Finite Group Databasebeta

← #11889751

Subgroups — #11889751

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595229C211yesmaximal, characteristic
2#10594537C211yesmaximal, characteristic, complemented
3#10592479C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4765C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591441C211yesmaximal, characteristic, complemented
8#10591417C211yesmaximal, characteristic, complemented
9#10590957C211yesmaximal, characteristic, complemented
10#10590848C211yesmaximal, characteristic, complemented
11#10590747C211yesmaximal, characteristic, complemented
12#10590726C211yesmaximal, characteristic, complemented
13#10590618C211yesmaximal, characteristic, complemented
14#10590517C211yesmaximal, characteristic, complemented
15#10590463C211yesmaximal, characteristic, complemented
16#81700—31nomaximal
17#78763—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64147C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C2×#3743C2211yescharacteristic, complemented
23#64106C2211yescharacteristic, complemented
24C3×#936C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#888C2211yescharacteristic, complemented
28#63977—21no—
29#63971—21no—
30#63969—21no—
31D3×#217—21no—
32#63904—21no—
33C4×#626C2211yescharacteristic
34#63900C2211yescharacteristic, complemented
35Dic3×D12C2211yescharacteristic
36#63888—21no—
37#63857C2211yescharacteristic
38#63856—21no—
39#63856C2211yescharacteristic
40#63845—21no—
41#63844C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63643C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54#63575C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5806—31no—
62#5730—31no—
63#5676—31no—
64#5511—31no—
65C3×#489—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5116—31no—
69#5111—31no—
70#5087—31no—
71#5054—31no—
72#4970—31no—
73#4813—31no—
74#4811—31no—
75#4808—31no—
76#4803—31no—
77#4783—31no—
78#4780—31no—
79#4780—31no—
80#4780—61no—
81#4776—31no—
82#4774—31no—
83#4774—31no—
84#4771—31no—
85D3×#102D311yescharacteristic, complemented
86#4767—31no—
87#4765D311yescharacteristic, complemented
88#4759—31no—
89#4757—31no—
90#4710—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C3×D3×D4—22no—
99C3×D3×D4—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3757—21no—
115#3754—41no—
116#3752—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3743—41no—
121C3×#217—21no—
122C3×#217—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131#3724—21no—
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3719—41no—
143#3716—22no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C2×D3×D4C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×C4⋊Q8—31no—
151C3×#124—31no—
152C2×C3×C4⋊C4—31no—
153#953—61no—
154C2×#217—61no—
155#946—31no—
156#946—61no—
157#946—61no—
158C2×#216—31no—
159#939—61no—
160#938—31no—
161#938—31no—
162#938—61no—
163#936C2×D311yescharacteristic
164#935—61no—
165D4×Dic3—31no—
166C2×#214—31no—
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—61no—
170C4×#67—31no—
171C4×#67—61no—
172#924—31no—
173#924—31no—
174#924—61no—
175C2×Dic12—31no—
176C2×#204—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—61no—
180C2×D3×C8C2×D311yescharacteristic
181#897—31no—
182#897—31no—
183#897—31no—
184#897—61no—
185#896—61no—
186#893—61no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4C2×D311yescharacteristic
190#890—61no—
191#889—61no—
192#888C2×D311yescharacteristic, complemented
193#887—31no—
194#884—61no—
195#883—61no—
196#882—61no—
197D3×C22⋊C4—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×Dic6—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×#97—31no—
211#835—31no—
212#832—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#830—31no—
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220#818—31no—
221#818—31no—
222#816—31no—
223#816—31no—
224#816—61no—
225#816C2×D311yescharacteristic, complemented
226#815C2×D311yescharacteristic, complemented
227Dic3⋊C8—31no—
228#810—31no—
229#810C2×D311yescharacteristic, complemented
230#809—31no—
231#809C2×D311yescharacteristic
232#807—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—81no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255#634—21no—
256#634—21no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—81no—
272#626—22no—
273#626—42no—
274#624—81no—
275D3×Dic3—42no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—31no—
284#484—91no—
285#480—91no—
286#474—91no—
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—31no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—62no—
304C2×C3×D4—121no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—121no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317#239—62no—
318#239—121no—
319#237—62no—
320#237—121no—
321D3×D4—22no—
322D3×D4—41no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—21no—
336C2×Dic6—31no—
337C2×Dic6—31no—
338C2×Dic6—61no—
339C2×Dic6C22×D311yescharacteristic
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—121no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356#217—21no—
357#217—21no—
358#217—31no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—121no—
365#216—121no—
366#214—62no—
367#214—121no—
368#214—121no—
369#214—122no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—121no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—121no—
408#204—62no—
409ΓL(1,𝔽25)—121no—
410ΓL(1,𝔽25)—121no—
411ΓL(1,𝔽25)—122no—
412D3×C8—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—84no—
426C2×C3×D3#13712yes—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×M16—91no—
445C22×C8—31no—
446C4⋊Q8—31no—
447#125—181no—
448#124—31no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—91no—
466#107—91no—
