531682C211yesmaximal, characteristic, complemented
18#14531593C211yesmaximal, characteristic, complemented
19#14531572C211yesmaximal, characteristic, complemented
20#14531566C211yesmaximal, characteristic, complemented
21#14531557C211yesmaximal, characteristic, complemented
22#14531494C211yesmaximal, characteristic, complemented
23#14531485C211yesmaximal, characteristic, complemented
24#14531470C211yesmaximal, characteristic, complemented
25#14531454C211yesmaximal, characteristic, complemented
26#14531442C211yesmaximal, characteristic, complemented
27#14531380C211yesmaximal, characteristic, complemented
28#120×Dic17C211yesmaximal, characteristic, complemented
29#14531283C211yesmaximal, characteristic, complemented
30C2×#11762681C211yesmaximal, characteristic, complemented
31C17×#2321C211yesmaximal, characteristic, complemented
32C24×Dic17C2211yescharacteristic
33#11763394C4116yescomplemented
34C2×#10587565C2211yescharacteristic
35C2×#10587565C2211yescharacteristic
36C2×#10587622C2211yescharacteristic
37C2×#10587571C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587621C2211yescharacteristic
40C2×#10587564C2211yescharacteristic
41C2×#10587625C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587624C2211yescharacteristic
44C2×#10587639C2211yescharacteristic
45C2×#10587573C2211yescharacteristic, complemented
46C2×D4×Dic17C2211yescharacteristic
47C2×D4×Dic17C2211yescharacteristic
48C2×D4×Dic17C2211yescharacteristic
49C2×D4×Dic17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×#10587567C2211yescharacteristic
52C2×#10587567C2211yescharacteristic
53C2×#10587567C2211yescharacteristic
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic, complemented
56C2×#10587563C2211yescharacteristic, complemented
57C22×#63225C2211yescharacteristic
58C22×#63225C2211yescharacteristic
59C2×C4⋊C4×D17C2211yescharacteristic, complemented
60C22×C22⋊Dic17C2211yescharacteristic
61#11762715C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762713C2211yescharacteristic, complemented
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic, complemented
67#11762707C2211yescharacteristic, complemented
68#11762706C2211yescharacteristic, complemented
69#11762706C2211yescharacteristic, complemented
70#11762705C2211yescharacteristic, complemented
71#11762705C2211yescharacteristic, complemented
72#11762704C2211yescharacteristic, complemented
73#11762704C2211yescharacteristic, complemented
74#11762704C2211yescharacteristic, complemented
75#11762703C2211yescharacteristic
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic
79#11762703C2211yescharacteristic
80#11762703C2211yescharacteristic
81#11762703C2211yescharacteristic, complemented
82#11762703C2211yescharacteristic, complemented
83#11762703C2211yescharacteristic, complemented
84#11762700C2211yescharacteristic, complemented
85#11762699C2211yescharacteristic, complemented
86#11762698C2211yescharacteristic, complemented
87#11762698C2211yescharacteristic, complemented
88#11762697C2211yescharacteristic
89#11762697C2211yescharacteristic
90#11762697C2211yescharacteristic
91#11762697C2211yescharacteristic
92#11762697C2211yescharacteristic
93#11762697C2211yescharacteristic
94#11762697C2211yescharacteristic, complemented
95#11762696C2211yescharacteristic, complemented
96#11762696C2211yescharacteristic, complemented
97#11762694C2211yescharacteristic, complemented
98#11762694C2211yescharacteristic, complemented
99#11762693C2211yescharacteristic, complemented
100#11762693C2211yescharacteristic, complemented
101#11762693C2211yescharacteristic, complemented
102#11762692C2211yescharacteristic, complemented
103#11762692C2211yescharacteristic, complemented
104#11762691C2211yescharacteristic, complemented
105#11762691C2211yescharacteristic, complemented
