Finite Group Databasebeta

← #29727851

Subgroups — #29727851

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839962C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839907C211yesmaximal, characteristic, complemented
4C2×#16839860C211yesmaximal, characteristic, complemented
5#21449407C211yesmaximal, characteristic, complemented
6#21447207C211yesmaximal, characteristic, complemented
7#21447008C211yesmaximal, characteristic, complemented
8#21447001C211yesmaximal, characteristic, complemented
9#21446889C211yesmaximal, characteristic, complemented
10#21446694C211yesmaximal, characteristic, complemented
11#21446434C211yesmaximal, characteristic, complemented
12#21446174C211yesmaximal, characteristic, complemented
13#21446170C211yesmaximal, characteristic, complemented
14#21446087C211yesmaximal, characteristic, complemented
15C61×#2341C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C2×#14519774C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519750—21no—
24C2×C4×D244C2211yescharacteristic
25#16839962—24no—
26#16839907—24no—
27#16839907—24no—
28#16839860—24no—
29C2×#14519710C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519688C2211yescharacteristic
43#16839680—21no—
44#16839671—21no—
45#16839664C2211yescharacteristic
46#16839660C2211yescharacteristic
47#16839640—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C61×#390—21no—
56C61×#390—21no—
57C61×#390C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#380—21no—
60C61×#380C2211yescharacteristic
61C4×C22⋊C4×C61—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×D244—21no—
64C22×D244—21no—
65C22×D244C2311yescharacteristic
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C22×C4×D61—21no—
70C2×#11758201—22no—
71C2×#11758201—22no—
72C2×#11758201—22no—
73C2×#11758201—22no—
74C2×#11758201—22no—
75C2×#11758201D414yescomplemented
76C2×#11758199—22no—
77C2×#11758199—22no—
78C2×#11758199—22no—
79C2×#11758199—22no—
80C2×#11758199—41no—
81C2×#11758199—41no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519774—22no—
87#14519774—41no—
88#14519751—22no—
89#14519751—22no—
90#14519751—41no—
91#14519751—41no—
92#14519750—44no—
93C4×D244—22no—
94C4×D244—41no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103#14519710—22no—
104#14519708—41no—
105C4⋊#92418—22no—
106#14519701—22no—
107#14519701D414yescomplemented
108#14519698—22no—
109#14519698—22no—
110#14519697—22no—
111#14519697—22no—
112#14519697—22no—
113#14519697—41no—
114C22⋊#92418—22no—
115C22⋊#92418—22no—
116#14519688—22no—
117#14519684—21no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—41no—
123C2×#41×C61—41no—
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61C2311yescharacteristic
129C4×Q8×C61—22no—
130C4×Q8×C61—22no—
131C4×Q8×C61—41no—
132C4×Q8×C61—41no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
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×C61—21no—
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61—21no—
152C24×C61C2×D411yescharacteristic
153C23×D61—21no—
154C23×D61—21no—
155#41×C61—44no—
156#41×C61—44no—
157#41×C61—44no—
158#41×C61—44no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C2×D412yes—
163C2×Q8×C61C2×D412yes—
164C2×Q8×C61#4112yes—
165C2×D4×C61—24no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61#4112yes—
174C22×C4×C61—21no—
175C22×C4×C61—24no—
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—42no—
185C22×C4×C61—42no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2411yescharacteristic
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—81no—
197C2×C22⋊D61—81no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—42no—
212C2×D244—42no—
213C2×D244—42no—
214C2×D244—42no—
215C2×D244—81no—
216C2×D244—81no—
217C2×D244C2×D412yes—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—81no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—42no—
226C4⋊C4×C61—42no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—41no—
229C22⋊C4×C61—42no—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—81no—
232C22⋊C4×C61—81no—
233C22⋊C4×C61—81no—
234C42×C61—21no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61—21no—
238C42×C61—42no—
239C42×C61—42no—
240#11758201—28no—
241#11758201—44no—
242#11758199—44no—
243#11758199—44no—
244#11758198—42no—
245#11758198—42no—
246#11758198—42no—
247#11758198—42no—
248#11758198—81no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C2×D412yes—
253#11758196—42no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418C2×D412yes—
