Finite Group Databasebeta

← #29730963

Subgroups — #29730963

Order 15616.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840013C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839974C211yesmaximal, characteristic, complemented
4C2×#16839834C211yesmaximal, characteristic, complemented
5#21450732C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446820C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446636C211yesmaximal, characteristic, complemented
11#21446582C211yesmaximal, characteristic, complemented
12#21446253C211yesmaximal, characteristic, complemented
13#21446248C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15C61×#2540C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519748—21no—
23C2×C4×D244C2211yescharacteristic
24#16840013—24no—
25#16839993—24no—
26#16839974—24no—
27#16839834—24no—
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519688C2211yescharacteristic
42#16839678—21no—
43#16839678—21no—
44#16839632C2211yescharacteristic
45#16839622C2211yescharacteristic
46#16839622C2211yescharacteristic
47#16839619—21no—
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—
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—
87#14519748—44no—
88C4×D244—22no—
89C4×D244—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100#14519708—22no—
101#14519708—22no—
102C4⋊#92418D414yescomplemented
103#14519701—22no—
104#14519701—22no—
105#14519701—41no—
106#14519698—22no—
107#14519698—22no—
108#14519698—41no—
109#14519697—22no—
110#14519697D414yescomplemented
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113#14519688—22no—
114#14519684—21no—
115#14519684—21no—
116C22×Q8×C61C2311yescharacteristic
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119C22×D4×C61D411yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123#124×C61—22no—
124#124×C61—22no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—22no—
127C22⋊Q8×C61—41no—
128C22⋊Q8×C61—41no—
129#121×C61—22no—
130#121×C61—22no—
131#121×C61—41no—
132#121×C61—41no—
133C4×D4×C61—22no—
134C4×D4×C61—22no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C22⋊C4×C61D411yescharacteristic
148C2×C42×C61—21no—
149C2×C42×C61C2311yescharacteristic
150#95×C61—21no—
151C24×C61—21no—
152C24×C61C2×D411yescharacteristic
153C24×C61C2×D411yescharacteristic
154C23×D61—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×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—41no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—42no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
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×C61—21no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61—81no—
201C2×C22⋊D61—81no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244C2×D412yes—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—42no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61C2×D412yes—
220C4⋊C4×C61#4112yes—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—42no—
227C22⋊C4×C61—42no—
228C22⋊C4×C61—42no—
229C42×C61—81no—
230C42×C61C2×D412yes—
231C42×C61#4112yes—
232C22⋊Dic61—42no—
233C22⋊Dic61—42no—
234#11758201—44no—
235#11758199—44no—
236#11758198—42no—
237#11758198—42no—
238#11758198—42no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—42no—
246C4⋊Dic61—81no—
247#11758194—44no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—44no—
258C2×#92418C2×D412yes—
259C2×#92418C2×D412yes—
260C2×#92418C2×D412yes—
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—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61AGL(1,ℤ/8)12yes—
282C23×C61C22×D411yescharacteristic
283C22×D61—22no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290Q8×C61—41no—
291Q8×C61—41no—
292Q8×C61—41no—
293Q8×C61—41no—
294D4×C61—44no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—41no—
298D4×C61—41no—
299D4×C61—84no—
300D4×C61—84no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