106#11762690C2211yescharacteristic, complemented
107#11762689C2211yescharacteristic
108#11762689C2211yescharacteristic
109#11762689C2211yescharacteristic
110#11762688C2211yescharacteristic
111#11762688C2211yescharacteristic, complemented
112#11762686C2211yescharacteristic
113#11762686C2211yescharacteristic
114#11762686C2211yescharacteristic
115#11762685C2211yescharacteristic
116#11762685C2211yescharacteristic
117#11762685C2211yescharacteristic, complemented
118#11762684C2211yescharacteristic
119#11762684C2211yescharacteristic
120#11762684C2211yescharacteristic
121#11762683C2211yescharacteristic, complemented
122#11762683C2211yescharacteristic, complemented
123#11762682C2211yescharacteristic
124#11762682C2211yescharacteristic, complemented
125#11762681C2211yescharacteristic
126#11762681C2211yescharacteristic
127#11762681C2211yescharacteristic
128#11762681C2211yescharacteristic
129#11762681C2211yescharacteristic
130#11762681C2211yescharacteristic
131#11762681C2211yescharacteristic
132#11762681C2211yescharacteristic
133#11762681C2211yescharacteristic
134#11762681C2211yescharacteristic
135#11762681C2211yescharacteristic
136#11762681C2211yescharacteristic, complemented
137#11762681C2211yescharacteristic, complemented
138#11762680C2211yescharacteristic, complemented
139#11762678C2211yescharacteristic, complemented
140#11762676C2211yescharacteristic, complemented
141#11762674C2211yescharacteristic, complemented
142#11762673C2211yescharacteristic, complemented
143#11762671C2211yescharacteristic, complemented
144#11762668C2211yescharacteristic, complemented
145#11762667C2211yescharacteristic
146#11762667C2211yescharacteristic
147#11762667C2211yescharacteristic, complemented
148#11762667C2211yescharacteristic, complemented
149#11762665C2211yescharacteristic
150C4×#63225C2211yescharacteristic, complemented
151C4×#63225C2211yescharacteristic, complemented
152C4×C4⋊Dic17C2211yescharacteristic, complemented
153#11762660C2211yescharacteristic, complemented
154#11762660C2211yescharacteristic, complemented
155#11762660C2211yescharacteristic, complemented
156#11762660C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C22⋊C4×Dic17C2211yescharacteristic
162C22⋊C4×Dic17C2211yescharacteristic
163C22⋊C4×Dic17C2211yescharacteristic
164C22⋊C4×Dic17C2211yescharacteristic
165C4×#63227C2211yescharacteristic, complemented
166C4×#63227C2211yescharacteristic, complemented
167C4×C22⋊Dic17C2211yescharacteristic
168C4×C22⋊Dic17C2211yescharacteristic, complemented
169#11762655C2211yescharacteristic, complemented
170C2×#10587502C2211yescharacteristic
171C2×#10587502C2211yescharacteristic
172C2×#10587502C2211yescharacteristic, complemented
173C2×C17×#120C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C22×C22⋊C4×C17C2211yescharacteristic
176C17×#390C2211yescharacteristic
177C17×#390C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#388C2211yescharacteristic
181C17×#388C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#385C2211yescharacteristic
186C17×#379C2211yescharacteristic
187C4×C22⋊C4×C17C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C23×Dic17—42no—
200C23×Dic17—42no—
201C23×Dic17—42no—
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×Dic34C2311yescharacteristic
216C17×#120C2×C418yescomplemented
217C4×D4×C17—42no—
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17—42no—
222C2×C22⋊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×C42×C17C2311yescharacteristic
239C2×C42×C17C2311yescharacteristic
240C2×C42×C17C2311yescharacteristic
241#10587639C2×C418yescomplemented
242C2×C22⋊Dic17C2×C418yescomplemented
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
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
261#10587625C2×C418yescomplemented
262#10587625C2×C418yescomplemented
