Finite Group Databasebeta

← #11889773

Subgroups — #11889773

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594630C211yesmaximal, characteristic
2#10594537C211yesmaximal, characteristic, complemented
3#10592586C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic, complemented
5C3×#4882C211yesmaximal, characteristic, complemented
6#10590969C211yesmaximal, characteristic, complemented
7#10590940C211yesmaximal, characteristic, complemented
8#10590861C211yesmaximal, characteristic, complemented
9#10590737C211yesmaximal, characteristic, complemented
10#10590607C211yesmaximal, characteristic, complemented
11#10590597C211yesmaximal, characteristic, complemented
12#10590590C211yesmaximal, characteristic, complemented
13#10590588C211yesmaximal, characteristic, complemented
14#10590531C211yesmaximal, characteristic, complemented
15#10590444C211yesmaximal, characteristic, complemented
16#81289—31nomaximal
17#80982—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×#3746C2211yescharacteristic, complemented
21C2×C8×C3⋊D3C2211yescharacteristic
22#64106C2211yescharacteristic
23#64106C2211yescharacteristic
24C3×#895C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic, complemented
27C3×#888C2211yescharacteristic, complemented
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63908—21no—
31#63904—21no—
32C4×#626C2211yescharacteristic
33#63900C2211yescharacteristic
34#63891—21no—
35#63888—21no—
36#63860C2211yescharacteristic
37#63857C2211yescharacteristic, complemented
38#63856—21no—
39#63845—21no—
40#63844C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5730—31no—
62#5612—31no—
63#5554—31no—
64#5511—31no—
65C3×#480—31no—
66C3×#474—31no—
67#5089—31no—
68#5042—31no—
69#5018—31no—
70#4966—31no—
71#4890D311yescharacteristic, complemented
72#4889—31no—
73#4887—31no—
74#4887—31no—
75#4887—61no—
76#4886—31no—
77#4884—31no—
78#4884—31no—
79#4882D311yescharacteristic, complemented
80#4845—31no—
81#4836—31no—
82#4783—31no—
83#4776—31no—
84#4776—31no—
85#4771—31no—
86D3×#102—31no—
87D3×#102—31no—
88#4767—31no—
89#4765—31no—
90#4733—31no—
91#4728—31no—
92C22×D32—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×#626D411yescharacteristic
104C2×#625—21no—
105C2×#625—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108#3802—22no—
109#3802—41no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3746—41no—
121C8×C3⋊D3—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3716—22no—
142#3716—41no—
143#3711—41no—
144#3314—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×#235—31no—
149C3×C4⋊Q8—31no—
150C3×#121—31no—
151C3×C4×D4—31no—
152C2×C3×C4⋊C4—31no—
153#946—61no—
154#946—61no—
155#938—61no—
156#937—61no—
157#936—31no—
158C2×#214—31no—
159C2×#214—31no—
160#930—61no—
161C4×#67—31no—
162C4×#67—61no—
163C2×(C2×D3)⋊C4—61no—
164#924—31no—
165#924—61no—
166C2×#208—31no—
167C2×Dic12—31no—
168C2×Dic12—31no—
169C2×Dic12—61no—
170C2×#204—31no—
171C2×#204—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—61no—
176#897—31no—
177#897—31no—
178#897—31no—
179#897—31no—
180#897—31no—
181#897—61no—
182#897—61no—
183#896—61no—
184#895C2×D311yescharacteristic
185#893—61no—
186#893C2×D311yescharacteristic
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4C2×D311yescharacteristic, complemented
190#890—61no—
191#889—61no—
192#888C2×D311yescharacteristic, complemented
193#887—31no—
194#886—61no—
195#883—61no—
196#882—61no—
197D3×C22⋊C4—61no—
198#875—31no—
199C4×D12—31no—
200C4×Dic6—31no—
201C3×#107—21no—
202C3×#107—31no—
203C3×#107—31no—
204C3×#107C2×D311yescharacteristic, complemented
205C3×#107C2×D311yescharacteristic, complemented
206C3×C4⋊C8—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—31no—
212#832—31no—
213#832—31no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic, complemented
219#816—31no—
220#816—31no—
221#815—31no—
222Dic3⋊C8C2×D311yescharacteristic, complemented
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—61no—
230#810—61no—
231#809—31no—
232#809—31no—
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic
235#807C2×D311yescharacteristic, complemented
236#807C2×D311yescharacteristic, complemented
237#803—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253#634—21no—
254#634—21no—
255#634—21no—
256#634—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—81no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271C3×Dic6—81no—
272#626—22no—
273#625—42no—
274#625—42no—
275#624—81no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—31no—
286#474—31no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—61no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C2×#67—31no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311#237—62no—
312#237—121no—
313D3×D4—62no—
314D3×D4—62no—
315D3×D4—121no—
316D3×D4—121no—
317#235—62no—
318#235—121no—
319C2×D12—21no—
320C2×D12—31no—
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6—21no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—31no—
357#217—31no—
358#217—61no—
359#217—61no—
360#217—61no—
361#214—62no—
362#214—121no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—121no—
376(C2×D3)⋊C4—121no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—121no—
384C4⋊Dic3—121no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3C22×D311yescharacteristic
398#208—121no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12—121no—
405Dic12—121no—
406Dic12—122no—
