Finite Group Databasebeta

← #29717724

Subgroups — #29717724

Order 15616.

1674 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839993C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839896C211yesmaximal, characteristic, complemented
4C22×#14519698C211yesmaximal, characteristic, complemented
5#21449259C211yesmaximal, characteristic, complemented
6#21447055C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446896C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446127C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446080C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic, complemented
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic, complemented
22C2×#14519749—21no—
23C22×C4⋊Dic61C2211yescharacteristic
24#16839993—24no—
25#16839907—24no—
26#16839896—24no—
27C2×#14519708C2211yescharacteristic, complemented
28C2×#14519701C2211yescharacteristic, complemented
29C2×#14519701C2211yescharacteristic, complemented
30C2×#14519701C2211yescharacteristic, complemented
31C2×#14519698—24no—
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519697C2211yescharacteristic, complemented
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic, complemented
41C2×C22⋊#92418C2211yescharacteristic, complemented
42#16839684—21no—
43#16839678—21no—
44#16839664C2211yescharacteristic, complemented
45#16839660C2211yescharacteristic, complemented
46#16839639—21no—
47#16839622C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C22×#41×C61C2211yescharacteristic
53C23×D4×C61C2211yescharacteristic
54C61×#546—24no—
55C61×#546—24no—
56C2×#124×C61C2211yescharacteristic
57C2×#123×C61—21no—
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#121×C61—21no—
60C2×#121×C61C2211yescharacteristic
61C2×#120×C61—21no—
62C2×C4×D4×C61C2211yescharacteristic
63C2×C4×D4×C61C2211yescharacteristic
64C22×C22⋊C4×C61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C23×Dic61—21no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201—41no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—41no—
77C2×#11758199—41no—
78C22×#92418—22no—
79C22×#92418—22no—
80C22×#92418—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#14519701—41no—
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—22no—
110#14519698—22no—
111#14519698D414yescomplemented
112#14519697—22no—
113C22⋊#92418—22no—
114C22⋊#92418—22no—
115C22⋊#92418—41no—
116#14519684—21no—
117#14519684—21no—
118C25×C61—21no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—22no—
123C2×#41×C61—41no—
124C2×#41×C61—41no—
125C22×Q8×C61C2311yescharacteristic
126C22×D4×C61—22no—
127C22×D4×C61—22no—
128C22×D4×C61—21no—
129C22×D4×C61—21no—
130C22×D4×C61—22no—
131C22×D4×C61—21no—
132C22×D4×C61—41no—
133C22×D4×C61—41no—
134C22×D4×C61D411yescharacteristic
135C22×D4×C61D414yescomplemented
136C22×D4×C61C2311yescharacteristic
137C22×D4×C61C2311yescharacteristic
138C23×C4×C61—21no—
139C23×C4×C61—21no—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142#124×C61—22no—
143#124×C61—22no—
144#123×C61—28no—
145C22⋊Q8×C61—22no—
146C22⋊Q8×C61D414yescomplemented
147#121×C61—28no—
148#121×C61—22no—
149#121×C61—22no—
150#120×C61—28no—
151C4×D4×C61—22no—
152C4×D4×C61—22no—
153C4×D4×C61—22no—
154C4×D4×C61—22no—
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61D411yescharacteristic
157C2×C4⋊C4×C61C2311yescharacteristic
158C2×C22⋊C4×C61—28no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61—21no—
163C2×C22⋊C4×C61—21no—
164C2×C22⋊C4×C61D411yescharacteristic
165C2×C22⋊C4×C61D411yescharacteristic
166C2×C42×C61C2311yescharacteristic
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—24no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—42no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61C2×D411yescharacteristic
177C24×C61C2×D411yescharacteristic
178C23×D61—21no—
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182#41×C61—44no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61C2×D412yes—
189C2×D4×C61—28no—
