Finite Group Databasebeta

← #17200262

Subgroups — #17200262

Order 4352.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763547C211yesmaximal, characteristic
2#14531935C211yesmaximal, characteristic, complemented
3#14531935C211yesmaximal, characteristic, complemented
4#14531930C211yesmaximal, characteristic, complemented
5#14531899C211yesmaximal, characteristic, complemented
6#14531898C211yesmaximal, characteristic, complemented
7#14531845C211yesmaximal, characteristic, complemented
8#14531836C211yesmaximal, characteristic, complemented
9#14531833C211yesmaximal, characteristic, complemented
10#14531822C211yesmaximal, characteristic, complemented
11#14531817C211yesmaximal, characteristic, complemented
12#14531781C211yesmaximal, characteristic, complemented
13#14531776C211yesmaximal, characteristic, complemented
14#14531765C211yesmaximal, characteristic, complemented
15#14531764C211yesmaximal, characteristic, complemented
16#14531760C211yesmaximal, characteristic, complemented
17#14531577C211yesmaximal, characteristic, complemented
18#14531570C211yesmaximal, characteristic, complemented
19#14531557C211yesmaximal, characteristic, complemented
20#14531552C211yesmaximal, characteristic, complemented
21#14531505C211yesmaximal, characteristic, complemented
22#14531484C211yesmaximal, characteristic, complemented
23#14531481C211yesmaximal, characteristic, complemented
24#14531480C211yesmaximal, characteristic, complemented
25#14531446C211yesmaximal, characteristic, complemented
26#14531443C211yesmaximal, characteristic, complemented
27#14531438C211yesmaximal, characteristic, complemented
28#14531303C211yesmaximal, characteristic, complemented
29#14531294C211yesmaximal, characteristic, complemented
30C4×#10587625C211yesmaximal, characteristic, complemented
31C17×#2324C211yesmaximal, characteristic, complemented
32#11763547C4116yescomplemented
33C2×#10587626C2211yescharacteristic
34C2×#10587584C2211yescharacteristic
35C2×#10587565C2211yescharacteristic
36C2×#10587580C2211yescharacteristic
37C2×#10587572C2211yescharacteristic
38C2×#10587615C2211yescharacteristic
39C2×#10587616C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587625C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587624C2211yescharacteristic
44C2×#10587568C2211yescharacteristic
45C2×#10587623C2211yescharacteristic
46C2×#10587623C2211yescharacteristic
47C2×C4×D68C2211yescharacteristic
48C2×D4×Dic17C2211yescharacteristic
49C2×D4×Dic17C2211yescharacteristic, complemented
50C2×#10587579C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×C4×C22⋊D17C2211yescharacteristic, complemented
53C2×#10587567C2211yescharacteristic
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic
56C2×#10587567C2211yescharacteristic
57C2×#10587567C2211yescharacteristic, complemented
58C2×#10587558C2211yescharacteristic, complemented
59C22×#63227C2211yescharacteristic
60C2×C22⋊C4×D17C2211yescharacteristic
61C2×C22⋊C4×D17C2211yescharacteristic
62C22×C4×Dic17C2211yescharacteristic, complemented
63#11762710C2211yescharacteristic
64#11762710C2211yescharacteristic
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#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic
79#11762703C2211yescharacteristic, complemented
80#11762702C2211yescharacteristic
81#11762702C2211yescharacteristic, complemented
82#11762701C2211yescharacteristic
83#11762701C2211yescharacteristic
84#11762700C2211yescharacteristic
85#11762700C2211yescharacteristic
86#11762700C2211yescharacteristic
