Finite Group Databasebeta

← #29717979

Subgroups — #29717979

Order 15616.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840013C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839907C211yesmaximal, characteristic, complemented
4C2×#16839763C211yesmaximal, characteristic, complemented
5#21449259C211yesmaximal, characteristic, complemented
6#21447050C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446890C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446137C211yesmaximal, characteristic, complemented
12#21446117C211yesmaximal, characteristic, complemented
13#21446087C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#550C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519749—21no—
23C22×C4⋊Dic61C2211yescharacteristic
24#16840013—24no—
25#16839907—24no—
26#16839907—24no—
27C2×#14519708C2211yescharacteristic
28#16839763—24no—
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42#16839684—21no—
43#16839678—21no—
44#16839664C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839639—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C22×#41×C61C2211yescharacteristic
54C61×#550—24no—
55C61×#550—24no—
56C2×#127×C61—21no—
57C2×#127×C61C2211yescharacteristic
58C2×#121×C61—21no—
59C2×#121×C61—21no—
60C2×#121×C61C2211yescharacteristic
61C2×#121×C61C2211yescharacteristic
62C2×C4×Q8×C61C2211yescharacteristic
63C2×C4×D4×C61—21no—
64C2×C4×D4×C61C2211yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C23×Dic61—21no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201—22no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—41no—
76C2×#11758199—41no—
77C2×#11758199—41no—
78C2×#11758194—22no—
79C2×#11758194—22no—
80C2×#11758194—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519751—22no—
86#14519751—22no—
87#14519751—22no—
88#14519751—41no—
89#14519749—44no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102#14519708—22no—
103#14519701—22no—
104#14519701—22no—
105#14519701D414yescomplemented
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—22no—
110#14519698—22no—
111#14519698—41no—
112#14519697—22no—
113C22⋊#92418—22no—
114C22⋊#92418—22no—
115C22⋊#92418—41no—
116#14519684—21no—
117#14519684—21no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—22no—
123C2×#41×C61—22no—
124C2×#41×C61—22no—
125C2×#41×C61—41no—
126C2×#41×C61—41no—
127C2×#41×C61—41no—
128C2×#41×C61—41no—
129C2×#41×C61D414yescomplemented
130C22×Q8×C61C2311yescharacteristic
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61—21no—
135C22×D4×C61—21no—
136C22×D4×C61—21no—
137C22×D4×C61D411yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C23×C4×C61—21no—
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144#127×C61—28no—
145#127×C61—22no—
146#127×C61—22no—
147#121×C61—28no—
148#121×C61—28no—
149#121×C61—22no—
150#121×C61—22no—
151#121×C61—22no—
152#121×C61D414yescomplemented
153C4×Q8×C61—22no—
154C4×Q8×C61—22no—
155C4×D4×C61—28no—
156C4×D4×C61—22no—
157C4×D4×C61—22no—
158C2×C4⋊C4×C61—21no—
159C2×C4⋊C4×C61D411yescharacteristic
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61—21no—
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C22⋊C4×C61D411yescharacteristic
165C2×C42×C61—21no—
166C2×C42×C61C2311yescharacteristic
167C24×C61—21no—
168C24×C61—21no—
169C24×C61C2×D411yescharacteristic
170C24×C61C2×D411yescharacteristic
171C23×D61—21no—
172#41×C61—28no—
173#41×C61—44no—
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—44no—
177#41×C61—44no—
178#41×C61—44no—
179#41×C61—44no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61C2×D412yes—
184C2×Q8×C61C2×D412yes—
185C2×Q8×C61#4112yes—
186C2×D4×C61—24no—
187C2×D4×C61—24no—
188C2×D4×C61—22no—
189C2×D4×C61—24no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—24no—
