Finite Group Databasebeta

← #16965009

Subgroups — #16965009

Order 4352.

1390 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762721C211yesmaximal, characteristic
2C2×#11762713C211yesmaximal, characteristic, complemented
3C2×#11762703C211yesmaximal, characteristic
4#14527054C211yesmaximal, characteristic, complemented
5#14527047C211yesmaximal, characteristic, complemented
6#14527043C211yesmaximal, characteristic, complemented
7#14527042C211yesmaximal, characteristic, complemented
8#14527042C211yesmaximal, characteristic, complemented
9#14527039C211yesmaximal, characteristic, complemented
10#14527033C211yesmaximal, characteristic
11#14527031C211yesmaximal, characteristic
12#14527027C211yesmaximal, characteristic
13#14527027C211yesmaximal, characteristic
14#14527008C211yesmaximal, characteristic, complemented
15C17×#1439C211yesmaximal, characteristic
16C23×Dic34C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25#11762721C418yescomplemented
26#11762713—24no—
27#11762703—24no—
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C22×C4⋊C4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C22⋊C4×C17C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17C2311yescharacteristic
62C23×Dic17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C22×Dic34—22no—
70C22×Dic34—22no—
71C22×Dic34—41no—
72C22×Dic34—41no—
73C22×Dic34—41no—
74C22×Dic34—41no—
75C22×Dic34C2×C414yes—
76C2×C4⋊C4×C17—41no—
77C2×C4⋊C4×C17—41no—
78C2×C4⋊C4×C17—41no—
79C2×C22⋊C4×C17—22no—
80C2×C22⋊C4×C17—41no—
81C2×C22⋊C4×C17—41no—
82C2×C22⋊C4×C17—41no—
83C2×C22⋊C4×C17—41no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17—41no—
86C2×C22⋊C4×C17—41no—
87C2×C22⋊C4×C17C2×C414yes—
88C2×C22⋊Dic17—22no—
89C2×C22⋊Dic17—22no—
90C2×C22⋊Dic17—22no—
91C2×C22⋊Dic17—41no—
92C2×C22⋊Dic17—41no—
93C2×C22⋊Dic17—41no—
94C2×C22⋊Dic17—41no—
95C2×C22⋊Dic17—41no—
96C2×C22⋊Dic17—41no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17C2×C414yes—
99C2×C22⋊Dic17C2×C414yes—
100C2×#63225—22no—
101C2×#63225—22no—
102C2×#63225—41no—
103C2×#63225—41no—
104C2×#63225—41no—
105C2×#63225—41no—
106C2×#63225—41no—
107C2×#63225—41no—
108C2×#63225—41no—
109C2×C4×Dic17—41no—
110C2×C4×Dic17—41no—
111C2×C4×Dic17D414yes—
112C17×#95—22no—
113C17×#95—41no—
114C17×#95—41no—
115#10587502—22no—
116#10587502—22no—
117#10587502—22no—
118#10587502—22no—
119#10587502—22no—
120#10587502—22no—
121#10587502—41no—
122#10587502—41no—
123#10587502—41no—
124#10587502—41no—
125#10587502—41no—
126#10587502—41no—
127#10587502—41no—
128#10587502—41no—
129#10587502—41no—
130#10587502—41no—
131#10587502C2×C414yes—
132#10587502C2×C414yes—
133#10587502C2×C414yes—
134C24×C17—21no—
135C24×C17—21no—
136C24×C17—21no—
137C24×C17—21no—
138C24×C17—21no—
139C24×C17—21no—
140C24×C17—21no—
141C24×C17—21no—
142C24×C17—21no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17C22×C412yes—
149C24×C17C2411yescharacteristic
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17C22×C412yes—
190C22×C4×C17C22×C412yes—
191C22×C4×C17C2×D412yes—
192C22×Dic17—21no—
193C22×Dic17—21no—