87#11762700C2211yescharacteristic
88#11762700C2211yescharacteristic, complemented
89#11762699C2211yescharacteristic
90#11762699C2211yescharacteristic
91#11762699C2211yescharacteristic
92#11762699C2211yescharacteristic
93#11762699C2211yescharacteristic, complemented
94#11762698C2211yescharacteristic
95#11762698C2211yescharacteristic
96#11762697C2211yescharacteristic
97#11762697C2211yescharacteristic
98#11762697C2211yescharacteristic, complemented
99#11762695C2211yescharacteristic, complemented
100#11762695C2211yescharacteristic, complemented
101#11762694C2211yescharacteristic, complemented
102#11762693C2211yescharacteristic, complemented
103#11762693C2211yescharacteristic, complemented
104#11762692C2211yescharacteristic, complemented
105#11762692C2211yescharacteristic, complemented
106#11762692C2211yescharacteristic, complemented
107#11762691C2211yescharacteristic, complemented
108#11762690C2211yescharacteristic, complemented
109#11762690C2211yescharacteristic, complemented
110#11762690C2211yescharacteristic, complemented
111#11762689C2211yescharacteristic
112#11762689C2211yescharacteristic
113#11762689C2211yescharacteristic
114#11762689C2211yescharacteristic, complemented
115#11762688C2211yescharacteristic
116#11762688C2211yescharacteristic
117#11762687C2211yescharacteristic
118#11762687C2211yescharacteristic
119#11762687C2211yescharacteristic
120#11762687C2211yescharacteristic
121#11762686C2211yescharacteristic
122#11762686C2211yescharacteristic
123#11762686C2211yescharacteristic
124#11762686C2211yescharacteristic, complemented
125#11762686C2211yescharacteristic, complemented
126#11762685C2211yescharacteristic
127#11762685C2211yescharacteristic
128#11762685C2211yescharacteristic
129#11762685C2211yescharacteristic
130#11762685C2211yescharacteristic
131#11762685C2211yescharacteristic, complemented
132#11762685C2211yescharacteristic, complemented
133#11762683C2211yescharacteristic
134#11762681C2211yescharacteristic
135#11762681C2211yescharacteristic
136#11762681C2211yescharacteristic, complemented
137#11762680C2211yescharacteristic
138#11762680C2211yescharacteristic
139#11762680C2211yescharacteristic
140#11762680C2211yescharacteristic
141#11762680C2211yescharacteristic
142#11762680C2211yescharacteristic, complemented
143#11762673C2211yescharacteristic, complemented
144#11762670C2211yescharacteristic, complemented
145#11762667C2211yescharacteristic, complemented
146#11762667C2211yescharacteristic, complemented
147#11762666C2211yescharacteristic, complemented
148#11762664C2211yescharacteristic
149C4⋊C4×Dic17C2211yescharacteristic, complemented
150C4⋊C4×Dic17C2211yescharacteristic, complemented
151C4⋊C4×Dic17C2211yescharacteristic, complemented
152C4×#63225C2211yescharacteristic, complemented
153C4×#63225C2211yescharacteristic, complemented
154#11762660C2211yescharacteristic, complemented
155#11762660C2211yescharacteristic, complemented
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic, complemented
158C22⋊C4×Dic17C2211yescharacteristic, complemented
159C4×#63227C2211yescharacteristic
160C4×#63227C2211yescharacteristic
161C4×#63227C2211yescharacteristic
162C4×#63227C2211yescharacteristic, complemented
163C4×C22⋊Dic17C2211yescharacteristic
164C4×C22⋊Dic17C2211yescharacteristic
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic
168#11762656C2211yescharacteristic
169#11762656C2211yescharacteristic, complemented
170#11762654C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#121C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C17×#117C2211yescharacteristic, complemented