193C2×D4×C61—22no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—41no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
209C2×D4×C61—42no—
210C2×D4×C61—42no—
211C2×D4×C61—81no—
212C2×D4×C61—81no—
213C2×D4×C61—81no—
214C2×D4×C61—81no—
215C2×D4×C61—81no—
216C2×D4×C61—81no—
217C2×D4×C61C2×D412yes—
218C2×D4×C61C2×D412yes—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—24no—
225C22×C4×C61—21no—
226C22×C4×C61—24no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—42no—
234C22×C4×C61—42no—
235C22×C4×C61—42no—
236C22×C4×C61—42no—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2411yescharacteristic
244C2×C22⋊D61—42no—
245C2×C22⋊D61—42no—
246C2×C22⋊D61—42no—
247C2×C22⋊D61—42no—
248C2×C22⋊D61—42no—
249C2×C22⋊D61—81no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—42no—
254C22×Dic61—42no—
255C22×Dic61—81no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—21no—
262C4⋊C4×C61—24no—
263C4⋊C4×C61—22no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61C2×D412yes—
266C22⋊C4×C61—24no—
267C22⋊C4×C61—22no—
268C22⋊C4×C61—24no—
269C22⋊C4×C61—22no—
270C42×C61—24no—
271C42×C61—21no—
272C42×C61—21no—
273C22⋊Dic61—42no—
274#11758201—44no—
275#11758199—44no—
276#11758199—44no—
277#11758198—42no—
278#11758198—42no—
279#11758198—42no—
280#11758198—81no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—42no—
287C4⋊Dic61C2×D412yes—
288#11758196—42no—
289#11758194—44no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—21no—
301C2×#92418C2×D412yes—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61#12012yes—
330C23×C61C22×D411yescharacteristic
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338Q8×C61—22no—
339Q8×C61—22no—
340Q8×C61—22no—
341Q8×C61#12114yescomplemented
342D4×C61—22no—
343D4×C61—22no—
344D4×C61—22no—
345D4×C61—22no—
346D4×C61—44no—
347D4×C61—48no—
348D4×C61—48no—
349D4×C61—48no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61—41no—
353D4×C61—41no—
354D4×C61—84no—
355D4×C61—84no—
356D4×C61—84no—
357C2×C4×C61—21no—
358C2×C4×C61—22no—
359C2×C4×C61—21no—
360C2×C4×C61—22no—
361C2×C4×C61—21no—
362C2×C4×C61—22no—
363C2×C4×C61—21no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—21no—
369C2×C4×C61—22no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—48no—
376C2×C4×C61—48no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61#12012yes—
384C2×C4×C61AGL(1,ℤ/8)12yes—
385C2×C4×C61C22×D411yescharacteristic
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61C22×D411yescharacteristic
388C2×C4×C61C2×#4111yescharacteristic
389C2×C4×C61H(5,𝔽2)11yescharacteristic
390C2×C4×C61H(5,𝔽2)11yescharacteristic
391C22⋊D61—84no—
392C22⋊D61—84no—
393C2×Dic61—22no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—84no—
403D244—41no—
404D244—41no—
405D244—41no—
406D244—41no—
407#92418—22no—
408#92418—41no—
409#92418—41no—
410#92418—41no—
411#24451—611nomaximal, Sylow
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—41no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61—81no—
440C22×C61C2×#12011yescharacteristic
441C22×C61D4211yescharacteristic
442C22×C61#54611yescharacteristic
443C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
444C22×C61#57511yescharacteristic
445C22×C61#57611yescharacteristic
446C22×C61#57711yescharacteristic
447C2×D61—81no—
448C2×D61—81no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C4×C61—22no—
455C4×C61—24no—
456C4×C61—22no—
457C4×C61—41no—
458C4×C61—41no—
459C4×C61—42no—
460C4×C61C2×#12111yescharacteristic
461C4×C61#53411yescharacteristic
462C4×C61D4211yescharacteristic
463C4×C61#54611yescharacteristic
464Dic61—42no—
465Dic61—81no—
466Dic61—81no—
467C2×#550D6111yescharacteristic, complemented
468C2×#469—611no—
469C2×#449—611no—
470C2×#449—611no—
471C2×#417—611no—
472#2416—611no—