190C2×D4×C61—24no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—24no—
195C2×D4×C61—24no—
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—44no—
205C2×D4×C61—44no—
206C2×D4×C61—44no—
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×C61C2×D412yes—
214C2×D4×C61C2×D412yes—
215C2×D4×C61C2×D412yes—
216C2×D4×C61#4112yes—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—24no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—24no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—42no—
232C22×C4×C61—42no—
233C22×C4×C61—81no—
234C22×C4×C61—81no—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2411yescharacteristic
242C2×C22⋊D61—42no—
243C2×C22⋊D61—42no—
244C2×C22⋊D61—42no—
245C2×C22⋊D61—42no—
246C2×C22⋊D61—42no—
247C2×C22⋊D61—81no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—42no—
252C22×Dic61—42no—
253C22×Dic61—81no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C4⋊C4×C61—24no—
261C4⋊C4×C61—22no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C2×D412yes—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—24no—
266C22⋊C4×C61—24no—
267C22⋊C4×C61—24no—
268C22⋊C4×C61—22no—
269C22⋊C4×C61—24no—
270C22⋊C4×C61—22no—
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—
289C2×#92418—21no—
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—44no—
301C2×#92418C2×D412yes—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—48no—
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—48no—
329C23×C61—84no—
330C23×C61—84no—
331C23×C61—84no—
332C23×C61—84no—
333C23×C61—84no—
334C23×C61#12012yes—
335C23×C61#13512yes—
336C23×C61AGL(1,ℤ/8)12yes—
337C23×C61C22×D411yescharacteristic
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345Q8×C61—22no—
346Q8×C61—22no—
347Q8×C61—41no—
348Q8×C61—41no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—22no—
353D4×C61—22no—
354D4×C61—48no—
355D4×C61—48no—
356D4×C61—44no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—84no—
360D4×C61#12114yescomplemented
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—22no—
370C2×C4×C61—21no—
371C2×C4×C61—22no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—48no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—84no—
388C2×C4×C61#12012yes—
389C2×C4×C61C22×D411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C2×C4×C61C22×D411yescharacteristic
392C2×C4×C61C2×#4111yescharacteristic
393C2×C4×C61H(5,𝔽2)11yescharacteristic
394C2×C4×C61H(5,𝔽2)11yescharacteristic
395C22⋊D61—84no—
396C22⋊D61—84no—
397C2×Dic61—22no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—84no—
407D244—41no—
408D244—41no—
409D244—41no—
410D244—41no—
411#92418—22no—
412#92418—41no—
413#92418—41no—
414#92418—41no—
415#24434—611nomaximal, Sylow
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—24no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—41no—
430C22×C61—42no—
431C22×C61—41no—
432C22×C61—42no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—42no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—816no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61#44914yescomplemented
445C22×C61C2×#12011yescharacteristic
446C22×C61D4211yescharacteristic
447C22×C61#54611yescharacteristic
448C22×C61C2×#13511yescharacteristic
449C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C61#57611yescharacteristic
451C22×C61#57711yescharacteristic
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61—81no—
459C4×C61—22no—
460C4×C61—41no—
461C4×C61—42no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61—42no—
465C4×C61C2×#12111yescharacteristic
466C4×C61#53411yescharacteristic
467C4×C61D4211yescharacteristic
468C4×C61#54611yescharacteristic
469Dic61—42no—
470Dic61—81no—
471Dic61—81no—
472C2×#546D6111yescharacteristic, complemented
473C2×#465—611no—
474C2×#449—611no—
475C2×#447—611no—
476C22×#102—611no—
477#2416—611no—
478#2042—611no—
479#2034—611no—
480#2012—611no—
481#1999—611no—
482#1879—611no—
483#1872—611no—
484#1869—611no—
485#1864—611no—
486#1788—611no—
487C2×C61—24no—
488C2×C61—44no—
489C2×C61—81no—
490C2×C61—82no—
