Finite Group Databasebeta

← #29730948

Subgroups — #29730948

Order 15616.

1048 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840010C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839964C211yesmaximal, characteristic, complemented
4C2×#16839834C211yesmaximal, characteristic, complemented
5#21450720C211yesmaximal, characteristic
6#21447019C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446820C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446640C211yesmaximal, characteristic, complemented
11#21446587C211yesmaximal, characteristic, complemented
12#21446253C211yesmaximal, characteristic, complemented
13#21446243C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15C61×#2542C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23#16840010—24no—
24#16839993—24no—
25#16839964—24no—
26#16839834—24no—
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519688C2211yescharacteristic
41#16839688—21no—
42#16839670—21no—
43#16839638—21no—
44#16839638—21no—
45#16839628C2211yescharacteristic
46#16839622C2211yescharacteristic
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#399—21no—
59C61×#399—21no—
60C61×#390—21no—
61C61×#384—21no—
62C4×C4⋊C4×C61C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C2×#11758201—22no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201—41no—
72C2×#11758201—41no—
73C2×#11758194—22no—
74C2×#11758194—22no—
75C2×#11758194—41no—
76C22×#92418—22no—
77C22×#92418—22no—
78C22×#92418—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519751—22no—
84#14519751—22no—
85#14519751—41no—
86#14519751—41no—
87C4×D244—22no—
88C4×D244—22no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97#14519710—22no—
98#14519708—22no—
99C4⋊#92418D414yescomplemented
100#14519701—22no—
101#14519701—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—41no—
105#14519701—41no—
106#14519697—22no—
107#14519697D414yescomplemented
108C22⋊#92418—22no—
109C22⋊#92418—22no—
110#14519688—22no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C22×Q8×C61C2311yescharacteristic
116C22×Q8×C61C2311yescharacteristic
117C22×D4×C61D411yescharacteristic
118C23×C4×C61C2311yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C4⋊Q8×C61—22no—
121C4⋊Q8×C61—22no—
122C22⋊Q8×C61—22no—
123C22⋊Q8×C61—22no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127C22⋊Q8×C61—41no—
128C22⋊Q8×C61—41no—
129C22⋊Q8×C61—41no—
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61D411yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
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×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—41no—
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×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—81no—
194C2×C22⋊D61—81no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244C2×D412yes—
204C2×C4×D61—42no—
205C2×C4×D61—81no—
206C2×C4×D61—81no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—42no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61C2×D412yes—
217C4⋊C4×C61#4112yes—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—42no—
224C42×C61—42no—
225C42×C61C2×D412yes—
226C42×C61#4112yes—
227C22⋊Dic61—81no—
228C22⋊Dic61—81no—
229#11758201—44no—
230#11758201—44no—
231#11758198—42no—
232#11758198—42no—
233#11758198—42no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240#11758194—44no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—44no—
251C2×#92418C2×D412yes—
252C2×#92418C2×D412yes—
253C2×#92418C2×D412yes—
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—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61#13712yes—
268C23×C61C22×D411yescharacteristic
269C22×D61—22no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276Q8×C61—41no—
277Q8×C61—41no—
278Q8×C61—41no—
279Q8×C61—41no—
280Q8×C61—41no—
281Q8×C61—41no—
282Q8×C61—41no—
283Q8×C61—41no—
284D4×C61—44no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
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—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61#12112yes—
316C2×C4×C61#12112yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C22⋊D61—84no—
324C22⋊D61—84no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334D244—22no—
335D244—22no—
336D244—41no—
337D244—41no—
338C4×D61—84no—
339#92418—22no—
340#92418—22no—
341#92418—22no—
342#92418—41no—
343#25400—611nomaximal, Sylow
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×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61C2×#12111yescharacteristic
359C22×C61D4211yescharacteristic
360C22×C61#54611yescharacteristic
361C22×C61C2×#13711yescharacteristic
362C22×C61#57511yescharacteristic
363C22×C61#57711yescharacteristic
364C22×C61#57711yescharacteristic
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C4×C61—22no—
373C4×C61—22no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61—81no—
379C4×C61—81no—
380C4×C61#53211yescharacteristic
381C4×C61#54011yescharacteristic
382C4×C61D4211yescharacteristic
383C4×C61#55011yescharacteristic
384Dic61—81no—
385Dic61—81no—
386Dic61—81no—
387C2×#468—611no—
388C2×#465—611no—
389C2×#461—611no—
390C2×#435—611no—
391#2542D6111yescharacteristic, complemented
392#2535—611no—
393#2036—611no—
394#2035—611no—
395#2000—611no—
396#2000—611no—
397#1960—611no—
398#1949—611no—
399#1894—611no—
400#1892—611no—
401#1762—611no—
402C2×C61—42no—
403C2×C61—81no—
404C2×C61#242811yescharacteristic
405C2×C61#305611yescharacteristic
406C2×C61#305711yescharacteristic
407C2×C61#326611yescharacteristic
408C2×C61#326711yescharacteristic
409C2×C61#330711yescharacteristic
410C2×C61#332011yescharacteristic
411D61—82no—
412C22×SD16—611no—
413C22×SD16—611no—
414C22×M16—611no—
415C23×C8—611no—
416C2×C4⋊Q8C2×D6111yescharacteristic
417C2×C22⋊Q8C2×D6111yescharacteristic