265C2×#92418C2×D412yes—
266C23×C61—21no—
267C23×C61—22no—
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×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—22no—
298Q8×C61#12114yescomplemented
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—48no—
302D4×C61—41no—
303D4×C61—41no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—48no—
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—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61AGL(1,ℤ/8)12yes—
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C2×#4111yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61H(5,𝔽2)11yescharacteristic
338C2×C4×C61H(5,𝔽2)11yescharacteristic
339C22⋊D61—84no—
340C22⋊D61—84no—
341C2×Dic61—22no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347D244—22no—
348D244—22no—
349D244—41no—
350D244—41no—
351D244—41no—
352D244—41no—
353D244—41no—
354D244—41no—
355D244—84no—
356D244—84no—
357C4×D61—84no—
358#92418—22no—
359#92418—22no—
360#92418—41no—
361#92418—41no—
362#25179—611nomaximal, Sylow
363C22×C61—41no—
364C22×C61—42no—
365C22×C61—41no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61#52511yescharacteristic
378C22×C61D4211yescharacteristic
379C22×C61D4211yescharacteristic
380C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
381C22×C61#57511yescharacteristic
382C22×C61#57611yescharacteristic
383C22×C61#57711yescharacteristic
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—81no—
393C2×D61—81no—
394C2×D61—81no—
395C2×D61—81no—
396C2×D61—81no—
397C2×D61—81no—
398C4×C61—24no—
399C4×C61—22no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—81no—
405C4×C61—81no—
406C4×C61C2×#12111yescharacteristic
407C4×C61#53811yescharacteristic
408C4×C61#54611yescharacteristic
409C4×C61#54611yescharacteristic
410Dic61—42no—
411Dic61—81no—
412C2×#460—611no—
413C2×#449—611no—
414C2×#449—611no—
415C2×#440—611no—
416#2428—611no—
417#2341D6111yescharacteristic, complemented
418#2067—611no—
419#2034—611no—
420#2033—611no—
421#2011—611no—
422#1972—611no—
423#1924—611no—
424#1880—611no—
425#1879—611no—
426#1865—611no—
427C2×C61—81no—
428C2×C61—82no—
429C2×C61#242411yescharacteristic
430C2×C61#311511yescharacteristic
431C2×C61#311911yescharacteristic
432C2×C61#326511yescharacteristic
433C2×C61#326811yescharacteristic
434C2×C61#327111yescharacteristic
435C2×C61#327411yescharacteristic
436D61—82no—
437D61—161no—
438C22×#41C2×D6111yescharacteristic
439C22×SD16—611no—
440C22×SD16—611no—
441C22×D8—611no—
442C22×D8—611no—
443C2×#127—611no—
444C2×#121—611no—
445C2×#121—611no—
446C2×#121—1221no—
447C2×C4×Q8C2×D6111yescharacteristic
448C2×C4×Q8C2×D6111yescharacteristic
449C2×C4×D4—611no—
450#460—1224no—
451#449—1224no—
452#449—1224no—
453#440—1224no—
454C2×#107—611no—
455C2×#106—611no—
456C2×C4⋊C8—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#102—611no—
460C2×#102—611no—
461C2×#102—611no—
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×C22⋊C8—611no—
466C2×C22⋊C8—611no—
467C2×#97—611no—
468#394—1221no—
469#392—1221no—
470#390—21no—
471#390—21no—
472#390—611no—
473#390C2×D6111yescharacteristic
474#390C2×D6111yescharacteristic
475#389—611no—
476#386—1221no—
477#380—21no—
478#380C2×D6111yescharacteristic
479C4×C22⋊C4—21no—
480C4×C22⋊C4C2×D6111yescharacteristic
481#340—611no—
482#340—611no—
483#336—611no—
484#336—611no—
485C61#2517911yescharacteristic, complemented, Sylow
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C22×D6111yescharacteristic
493C22×D4—21no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4C22×D6111yescharacteristic
501C23×C4—21no—
502C23×C4—1221no—
503C23×C4C22×D6111yescharacteristic
504C2×SD16—614no—
505C2×SD16—1222no—
506C2×SD16—1222no—
507C2×SD16—1222no—
508C2×SD16—1222no—
509C2×SD16—1222no—
510C2×D8—1222no—
511C2×D8—1222no—
512C2×D8—1222no—
513C2×D8—1222no—
514C2×D8—2441no—
515C2×D8—2441no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520#127—1222no—
521#127—2441no—
522#121—1222no—
523#121—1222no—
524#121—2444no—
525#121—2441no—
526#121—2441no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—1222no—
532C4×D4—2441no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4C22×D6111yescharacteristic
539C2×C4⋊C4C22×D6111yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4C22⋊D6111yescharacteristic
551C2×C22⋊C4C22⋊D6111yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C22×D6111yescharacteristic
555C2×C42C22×D6111yescharacteristic
556#107—1222no—
557#106—2441no—
558C4⋊C8—1222no—