194C22×Dic17—21no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17C22×C412yes—
242C22×Dic17C22×C412yes—
243C22×Dic17C22×C412yes—
244C22×Dic17C22×C412yes—
245C22×Dic17C2×D412yes—
246C22×Dic17C2×D412yes—
247C22×Dic17#4112yes—
248C2×Dic34—28no—
249C2×Dic34—44no—
250C2×Dic34—44no—
251C2×Dic34—44no—
252C2×Dic34—44no—
253C2×Dic34—44no—
254C2×Dic34—44no—
255C4⋊C4×C17—44no—
256C22⋊C4×C17—44no—
257C22⋊C4×C17—44no—
258C22⋊C4×C17—44no—
259C22⋊Dic17—28no—
260C22⋊Dic17—44no—
261C22⋊Dic17—44no—
262C22⋊Dic17—44no—
263#63225—44no—
264#63225—44no—
265#63225—44no—
266C4×Dic17—44no—
267#14625—171nomaximal, Sylow
268C23×C17—22no—
269C23×C17—22no—
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—41no—
276C23×C17—41no—
277C23×C17—41no—
278C23×C17—41no—
279C23×C17—41no—
280C23×C17—41no—
281C23×C17—41no—
282C23×C17—41no—
283C23×C17—41no—
284C23×C17—41no—
285C23×C17—41no—
286C23×C17—41no—
287C23×C17—41no—
288C23×C17—41no—
289C23×C17—41no—
290C23×C17—41no—
291C23×C17—41no—
292C23×C17—41no—
293C23×C17—41no—
294C23×C17—41no—
295C23×C17—41no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—41no—
299C23×C17—41no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17C23×C411yescharacteristic
304C23×C17C22×D411yescharacteristic
305C23×C17C2×#4111yescharacteristic
306C23×C17H(5,𝔽2)11yescharacteristic
307C23×C17H(5,𝔽2)11yescharacteristic
308C23×C17H(5,𝔽2)11yescharacteristic
309C23×C17H(5,𝔽2)11yescharacteristic
310C23×C17H(5,𝔽2)11yescharacteristic
311C23×C17H(5,𝔽2)11yescharacteristic
312C23×C17H(5,𝔽2)11yescharacteristic
313C23×C172−1+411yescharacteristic
314C23×C172−1+411yescharacteristic
315C23×C172−1+411yescharacteristic
316C23×C172−1+411yescharacteristic
317C23×C172−1+411yescharacteristic
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—41no—
328C2×C4×C17—41no—
329C2×C4×C17—41no—
330C2×C4×C17—41no—
331C2×C4×C17—41no—
332C2×C4×C17—41no—
333C2×C4×C17—41no—
334C2×C4×C17—41no—
335C2×C4×C17—41no—
336C2×C4×C17—41no—
337C2×C4×C17—41no—
338C2×C4×C17—41no—
339C2×C4×C17—41no—
340C2×C4×C17—41no—
341C2×C4×C17—41no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17—41no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×Dic17—22no—
361C2×Dic17—22no—
362C2×Dic17—22no—
363C2×Dic17—22no—
364C2×Dic17—22no—
365C2×Dic17—22no—
366C2×Dic17—22no—
367C2×Dic17—22no—
368C2×Dic17—22no—
369C2×Dic17—22no—
370C2×Dic17—22no—
371C2×Dic17—22no—
372C2×Dic17—22no—
373C2×Dic17—22no—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—41no—
379C2×Dic17—41no—
380C2×Dic17—41no—
381C2×Dic17—41no—
382C2×Dic17—41no—
383C2×Dic17—41no—
384C2×Dic17—41no—
385C2×Dic17—41no—
386C2×Dic17—41no—
387C2×Dic17—41no—
388C2×Dic17—41no—
389C2×Dic17—41no—
390C2×Dic17—41no—
391C2×Dic17—41no—
392C2×Dic17—41no—
393C2×Dic17—41no—
394C2×Dic17—41no—
395C2×Dic17—41no—
396C2×Dic17—41no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17C4×D414yes—
416Dic34—416no—
417C2×#393—171no—
418C2×#391—171no—
419C2×#388—171no—
420#1446—171no—
421#1444—171no—
422#1442—171no—
423#1442—171no—
424#1442—171no—
425#1442—171no—
426#1440—171no—
427#1440—171no—