418C2×C22⋊Q8C2×D6111yescharacteristic
419C2×C22⋊Q8C2×D6111yescharacteristic
420C2×C22⋊Q8C2×D6111yescharacteristic
421C2×#121—611no—
422C2×#121—611no—
423C2×C4×D4—611no—
424C2×C4×D4C2×D6111yescharacteristic
425#468—1224no—
426#465—1224no—
427#461—1224no—
428#435—1224no—
429C2×#107—611no—
430C2×#106—611no—
431C2×C4⋊C8—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×#97—611no—
443#399—21no—
444#399—21no—
445#397—1221no—
446#392—1221no—
447#390—21no—
448#386—1221no—
449#386—1221no—
450#384—21no—
451#382—611no—
452#380—611no—
453#380—611no—
454C4×C4⋊C4C2×D6111yescharacteristic
455#340—611no—
456#340—611no—
457#340—611no—
458#340—611no—
459C61#2540011yescharacteristic, complemented, Sylow
460C22×Q8C22×D6111yescharacteristic
461C22×Q8C22×D6111yescharacteristic
462C22×D4—611no—
463C22×D4—1221no—
464C22×D4—1221no—
465C22×D4C22⋊D6111yescharacteristic
466C23×C4—1221no—
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C2×SD16—1222no—
470C2×SD16—1222no—
471C2×SD16—1222no—
472C2×SD16—1222no—
473C2×SD16—2441no—
474C2×SD16—2441no—
475C2×M16—1222no—
476C2×M16—1222no—
477C2×M16—2441no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—1222no—
483C22×C8—1222no—
484C22×C8—2441no—
485C4⋊Q8—22no—
486C4⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—41no—
492C22⋊Q8—41no—
493C22⋊Q8—41no—
494C22⋊Q8—41no—
495#121—1222no—
496#121—1222no—
497#121—2441no—
498#121—2441no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—1222no—
502C4×D4—1222no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4C22⋊D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4C22⋊D6111yescharacteristic
525C2×C22⋊C4C22⋊D6111yescharacteristic
526C2×C42—21no—
527C2×C42C22×D6111yescharacteristic
528#107—1222no—
529#106—1222no—
530C4⋊C8—614no—
531#103—1222no—
532#103—1222no—
533#103—1222no—
534#103—1222no—
535#103—2441no—
536#103—2441no—
537#102—614no—
538#102—1222no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541#97—1222no—
542#95—21no—
543#95—1221no—
544#95—1221no—
545#95—1221no—
546#95—1221no—
547C24—1221no—
548C24C2×C22⋊D6111yescharacteristic
549C24C2×C22⋊D6111yescharacteristic
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—612no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—4881no—
572C2×D4—4881no—
573C2×D4—2442no—
574C2×D4—2442no—
575C2×D4—2442no—
576C2×D4—2442no—
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—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—4881no—
597C22×C4—4881no—
598C22×C4—2442no—
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C23×D6111yescharacteristic
604SD16—2444no—
605SD16—2444no—
606M16—2444no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—2444no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—22no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4D4×D6112yes—
636C4⋊C4#1175822412yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—4881no—
644C22⋊C4—4881no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C22⋊C4—2442no—
648C42—42no—
649C42D4×D6112yes—
650C42#1175822412yes—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—1222no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23#1451980812yes—
672C23C22×C22⋊D6111yescharacteristic
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681D4—44no—
682D4—1222no—
683D4—1222no—
684D4—4884no—
685D4—4884no—
686D4—2441no—
687D4—2441no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
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—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—4884no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4#1451974912yes—
729C2×C4#1451974912yes—
730C2×C4C2×D4×D6111yescharacteristic
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4C2×#1175822411yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4#1451982211yescharacteristic
735C2×C4#1451982211yescharacteristic
736C8—1222no—
737C8—1222no—
738C8—1222no—
739C8—2441no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—4881no—
755C22—4881no—
756C22—4881no—
757C22—4881no—
758C22—2442no—
759C22—2442no—
760C22—2442no—
761C22C2×#1451974911yescharacteristic
762C22D4×C22⋊D6111yescharacteristic
763C22#1684040611yescharacteristic
764C22C2×#1451980811yescharacteristic
765C22#1684056011yescharacteristic
766C22#1684057011yescharacteristic
767C22#1684057011yescharacteristic
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4—4881no—
777C4—4881no—
778C4—4881no—
779C4#1684031011yescharacteristic
780C4#1684036611yescharacteristic
781C4#1684039711yescharacteristic
782C4#1684043211yescharacteristic
783C2—42no—
784C2—81no—
785C2—4882no—
786C2#2144941011yescharacteristic
787C2#2145544511yescharacteristic
788C2#2145546011yescharacteristic
789C2#2145733011yescharacteristic
790C2#2145734511yescharacteristic
791C2#2145779511yescharacteristic
792C2#2145799011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2542C2
socleC23×C61C22×D4
prime radical#21450720C2
hypercenter#2542D61
hypocenterC61#25400
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#16840010C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839964C2semidirect
4. C2×#16839834C2semidirect
6. #21447019C2semidirect
7. #21447012C2semidirect
8. #21446820C2semidirect
9. #21446820C2semidirect
10. #21446640C2semidirect
11. #21446587C2semidirect
12. #21446253C2semidirect
13. #21446243C2semidirect
14. #21445647C2semidirect
15. C61×#2542C2semidirect
99. C4⋊#92418D4semidirect
107. #14519697D4semidirect
391. #2542D61semidirect
459. C61#25400semidirect

Maximal subgroups

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

subgroupindex
C2×#168400102
C2×#168399932
C2×#168399642
C2×#168398342
#214507202
#214470192
#214470122
#214468202
#214466402
#214465872
#214462532
#214462432
#214456472
C61×#25422
#2540061