Finite Group Databasebeta

← #29730797

Subgroups — #29730797

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840001C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839984C211yesmaximal, characteristic, complemented
4C2×D4×#92418C211yesmaximal, characteristic, complemented
5#21450758C211yesmaximal, characteristic
6#21447015C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446628C211yesmaximal, characteristic, complemented
11#21446585C211yesmaximal, characteristic, complemented
12#21446245C211yesmaximal, characteristic, complemented
13#21446240C211yesmaximal, characteristic, complemented
14C4×#14519701C211yesmaximal, characteristic, complemented
15C61×#2536C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519765C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25#16840001—24no—
26#16839993—24no—
27#16839984—24no—
28D4×#92418—24no—
29C2×#14519710C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C4×#92418C2211yescharacteristic
43#16839697—21no—
44#16839670—21no—
45#16839662—21no—
46#16839662—21no—
47C4×C4⋊Dic61C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#398—21no—
57C61×#394—21no—
58C61×#388—21no—
59C61×#388—21no—
60C61×#382C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—41no—
70C2×#11758201—22no—
71C2×#11758201—22no—
72C2×#11758201—41no—
73C22×#92418—22no—
74C22×#92418—22no—
75C22×#92418—22no—
76C22×#92418—22no—
77C22×#92418—41no—
78C22×#92418—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519765—22no—
84#14519765—22no—
85#14519756—22no—
86#14519756—22no—
87#14519756—41no—
88#14519756—41no—
89#14519751—22no—
90#14519751—22no—
91#14519751—41no—
92#14519751—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61—21no—
104#14519710—22no—
105#14519708—22no—
106C4⋊#92418D414yescomplemented
107#14519701—22no—
108#14519701D414yescomplemented
109#14519700—22no—
110#14519700—22no—
111#14519700—41no—
112#14519697—22no—
113#14519697—22no—
114#14519697—41no—
115C22⋊#92418—22no—
116C22⋊#92418—22no—
117C4×#92418—22no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×D4×C61D411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C22⋊Q8×C61—22no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—41no—
126C22⋊Q8×C61—41no—
127C4×Q8×C61—22no—
128C4×Q8×C61—22no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61—21no—
150C24×C61C2×D411yescharacteristic
151C24×C61C2×D411yescharacteristic
152C23×D61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61C2×D412yes—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—81no—
188C2×C22⋊D61—81no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—42no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C42×C61—42no—
221C42×C61C2×D412yes—
222C42×C61#4112yes—
223C22⋊Dic61—42no—
224C22⋊Dic61—42no—
225#11758202—44no—
226#11758201—44no—
227#11758198—42no—
228#11758198—42no—
229#11758198—42no—
230#11758198—42no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61C2×D412yes—
234C4⋊Dic61#4112yes—
235#11758196—42no—
236#11758196—42no—
237C4×Dic61—81no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—44no—
248C2×#92418—44no—
249C2×#92418C2×D412yes—
250C2×#92418C2×D412yes—
251C2×#92418C2×D412yes—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61#13512yes—
265C23×C61#13512yes—
266C23×C61C22×D411yescharacteristic
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—41no—
277Q8×C61—41no—
278D4×C61—28no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61#12112yes—
310C2×C4×C61#12112yes—
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C22⋊D61—84no—
318C22⋊D61—84no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328D244—41no—
329D244—41no—
330D244—41no—
331D244—41no—
332Dic122—41no—
333Dic122—41no—
334Dic122—41no—
335Dic122—41no—
336#92418—22no—
337#92418—22no—
338#92418—22no—
339#92418—41no—
340#25389—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61C2×#12111yescharacteristic
356C22×C61D4211yescharacteristic
357C22×C61#54611yescharacteristic
358C22×C61C2×#13511yescharacteristic
359C22×C61C2×#13511yescharacteristic
360C22×C61#57711yescharacteristic
361C22×C61#57811yescharacteristic
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C4×C61—22no—
370C4×C61—22no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61—42no—
374C4×C61—81no—
375C4×C61—81no—
376C4×C61—81no—
377C4×C61#53211yescharacteristic
378C4×C61#54011yescharacteristic
379C4×C61D4211yescharacteristic
380C4×C61#55011yescharacteristic
381Dic61—42no—
382Dic61—42no—
383Dic61—81no—
384C2×#467—611no—
385C2×#465—611no—
386C2×#464—611no—
387C2×C8×D4—611no—
388#2540—611no—
389#2536D6111yescharacteristic, complemented
390#2035—611no—
391#2033—611no—
392#2001—611no—
393#2000—611no—
394#1958—611no—
395#1949—611no—
396#1893—611no—
397#1892—611no—
398C4×#103—611no—
399C2×C61—42no—
400C2×C61—42no—
401C2×C61#242811yescharacteristic
402C2×C61#305011yescharacteristic
403C2×C61#306311yescharacteristic
404C2×C61#328211yescharacteristic
405C2×C61#328511yescharacteristic
406C2×C61#329611yescharacteristic
407C2×C61#330011yescharacteristic
408D61—161no—
409C22×Q16—611no—
410C22×SD16—611no—
411C23×C8—611no—
412C23×C8—611no—
413C2×#124—611no—
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8C2×D6111yescharacteristic
417C2×C22⋊Q8C2×D6111yescharacteristic
418C2×#121—611no—
419C2×#121—611no—
420C2×C4×Q8C2×D6111yescharacteristic
421C2×C4×D4C2×D6111yescharacteristic
422#467—1224no—
423#465—1224no—
424#464—1224no—