263#10587624C2×C418yescomplemented
264#10587622C2×C418yescomplemented
265#10587621C2×C418yescomplemented
266D4×Dic17—42no—
267D4×Dic17—42no—
268D4×Dic17—42no—
269D4×Dic17C2×C418yescomplemented
270C4×C22⋊D17—42no—
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×#63225—42no—
285C2×#63225—42no—
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
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×#63225C2311yescharacteristic
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#10587573—42no—
325#10587571C2×C418yescomplemented
326#10587569C2×C418yescomplemented
327#10587567—42no—
328#10587567—42no—
329#10587567—42no—
330#10587567—42no—
331#10587567C2×C418yescomplemented
332#10587565C2×C418yescomplemented
333#10587565C2×C418yescomplemented
334#10587564C2×C418yescomplemented
335#10587563—42no—
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
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—22no—
377C24×C17—22no—
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
388C2×D4×C17—22no—
389C2×D4×C17—22no—
390C2×D4×C17—41no—
391C2×D4×C17—41no—
392C2×D4×C17—41no—
393C2×D4×C17—41no—
394C2×D4×C17C22×C414yes—
395C2×D4×C17C22×C414yes—
396C2×D4×C17C22×C414yes—
397C22×C4×C17—22no—
398C22×C4×C17—22no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C2×C22⋊D17—22no—
418C2×C22⋊D17—22no—
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⋊D17C22×C414yes—
426C2×C22⋊D17C22×C414yes—
427C2×C22⋊D17C22×C414yes—
428C2×C22⋊D17C22×C414yescomplemented
429C22×Dic17—22no—
430C22×Dic17—22no—
431C22×Dic17—22no—
432C22×Dic17—22no—
433C22×Dic17—22no—
434C22×Dic17—22no—
435C22×Dic17—22no—
436C22×Dic17—22no—
437C22×Dic17—22no—
438C22×Dic17—41no—
439C22×Dic17—41no—
440C22×Dic17—41no—
441C22×Dic17—41no—
442C22×Dic17—41no—
443C22×Dic17—41no—
444C22×Dic17—41no—
445C22×Dic17—41no—
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—416no—
457C22×Dic17C22×C414yes—
458C22×Dic17C22×C414yes—
459C22×Dic17C22×C414yescomplemented
460C22×Dic17C2411yescharacteristic
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×C4×D17—22no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17C22×C414yescomplemented
484C2×Dic34—41no—
485C2×Dic34—41no—
486C2×Dic34C22×C414yescomplemented
487C4⋊C4×C17—41no—
488C4⋊C4×C17—41no—
489C4⋊C4×C17—41no—
490C22⋊C4×C17—22no—
491C22⋊C4×C17—22no—
492C22⋊C4×C17—41no—
493C22⋊C4×C17—41no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17—41no—
501C22⋊C4×C17—41no—
502C22⋊C4×C17—41no—
503C22⋊C4×C17C22×C414yes—
504C22⋊C4×C17C22×C414yes—
505C22⋊C4×C17C22×C414yes—
506C42×C17—41no—
507C42×C17—41no—
508C42×C17—41no—
509C22⋊Dic17—22no—
510C22⋊Dic17—22no—
511C22⋊Dic17—22no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17—41no—
518C22⋊Dic17C22×C414yes—
519C22⋊Dic17C22×C414yes—
520C22⋊Dic17C22×C414yes—
521C22⋊Dic17C22×C414yes—
522C22⋊Dic17C22×C414yes—
523C22⋊Dic17C22×C414yes—
524C22⋊Dic17C22×C414yes—
525C22⋊Dic17C22×C414yescomplemented
526C22⋊Dic17C22×C414yescomplemented
527#63227—22no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227C22×C414yescomplemented
534#63227C22×C414yescomplemented
535C4⋊Dic17—22no—
536C4⋊Dic17—41no—
537C4⋊Dic17—41no—
538C4⋊Dic17C22×C414yescomplemented
539C4⋊Dic17C22×C414yescomplemented
540#63225—22no—
541#63225—22no—
542#63225—22no—
543#63225—22no—
544#63225—22no—
545#63225—41no—
546#63225—41no—
547#63225—41no—
548#63225—41no—
549#63225—41no—
550#63225—41no—
551#63225—41no—
552#63225—41no—
553#63225—41no—
554#63225—41no—
555#63225—41no—
556#63225—41no—
557#63225—41no—
558#63225C22×C414yescomplemented
559#63225C22×C414yescomplemented
560#63225C22×C414yescomplemented
561#63225C22×C414yescomplemented
562C4×Dic17—22no—
563C4×Dic17—22no—
564C4×Dic17—41no—
565C4×Dic17—41no—
566C4×Dic17—41no—
567C4×Dic17—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573C4×Dic17—41no—