491C2×C61#241011yescharacteristic
492C2×C61C2×#44911yescharacteristic
493C2×C61#301211yescharacteristic
494C2×C61#326411yescharacteristic
495C2×C61#328211yescharacteristic
496C2×C61#329711yescharacteristic
497C2×C61#330611yescharacteristic
498D61—161no—
499C22×#41C2×D6111yescharacteristic
500C23×D4C2×D6111yescharacteristic
501C22×SD16—611no—
502C22×D8—611no—
503C22×D8—611no—
504C23×C8—611no—
505#546—24no—
506#546—24no—
507C2×#124C2×D6111yescharacteristic
508C2×#123—21no—
509C2×C22⋊Q8C2×D6111yescharacteristic
510C2×#121—21no—
511C2×#121—611no—
512C2×#121—611no—
513C2×#121—1221no—
514C2×#121C2×D6111yescharacteristic
515C2×#120—21no—
516C2×C4×D4C2×D6111yescharacteristic
517C2×C4×D4C2×D6111yescharacteristic
518C22×C4⋊C4—611no—
519C22×C22⋊C4—21no—
520#465—1224no—
521#449—1224no—
522#447—1224no—
523C2×#106—611no—
524C2×#103—611no—
525C2×#103—611no—
526C2×#103—611no—
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×#102—611no—
531C2×#102—611no—
532C2×#102—611no—
533C2×#102—611no—
534C2×#102—1224no—
535C2×C22⋊C8—611no—
536C2×C22⋊C8—611no—
537C2×C22⋊C8—611no—
538#396—1221no—
539#394—1221no—
540#390—611no—
541#389—611no—
542#386—1221no—
543#380—611no—
544#340—611no—
545#340—611no—
546#336—611no—
547#336—611no—
548C61#2443411yescharacteristic, complemented, Sylow
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—41no—
555C2×#41—41no—
556C22×Q8C22×D6111yescharacteristic
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—22no—
563C22×D4—41no—
564C22×D4—41no—
565C22×D4—611no—
566C22×D4—1221no—
567C22×D4—1221no—
568C22×D4C22⋊D6111yescharacteristic
569C22×D4C22⋊D6114yescomplemented
570C22×D4C22×D6111yescharacteristic
571C22×D4C22×D6111yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—1221no—
575C23×C4C22×D6111yescharacteristic
576C23×C4C22×D6111yescharacteristic
577C2×SD16—1222no—
578C2×SD16—1222no—
579C2×SD16—2441no—
580C2×D8—1222no—
581C2×D8—1222no—
582C2×D8—1222no—
583C2×D8—1222no—
584C2×D8—2441no—
585C2×D8—2441no—
586C22×C8—611no—
587C22×C8—611no—
588C22×C8—611no—
589C22×C8—611no—
590C22×C8—1222no—
591C22×C8—1222no—
592C22×C8—2441no—
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8C22⋊D6114yescomplemented
598#121—28no—
599#121—22no—
600#121—22no—
601#121—1222no—
602#121—1222no—
603#121—1222no—
604#121—2441no—
605#121—2444no—
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—1222no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—2441no—
619C2×C4⋊C4C22⋊D6111yescharacteristic
620C2×C4⋊C4C22×D6111yescharacteristic
621C2×C22⋊C4—28no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4C22⋊D6111yescharacteristic
633C2×C22⋊C4C22⋊D6111yescharacteristic
634C2×C42C22×D6111yescharacteristic
635#106—1222no—
636#103—1222no—
637#103—1222no—
638#103—2441no—
639#102—614no—
640#102—1222no—
641#102—1222no—
642#102—1222no—
643#102—1222no—
644#102—1222no—
645#102—1222no—
646C22⋊C8—1222no—
647C22⋊C8—1222no—
648C22⋊C8—2441no—
649#95—1221no—
650#95—1221no—
651C24—21no—
652C24—21no—
653C24—24no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24—1221no—
661C24C2×C22⋊D6111yescharacteristic
662C24C2×C22⋊D6111yescharacteristic
663#41—44no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×C22⋊D6112yes—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—24no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—4881no—
704C2×D4—2442no—
705C2×D4—2442no—
706C2×D4—2442no—
707C2×D4—2442no—
708C2×D4—2442no—
709C2×D4D4×D6112yes—
710C2×D4#1175822412yes—
711C2×D4C2×C22⋊D6112yes—
712C2×D4C2×C22⋊D6112yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—81no—
730C22×C4—81no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—4881no—
735C22×C4—2442no—
736C22×C4—2442no—
737C22×C4C2×C22⋊D6111yescharacteristic
738C22×C4C2×C22⋊D6111yescharacteristic
739C22×C4C2×C22⋊D6111yescharacteristic
740C22×C4C2×C22⋊D6112yes—
741C22×C4C2×C22⋊D6112yes—
742C22×C4C2×C22⋊D6111yescharacteristic
743C22×C4C23×D6111yescharacteristic
744SD16—2444no—
745D8—2444no—
746D8—2444no—
747C2×C8—612no—
