Finite Group Databasebeta

← #29730784

Subgroups — #29730784

Order 15616.

1116 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839996C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839974C211yesmaximal, characteristic, complemented
4C2×D4×#92418C211yesmaximal, characteristic, complemented
5#21450720C211yesmaximal, characteristic, complemented
6#21447019C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446820C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446631C211yesmaximal, characteristic, complemented
11#21446587C211yesmaximal, characteristic, complemented
12#21446248C211yesmaximal, characteristic, complemented
13#21446243C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2540C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23#16839996—24no—
24#16839993—24no—
25#16839974—24no—
26D4×#92418—24no—
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
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×#124×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#399—21no—
59C61×#392—21no—
60C61×#390—21no—
61C61×#390—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—41no—
70C2×#11758199—22no—
71C2×#11758199—22no—
72C2×#11758199—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#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—41no—
103#14519698—22no—
104#14519698—22no—
105#14519698—41no—
106#14519697—22no—
107#14519697D414yescomplemented
108C22⋊#92418—22no—
109C22⋊#92418—22no—
110C4×#92418—22no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C22×Q8×C61C2311yescharacteristic
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61D411yescharacteristic
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122#124×C61—22no—
123#124×C61—22no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127C22⋊Q8×C61—41no—
128#121×C61—22no—
129#121×C61—22no—
130#121×C61—41no—
131#121×C61—41no—
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61D411yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
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×C61—21no—
151C24×C61C2×D411yescharacteristic
152C24×C61C2×D411yescharacteristic
153C23×D61—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×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—81no—
174C2×D4×C61—81no—
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×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—81no—
200C2×C22⋊D61—81no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244C2×D412yes—
210C2×C4×D61—42no—
211C2×C4×D61—81no—
212C2×C4×D61—81no—
213C4⋊C4×C61—22no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—42no—
217C4⋊C4×C61—42no—
218C4⋊C4×C61C2×D412yes—
219C4⋊C4×C61#4112yes—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—42no—
227C22⋊C4×C61—42no—
228C42×C61—81no—
229C42×C61C2×D412yes—
230C42×C61#4112yes—
231C22⋊Dic61—81no—
232C22⋊Dic61—81no—
233#11758201—44no—
234#11758199—44no—
235#11758198—42no—
236#11758198—42no—
237#11758198—42no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—44no—
254C2×#92418—44no—
255C2×#92418C2×D412yes—
256C2×#92418C2×D412yes—
257C2×#92418C2×D412yes—
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—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61#13512yes—
278C23×C61#13512yes—
279C23×C61C22×D411yescharacteristic
280C22×D61—22no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287Q8×C61—41no—
288Q8×C61—41no—
289Q8×C61—41no—
290Q8×C61—41no—
291D4×C61—28no—
292D4×C61—41no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61—41no—
296D4×C61—84no—
297D4×C61—84no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61#12112yes—
326C2×C4×C61#12112yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C22⋊D61—84no—
334C22⋊D61—84no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344D244—22no—
345D244—22no—
346D244—41no—
347D244—41no—
348C4×D61—84no—
349#92418—22no—
350#92418—22no—
351#92418—22no—
352#92418—41no—
353#25388—611nomaximal, Sylow
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61C2×#12111yescharacteristic
376C22×C61D4211yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61C2×#13511yescharacteristic
379C22×C61C2×#13511yescharacteristic
380C22×C61#57611yescharacteristic
381C22×C61#57711yescharacteristic
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C4×C61—22no—
390C4×C61—22no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61—81no—
396C4×C61#53211yescharacteristic
397C4×C61#54011yescharacteristic
398C4×C61D4211yescharacteristic
399C4×C61#55011yescharacteristic
400Dic61—81no—
401Dic61—81no—
402Dic61—81no—
403C2×#466—611no—
404C2×#465—611no—
405C2×#463—611no—
406C2×C8×D4—611no—
407#2540D6111yescharacteristic, complemented
408#2535—611no—
409#2036—611no—
410#2034—611no—
411#2000—611no—
412#1999—611no—
413#1958—611no—
414#1949—611no—
415#1893—611no—
416#1892—611no—
417C4×#102—611no—
418C2×C61—42no—
419C2×C61—42no—
420C2×C61—161no—
421C2×C61#242811yescharacteristic
422C2×C61#305011yescharacteristic
423C2×C61#306211yescharacteristic
424C2×C61#328011yescharacteristic
425C2×C61#328211yescharacteristic
426C2×C61#329711yescharacteristic
427C2×C61#330111yescharacteristic
428D61—82no—
429C22×SD16—611no—
430C22×D8—611no—
431C23×C8—611no—
432C23×C8—611no—
433C2×#124C2×D6111yescharacteristic
434C2×C22⋊Q8C2×D6111yescharacteristic
435C2×C22⋊Q8C2×D6111yescharacteristic
436C2×#121—611no—
437C2×#121—611no—
438C2×#121C2×D6111yescharacteristic
439C2×#121C2×D6111yescharacteristic
440C2×C4×D4—611no—
441C2×C4×D4C2×D6111yescharacteristic
442#466—1224no—
443#465—1224no—
444#463—1224no—
445C8×D4—1224no—
446C2×#107—611no—
447C2×#106—611no—