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—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61#12112yes—
329C2×C4×C61#12112yes—
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C22⋊D61—84no—
337C22⋊D61—84no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347D244—22no—
348D244—22no—
349D244—41no—
350D244—41no—
351C4×D61—84no—
352#92418—22no—
353#92418—22no—
354#92418—22no—
355#92418—41no—
356#25401—611nomaximal, Sylow
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—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61C2×#12111yescharacteristic
379C22×C61D4211yescharacteristic
380C22×C61#54611yescharacteristic
381C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C61#57511yescharacteristic
383C22×C61#57711yescharacteristic
384C22×C61#57711yescharacteristic
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C4×C61—22no—
393C4×C61—22no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61—42no—
397C4×C61—42no—
398C4×C61—81no—
399C4×C61#53211yescharacteristic
400C4×C61#54011yescharacteristic
401C4×C61D4211yescharacteristic
402C4×C61#55011yescharacteristic
403Dic61—81no—
404Dic61—81no—
405Dic61—81no—
406C2×#469—611no—
407C2×#465—611no—
408C2×#463—611no—
409C2×#435—611no—
410#2540D6111yescharacteristic, complemented
411#2537—611no—
412#2035—611no—
413#2034—611no—
414#2000—611no—
415#1999—611no—
416#1959—611no—
417#1948—611no—
418#1894—611no—
419#1893—611no—
420#1762—611no—
421C2×C61—42no—
422C2×C61—81no—
423C2×C61—161no—
424C2×C61#242811yescharacteristic
425C2×C61#305511yescharacteristic
426C2×C61#306011yescharacteristic
427C2×C61#326511yescharacteristic
428C2×C61#326711yescharacteristic
429C2×C61#330611yescharacteristic
430C2×C61#332111yescharacteristic
431D61—82no—
432C22×SD16—611no—
433C22×D8—611no—
434C22×M16—611no—
435C23×C8—611no—
436C2×#124C2×D6111yescharacteristic
437C2×C22⋊Q8C2×D6111yescharacteristic
438C2×C22⋊Q8C2×D6111yescharacteristic
439C2×#121—611no—
440C2×#121—611no—
441C2×#121—1221no—
442C2×#121C2×D6111yescharacteristic
443C2×#121C2×D6111yescharacteristic
444C2×C4×D4—611no—
445C2×C4×D4C2×D6111yescharacteristic
446#469—1224no—
447#465—1224no—
448#463—1224no—
449#435—1224no—
450C2×#106—611no—
451C2×#106—611no—
452C2×C4⋊C8—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×#102—611no—
460C2×#102—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8—611no—
463C2×#97—611no—
464#399—21no—
465#394—1221no—
466#394—1221no—
467#392—21no—
468#390—21no—
469#390—21no—
470#384—611no—
471#380—611no—
472#380—611no—
473#380—1221no—
474C4×C4⋊C4C2×D6111yescharacteristic
475#340—611no—
476#340—611no—
477#340—611no—
478#340—611no—
479C61#2540111yescharacteristic, complemented, Sylow
480C22×Q8C22×D6111yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—611no—
484C22×D4—1221no—
485C22×D4—1221no—
486C22×D4C22⋊D6111yescharacteristic
487C22×D4C22×D6111yescharacteristic
488C23×C4—1221no—
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6111yescharacteristic
491C2×SD16—1222no—
492C2×SD16—1222no—
493C2×SD16—2441no—
494C2×D8—1222no—
495C2×D8—1222no—
496C2×D8—2441no—
497C2×M16—1222no—
498C2×M16—1222no—
499C2×M16—2441no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—1222no—
505C22×C8—1222no—
506C22×C8—2441no—
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—41no—
512C22⋊Q8—41no—
513#121—22no—
514#121—22no—
515#121—41no—
516#121—41no—
517#121—1222no—
518#121—1222no—
519#121—2441no—
520#121—2441no—
521#121—2444no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—1222no—
525C4×D4—1222no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4C22⋊D6111yescharacteristic
534C2×C4⋊C4C22×D6111yescharacteristic
535C2×C4⋊C4C22×D6111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4C22⋊D6111yescharacteristic
548C2×C22⋊C4C22⋊D6111yescharacteristic
549C2×C42—21no—
550C2×C42C22×D6111yescharacteristic
551#106—1222no—
552#106—1222no—
553C4⋊C8—614no—
554#103—1222no—
555#103—1222no—
556#103—2441no—
557#102—614no—
558#102—1222no—