176C17×#390C2211yescharacteristic
177C17×#390C2211yescharacteristic
178C17×#390C2211yescharacteristic, complemented
179C17×#389C2211yescharacteristic, complemented
180C17×#388C2211yescharacteristic
181C17×#388C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic, complemented
184C17×#385C2211yescharacteristic
185C17×#385C2211yescharacteristic, complemented
186C17×#380C2211yescharacteristic, complemented
187C4×C4⋊C4×C17C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
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
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C22×D68C2311yescharacteristic
208C22×D68C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C17×#121C2×C418yescomplemented
217C4×D4×C17—42no—
218C17×#117—42no—
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊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
241C2×C42×C17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
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
253#10587626C2×C418yescomplemented
254#10587625C2×C418yescomplemented
255#10587625C2×C418yescomplemented
256#10587624C2×C418yescomplemented
257#10587623C2×C418yescomplemented
258#10587623C2×C418yescomplemented
259D4×Dic17—42no—
260D4×Dic17—42no—
261#10587616C2×C418yescomplemented
262#10587615C2×C418yescomplemented
263C4×C22⋊D17—42no—
264C4×C22⋊D17—42no—
265C2×#63227—42no—
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
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×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
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×Dic17—42no—
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
323C2×C4×Dic17C2311yescharacteristic
324#10587584C2×C418yescomplemented
325#10587580C2×C418yescomplemented
326#10587579—42no—
327#10587572C2×C418yescomplemented
328#10587570C2×C418yescomplemented
329#10587568C2×C418yescomplemented
330#10587567—42no—
331#10587567—42no—
332#10587567—42no—
333#10587567—42no—
334#10587567—42no—
335C22⋊C4×D17—42no—
336C22⋊C4×D17—42no—
337#10587565C2×C418yescomplemented
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×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C24×C17C2411yescharacteristic
379C23×D17—41no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17C22×C414yes—
386C23×D17C2411yescharacteristic
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—22no—
399C22×C4×C17—22no—
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×C17C22×C414yes—
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
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
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⋊D17—41no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17—41no—
432C2×C22⋊D17—41no—
433C2×C22⋊D17C22×C414yes—
434C2×C22⋊D17C22×C414yes—
435C2×C22⋊D17C22×C414yes—
436C2×C22⋊D17C22×C414yes—
437C2×C22⋊D17C22×C414yes—
438C2×C22⋊D17C22×C414yes—
439C2×C22⋊D17C22×C414yes—
440C22×Dic17—22no—
441C22×Dic17—22no—
442C22×Dic17—22no—
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×Dic17C22×C414yes—
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C2×D68—41no—
469C2×D68—41no—
470C2×D68—41no—
471C2×D68—41no—
472C2×D68C22×C414yes—
473C2×D68C22×C414yes—
474C2×C4×D17—22no—
475C2×C4×D17—22no—
476C2×C4×D17—22no—
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×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×C414yes—
495C4⋊C4×C17—22no—
496C4⋊C4×C17—41no—
497C4⋊C4×C17—41no—
498C4⋊C4×C17—41no—
499C4⋊C4×C17—41no—