425C8×D4—1224no—
426C2×#107—611no—
427C2×#106—611no—
428C2×C4⋊C8—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×C22⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C4×C8—611no—
440#399—1221no—
441#398—21no—
442#394—21no—
443#392—1221no—
444#390—1221no—
445#390—1221no—
446#388—21no—
447#388—21no—
448#382C2×D6111yescharacteristic
449#380C2×D6111yescharacteristic
450#380C2×D6111yescharacteristic
451C4×C4⋊C4—611no—
452#340—611no—
453#340—611no—
454#340—611no—
455#340—611no—
456C61#2538911yescharacteristic, complemented, Sylow
457C22×Q8—611no—
458C22×Q8C22×D6111yescharacteristic
459C22×D4—611no—
460C22×D4—1221no—
461C22×D4—1221no—
462C22×D4C22⋊D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C2×Q16—1222no—
466C2×Q16—1222no—
467C2×Q16—2441no—
468C2×SD16—1222no—
469C2×SD16—1222no—
470C2×SD16—2441no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—1222no—
476C22×C8—1222no—
477C22×C8—1222no—
478C22×C8—1222no—
479C22×C8—2441no—
480C22×C8—2441no—
481#124—1222no—
482#124—1222no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—41no—
486C22⋊Q8—41no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—2441no—
490C22⋊Q8—2441no—
491#121—1222no—
492#121—1222no—
493#121—2441no—
494#121—2441no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×D4—22no—
498C4×D4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4C22⋊D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C4⋊C4C22×D6111yescharacteristic
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4C22⋊D6111yescharacteristic
521C2×C22⋊C4C22⋊D6111yescharacteristic
522C2×C42—21no—
523C2×C42—1221no—
524C2×C42C22×D6111yescharacteristic
525#107—1222no—
526#106—1222no—
527C4⋊C8—614no—
528#103—614no—
529#103—1222no—
530#103—1222no—
531#103—1222no—
532#103—2441no—
533#102—1222no—
534#102—1222no—
535#102—2441no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C4×C8—1222no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—1221no—
544C24—1221no—
545C24C2×C22⋊D6111yescharacteristic
546C24C2×C22⋊D6111yescharacteristic
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8D4×D6112yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—4881no—
569C2×D4—4881no—
570C2×D4—2442no—
571C2×D4—2442no—
572C2×D4—2442no—
573C2×D4—2442no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598Q16—2444no—
599SD16—2444no—
600C2×C8—612no—
601C2×C8—612no—
602C2×C8—612no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—2444no—
613C2×C8—2444no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—612no—
625C4⋊C4—612no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—2442no—
629C4⋊C4—2442no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—2442no—
637C22⋊C4—2442no—
638C22⋊C4—2442no—
639C22⋊C4—2442no—
640C22⋊C4—2442no—
641C22⋊C4—2442no—
642C42—42no—
643C42—4881no—
644C42D4×D6112yes—
645C42#1175822412yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—2441no—
665C23#1451979712yes—
666C23#1451979712yes—
667C23C22×C22⋊D6111yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672Q8—2441no—
673Q8—2441no—
674Q8—2441no—
675Q8—2441no—
676D4—28no—
677D4—4884no—
678D4—4884no—
679D4—2441no—
680D4—2441no—
681D4—2441no—
682D4—2441no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4#1451974912yes—
723C2×C4#1451974912yes—
724C2×C4C2×D4×D6111yescharacteristic
725C2×C4C2×D4×D6111yescharacteristic
726C2×C4#41×D6111yescharacteristic
727C2×C4C2×#1175822411yescharacteristic
728C2×C4#1451982211yescharacteristic
729C2×C4#1451982311yescharacteristic
730C8—1222no—
731C8—1222no—
732C8—1222no—
733C8—2441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—4881no—
749C22—4881no—
750C22—4881no—
751C22—4881no—
752C22—4881no—
753C22—4881no—
754C22—4881no—
755C22C2×#1451974911yescharacteristic
756C22D4×C22⋊D6111yescharacteristic
757C22#1684040011yescharacteristic
758C22C2×#1451979711yescharacteristic
759C22C2×#1451979711yescharacteristic
760C22#1684057011yescharacteristic
761C22#1684057711yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4—81no—
770C4—4881no—
771C4—2442no—
772C4—2442no—
773C4#1684030711yescharacteristic
774C4#1684036511yescharacteristic
775C4#1684039611yescharacteristic
776C4#1684043011yescharacteristic
777C2—42no—
778C2—42no—
779C2—9761no—
780C2#2144940911yescharacteristic
781C2#2145539711yescharacteristic
782C2#2145550611yescharacteristic
783C2#2145752711yescharacteristic
784C2#2145755611yescharacteristic
785C2#2145764811yescharacteristic
786C2#2145770011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2536C2
socleC23×C61C22×D4
prime radical#21450758C2
hypercenter#2536D61
hypocenterC61#25389
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. C2×#16840001C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839984C2semidirect
4. C2×D4×#92418C2semidirect
6. #21447015C2semidirect
7. #21447001C2semidirect
8. #21446827C2semidirect
9. #21446820C2semidirect
10. #21446628C2semidirect
11. #21446585C2semidirect
12. #21446245C2semidirect
13. #21446240C2semidirect
14. C4×#14519701C2semidirect
15. C61×#2536C2semidirect
106. C4⋊#92418D4semidirect
108. #14519701D4semidirect
389. #2536D61semidirect
456. C61#25389semidirect

Maximal subgroups

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

subgroupindex
C2×#168400012
C2×#168399932
C2×#168399842
C2×D4×#924182
#214507582
#214470152
#214470012
#214468272
#214468202
#214466282
#214465852
#214462452
#214462402
C4×#145197012
C61×#25362
#2538961