559#102—1222no—
560#102—1222no—
561#102—2441no—
562C22⋊C8—1222no—
563C22⋊C8—1222no—
564#97—1222no—
565#95—21no—
566#95—1221no—
567#95—1221no—
568C24—21no—
569C24—1221no—
570C24C2×C22⋊D6111yescharacteristic
571C24C2×C22⋊D6111yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—612no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1221no—
599C2×D4—4881no—
600C2×D4—4881no—
601C2×D4—2442no—
602C2×D4—2442no—
603C2×D4—2442no—
604C2×D4—2442no—
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—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C22×C4C2×C22⋊D6111yescharacteristic
629C22×C4C2×C22⋊D6111yescharacteristic
630C22×C4C23×D6111yescharacteristic
631SD16—2444no—
632D8—2444no—
633M16—2444no—
634C2×C8—612no—
635C2×C8—612no—
636C2×C8—612no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—2444no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—4881no—
659C4⋊C4—2442no—
660C4⋊C4D4×D6112yes—
661C4⋊C4#1175822412yes—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—2442no—
671C22⋊C4—2442no—
672C22⋊C4—2442no—
673C22⋊C4—2442no—
674C22⋊C4—2442no—
675C42—81no—
676C42D4×D6112yes—
677C42#1175822412yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—1222no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23#1451980212yes—
706C23C22×C22⋊D6111yescharacteristic
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—44no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—84no—
717D4—84no—
718D4—1222no—
719D4—1222no—
720D4—4884no—
721D4—4884no—
722D4—2441no—
723D4—2441no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
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—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—4884no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4#1451974912yes—
762C2×C4#1451974912yes—
763C2×C4C2×D4×D6111yescharacteristic
764C2×C4C2×D4×D6111yescharacteristic
765C2×C4C2×#1175822411yescharacteristic
766C2×C4C2×#1175822411yescharacteristic
767C2×C4#1451982211yescharacteristic
768C2×C4#1451982211yescharacteristic
769C8—1222no—
770C8—1222no—
771C8—1222no—
772C8—2441no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—4881no—
795C22—4881no—
796C22—4881no—
797C22—4881no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22C2×#1451974911yescharacteristic
802C22D4×C22⋊D6111yescharacteristic
803C22#1684040611yescharacteristic
804C22C2×#1451980211yescharacteristic
805C22#1684056011yescharacteristic
806C22#1684057011yescharacteristic
807C22#1684057311yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—81no—
815C4—4881no—
816C4—4881no—
817C4—4881no—
818C4#1684031011yescharacteristic
819C4#1684036611yescharacteristic
820C4#1684039711yescharacteristic
821C4#1684043211yescharacteristic
822C2—42no—
823C2—81no—
824C2—161no—
825C2—4882no—
826C2#2144941011yescharacteristic
827C2#2145544011yescharacteristic
828C2#2145547811yescharacteristic
829C2#2145731511yescharacteristic
830C2#2145734011yescharacteristic
831C2#2145778011yescharacteristic
832C2#2145800511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2540C2
socleC23×C61C22×D4
hypercenter#2540D61
hypocenterC61#25401
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×#16840013C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839974C2semidirect
4. C2×#16839834C2semidirect
5. #21450732C2semidirect
6. #21447012C2semidirect
7. #21447005C2semidirect
8. #21446820C2semidirect
9. #21446815C2semidirect
10. #21446636C2semidirect
11. #21446582C2semidirect
12. #21446253C2semidirect
13. #21446248C2semidirect
14. #21445647C2semidirect
15. C61×#2540C2semidirect
102. C4⋊#92418D4semidirect
110. #14519697D4semidirect
410. #2540D61semidirect
479. C61#25401semidirect

Maximal subgroups

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

subgroupindex
C2×#168400132
C2×#168399932
C2×#168399742
C2×#168398342
#214507322
#214470122
#214470052
#214468202
#214468152
#214466362
#214465822
#214462532
#214462482
#214456472
C61×#25402
#2540161