473#2041—611no—
474#2034—611no—
475#2011—611no—
476#1999—611no—
477#1880—611no—
478#1874—611no—
479#1870—611no—
480#1865—611no—
481#1788—611no—
482C2×C61—42no—
483C2×C61—81no—
484C2×C61—82no—
485C2×C61—82no—
486C2×C61#241011yescharacteristic
487C2×C61#300611yescharacteristic
488C2×C61#301211yescharacteristic
489C2×C61#327111yescharacteristic
490C2×C61#327411yescharacteristic
491C2×C61#330911yescharacteristic
492C2×C61#333211yescharacteristic
493D61—161no—
494C22×#41C2×D6111yescharacteristic
495C22×#41C2×D6111yescharacteristic
496C22×SD16—611no—
497C22×D8—611no—
498C22×D8—611no—
499C22×M16—611no—
500#550—24no—
501#550—24no—
502C2×#127—21no—
503C2×#127C2×D6111yescharacteristic
504C2×#121—21no—
505C2×#121—21no—
506C2×#121—611no—
507C2×#121—611no—
508C2×#121—1221no—
509C2×#121C2×D6111yescharacteristic
510C2×#121C2×D6111yescharacteristic
511C2×C4×Q8C2×D6111yescharacteristic
512C2×C4×D4—21no—
513C2×C4×D4C2×D6111yescharacteristic
514C22×C4⋊C4—611no—
515#469—1224no—
516#449—1224no—
517#449—1224no—
518C2×#106—611no—
519#417—1224no—
520C2×#103—611no—
521C2×#103—611no—
522C2×#103—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×C22⋊C8—611no—
531C2×C22⋊C8—611no—
532C2×C22⋊C8—611no—
533#396—1221no—
534#394—1221no—
535#390—611no—
536#389—611no—
537#386—1221no—
538#380—611no—
539#340—611no—
540#340—611no—
541#336—611no—
542#336—611no—
543C61#2445111yescharacteristic, complemented, Sylow
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41C22⋊D6114yescomplemented
556C22×Q8C22×D6111yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—611no—
564C22×D4—1221no—
565C22×D4—1221no—
566C22×D4C22⋊D6111yescharacteristic
567C22×D4C22×D6111yescharacteristic
568C22×D4C22×D6111yescharacteristic
569C23×C4—21no—
570C23×C4—21no—
571C23×C4—1221no—
572C23×C4C22×D6111yescharacteristic
573C23×C4C22×D6111yescharacteristic
574C2×SD16—1222no—
575C2×SD16—1222no—
576C2×SD16—1222no—
577C2×D8—1222no—
578C2×D8—1222no—
579C2×D8—1222no—
580C2×D8—2441no—
581C2×D8—2441no—
582C2×D8—2441no—
583C2×M16—1222no—
584C2×M16—1222no—
585C2×M16—2441no—
586C22×C8—611no—
587C22×C8—611no—
588C22×C8—611no—
589C22×C8—611no—
590#127—28no—
591#127—22no—
592#127—22no—
593#121—28no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—1222no—
599#121—1222no—
600#121—1222no—
601#121—2441no—
602#121—2444no—
603#121C22⋊D6114yescomplemented
604C4×Q8—22no—
605C4×Q8—22no—
606C4×D4—28no—
607C4×D4—22no—
608C4×D4—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—1222no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—2441no—
617C2×C4⋊C4C22⋊D6111yescharacteristic
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4C22⋊D6111yescharacteristic
627C2×C22⋊C4C22⋊D6111yescharacteristic
628C2×C42—21no—
629C2×C42C22×D6111yescharacteristic
630#106—1222no—
631#103—614no—
632#103—1222no—
633#103—1222no—
634#102—1222no—
635#102—1222no—
636#102—1222no—
637#102—1222no—
638#102—1222no—
639#102—1222no—
640#102—2441no—
641C22⋊C8—1222no—
642C22⋊C8—1222no—
643C22⋊C8—2441no—
644#95—1221no—
645#95—1221no—
646C24—21no—
647C24—21no—
648C24—1221no—
649C24C2×C22⋊D6111yescharacteristic
650C24C2×C22⋊D6111yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656#41—44no—
657#41—44no—
658#41—44no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8D4×D6112yes—
663C2×Q8#1175822412yes—
664C2×Q8C2×C22⋊D6112yes—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—22no—
683C2×D4—41no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—81no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—4881no—
703C2×D4—2442no—
704C2×D4—2442no—
705C2×D4—2442no—
706C2×D4—2442no—
707C2×D4—2442no—
708C2×D4C2×C22⋊D6112yes—
709C2×D4C2×C22⋊D6112yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—4881no—
732C22×C4—2442no—
733C22×C4—2442no—