407#204—62no—
408#204—121no—
409ΓL(1,𝔽25)—121no—
410D3×C8—121no—
411D3×C8—121no—
412D3×C8—122no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3#13712yes—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426D32—84no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447#125—181no—
448#124—91no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—31no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—31no—
466#107—31no—
467#107D3211yescharacteristic, complemented
468C4⋊C8—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—31no—
483C23×C3—61no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3D3×D411yescharacteristic
497C3×Q8—241no—
498C3×D4—32no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—241no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—62no—
522#67—122no—
523#67—122no—
524#67—122no—
525#67—122no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—122no—
538C2×Dic3D3×D411yescharacteristic
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541D12—21no—
542D12—21no—
543D12—21no—
544D12—62no—
545D12—81no—
546D12#23912yes—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—81no—
554C4×D3—81no—
555C4×D3—121no—
556C4×D3—121no—
557C4×D3—122no—
558C4×D3—241no—
559C4×D3—241no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—81no—
569Dic6—121no—
570Dic6—121no—
571Dic6—121no—
572Dic6—121no—
573C3×C8—22no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32#54611yescharacteristic
584C2×C32C2×#13711yescharacteristic
585C2×C32#57611yescharacteristic
586C3⋊D3—22no—
587C3×D3—42no—
588C3×D3—41no—
589C3×D3—81no—
590C24—181no—
591#41—182no—
592#41—361no—
593C2×Q8—61no—
594C2×Q8—91no—
595C2×Q8—91no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—182no—
602C2×D4—181no—
603C2×D4—361no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—91no—
608C22×C4—181no—
609C22×C4—181no—
610Q16—361no—
611SD16—182no—
612SD16—361no—
613M16—361no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—361no—
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4C2×D3211yescharacteristic
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—181no—
642C22×C3—21no—
643C22×C3—62no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—22no—
658C2×D3—32no—
659C2×D3—32no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—62no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—244no—
673C2×D3—244no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4C2×#23911yescharacteristic
688C3×C4D3×#4111yescharacteristic
689C3×C4#100911yescharacteristic
690C3×C4#100911yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—31no—
707C23—61no—
708C23—61no—
709C23—91no—
710C23—362no—
711C23—362no—
712C23—721no—
713Q8—181no—
714Q8—181no—
715Q8—181no—
716Q8—181no—
717Q8—241no—
718D4—32no—
719D4—61no—
720D4—61no—
721D4—61no—
722D4—182no—
723D4—241no—
724D4—362no—
725D4—362no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—362no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—121no—
753C2×C3—122no—
754C2×C3—241no—
755C2×C3#563011yescharacteristic
756C2×C3#565411yescharacteristic
757C2×C3#575711yescharacteristic
758C2×C3#575711yescharacteristic
759C2×C3D3×#13711yescharacteristic
760C2×C3D3×#13711yescharacteristic
761D3—42no—
762D3—41no—
763D3—62no—
764D3—62no—
765D3—81no—
766D3—122no—
767C22—61no—
768C22—62no—
769C22—61no—
770C22—61no—
771C22—92no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—181no—
778C22—181no—
779C22—724no—
780C22D32×D411yescharacteristic
781C4—41no—
782C4—41no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—181no—
789C4—361no—
790C4—361no—
791C4#6430811yescharacteristic
792C4D3×#23911yescharacteristic
793C3—21no—
794C3#8098211yescharacteristic, complemented
795C3#8128911yescharacteristic, complemented
796C2—121no—
797C2—122no—
798C2—182no—
799C2—241no—
800C2#1059462011yescharacteristic
801C2#1059473111yescharacteristic
802C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594630C2
hypercenter#107D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594537C2semidirect
3. #10592586C2semidirect
4. C3×#4890C2semidirect
5. C3×#4882C2semidirect
6. #10590969C2semidirect
7. #10590940C2semidirect
8. #10590861C2semidirect
9. #10590737C2semidirect
10. #10590607C2semidirect
11. #10590597C2semidirect
12. #10590590C2semidirect
13. #10590588C2semidirect
14. #10590531C2semidirect
15. #10590444C2semidirect
20. C2×#3746C22semidirect
26. C3×D3×C4⋊C4C22semidirect
27. C3×#888C22semidirect
37. #63857C22semidirect
40. #63844C22semidirect
43. C2×#3711C22semidirect
44. C32×#107C22semidirect
45. #63637C22semidirect
46. #63637C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×Dic3⋊C8C22semidirect
53. C3×#807C22semidirect
54. C3×#807C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
60. #63554C22semidirect
71. #4890D3semidirect
79. #4882D3semidirect
189. D3×C4⋊C4C2×D3semidirect
192. #888C2×D3semidirect
204. C3×#107C2×D3semidirect
205. C3×#107C2×D3semidirect
218. (C2×D3)⋊C8C2×D3semidirect
222. Dic3⋊C8C2×D3semidirect
235. #807C2×D3semidirect
236. #807C2×D3semidirect
467. #107D32semidirect
705. C32#3314semidirect
794. C3#80982semidirect
795. C3#81289semidirect

Maximal subgroups

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

subgroupindex
#105946302
#105945372
#105925862
C3×#48902
C3×#48822
#105909692
#105909402
#105908612
#105907372
#105906072
#105905972
#105905902
#105905882
#105905312
#105904442
#812893
#809823