574C4×Dic17—41no—
575C4×Dic17C22×C414yescomplemented
576C4×Dic17C22×C414yescomplemented
577#34416—171nomaximal, Sylow
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—28no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
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—44no—
602C23×C17—44no—
603C23×C17—44no—
604C23×C17—44no—
605C23×C17—44no—
606C23×C17—44no—
607C23×C17C23×C412yes—
608C23×C17C23×C412yes—
609C23×C17C23×C412yes—
610C23×C17C23×C412yes—
611C23×C17H(5,𝔽2)12yes—
612C23×C172−1+412yes—
613C23×C17C2511yescharacteristic
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17C23×C412yes—
621D4×C17—28no—
622D4×C17—44no—
623D4×C17—44no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
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—82no—
655C2×C4×C17—82no—
656C2×C4×C17—82no—
657C2×C4×C17C23×C412yes—
658C2×C4×C17C23×C412yes—
659C2×C4×C17C23×C412yes—
660C22⋊D17—28no—
661C22⋊D17—44no—
662C22⋊D17—44no—
663C22⋊D17—44no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
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—44no—
701C2×Dic17—44no—
702C2×Dic17—44no—
703C2×Dic17—44no—
704C2×Dic17—44no—
705C2×Dic17—44no—
706C2×Dic17—44no—
707C2×Dic17—44no—
708C2×Dic17—44no—
709C2×Dic17—82no—
710C2×Dic17C23×C412yes—
711C2×Dic17C23×C412yes—
712C2×Dic17C23×C412yes—
713C2×Dic17C23×C412yes—
714C2×Dic17C23×C412yes—
715C2×Dic17C23×C412yes—
716C2×Dic17C23×C412yes—
717C2×Dic17H(5,𝔽2)12yes—
718C2×Dic17H(5,𝔽2)12yes—
719C4×D17—44no—
720C4×D17—82no—
721C4×D17—82no—
722Dic34—44no—
723C2×#538—171no—
724#2383—171no—
725#2379—171no—
726#2377—171no—
727#2376—171no—
728#2373—171no—
729#2368—171no—
730#2367—171no—
731#2364—171no—
732#2361—171no—
733#2361—171no—
734#2360—171no—
735#2359—171no—
736#2353—171no—
737#2352—171no—
738#2349—171no—
739D4×C4⋊C4—171no—
740#2337—171no—
741#2335—171no—
742#2334—171no—
743#2334—171no—
744#2326—171no—
745#2325—171no—
746#2324—171no—
747#2322—171no—
748#2321—171no—
749#2321D1711yescharacteristic, complemented
750#2312—171no—
751C4×#120—171no—
752C4×#120—171no—
753C2×#385—171no—
754C22×C17—22no—
755C22×C17—22no—
756C22×C17—22no—
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—22no—
764C22×C17—22no—
765C22×C17—22no—
766C22×C17—22no—
767C22×C17—22no—
768C22×C17—22no—
769C22×C17—416no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17—41no—
776C22×C17—41no—
777C22×C17—41no—
778C22×C17—41no—
779C22×C17—41no—
780C22×C17—41no—
781C22×C17—41no—
782C22×C17#52014yes—
783C22×C17C24×C411yescharacteristic
784C22×C17C2×H(5,𝔽2)11yescharacteristic
785C22×C17C2×H(5,𝔽2)11yescharacteristic
786C22×C17C2×H(5,𝔽2)11yescharacteristic
787C22×C17C2×2−1+411yescharacteristic
788C22×C17#58511yescharacteristic
789C22×C17#58511yescharacteristic
790C2×D17—22no—
791C2×D17—22no—
792C2×D17—22no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17—41no—
797C4×C17—22no—
798C4×C17—22no—
799C4×C17—22no—
800C4×C17—41no—
801C4×C17—41no—
802C4×C17—41no—
803C4×C17—41no—
804C4×C17—41no—
805C4×C17—41no—
806C4×C17—41no—
807C4×C17—41no—
808Dic17—22no—
809Dic17—22no—
810Dic17—22no—
811Dic17—22no—
812Dic17—22no—
813Dic17—22no—
814Dic17—22no—
815Dic17—22no—
816Dic17—22no—
817Dic17—41no—
818Dic17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822Dic17—41no—
823C24×C4—171no—
824#538—1716no—
825C2×#126—171no—
826C2×#126—171no—
827C2×#124—171no—
828C2×#124—171no—
829C2×#123—171no—
830C2×#123—171no—
831C2×C22⋊Q8—171no—
832C2×#121—171no—
833C2×#121—171no—
834C2×#121—171no—
835C2×#120—171no—
836C2×#120C2×D1711yescharacteristic
837C2×C4×Q8—171no—
838C2×C4×D4—171no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4—171no—
842C2×C4×D4—171no—
843C2×C4×D4—171no—
844C2×C4×D4—171no—
845C2×C4×D4—171no—
846C2×C4×D4—171no—
847C2×C4×D4—171no—
848C2×C4×D4C2×D1711yescharacteristic
849C2×#117—171no—