559#103—614no—
560#103—1222no—
561#102—1222no—
562#102—1222no—
563#102—1222no—
564#102—1222no—
565#102—1222no—
566#102—2441no—
567C22⋊C8—1222no—
568C22⋊C8—1222no—
569#97—1222no—
570#95—21no—
571#95—1221no—
572#95C22⋊D6111yescharacteristic
573#95C22⋊D6111yescharacteristic
574C24—21no—
575C24—1221no—
576C24—1221no—
577C24C2×C22⋊D6111yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8#1175822212yes—
586C2×Q8D4×D6112yes—
587C2×Q8D4×D6112yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—612no—
597C2×D4—1221no—
598C2×D4—1221no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—4881no—
609C2×D4—4881no—
610C2×D4—4881no—
611C2×D4—4881no—
612C2×D4—2442no—
613C2×D4—2442no—
614C2×D4—2442no—
615C2×D4—2442no—
616C2×D4—2442no—
617C2×D4—2442no—
618C2×D4—2442no—
619C2×D4—2442no—
620C2×D4#1175822212yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—4881no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4C2×C22⋊D6111yescharacteristic
639C22×C4C2×C22⋊D6111yescharacteristic
640C22×C4C2×C22⋊D6111yescharacteristic
641C22×C4C2×C22⋊D6111yescharacteristic
642C22×C4C2×C22⋊D6111yescharacteristic
643C22×C4C23×D6111yescharacteristic
644SD16—1228no—
645SD16—2444no—
646D8—2444no—
647D8—2444no—
648C2×C8—612no—
649C2×C8—612no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—612no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—2442no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C22⋊C4—81no—
678C22⋊C4—4881no—
679C22⋊C4—2442no—
680C22⋊C4—2442no—
681C22⋊C4—2442no—
682C22⋊C4—2442no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—1222no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23—2441no—
716C23—2441no—
717C23C22×C22⋊D6111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#1451975014yescomplemented
722D4—22no—
723D4—22no—
724D4—48no—
725D4—41no—
726D4—41no—
727D4—1222no—
728D4—1222no—
729D4—4884no—
730D4—4884no—
731D4—4884no—
732D4—4884no—
733D4—2441no—
734D4—2441no—
735D4—2441no—
736D4—2441no—
737D4—2441no—
738D4—2441no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—1222no—
768C2×C4—4884no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4#1451980212yes—
775C2×C4C2×D4×D6111yescharacteristic
776C2×C4C2×D4×D6111yescharacteristic
777C2×C4C2×#1175822211yescharacteristic
778C2×C4C2×#1175822211yescharacteristic
779C2×C4#1451982211yescharacteristic
780C2×C4#1451982211yescharacteristic
781C8—1222no—
782C8—1222no—
783C8—2441no—
784C8—2441no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—4881no—
800C22—4881no—
801C22—4881no—
802C22—4881no—
803C22—4881no—
804C22—4881no—
805C22—4881no—
806C22—4881no—
807C22—4881no—
808C22—4881no—
809C22—4881no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22#1684027311yescharacteristic
814C22D4×C22⋊D6111yescharacteristic
815C22D4×C22⋊D6111yescharacteristic
816C22C2×#1451980211yescharacteristic
817C22#1684056011yescharacteristic
818C22#1684056511yescharacteristic
819C22#1684057011yescharacteristic
820C4—24no—
821C4—22no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—81no—
827C4—81no—
828C4—4881no—
829C4—2442no—
830C4C2×#1451975011yescharacteristic
831C4#1684035011yescharacteristic
832C4#1684040211yescharacteristic
833C4#1684040211yescharacteristic
834C2—81no—
835C2—82no—
836C2—9761no—
837C2—4882no—
838C2#2144935511yescharacteristic
839C2#2145597011yescharacteristic
840C2#2145601811yescharacteristic
841C2#2145731511yescharacteristic
842C2#2145736011yescharacteristic
843C2#2145740511yescharacteristic
844C2#2145743911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2341C2
socleC23×C61C22×D4
hypercenter#2341D61
hypocenterC61#25179
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
1. C2×#16839962C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839907C2semidirect
4. C2×#16839860C2semidirect
5. #21449407C2semidirect
6. #21447207C2semidirect
7. #21447008C2semidirect
8. #21447001C2semidirect
9. #21446889C2semidirect
10. #21446694C2semidirect
11. #21446434C2semidirect
12. #21446174C2semidirect
13. #21446170C2semidirect
14. #21446087C2semidirect
15. C61×#2341C2semidirect
75. C2×#11758201D4semidirect
107. #14519701D4semidirect
298. Q8×C61#121semidirect
417. #2341D61semidirect
485. C61#25179semidirect
721. Q8#14519750semidirect

Maximal subgroups

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

subgroupindex
C2×#168399622
C2×#168399072
C2×#168398602
#214494072
#214472072
#214470082
#214470012
#214468892
#214466942
#214464342
#214461742
#214461702
#214460872
C61×#23412
#2517961