500C4⋊C4×C17—41no—
501C4⋊C4×C17C22×C414yes—
502C22⋊C4×C17—22no—
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×C17C22×C414yes—
513C22⋊C4×C17C22×C414yes—
514C42×C17—22no—
515C42×C17—41no—
516C42×C17—41no—
517C42×C17—41no—
518C22⋊Dic17—22no—
519C22⋊Dic17—22no—
520C22⋊Dic17—22no—
521C22⋊Dic17—41no—
522C22⋊Dic17—41no—
523C22⋊Dic17—41no—
524C22⋊Dic17—41no—
525C22⋊Dic17—41no—
526C22⋊Dic17C22×C414yes—
527C22⋊Dic17C22×C414yes—
528C22⋊Dic17C22×C414yes—
529#63227—22no—
530#63227—22no—
531#63227—22no—
532#63227—22no—
533#63227—22no—
534#63227—22no—
535#63227—41no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545#63227—41no—
546#63227—41no—
547#63227C22×C414yes—
548#63227C22×C414yes—
549#63227C22×C414yes—
550#63227C22×C414yes—
551#63227C22×C414yes—
552#63227C22×C414yes—
553#63227C22×C414yes—
554C4⋊Dic17—22no—
555C4⋊Dic17—41no—
556C4⋊Dic17C22×C414yes—
557C4⋊Dic17C22×C414yes—
558#63225—22no—
559#63225—22no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225C22×C414yes—
569#63225C22×C414yes—
570#63225C22×C414yes—
571C4×Dic17—22no—
572C4×Dic17—22no—
573C4×Dic17—22no—
574C4×Dic17—22no—
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×Dic17C22×C414yes—
586#34517—171nomaximal, Sylow
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—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17C23×C412yes—
606C23×C17C23×C412yes—
607C23×C17C23×C412yes—
608C23×C17C2511yescharacteristic
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—44no—
628C22×D17—44no—
629C22×D17—44no—
630C22×D17—82no—
631C22×D17—82no—
632C22×D17—82no—
633C22×D17—82no—
634C22×D17C23×C412yes—
635C22×D17C23×C412yes—
636C22×D17C23×C412yes—
637D4×C17—44no—
638D4×C17—44no—
639D4×C17—44no—
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—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—44no—
672C2×C4×C17—44no—
673C2×C4×C17—82no—
674C2×C4×C17C23×C412yes—
675C2×C4×C17C23×C412yes—
676C2×C4×C17C23×C412yes—
677C2×C4×C17C23×C412yes—
678C2×C4×C17H(5,𝔽2)12yes—
679C22⋊D17—44no—
680C22⋊D17—44no—
681C22⋊D17—44no—
682C22⋊D17—44no—
683C22⋊D17—44no—
684C22⋊D17—44no—
685C22⋊D17—44no—
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—21no—
717C2×Dic17—21no—
718C2×Dic17—44no—
719C2×Dic17—44no—
720C2×Dic17—82no—
721C2×Dic17—82no—
722C2×Dic17—82no—
723C2×Dic17C23×C412yes—
724C2×Dic17C23×C412yes—
725C2×Dic17C23×C412yes—
726C2×Dic17C23×C412yes—
727C2×Dic17C23×C412yes—
728C2×Dic17H(5,𝔽2)12yes—
729C2×Dic17H(5,𝔽2)12yes—
730D68—44no—
731D68—44no—
732C4×D17—44no—
733C4×D17—82no—
734C4×D17—82no—
735C4×D17—82no—
736C4×D17—82no—
737C4×D17—82no—
738C4×D17—82no—
739C2×#560—171no—
740#2377—171no—
741#2377—171no—
742#2376—171no—
743#2373—171no—
744#2373—171no—
745#2366—171no—
746#2364—171no—
747#2364—171no—
748#2363—171no—
749#2363—171no—
750#2359—171no—
751#2359—171no—
752#2358—171no—
753#2358—171no—
754#2358—171no—
755#2335—171no—
756#2335—171no—
757#2334—171no—
758#2334—171no—
759#2328—171no—
760#2325—171no—
761#2325—171no—
762#2324—171no—
763#2324D1711yescharacteristic, complemented
764#2321—171no—
765#2321—171no—
766#2321—171no—
767C4×#123—171no—
768C4×#121—171no—
769C4×#121—171no—
770C22×C17—22no—
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—41no—
780C22×C17—41no—
781C22×C17—41no—
782C22×C17—41no—
783C22×C17—41no—
784C22×C17—41no—
785C22×C17—41no—
786C22×C17—41no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17C24×C411yescharacteristic
792C22×C17C2×H(5,𝔽2)11yescharacteristic
793C22×C17C2×H(5,𝔽2)11yescharacteristic
794C22×C17C2×H(5,𝔽2)11yescharacteristic