850C22×C4⋊C4—171no—
851C22×C4⋊C4—171no—
852C22×C4⋊C4—171no—
853C22×C22⋊C4—171no—
854C22×C22⋊C4C2×D1711yescharacteristic
855#391—171no—
856#391—171no—
857#391—171no—
858#390—171no—
859#390—171no—
860#390—171no—
861#390C2×D1711yescharacteristic
862#390C2×D1711yescharacteristic
863#389—171no—
864#389—171no—
865#389—171no—
866#389—171no—
867#389—171no—
868#389—171no—
869#389—171no—
870#389—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388—171no—
881#388—171no—
882#388—171no—
883#388—171no—
884#388—171no—
885#388—171no—
886#388—171no—
887#388—171no—
888#388—171no—
889#388—171no—
890#388—171no—
891#388C2×D1711yescharacteristic
892#388C2×D1711yescharacteristic
893#388C2×D1711yescharacteristic
894#388C2×D1711yescharacteristic
895#387—171no—
896#387—171no—
897#387—171no—
898#387—171no—
899#387—171no—
900#387—171no—
901#387—171no—
902#387—171no—
903#387—171no—
904#387—171no—
905#387—171no—
906#387—171no—
907#386—171no—
908#386—171no—
909#386—171no—
910#386—171no—
911#386—171no—
912#386—171no—
913#386—171no—
914#386—171no—
915#386—171no—
916#386—171no—
917#386—171no—
918#386C2×D1711yescharacteristic
919#386C2×D1711yescharacteristic
920#386C2×D1711yescharacteristic
921#385—171no—
922#385—171no—
923#385—171no—
924#385—171no—
925#385—171no—
926#385—171no—
927#385—171no—
928#385—171no—
929#385—171no—
930#385—171no—
931#385—171no—
932#385—171no—
933#385—171no—
934#385—171no—
935#385—171no—
936#385—171no—
937#385—171no—
938#385—171no—
939#385—171no—
940#385—171no—
941#385—171no—
942#385C2×D1711yescharacteristic
943#384—171no—
944#383—171no—
945#382—171no—
946#382—171no—
947#381—171no—
948#380—171no—
949#380—171no—
950#380—171no—
951#380—171no—
952#380—171no—
953#379—171no—
954#379C2×D1711yescharacteristic
955C4×C4⋊C4—171no—
956C4×C4⋊C4—171no—
957C4×C4⋊C4—171no—
958C4×C4⋊C4—171no—
959C4×C4⋊C4—171no—
960C4×C4⋊C4—171no—
961C4×C4⋊C4—171no—
962C4×C22⋊C4—171no—
963C4×C22⋊C4—171no—
964C4×C22⋊C4—171no—
965C4×C22⋊C4—171no—
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4—171no—
971C4×C22⋊C4—171no—
972C4×C22⋊C4—171no—
973C4×C22⋊C4—171no—
974C4×C22⋊C4C2×D1711yescharacteristic
975#376—171no—
976C2×#95—171no—
977C2×#95—171no—
978C2×#95—171no—
979C2×C17—24no—
980C2×C17—42no—
981C2×C17—42no—
982C2×C17—42no—
983C2×C17C2×#52011yescharacteristic
984C2×C17C4×H(5,𝔽2)11yescharacteristic
985C2×C17C4×H(5,𝔽2)11yescharacteristic
986C2×C17#353211yescharacteristic
987C2×C17#353311yescharacteristic
988C2×C17#354111yescharacteristic
989C2×C17#354111yescharacteristic
990D17—42no—
991C25C22×D1711yescharacteristic
992C22×Q8—171no—
993C22×D4—171no—
994C22×D4—171no—
995C22×D4—171no—
996C22×D4—171no—
997C22×D4C22×D1711yescharacteristic
998C22×D4C22×D1711yescharacteristic
999C22×D4C22×D1711yescharacteristic
1000C23×C4—171no—
1001C23×C4—171no—
1002C23×C4—171no—
1003C23×C4—171no—
1004C23×C4—171no—
1005C23×C4—171no—
1006C23×C4—171no—
1007C23×C4—171no—
1008C23×C4—171no—
1009C23×C4—171no—
1010C23×C4—171no—
1011C23×C4—171no—
1012C23×C4—171no—
1013C23×C4—682no—
1014C23×C4—682no—
1015C23×C4—682no—
1016C23×C4C22×D1711yescharacteristic
1017C23×C4C22×D1711yescharacteristic
1018C23×C4C22×D1711yescharacteristic
1019#126—178no—
1020#126—178no—
1021#124—178no—
1022#124—178no—
1023#123—178no—
1024#123—178no—
1025C22⋊Q8—178no—
1026#121—178no—
1027#121—178no—
1028#121—178no—
1029#120—178no—
1030#120C4×D1718yescomplemented
1031C4×Q8—682no—
1032C4×D4—42no—
1033C4×D4—178no—
1034C4×D4—178no—
1035C4×D4—682no—
1036C4×D4—682no—
1037C4×D4—682no—
1038C4×D4—682no—
1039C4×D4—682no—
1040C4×D4—682no—
1041C4×D4—682no—
1042C4×D4—682no—
1043#117—682no—
1044C2×C4⋊C4—171no—
1045C2×C4⋊C4—171no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—682no—
1072C2×C4⋊C4—682no—
1073C2×C4⋊C4—682no—
1074C2×C4⋊C4C22×D1711yescharacteristic
1075C2×C4⋊C4C22×D1711yescharacteristic