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—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—2444no—
760C4⋊C4—21no—
761C4⋊C4—24no—
762C4⋊C4—22no—
763C4⋊C4—612no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—2442no—
770C4⋊C4—2442no—
771C4⋊C4C2×C22⋊D6112yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—24no—
778C22⋊C4—22no—
779C22⋊C4—4881no—
780C22⋊C4—2442no—
781C22⋊C4—2442no—
782C22⋊C4—2442no—
783C22⋊C4—2442no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—48no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—48no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—2441no—
819C23—2441no—
820C23—2441no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23#1451974612yes—
826C23#1451979712yes—
827C23#1451980212yes—
828C23C22×C22⋊D6111yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—44no—
841D4—41no—
842D4—41no—
843D4—84no—
844D4—4884no—
845D4—4884no—
846D4—2441no—
847D4—2441no—
848D4—2441no—
849D4—2441no—
850D4#1451974914yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—48no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—1222no—
879C2×C4—4884no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4#1451974612yes—
889C2×C4C2×D4×D6111yescharacteristic
890C2×C4C22×C22⋊D6111yescharacteristic
891C2×C4C22×C22⋊D6111yescharacteristic
892C2×C4C2×#1175822411yescharacteristic
893C2×C4#1451982211yescharacteristic
894C2×C4#1451982211yescharacteristic
895C8—1222no—
896C8—2441no—
897C8—2441no—
898C8—2441no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—24no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—42no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—4881no—
928C22—4881no—
929C22—4881no—
930C22—4881no—
931C22—4881no—
932C22—4881no—
933C22—4881no—
934C22#1683990714yescomplemented
935C22C2×#1451974611yescharacteristic
936C22D4×C22⋊D6111yescharacteristic
937C22#1684040611yescharacteristic
938C22C2×#1451979711yescharacteristic
939C22C2×#1451980211yescharacteristic
940C22#1684056511yescharacteristic
941C22#1684057311yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—4881no—
949C4—4881no—
950C4—2442no—
951C4C2×#1451974911yescharacteristic
952C4#1684032111yescharacteristic
953C4D4×C22⋊D6111yescharacteristic
954C4#1684040611yescharacteristic
955C2—24no—
956C2—44no—
957C2—81no—
958C2—82no—
959C2—9761no—
960C2#2144919311yescharacteristic
961C2C2×#1683990711yescharacteristic
962C2#2145512311yescharacteristic
963C2#2145730011yescharacteristic
964C2#2145752211yescharacteristic
965C2#2145766911yescharacteristic
966C2#2145778011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61#24434
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16839993C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839896C2semidirect
4. C22×#14519698C2semidirect
5. #21449259C2semidirect
6. #21447055C2semidirect
7. #21447005C2semidirect
8. #21446896C2semidirect
9. #21446815C2semidirect
10. #21446167C2semidirect
11. #21446127C2semidirect
12. #21446112C2semidirect
13. #21446080C2semidirect
14. #21445759C2semidirect
15. C2×C61×#546C2semidirect
16. C22×#11758201C22semidirect
21. C2×#14519751C22semidirect
27. C2×#14519708C22semidirect
28. C2×#14519701C22semidirect
29. C2×#14519701C22semidirect
30. C2×#14519701C22semidirect
38. C2×#14519697C22semidirect
40. C2×C22⋊#92418C22semidirect
41. C2×C22⋊#92418C22semidirect
44. #16839664C22semidirect
45. #16839660C22semidirect
47. #16839622C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
111. #14519698D4semidirect
135. C22×D4×C61D4semidirect
146. C22⋊Q8×C61D4semidirect
360. D4×C61#121semidirect
444. C22×C61#449semidirect
472. C2×#546D61semidirect
548. C61#24434semidirect
569. C22×D4C22⋊D61semidirect
597. C22⋊Q8C22⋊D61semidirect
850. D4#14519749semidirect
934. C22#16839907semidirect

Maximal subgroups

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

subgroupindex
C2×#168399932
C2×#168399072
C2×#168398962
C22×#145196982
#214492592
#214470552
#214470052
#214468962
#214468152
#214461672
#214461272
#214461122
#214460802
#214457592
C2×C61×#5462
#2443461