795C22×C17#58511yescharacteristic
796C22×C17#58511yescharacteristic
797C22×C17#58511yescharacteristic
798C2×D17—22no—
799C2×D17—22no—
800C2×D17—22no—
801C2×D17—22no—
802C2×D17—22no—
803C2×D17—22no—
804C2×D17—22no—
805C2×D17—22no—
806C2×D17—22no—
807C2×D17—41no—
808C2×D17—41no—
809C2×D17—41no—
810C2×D17—41no—
811C2×D17—41no—
812C2×D17—41no—
813C2×D17—41no—
814C2×D17—41no—
815C2×D17—41no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—88no—
820C4×C17—22no—
821C4×C17—22no—
822C4×C17—22no—
823C4×C17—22no—
824C4×C17—22no—
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—41no—
840Dic17—41no—
841Dic17—41no—
842Dic17—41no—
843Dic17—41no—
844Dic17—41no—
845#560—1716no—
846C2×#127—171no—
847C2×#126—171no—
848C2×#126—171no—
849C2×#123—171no—
850C2×#123—171no—
851C2×#123—171no—
852C2×#121—171no—
853C2×#121—171no—
854C2×#121—171no—
855C2×#121—171no—
856C2×#121—171no—
857C2×#121C2×D1711yescharacteristic
858C2×#120—171no—
859C2×#120—171no—
860C2×#120—171no—
861C2×C4×D4—171no—
862C2×C4×D4—171no—
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×D4C2×D1711yescharacteristic
873C2×#117—171no—
874C2×#117C2×D1711yescharacteristic, complemented
875C22×C22⋊C4—171no—
876C22×C22⋊C4—171no—
877C22×C22⋊C4—171no—
878C22×C42—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#390—171no—
888#390C2×D1711yescharacteristic
889#390C2×D1711yescharacteristic
890#390C2×D1711yescharacteristic, complemented
891#389—171no—
892#389—171no—
893#389—171no—
894#389—171no—
895#389—171no—
896#389C2×D1711yescharacteristic, complemented
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#388—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388C2×D1711yescharacteristic
920#388C2×D1711yescharacteristic, complemented
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#387—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#386—171no—
954#386—171no—
955#386C2×D1711yescharacteristic
956#386C2×D1711yescharacteristic, complemented
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#385C2×D1711yescharacteristic
968#385C2×D1711yescharacteristic, complemented
969#382—171no—
970#381—171no—
971#380—171no—
972#380—171no—
973#380—171no—
974#380C2×D1711yescharacteristic, complemented
975#379—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×C4⋊C4C2×D1711yescharacteristic, complemented
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—
998#376—171no—
999C2×#95—171no—
1000C2×#95—171no—
1001C2×C17—42no—
1002C2×C17—42no—
1003C2×C17—42no—
1004C2×C17C4×H(5,𝔽2)11yescharacteristic
1005C2×C17C4×H(5,𝔽2)11yescharacteristic
1006C2×C17C4×H(5,𝔽2)11yescharacteristic
1007C2×C17#353411yescharacteristic
1008C2×C17#354211yescharacteristic
1009C2×C17#354611yescharacteristic
1010C2×C17#356611yescharacteristic
1011D17—42no—
1012D17—42no—
1013D17—42no—
1014C25—171no—
1015C22×D4—171no—
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×D4C22×D1711yescharacteristic
1025C22×D4C22×D1711yescharacteristic
1026C22×D4C22×D1711yescharacteristic
1027C23×C4—171no—
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×C4C22×D1711yescharacteristic
1040C23×C4C22×D1711yescharacteristic
1041C23×C4C22×D1711yescharacteristic
1042#127—178no—
1043#126—178no—
1044#126—178no—
1045#123—178no—
1046#123—178no—
1047#123—178no—
1048#121—178no—
1049#121—178no—
1050#121—178no—
1051#121—178no—
1052#121—178no—
1053#121C4×D1718yescomplemented
1054#120—178no—
1055#120—178no—
1056#120—178no—
1057C4×D4—42no—
1058C4×D4—682no—
1059C4×D4—682no—
1060C4×D4—682no—
1061C4×D4—682no—
1062C4×D4—682no—