1076C2×C4⋊C4C22×D1711yescharacteristic
1077C2×C22⋊C4—42no—
1078C2×C22⋊C4—178no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4C22×D1711yescharacteristic
1106C2×C22⋊C4C22×D1711yescharacteristic
1107C2×C22⋊C4C22×D1711yescharacteristic
1108C2×C22⋊C4C22×D1711yescharacteristic
1109C2×C22⋊C4C22×D1711yescharacteristic
1110C2×C22⋊C4C22×D1711yescharacteristic
1111C2×C22⋊C4C22×D1711yescharacteristic
1112C2×C22⋊C4C22×D1711yescharacteristic
1113C2×C22⋊C4C22×D1711yescharacteristic
1114C2×C22⋊C4C22×D1711yescharacteristic
1115C2×C22⋊C4C22×D1711yescharacteristic
1116C2×C22⋊C4C22×D1711yescharacteristic
1117C2×C22⋊C4C22×D1711yescharacteristic
1118C2×C22⋊C4C22×D1711yescharacteristic
1119C2×C22⋊C4C22×D1711yescharacteristic
1120C2×C22⋊C4C22×D1711yescharacteristic
1121C2×C42—171no—
1122C2×C42—171no—
1123C2×C42—171no—
1124C2×C42—171no—
1125C2×C42—171no—
1126C2×C42—171no—
1127C2×C42—171no—
1128C2×C42—171no—
1129C2×C42—171no—
1130C2×C42—171no—
1131C2×C42—171no—
1132C2×C42—171no—
1133C2×C42—171no—
1134C2×C42—171no—
1135C2×C42—171no—
1136C2×C42C22×D1711yescharacteristic
1137C2×C42C22×D1711yescharacteristic
1138C2×C42C22×D1711yescharacteristic
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179C17#3441611yescharacteristic, complemented, Sylow
1180C24—22no—
1181C24—22no—
1182C24—41no—
1183C24—41no—
1184C24—41no—
1185C24—41no—
1186C24—171no—
1187C24C2×C4×D1714yes—
1188C24C23×D1711yescharacteristic
1189C24C23×D1711yescharacteristic
1190C24C23×D1711yescharacteristic
1191C24C23×D1711yescharacteristic
1192C2×Q8—174no—
1193C2×Q8—681no—
1194C2×Q8—681no—
1195C2×D4—22no—
1196C2×D4—22no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—41no—
1200C2×D4—41no—
1201C2×D4—174no—
1202C2×D4—174no—
1203C2×D4—174no—
1204C2×D4—174no—
1205C2×D4—342no—
1206C2×D4—342no—
1207C2×D4—681no—
1208C2×D4—681no—
1209C2×D4—681no—
1210C2×D4—681no—
1211C2×D4—681no—
1212C2×D4—681no—
1213C2×D4C2×C4×D1714yes—
1214C2×D4C2×C4×D1714yes—
1215C2×D4C2×C4×D1714yes—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—171no—
1226C22×C4—171no—
1227C22×C4—171no—
1228C22×C4—171no—
1229C22×C4—171no—
1230C22×C4—171no—
1231C22×C4—171no—
1232C22×C4—171no—
1233C22×C4—171no—
1234C22×C4—174no—
1235C22×C4—174no—
1236C22×C4—174no—
1237C22×C4—174no—
1238C22×C4—171no—
1239C22×C4—171no—
1240C22×C4—171no—
1241C22×C4—171no—
1242C22×C4—171no—
1243C22×C4—171no—
1244C22×C4—342no—
1245C22×C4—342no—
1246C22×C4—342no—
1247C22×C4—342no—
1248C22×C4—342no—
1249C22×C4—342no—
1250C22×C4—342no—
1251C22×C4—342no—
1252C22×C4—342no—
1253C22×C4—342no—
1254C22×C4—681no—
1255C22×C4—681no—
1256C22×C4—681no—
1257C22×C4—681no—
1258C22×C4—681no—
1259C22×C4—681no—
1260C22×C4—681no—
1261C22×C4—681no—
1262C22×C4—681no—
1263C22×C4—681no—
1264C22×C4—681no—
1265C22×C4—681no—
1266C22×C4—681no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—681no—
1278C22×C4—681no—
1279C22×C4—6816no—
1280C22×C4C23×D1711yescharacteristic
1281C22×C4C23×D1711yescharacteristic
1282C22×C4C23×D1711yescharacteristic
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4—41no—
1294C4⋊C4—174no—
1295C4⋊C4—174no—
1296C4⋊C4—174no—
1297C4⋊C4—174no—
1298C4⋊C4—174no—
1299C4⋊C4—174no—
1300C4⋊C4—342no—
1301C4⋊C4—342no—
1302C4⋊C4—342no—
1303C4⋊C4—342no—
1304C4⋊C4—342no—
1305C4⋊C4—342no—
1306C4⋊C4—681no—
1307C4⋊C4—681no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4—681no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4—681no—
1319C4⋊C4—681no—
1320C4⋊C4—681no—
1321C22⋊C4—22no—
1322C22⋊C4—22no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—41no—
1328C22⋊C4—41no—
1329C22⋊C4—41no—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—174no—
1335C22⋊C4—174no—
1336C22⋊C4—174no—
1337C22⋊C4—174no—
1338C22⋊C4—174no—
1339C22⋊C4—174no—
1340C22⋊C4—174no—
1341C22⋊C4—174no—
1342C22⋊C4—174no—