734C22×C4C2×C22⋊D6111yescharacteristic
735C22×C4C2×C22⋊D6111yescharacteristic
736C22×C4C2×C22⋊D6112yes—
737C22×C4C2×C22⋊D6112yes—
738C22×C4C2×C22⋊D6111yescharacteristic
739C22×C4C2×C22⋊D6111yescharacteristic
740C22×C4C23×D6111yescharacteristic
741SD16—2444no—
742D8—2444no—
743D8—2444no—
744M16—2444no—
745C2×C8—612no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C4⋊C4—24no—
758C4⋊C4—21no—
759C4⋊C4—22no—
760C4⋊C4—612no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—2442no—
767C4⋊C4—2442no—
768C4⋊C4C2×C22⋊D6112yes—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—4881no—
774C22⋊C4—2442no—
775C22⋊C4—2442no—
776C22⋊C4—2442no—
777C22⋊C4—2442no—
778C42—24no—
779C42—21no—
780C42—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—2441no—
809C23—2441no—
810C23—2441no—
811C23—2441no—
812C23—2441no—
813C23—2441no—
814C23—2441no—
815C23#1451974612yes—
816C23C22×C22⋊D6111yescharacteristic
817Q8—22no—
818Q8—22no—
819Q8—22no—
820Q8#1451974914yescomplemented
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—44no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—84no—
834D4—84no—
835D4—84no—
836D4—4884no—
837D4—4884no—
838D4—2441no—
839D4—2441no—
840D4—2441no—
841D4—2441no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—48no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—1222no—
869C2×C4—4884no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4#1451974612yes—
879C2×C4#1451980212yes—
880C2×C4C2×D4×D6111yescharacteristic
881C2×C4C22×C22⋊D6111yescharacteristic
882C2×C4C22×C22⋊D6111yescharacteristic
883C2×C4C2×#1175822411yescharacteristic
884C2×C4#1451982211yescharacteristic
885C2×C4#1451982211yescharacteristic
886C8—1222no—
887C8—2441no—
888C8—2441no—
889C8—2441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—4881no—
919C22—4881no—
920C22—4881no—
921C22—4881no—
922C22—4881no—
923C22—4881no—
924C22—4881no—
925C22C2×#1451974611yescharacteristic
926C22D4×C22⋊D6111yescharacteristic
927C22#1684040611yescharacteristic
928C22C2×#1451980211yescharacteristic
929C22#1684056011yescharacteristic
930C22#1684056511yescharacteristic
931C22#1684057311yescharacteristic
932C4—22no—
933C4—22no—
934C4—24no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—4881no—
939C4—4881no—
940C4—2442no—
941C4C2×#1451974911yescharacteristic
942C4#1684032111yescharacteristic
943C4D4×C22⋊D6111yescharacteristic
944C4#1684040611yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—9761no—
950C2#2144919311yescharacteristic
951C2#2145507111yescharacteristic
952C2#2145512311yescharacteristic
953C2#2145740011yescharacteristic
954C2#2145743911yescharacteristic
955C2#2145782511yescharacteristic
956C2#2145814611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#550C2
socleC23×C61C22×D4
hypercenterC2×#550D61
hypocenterC61#24451
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16840013C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839907C2semidirect
4. C2×#16839763C2semidirect
5. #21449259C2semidirect
6. #21447050C2semidirect
7. #21447005C2semidirect
8. #21446890C2semidirect
9. #21446815C2semidirect
10. #21446174C2semidirect
11. #21446137C2semidirect
12. #21446117C2semidirect
13. #21446087C2semidirect
14. #21445759C2semidirect
15. C2×C61×#550C2semidirect
105. #14519701D4semidirect
129. C2×#41×C61D4semidirect
152. #121×C61D4semidirect
341. Q8×C61#121semidirect
467. C2×#550D61semidirect
543. C61#24451semidirect
555. C2×#41C22⋊D61semidirect
603. #121C22⋊D61semidirect
820. Q8#14519749semidirect

Maximal subgroups

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

subgroupindex
C2×#168400132
C2×#168399072
C2×#168397632
#214492592
#214470502
#214470052
#214468902
#214468152
#214461742
#214461372
#214461172
#214460872
#214457592
C2×C61×#5502
#2445161