428#1439—171no—
429#1439—171no—
430#1439D1711yescharacteristic
431#1434—171no—
432C22×C17—42no—
433C22×C17—42no—
434C22×C17—42no—
435C22×C17—42no—
436C22×C17—42no—
437C22×C17—42no—
438C22×C17—42no—
439C22×C17—81no—
440C22×C17—81no—
441C22×C17—81no—
442C22×C17—81no—
443C22×C17—81no—
444C22×C17—81no—
445C22×C17—81no—
446C22×C17—81no—
447C22×C17C2×C4×D411yescharacteristic
448C22×C17#51811yescharacteristic
449C22×C17#51811yescharacteristic
450C22×C17#51911yescharacteristic
451C22×C17#52011yescharacteristic
452C22×C17#52011yescharacteristic
453C22×C17#52011yescharacteristic
454C22×C17#53411yescharacteristic
455C22×C17#53511yescharacteristic
456C22×C17#53511yescharacteristic
457C22×C17#53611yescharacteristic
458C22×C17#53611yescharacteristic
459C22×C17#53711yescharacteristic
460C22×C17#53811yescharacteristic
461C22×C17#53811yescharacteristic
462C22×C17#54111yescharacteristic
463C22×C17#54211yescharacteristic
464C22×C17#54211yescharacteristic
465C22×C17#54211yescharacteristic
466C22×C17H(3,𝔽4)11yescharacteristic
467C22×C17H(3,𝔽4)11yescharacteristic
468C22×C17#56211yescharacteristic
469C22×C17#56211yescharacteristic
470C22×C17#56211yescharacteristic
471C22×C17#56211yescharacteristic
472C22×C17#56211yescharacteristic
473C22×C17#56211yescharacteristic
474C22×C17#56211yescharacteristic
475C22×C17#56211yescharacteristic
476C22×C17#56311yescharacteristic
477C22×C17#56311yescharacteristic
478C22×C17#56311yescharacteristic
479C22×C17#56311yescharacteristic
480C22×C17#56311yescharacteristic
481C22×C17#56311yescharacteristic
482C4×C17—42no—
483C4×C17—42no—
484C4×C17—42no—
485C4×C17—81no—
486C4×C17—81no—
487C4×C17—81no—
488Dic17—24no—
489Dic17—42no—
490Dic17—42no—
491Dic17—42no—
492Dic17—42no—
493Dic17—81no—
494Dic17—81no—
495Dic17—81no—
496C23×Q8—171no—
497C22×C4⋊C4—171no—
498C22×C4⋊C4—171no—
499C22×C4⋊C4—171no—
500C22×C4⋊C4C2×D1711yescharacteristic
501C22×C22⋊C4—171no—
502C22×C22⋊C4—171no—
503C22×C22⋊C4—171no—
504C22×C22⋊C4—171no—
505C22×C22⋊C4C2×D1711yescharacteristic
506C22×C22⋊C4C2×D1711yescharacteristic
507C22×C22⋊C4C2×D1711yescharacteristic
508C22×C42—171no—
509#393—178no—
510#391—344no—
511#388—344no—
512C2×#95—171no—
513C2×#95—171no—
514C2×#95—171no—
515C2×#95—171no—
516C2×#95—171no—
517C2×#95—171no—
518C2×#95—171no—
519C2×#95—171no—
520C2×#95—171no—
521C2×#95—171no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×#95—171no—
528C2×#95—171no—
529C2×#95—171no—
530C2×#95—171no—
531C2×#95C2×D1711yescharacteristic
532C2×#95C2×D1711yescharacteristic
533C2×#95C2×D1711yescharacteristic
534C2×C17—82no—
535C2×C17#232111yescharacteristic
536C2×C17#232311yescharacteristic
537C2×C17#232611yescharacteristic
538C2×C17#237811yescharacteristic
539C2×C17#237811yescharacteristic
540C2×C17#237911yescharacteristic
541C2×C17#237911yescharacteristic
542C2×C17#281411yescharacteristic
543C2×C17#281611yescharacteristic
544C2×C17#281911yescharacteristic
545C2×C17#282111yescharacteristic
546C2×C17#283111yescharacteristic
547C2×C17#283111yescharacteristic
548C2×C17#283211yescharacteristic
549C2×C17#283211yescharacteristic