1343C22⋊C4—174no—
1344C22⋊C4—174no—
1345C22⋊C4—342no—
1346C22⋊C4—342no—
1347C22⋊C4—342no—
1348C22⋊C4—342no—
1349C22⋊C4—681no—
1350C22⋊C4—681no—
1351C22⋊C4—681no—
1352C22⋊C4—681no—
1353C22⋊C4—681no—
1354C22⋊C4—681no—
1355C22⋊C4—681no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4—681no—
1359C22⋊C4—681no—
1360C22⋊C4C2×C4×D1714yes—
1361C22⋊C4C2×C4×D1714yes—
1362C22⋊C4C2×C4×D1714yes—
1363C42—41no—
1364C42—41no—
1365C42—41no—
1366C42—174no—
1367C42—174no—
1368C42—342no—
1369C42—342no—
1370C42—681no—
1371C42—681no—
1372C42—681no—
1373C42—681no—
1374C42—681no—
1375C42—681no—
1376C42—681no—
1377C42—681no—
1378C42—681no—
1379C42—681no—
1380C42—681no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—28no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—44no—
1405C23—44no—
1406C23—44no—
1407C23—44no—
1408C23—44no—
1409C23—44no—
1410C23—172no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23C22×C4×D1712yes—
1418C23C22×C4×D1712yes—
1419C23C22×C4×D1712yes—
1420C23C22×C4×D1712yes—
1421C23#1058769112yes—
1422C23#1058769712yes—
1423C23C24×D1711yescharacteristic
1424Q8—684no—
1425D4—28no—
1426D4—44no—
1427D4—44no—
1428D4—348no—
1429D4—684no—
1430D4—684no—
1431D4—684no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—82no—
1463C2×C4—82no—
1464C2×C4—82no—
1465C2×C4—172no—
1466C2×C4—172no—
1467C2×C4—172no—
1468C2×C4—172no—
1469C2×C4—172no—
1470C2×C4—172no—
1471C2×C4—172no—
1472C2×C4—172no—
1473C2×C4—172no—
1474C2×C4—341no—
1475C2×C4—341no—
1476C2×C4—341no—
1477C2×C4—341no—
1478C2×C4—341no—
1479C2×C4—341no—
1480C2×C4—341no—
1481C2×C4—341no—
1482C2×C4—341no—
1483C2×C4—341no—
1484C2×C4—341no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—684no—
1511C2×C4—684no—
1512C2×C4—684no—
1513C2×C4—684no—
1514C2×C4—684no—
1515C2×C4—684no—
1516C2×C4—684no—
1517C2×C4—684no—
1518C2×C4—684no—
1519C2×C4—684no—
1520C2×C4—1362no—
1521C2×C4—1362no—
1522C2×C4—1362no—
1523C2×C4C22×C4×D1712yes—
1524C2×C4C22×C4×D1712yes—
1525C2×C4C22×C4×D1712yes—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—22no—
1534C22—22no—
1535C22—22no—
1536C22—22no—
1537C22—22no—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—416no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—342no—
1555C22—342no—
1556C22—342no—
1557C22—681no—
1558C22—681no—
1559C22—681no—
1560C22—681no—
1561C22#1176328814yes—
1562C22C23×C4×D1711yescharacteristic
1563C22H(5,𝔽2)×D1711yescharacteristic
1564C22H(5,𝔽2)×D1711yescharacteristic
1565C22C2×#1058769111yescharacteristic
1566C22C2×#1058769711yescharacteristic
1567C22#1176364411yescharacteristic
1568C22#1176364411yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—41no—
1573C4—41no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—342no—
1581C4—342no—
1582C4—342no—
1583C4—342no—
1584C4—342no—
1585C4—342no—
1586C4—342no—
1587C4—342no—
1588C4—342no—
1589C4—681no—
1590C4—681no—
1591C4—681no—
1592C4—681no—
1593C4—681no—
1594C4—681no—
1595C2—24no—
1596C2—42no—
1597C2—42no—
1598C2—42no—
1599C2—682no—
1600C2C2×#1176328811yescharacteristic
1601C2#1454198811yescharacteristic
1602C2#1454198811yescharacteristic
1603C2#1454293811yescharacteristic
1604C2#1454294511yescharacteristic
1605C2#1454306411yescharacteristic
1606C2#1454306411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2321C2
socle, cosocleC23×C17C25
prime radicalC2×#11763394C2
hypercenter#2321D17
hypocenterC17#34416
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2321

Complements

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

NH ≅ G/Ntype
2. #14531971C2semidirect
3. #14531953C2semidirect
4. #14531936C2semidirect
5. #14531934C2semidirect
6. #14531901C2semidirect
7. #14531862C2semidirect
8. #14531850C2semidirect
9. #14531829C2semidirect
10. #14531805C2semidirect
11. #14531795C2semidirect
12. #14531784C2semidirect