1063C4×D4—682no—
1064C4×D4—682no—
1065C4×D4—682no—
1066C4×D4—682no—
1067C4×D4—682no—
1068C4×D4—682no—
1069#117—42no—
1070#117—682no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
1089C2×C4⋊C4C22×D1711yescharacteristic
1090C2×C4⋊C4C22×D1711yescharacteristic
1091C2×C4⋊C4C22×D1711yescharacteristic
1092C2×C4⋊C4C22×D1711yescharacteristic
1093C2×C4⋊C4C22×D1711yescharacteristic
1094C2×C4⋊C4C22×D1711yescharacteristic
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⋊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⋊C4—171no—
1131C2×C22⋊C4—682no—
1132C2×C22⋊C4—682no—
1133C2×C22⋊C4—682no—
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×C42—171no—
1147C2×C42—171no—
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—682no—
1162C2×C42C22×D1711yescharacteristic
1163C2×C42C22×D1711yescharacteristic
1164C2×C42C22×D1711yescharacteristic
1165C2×C42C22×D1711yescharacteristic
1166#95—171no—
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#95C22×D1711yescharacteristic
1197#95C22×D1711yescharacteristic
1198#95C22×D1711yescharacteristic
1199#95C22×D1711yescharacteristic
1200#95C22×D1711yescharacteristic
1201#95C22×D1711yescharacteristic
1202C17#3451711yescharacteristic, complemented, Sylow
1203C24—171no—
1204C24—171no—
1205C24—171no—
1206C24—174no—
1207C24—681no—
1208C24—681no—
1209C24—681no—
1210C24—681no—
1211C24—681no—
1212C24—681no—
1213C24C23×D1711yescharacteristic
1214C24C23×D1711yescharacteristic
1215C24C23×D1711yescharacteristic
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—174no—
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—681no—
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×D4C2×C4×D1714yes—
1250C2×D4C2×C4×D1714yes—
1251C2×D4C2×C4×D1714yes—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—41no—
1259C22×C4—41no—
1260C22×C4—171no—
1261C22×C4—171no—
1262C22×C4—171no—
1263C22×C4—171no—
1264C22×C4—171no—
1265C22×C4—171no—
1266C22×C4—171no—
1267C22×C4—174no—
1268C22×C4—174no—
1269C22×C4—171no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—171no—
1273C22×C4—171no—
1274C22×C4—171no—
1275C22×C4—342no—
1276C22×C4—342no—
1277C22×C4—342no—
1278C22×C4—342no—
1279C22×C4—342no—
1280C22×C4—342no—
1281C22×C4—681no—
1282C22×C4—681no—
1283C22×C4—681no—
1284C22×C4—681no—
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×C4C2×C4×D1714yes—
1310C22×C4C23×D1711yescharacteristic
1311C22×C4C23×D1711yescharacteristic
1312C22×C4C23×D1711yescharacteristic
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
1322C4⋊C4—22no—
1323C4⋊C4—41no—
1324C4⋊C4—41no—
1325C4⋊C4—41no—
1326C4⋊C4—41no—
1327C4⋊C4—41no—
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—681no—
1337C4⋊C4—681no—
1338C4⋊C4—681no—
1339C4⋊C4—681no—
1340C4⋊C4—681no—
1341C4⋊C4—681no—
1342C4⋊C4—681no—
1343C4⋊C4—681no—
1344C4⋊C4—681no—
1345C4⋊C4C2×C4×D1714yes—
1346C22⋊C4—22no—
1347C22⋊C4—41no—
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—174no—
1357C22⋊C4—174no—
1358C22⋊C4—174no—
1359C22⋊C4—174no—
1360C22⋊C4—174no—
1361C22⋊C4—174no—
1362C22⋊C4—174no—
1363C22⋊C4—174no—
1364C22⋊C4—174no—
1365C22⋊C4—174no—
1366C22⋊C4—342no—
1367C22⋊C4—342no—
1368C22⋊C4—342no—
1369C22⋊C4—342no—
1370C22⋊C4—342no—
1371C22⋊C4—342no—
1372C22⋊C4—342no—
1373C22⋊C4—342no—
1374C22⋊C4—342no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
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⋊C4C2×C4×D1714yes—
1393C22⋊C4C2×C4×D1714yes—
1394C42—22no—
1395C42—41no—
1396C42—41no—
1397C42—41no—
1398C42—174no—
1399C42—342no—
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—