550C25C22×D1711yescharacteristic
551C22×Q8—174no—
552C22×Q8—342no—
553C22×Q8—342no—
554C22×Q8—681no—
555C22×Q8—681no—
556C22×Q8—681no—
557C22×Q8—681no—
558C23×C4—171no—
559C23×C4—171no—
560C23×C4—171no—
561C23×C4—171no—
562C23×C4—171no—
563C23×C4—171no—
564C23×C4—171no—
565C23×C4—171no—
566C23×C4C22×D1711yescharacteristic
567C23×C4C22×D1711yescharacteristic
568C23×C4C22×D1711yescharacteristic
569C23×C4C22×D1711yescharacteristic
570C23×C4C22×D1711yescharacteristic
571C23×C4C22×D1711yescharacteristic
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—342no—
576C2×C4⋊C4—342no—
577C2×C4⋊C4—681no—
578C2×C4⋊C4—681no—
579C2×C4⋊C4—681no—
580C2×C4⋊C4—681no—
581C2×C4⋊C4—681no—
582C2×C4⋊C4—681no—
583C2×C4⋊C4—681no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—174no—
593C2×C22⋊C4—174no—
594C2×C22⋊C4—342no—
595C2×C22⋊C4—342no—
596C2×C22⋊C4—342no—
597C2×C22⋊C4—681no—
598C2×C22⋊C4—681no—
599C2×C22⋊C4—681no—
600C2×C22⋊C4—681no—
601C2×C22⋊C4—681no—
602C2×C22⋊C4—681no—
603C2×C22⋊C4—681no—
604C2×C22⋊C4C4×D1714yes—
605C2×C42—174no—
606C2×C42—681no—
607C2×C42—681no—
608#95—22no—
609#95—41no—
610#95—41no—
611#95—174no—
612#95—174no—
613#95—174no—
614#95—342no—
615#95—342no—
616#95—342no—
617#95—342no—
618#95—342no—
619#95—342no—
620#95—681no—
621#95—681no—
622#95—681no—
623#95—681no—
624#95—681no—
625#95—681no—
626#95—681no—
627#95—681no—
628#95—681no—
629#95—681no—
630C17#1462511yescharacteristic, complemented, Sylow
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24C2×C4×D1712yes—
646C24C23×D1711yescharacteristic
647C2×Q8—348no—
648C2×Q8—684no—
649C2×Q8—684no—
650C2×Q8—684no—
651C2×Q8—684no—
652C2×Q8—684no—
653C2×Q8—684no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—172no—
694C22×C4—172no—
695C22×C4—172no—
696C22×C4—172no—
697C22×C4—172no—
698C22×C4—172no—
699C22×C4—172no—
700C22×C4—341no—
701C22×C4—341no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4C2×C4×D1712yes—
750C22×C4C2×C4×D1712yes—
751C22×C4D4×D1712yes—
752C4⋊C4—44no—
753C4⋊C4—684no—
754C4⋊C4—684no—
755C4⋊C4—684no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—348no—
760C22⋊C4—684no—
761C22⋊C4—684no—
762C22⋊C4—684no—
763C42—684no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23C22×C4×D1711yescharacteristic
800C23C2×D4×D1711yescharacteristic
801C23#1058769111yescharacteristic
802C23#1058769111yescharacteristic
803C23#1058769111yescharacteristic
804C23#1058769111yescharacteristic
805C23#1058769111yescharacteristic
806C23#1058769111yescharacteristic
807C23#1058769411yescharacteristic
808C23#41×D1711yescharacteristic
809C23#1058769611yescharacteristic
810C23#1058769711yescharacteristic
811C23#1058769711yescharacteristic
812C23#1058769711yescharacteristic
813C23#1058769711yescharacteristic
814Q8—6816no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—174no—
858C2×C4—342no—
859C2×C4—342no—
860C2×C4—342no—
861C2×C4—342no—
862C2×C4—342no—
863C2×C4—342no—
864C2×C4—342no—
865C2×C4—342no—
866C2×C4—342no—
867C2×C4—342no—
868C2×C4—342no—
869C2×C4—342no—
870C2×C4—342no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—681no—