467#107—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102D3211yescharacteristic
479C22⋊C8—91no—
480C22⋊C8—91no—
481#97—31no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—61no—
487C23×C3—122no—
488C23×C3—122no—
489C23×C3—241no—
490C22×D3—21no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—61no—
496C22×D3—81no—
497C22×D3D3×D411yescharacteristic
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—241no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—32no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—61no—
509C3×D4—122no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—241no—
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—42no—
526#67—62no—
527#67—122no—
528#67—241no—
529#67—241no—
530#67—242no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—122no—
544C2×Dic3—241no—
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548D12—21no—
549D12—62no—
550D12—122no—
551D12#23512yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—81no—
559C4×D3—121no—
560C4×D3—121no—
561C4×D3—122no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565Dic6—21no—
566Dic6—21no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—81no—
572Dic6—121no—
573Dic6—121no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—41no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—62no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C2×C32—81no—
585C2×C32#54611yescharacteristic
586C2×C32C2×#13711yescharacteristic
587C2×C32#57611yescharacteristic
588C3⋊D3—41no—
589C3×D3—22no—
590C3×D3—42no—
591C24—61no—
592#41—182no—
593#41—361no—
594C2×Q8—31no—
595C2×Q8—61no—
596C2×Q8—91no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—62no—
600C2×D4—91no—
601C2×D4—121no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4C2×D3211yescharacteristic
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—91no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611Q16—361no—
612SD16—182no—
613SD16—361no—
614M16—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—121no—
619C2×C8C2×D3211yescharacteristic
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—181no—
643C22×C3—21no—
644C22×C3—32no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—62no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—244no—
660C22×C3C2×D3×D411yescharacteristic
661C22×C3C2×D3×D411yescharacteristic
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—22no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—84no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3#91512yes—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×#23511yescharacteristic
690C3×C4#100411yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4#100911yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—61no—
700Dic3—61no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707Dic3—241no—
708C32#331411yescharacteristic, complemented, Sylow
709C23—21no—
710C23—31no—
711C23—61no—
712C23—91no—
713C23—122no—
714C23—122no—
715C23—241no—
716Q8—61no—
717Q8—61no—
718Q8—181no—
719Q8—181no—
720Q8—241no—
721D4—21no—
722D4—21no—
723D4—32no—
724D4—61no—
725D4—122no—
726D4—182no—
727D4—362no—
728D4—721no—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—91no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—241no—
744C2×C4—362no—
745C2×C4—721no—
746C2×C4—721no—
747C2×C4C22×D3211yescharacteristic
748C8—21no—
749C8—61no—
750C8—61no—
751C8—181no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—62no—
756C2×C3—81no—
757C2×C3—81no—
758C2×C3—122no—
759C2×C3—161no—
760C2×C3#549011yescharacteristic
761C2×C3#567611yescharacteristic
762C2×C3#575711yescharacteristic
763C2×C3C2×#91511yescharacteristic
764C2×C3#577411yescharacteristic
765C2×C3D3×#13711yescharacteristic
766D3—22no—
767D3—42no—
768D3—121no—
769D3—121no—
770D3—241no—
771C22—32no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—61no—
776C22—61no—
777C22—62no—
778C22—121no—
779C22—121no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—244no—
784C22D32×D411yescharacteristic
785C4—41no—
786C4—61no—
787C4—61no—
788C4—61no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—181no—
793C4—361no—
794C4—361no—
795C4D3×#23511yescharacteristic
796C4#6431411yescharacteristic
797C3—21no—
798C3#7876311yescharacteristic, complemented
799C3#8170011yescharacteristic, complemented
800C2—62no—
801C2—81no—
802C2—122no—
803C2—361no—
804C2#1059428011yescharacteristic
805C2#1059473211yescharacteristic
806C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595229C2
hypercenter#102D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594537C2semidirect
3. #10592479C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4765C2semidirect
6. #10591459C2semidirect
7. #10591441C2semidirect
8. #10591417C2semidirect
9. #10590957C2semidirect
10. #10590848C2semidirect
11. #10590747C2semidirect
12. #10590726C2semidirect
13. #10590618C2semidirect
14. #10590517C2semidirect
15. #10590463C2semidirect
22. C2×#3743C22semidirect
23. #64106C22semidirect
27. C3×#888C22semidirect
34. #63900C22semidirect
41. #63844C22semidirect
42. C2×#3719C22semidirect
45. #63643C22semidirect
46. #63634C22semidirect
50. C3×#816C22semidirect
51. C3×#815C22semidirect
52. C3×#810C22semidirect
54. #63575C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
59. #63557C22semidirect
85. D3×#102D3semidirect
87. #4765D3semidirect
192. #888C2×D3semidirect
225. #816C2×D3semidirect
226. #815C2×D3semidirect
229. #810C2×D3semidirect
708. C32#3314semidirect
798. C3#78763semidirect
799. C3#81700semidirect

Maximal subgroups

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

subgroupindex
#105952292
#105945372
#105924792
C3×D3×#1022
C3×#47652
#105914592
#105914412
#105914172
#105909572
#105908482
#105907472
#105907262
#105906182
#105905172
#105904632
#817003
#787633