1413C23—21no—
1414C23—21no—
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—172no—
1432C23—172no—
1433C23—172no—
1434C23—341no—
1435C23—341no—
1436C23—341no—
1437C23—341no—
1438C23—341no—
1439C23—341no—
1440C23—341no—
1441C23—341no—
1442C23—341no—
1443C23—341no—
1444C23—341no—
1445C23—341no—
1446C23—341no—
1447C23—341no—
1448C23—341no—
1449C23—341no—
1450C23—341no—
1451C23—341no—
1452C23—684no—
1453C23—684no—
1454C23—684no—
1455C23—1362no—
1456C23—1362no—
1457C23—1362no—
1458C23—1362no—
1459C23C22×C4×D1712yes—
1460C23C22×C4×D1712yes—
1461C23C22×C4×D1712yes—
1462C23C24×D1711yescharacteristic
1463D4—44no—
1464D4—44no—
1465D4—44no—
1466D4—684no—
1467D4—684no—
1468D4—684no—
1469D4—684no—
1470D4—684no—
1471D4—684no—
1472D4—684no—
1473D4—684no—
1474D4—684no—
1475C2×C4—21no—
1476C2×C4—21no—
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—44no—
1507C2×C4—44no—
1508C2×C4—82no—
1509C2×C4—172no—
1510C2×C4—172no—
1511C2×C4—172no—
1512C2×C4—172no—
1513C2×C4—172no—
1514C2×C4—172no—
1515C2×C4—172no—
1516C2×C4—341no—
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—684no—
1549C2×C4—684no—
1550C2×C4—684no—
1551C2×C4—1362no—
1552C2×C4—1362no—
1553C2×C4—1362no—
1554C2×C4—1362no—
1555C2×C4—1362no—
1556C2×C4—1362no—
1557C2×C4—1362no—
1558C2×C4—1362no—
1559C2×C4—1362no—
1560C2×C4C22×C4×D1712yes—
1561C2×C4C22×C4×D1712yes—
1562C2×C4C22×C4×D1712yes—
1563C2×C4C22×C4×D1712yes—
1564C2×C4#1058769112yes—
1565C22—22no—
1566C22—22no—
1567C22—22no—
1568C22—22no—
1569C22—22no—
1570C22—22no—
1571C22—22no—
1572C22—22no—
1573C22—22no—
1574C22—41no—
1575C22—41no—
1576C22—41no—
1577C22—41no—
1578C22—41no—
1579C22—41no—
1580C22—41no—
1581C22—41no—
1582C22—41no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—342no—
1587C22—342no—
1588C22—342no—
1589C22—342no—
1590C22—342no—
1591C22—342no—
1592C22—342no—
1593C22—342no—
1594C22—342no—
1595C22—681no—
1596C22—681no—
1597C22—681no—
1598C22—681no—
1599C22—681no—
1600C22—681no—
1601C22—681no—
1602C22—681no—
1603C22—681no—
1604C22—681no—
1605C22—681no—
1606C22—681no—
1607C22—1368no—
1608C22C23×C4×D1711yescharacteristic
1609C22H(5,𝔽2)×D1711yescharacteristic
1610C22H(5,𝔽2)×D1711yescharacteristic
1611C22C2×#1058769111yescharacteristic
1612C22#1176364411yescharacteristic
1613C22#1176364511yescharacteristic
1614C22#1176364611yescharacteristic
1615C4—22no—
1616C4—22no—
1617C4—22no—
1618C4—22no—
1619C4—22no—
1620C4—41no—
1621C4—41no—
1622C4—41no—
1623C4—41no—
1624C4—41no—
1625C4—41no—
1626C4—41no—
1627C4—342no—
1628C4—342no—
1629C4—342no—
1630C4—342no—
1631C4—342no—
1632C4—342no—
1633C4—342no—
1634C4—681no—
1635C4—681no—
1636C4—681no—
1637C4—681no—
1638C4—681no—
1639C4—681no—
1640C2—42no—
1641C2—42no—
1642C2—42no—
1643C2—682no—
1644C2—682no—
1645C2—682no—
1646C2#1454198811yescharacteristic
1647C2C4×#1058769111yescharacteristic
1648C2#1454199011yescharacteristic
1649C2#1454296711yescharacteristic
1650C2#1454308711yescharacteristic
1651C2#1454314611yescharacteristic
1652C2#1454346411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2324C2
socle, cosocleC23×C17C25
prime radicalC2×#11763547C2
hypercenter#2324D17
hypocenterC17#34517
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #14531935C2semidirect
3. #14531935C2semidirect
4. #14531930C2semidirect
5. #14531899C2semidirect
6. #14531898C2semidirect
7. #14531845C2semidirect
8. #14531836C2semidirect
9. #14531833C2semidirect
10. #14531822C2semidirect
11. #14531817C2semidirect
12. #14531781C2semidirect
13. #14531776C2semidirect