877C2×C4—681no—
878C2×C4—681no—
879C2×C4—681no—
880C2×C4—681no—
881C2×C4—681no—
882C2×C4—681no—
883C2×C4—681no—
884C2×C4—681no—
885C2×C4—681no—
886C2×C4—681no—
887C2×C4—681no—
888C2×C4—681no—
889C2×C4—681no—
890C2×C4—681no—
891C2×C4—681no—
892C2×C4—681no—
893C2×C4—681no—
894C2×C4—681no—
895C2×C4—681no—
896C2×C4—681no—
897C2×C4—681no—
898C2×C4—681no—
899C2×C4—681no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—681no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22C4×D4×D1711yescharacteristic
929C22#1176328111yescharacteristic
930C22#1176328211yescharacteristic
931C22#1176328611yescharacteristic
932C22#1176328811yescharacteristic
933C22#1176328811yescharacteristic
934C22#1176329011yescharacteristic
935C22#1176336711yescharacteristic
936C22#1176337211yescharacteristic
937C22#1176337411yescharacteristic
938C22#1176338111yescharacteristic
939C22#1176338211yescharacteristic
940C22#1176338811yescharacteristic
941C22#1176339111yescharacteristic
942C22#1176339311yescharacteristic
943C22#1176341611yescharacteristic
944C22#1176342311yescharacteristic
945C22#1176342711yescharacteristic
946C22#1176342911yescharacteristic
947C22#1176355211yescharacteristic
948C22#1176355211yescharacteristic
949C22#1176355311yescharacteristic
950C22#1176355411yescharacteristic
951C22#1176355411yescharacteristic
952C22#1176355411yescharacteristic
953C22#1176355411yescharacteristic
954C22#1176355411yescharacteristic
955C22#1176355511yescharacteristic
956C22#1176355611yescharacteristic
957C22#1176356011yescharacteristic
958C22#1176356011yescharacteristic
959C22#1176356011yescharacteristic
960C22#1176356111yescharacteristic
961C22#1176356211yescharacteristic
962C22#1176356211yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—81no—
967C4—81no—
968C4—81no—
969C4—344no—
970C4—682no—
971C4—682no—
972C4—682no—
973C4—682no—
974C4—1361no—
975C4—1361no—
976C4—1361no—
977C2—82no—
978C2#1453144311yescharacteristic
979C2#1453146311yescharacteristic
980C2#1453149011yescharacteristic
981C2#1453194711yescharacteristic
982C2#1453195111yescharacteristic
983C2#1453195411yescharacteristic
984C2#1453195711yescharacteristic
985C2#1453680211yescharacteristic
986C2#1453681611yescharacteristic
987C2#1453683111yescharacteristic
988C2#1453684711yescharacteristic
989C2#1453694111yescharacteristic
990C2#1453694311yescharacteristic
991C2#1453695011yescharacteristic
992C2#1453695211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenter#1439D17
hypocenterC17#14625
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#11762713C2semidirect
4. #14527054C2semidirect
5. #14527047C2semidirect
6. #14527043C2semidirect
7. #14527042C2semidirect
8. #14527042C2semidirect
9. #14527039C2semidirect
14. #14527008C2semidirect
25. #11762721C4semidirect
630. C17#14625semidirect

Maximal subgroups

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

subgroupindex
C2×#117627212
C2×#117627132
C2×#117627032
#145270542
#145270472
#145270432
#145270422
#145270392
#145270332
#145270312
#145270272
#145270082
C17×#14392
#1462517