13. #14531782C2semidirect
14. #14531718C2semidirect
15. #14531711C2semidirect
16. #14531689C2semidirect
17. #14531682C2semidirect
18. #14531593C2semidirect
19. #14531572C2semidirect
20. #14531566C2semidirect
21. #14531557C2semidirect
22. #14531494C2semidirect
23. #14531485C2semidirect
24. #14531470C2semidirect
25. #14531454C2semidirect
26. #14531442C2semidirect
27. #14531380C2semidirect
28. #120×Dic17C2semidirect
29. #14531283C2semidirect
30. C2×#11762681C2semidirect
31. C17×#2321C2semidirect
33. #11763394C4semidirect
45. C2×#10587573C22semidirect
55. C2×#10587567C22semidirect
56. C2×#10587563C22semidirect
59. C2×C4⋊C4×D17C22semidirect
61. #11762715C22semidirect
62. #11762713C22semidirect
63. #11762713C22semidirect
66. #11762709C22semidirect
67. #11762707C22semidirect
68. #11762706C22semidirect
69. #11762706C22semidirect
70. #11762705C22semidirect
71. #11762705C22semidirect
72. #11762704C22semidirect
73. #11762704C22semidirect
74. #11762704C22semidirect
81. #11762703C22semidirect
82. #11762703C22semidirect
83. #11762703C22semidirect
84. #11762700C22semidirect
85. #11762699C22semidirect
86. #11762698C22semidirect
87. #11762698C22semidirect
94. #11762697C22semidirect
95. #11762696C22semidirect
96. #11762696C22semidirect
97. #11762694C22semidirect
98. #11762694C22semidirect
99. #11762693C22semidirect
100. #11762693C22semidirect
101. #11762693C22semidirect
102. #11762692C22semidirect
103. #11762692C22semidirect
104. #11762691C22semidirect
105. #11762691C22semidirect
106. #11762690C22semidirect
111. #11762688C22semidirect
117. #11762685C22semidirect
121. #11762683C22semidirect
122. #11762683C22semidirect
124. #11762682C22semidirect
136. #11762681C22semidirect
137. #11762681C22semidirect
138. #11762680C22semidirect
139. #11762678C22semidirect
140. #11762676C22semidirect
141. #11762674C22semidirect
142. #11762673C22semidirect
143. #11762671C22semidirect
144. #11762668C22semidirect
147. #11762667C22semidirect
148. #11762667C22semidirect
150. C4×#63225C22semidirect
151. C4×#63225C22semidirect
152. C4×C4⋊Dic17C22semidirect
153. #11762660C22semidirect
154. #11762660C22semidirect
155. #11762660C22semidirect
156. #11762660C22semidirect
165. C4×#63227C22semidirect
166. C4×#63227C22semidirect
168. C4×C22⋊Dic17C22semidirect
169. #11762655C22semidirect
172. C2×#10587502C22semidirect
216. C17×#120C2×C4semidirect
241. #10587639C2×C4semidirect
242. C2×C22⋊Dic17C2×C4semidirect
261. #10587625C2×C4semidirect
262. #10587625C2×C4semidirect
263. #10587624C2×C4semidirect
264. #10587622C2×C4semidirect
265. #10587621C2×C4semidirect
269. D4×Dic17C2×C4semidirect
325. #10587571C2×C4semidirect
326. #10587569C2×C4semidirect
331. #10587567C2×C4semidirect
332. #10587565C2×C4semidirect
333. #10587565C2×C4semidirect
334. #10587564C2×C4semidirect
428. C2×C22⋊D17C22×C4semidirect
459. C22×Dic17C22×C4semidirect
483. C2×C4×D17C22×C4semidirect
486. C2×Dic34C22×C4semidirect
525. C22⋊Dic17C22×C4semidirect
526. C22⋊Dic17C22×C4semidirect
533. #63227C22×C4semidirect
534. #63227C22×C4semidirect
538. C4⋊Dic17C22×C4semidirect
539. C4⋊Dic17C22×C4semidirect
558. #63225C22×C4semidirect
559. #63225C22×C4semidirect
560. #63225C22×C4semidirect
561. #63225C22×C4semidirect
575. C4×Dic17C22×C4semidirect
576. C4×Dic17C22×C4semidirect
749. #2321D17semidirect
1030. #120C4×D17semidirect
1179. C17#34416semidirect

Maximal subgroups

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

subgroupindex
C2×#117633942
#145319712
#145319532
#145319362
#145319342
#145319012
#145318622
#145318502
#145318292
#145318052
#145317952
#145317842
#145317822
#145317182
#145317112
#145316892
#145316822
#145315932
#145315722
#145315662
#145315572
#145314942
#145314852
#145314702
#145314542
#145314422
#145313802
#120×Dic172
#145312832
C2×#117626812
C17×#23212
#3441617