14. #14531765C2semidirect
15. #14531764C2semidirect
16. #14531760C2semidirect
17. #14531577C2semidirect
18. #14531570C2semidirect
19. #14531557C2semidirect
20. #14531552C2semidirect
21. #14531505C2semidirect
22. #14531484C2semidirect
23. #14531481C2semidirect
24. #14531480C2semidirect
25. #14531446C2semidirect
26. #14531443C2semidirect
27. #14531438C2semidirect
28. #14531303C2semidirect
29. #14531294C2semidirect
30. C4×#10587625C2semidirect
31. C17×#2324C2semidirect
32. #11763547C4semidirect
49. C2×D4×Dic17C22semidirect
52. C2×C4×C22⋊D17C22semidirect
57. C2×#10587567C22semidirect
58. C2×#10587558C22semidirect
62. C22×C4×Dic17C22semidirect
70. #11762709C22semidirect
71. #11762709C22semidirect
72. #11762707C22semidirect
73. #11762706C22semidirect
74. #11762705C22semidirect
75. #11762704C22semidirect
76. #11762704C22semidirect
79. #11762703C22semidirect
81. #11762702C22semidirect
88. #11762700C22semidirect
93. #11762699C22semidirect
98. #11762697C22semidirect
99. #11762695C22semidirect
100. #11762695C22semidirect
101. #11762694C22semidirect
102. #11762693C22semidirect
103. #11762693C22semidirect
104. #11762692C22semidirect
105. #11762692C22semidirect
106. #11762692C22semidirect
107. #11762691C22semidirect
108. #11762690C22semidirect
109. #11762690C22semidirect
110. #11762690C22semidirect
114. #11762689C22semidirect
124. #11762686C22semidirect
125. #11762686C22semidirect
131. #11762685C22semidirect
132. #11762685C22semidirect
136. #11762681C22semidirect
142. #11762680C22semidirect
143. #11762673C22semidirect
144. #11762670C22semidirect
145. #11762667C22semidirect
146. #11762667C22semidirect
147. #11762666C22semidirect
149. C4⋊C4×Dic17C22semidirect
150. C4⋊C4×Dic17C22semidirect
151. C4⋊C4×Dic17C22semidirect
152. C4×#63225C22semidirect
153. C4×#63225C22semidirect
154. #11762660C22semidirect
155. #11762660C22semidirect
157. C22⋊C4×Dic17C22semidirect
158. C22⋊C4×Dic17C22semidirect
162. C4×#63227C22semidirect
165. C4×C22⋊Dic17C22semidirect
169. #11762656C22semidirect
170. #11762654C22semidirect
171. C2×#10587502C22semidirect
172. #95×D17C22semidirect
175. C2×C17×#117C22semidirect
178. C17×#390C22semidirect
179. C17×#389C22semidirect
181. C17×#388C22semidirect
183. C17×#386C22semidirect
185. C17×#385C22semidirect
186. C17×#380C22semidirect
187. C4×C4⋊C4×C17C22semidirect
216. C17×#121C2×C4semidirect
253. #10587626C2×C4semidirect
254. #10587625C2×C4semidirect
255. #10587625C2×C4semidirect
256. #10587624C2×C4semidirect
257. #10587623C2×C4semidirect
258. #10587623C2×C4semidirect
261. #10587616C2×C4semidirect
262. #10587615C2×C4semidirect
324. #10587584C2×C4semidirect
325. #10587580C2×C4semidirect
327. #10587572C2×C4semidirect
328. #10587570C2×C4semidirect
329. #10587568C2×C4semidirect
337. #10587565C2×C4semidirect
763. #2324D17semidirect
874. C2×#117C2×D17semidirect
890. #390C2×D17semidirect
896. #389C2×D17semidirect
920. #388C2×D17semidirect
956. #386C2×D17semidirect
968. #385C2×D17semidirect
974. #380C2×D17semidirect
983. C4×C4⋊C4C2×D17semidirect
1053. #121C4×D17semidirect
1202. C17#34517semidirect

Maximal subgroups

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

subgroupindex
C2×#117635472
#145319352
#145319302
#145318992
#145318982
#145318452
#145318362
#145318332
#145318222
#145318172
#145317812
#145317762
#145317652
#145317642
#145317602
#145315772
#145315702
#145315572
#145315522
#145315052
#145314842
#145314812
#145314802
#145314462
#145314432
#145314382
#145313032
#145312942
C4×#105876252
C17×#23242
#3451717