448C2×C4⋊C8—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C4×C8—611no—
460#399—21no—
461#397—1221no—
462#392—21no—
463#392—1221no—
464#390—21no—
465#390—21no—
466#386—1221no—
467#386—1221no—
468#382—611no—
469#380—611no—
470#380—611no—
471C4×C4⋊C4C2×D6111yescharacteristic
472#340—611no—
473#340—611no—
474#340—611no—
475#340—611no—
476C61#2538811yescharacteristic, complemented, Sylow
477C22×Q8C22×D6111yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—611no—
481C22×D4—1221no—
482C22×D4—1221no—
483C22×D4C22⋊D6111yescharacteristic
484C22×D4C22×D6111yescharacteristic
485C23×C4—1221no—
486C23×C4C22×D6111yescharacteristic
487C23×C4C22×D6111yescharacteristic
488C2×SD16—1222no—
489C2×SD16—1222no—
490C2×SD16—2441no—
491C2×D8—1222no—
492C2×D8—1222no—
493C2×D8—2441no—
494C22×C8—611no—
495C22×C8—611no—
496C22×C8—611no—
497C22×C8—611no—
498C22×C8—1222no—
499C22×C8—1222no—
500C22×C8—1222no—
501C22×C8—1222no—
502C22×C8—2441no—
503C22×C8—2441no—
504#124—22no—
505#124—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510#121—22no—
511#121—22no—
512#121—41no—
513#121—41no—
514#121—1222no—
515#121—1222no—
516#121—2441no—
517#121—2441no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—1222no—
521C4×D4—1222no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4C22⋊D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C4⋊C4C22×D6111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4C22⋊D6111yescharacteristic
542C2×C22⋊C4C22⋊D6111yescharacteristic
543C2×C42—21no—
544C2×C42C22×D6111yescharacteristic
545#107—1222no—
546#106—1222no—
547C4⋊C8—614no—
548#103—1222no—
549#103—1222no—
550#103—2441no—
551#102—614no—
552#102—1222no—
553#102—1222no—
554#102—1222no—
555#102—2441no—
556C22⋊C8—1222no—
557C22⋊C8—1222no—
558C4×C8—1222no—
559#95—21no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564C24—21no—
565C24—1221no—
566C24C2×C22⋊D6111yescharacteristic
567C24C2×C22⋊D6111yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—612no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—4881no—
596C2×D4—4881no—
597C2×D4—2442no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4—2442no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—4881no—
620C22×C4—4881no—
621C22×C4—2442no—
622C22×C4C2×C22⋊D6111yescharacteristic
623C22×C4C2×C22⋊D6111yescharacteristic
624C22×C4C2×C22⋊D6111yescharacteristic
625C22×C4C2×C22⋊D6111yescharacteristic
626C22×C4C23×D6111yescharacteristic
627SD16—2444no—
628D8—2444no—
629C2×C8—612no—
630C2×C8—612no—
631C2×C8—612no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—2444no—
642C2×C8—2444no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4D4×D6112yes—
655C4⋊C4#1175822412yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—4881no—
665C22⋊C4—4881no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4—2442no—
669C42—81no—
670C42D4×D6112yes—
671C42#1175822412yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—1222no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23#1451979712yes—
699C23#1451979712yes—
700C23C22×C22⋊D6111yescharacteristic
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705D4—28no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712D4—1222no—
713D4—1222no—
714D4—4884no—
715D4—4884no—
716D4—2441no—
717D4—2441no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—4884no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4#1451974912yes—
756C2×C4#1451974912yes—
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C2×#1175822411yescharacteristic
760C2×C4C2×#1175822411yescharacteristic
761C2×C4#1451982211yescharacteristic
762C2×C4#1451982211yescharacteristic
763C8—1222no—
764C8—1222no—
765C8—1222no—
766C8—2441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—4881no—
789C22—4881no—
790C22—4881no—
791C22—4881no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22C2×#1451974911yescharacteristic
796C22D4×C22⋊D6111yescharacteristic
797C22#1684040611yescharacteristic
798C22C2×#1451979711yescharacteristic
799C22C2×#1451979711yescharacteristic
800C22#1684056511yescharacteristic
801C22#1684057011yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—41no—
807C4—41no—
808C4—81no—
809C4—4881no—
810C4—4881no—
811C4—4881no—
812C4#1684031011yescharacteristic
813C4#1684036611yescharacteristic
814C4#1684039711yescharacteristic
815C4#1684043211yescharacteristic
816C2—42no—
817C2—42no—
818C2—161no—
819C2—4882no—
820C2#2144941011yescharacteristic
821C2#2145539711yescharacteristic
822C2#2145550111yescharacteristic
823C2#2145750011yescharacteristic
824C2#2145752711yescharacteristic
825C2#2145766911yescharacteristic
826C2#2145772111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2540C2
socleC23×C61C22×D4
hypercenter#2540D61
hypocenterC61#25388
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#16839996C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839974C2semidirect
4. C2×D4×#92418C2semidirect
5. #21450720C2semidirect
6. #21447019C2semidirect
7. #21447005C2semidirect
8. #21446820C2semidirect
9. #21446815C2semidirect
10. #21446631C2semidirect
11. #21446587C2semidirect
12. #21446248C2semidirect
13. #21446243C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2540C2semidirect
99. C4⋊#92418D4semidirect
107. #14519697D4semidirect
407. #2540D61semidirect
476. C61#25388semidirect

Maximal subgroups

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

subgroupindex
C2×#168399962
C2×#168399932
C2×#168399742
C2×D4×#924182
#214507202
#214470192
#214470052
#214468202
#214468152
#214466312
#214465872
#214462482
#214462432
C4×#145196972
C61×#25402
#2538861