Finite Group Databasebeta

← #11889771

Subgroups — #11889771

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#10594629C211yesmaximal, characteristic
2#10594537C211yesmaximal, characteristic, complemented
3#10592585C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic, complemented
5C3×#4884C211yesmaximal, characteristic, complemented
6#10590957C211yesmaximal, characteristic, complemented
7#10590946C211yesmaximal, characteristic, complemented
8#10590907C211yesmaximal, characteristic, complemented
9#10590813C211yesmaximal, characteristic, complemented
10#10590618C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590590C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590535C211yesmaximal, characteristic, complemented
15#10590442C211yesmaximal, characteristic, complemented
16#81486—31nomaximal
17#80982—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C2×#3743C2211yescharacteristic, complemented
22#64106C2211yescharacteristic, complemented
23#64104C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#888C2211yescharacteristic, complemented
28#63923—21no—
29D3×(C2×D3)⋊C4—21no—
30#63909—21no—
31#63904—21no—
32C4×#626C2211yescharacteristic
33#63900C2211yescharacteristic, complemented
34#63890—21no—
35#63888—21no—
36#63864C2211yescharacteristic
37#63857C2211yescharacteristic
38#63856—21no—
39#63845—21no—
40#63844C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#107C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5730—31no—
62#5630—31no—
63#5554—31no—
64#5511—31no—
65C3×#484—31no—
66C3×#474—31no—
67#5089—31no—
68#5051—31no—
69#5018—31no—
70C2×#809—31no—
71#4890D311yescharacteristic, complemented
72#4889—31no—
73#4887—31no—
74#4886—31no—
75#4886—31no—
76#4886—61no—
77#4884D311yescharacteristic, complemented
78#4882—31no—
79#4882—31no—
80#4845—31no—
81#4836—31no—
82#4808—31no—
83#4803—31no—
84#4798—31no—
85#4794—31no—
86#4783—31no—
87#4776—31no—
88#4771—31no—
89D3×#102—31no—
90#4731—31no—
91#4730—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×#624—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3796—22no—
111#3796—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3744—41no—
120#3743—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—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#3722—21no—
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3719—41no—
142#3716—22no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C22×D12—31no—
149C3×C4⋊Q8—31no—
150C3×C22⋊Q8—31no—
151C3×C4×D4—31no—
152C2×C3×C4⋊C4—31no—
153#947—31no—
154#946—61no—
155#946—61no—
156C2×#216—31no—
157C2×#214—31no—
158#930—61no—
159C4×#67—31no—
160C4×#67—61no—
161C2×(C2×D3)⋊C4—61no—
162#924—31no—
163#924—61no—
164C22×C3⋊C8—31no—
165C2×Dic12—31no—
166C2×#204—31no—
167C2×#204—31no—
168C2×#204—31no—
169C2×#204—61no—
170C2×ΓL(1,𝔽25)—31no—
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—61no—
173C2×D3×C8—31no—
174#897—31no—
175#897—31no—
176#897—31no—
177#897—61no—
178#897C2×D311yescharacteristic
179#896—61no—
180#895—31no—
181#895—31no—
182#895—61no—
183#895—61no—
184#894—61no—
185#893—61no—
186#893C2×D311yescharacteristic
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#886—61no—
195#882—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×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—31no—
212#835—31no—
213#832—31no—
214#821—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#816C2×D311yescharacteristic, complemented
221#815—31no—
222Dic3⋊C8C2×D311yescharacteristic, complemented
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#807C2×D311yescharacteristic, complemented
236#807C2×D311yescharacteristic, complemented
237#803—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—81no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255#634—21no—
256#634—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—81no—
272#626—22no—
273#626—42no—
274#626—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—31no—
285#480—91no—
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—31no—
299C2×C3×Q8—61no—
300C2×C3×D4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—31no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308#239—62no—
309#239—121no—
310#237—62no—
311#237—121no—
312D3×D4—62no—
313D3×D4—121no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—62no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—121no—
324C2×D12—121no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
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×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359#217—31no—
360#217—61no—
361#216—121no—
362#214—62no—
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—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
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
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12—121no—
405#204—62no—
406#204—121no—
407#204—121no—
408#204—122no—
409ΓL(1,𝔽25)—121no—
410ΓL(1,𝔽25)—121no—
411ΓL(1,𝔽25)—122no—
412D3×C8—121no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13712yes—
426D32—84no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
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—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—31no—
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—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—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—241no—
496C22×D3—241no—
497C22×D3D3×D411yescharacteristic
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—241no—
501C3×D4—32no—
502C3×D4—61no—
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—61no—
518C2×C3×C4—241no—
519C2×C3×C4—241no—
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—62no—
523#67—122no—
524#67—122no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—122no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538D12—21no—
539D12—62no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12—121no—
546D12—122no—
547D12—122no—
548D12—241no—
549D12—241no—
550D12—242no—
551D12#23912yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—81no—
559C4×D3—81no—
560C4×D3—121no—
561C4×D3—121no—
562C4×D3—122no—
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—22no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13711yescharacteristic
586C2×C32#57611yescharacteristic
587C3⋊D3—41no—
588C3⋊D3—81no—
589C3×D3—22no—
590C3×D3—42no—
591C24—181no—
592#41—182no—
593#41—361no—
594C2×Q8—31no—
595C2×Q8—61no—
596C2×Q8—91no—
597C2×D4—31no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—182no—
603C2×D4—181no—
604C2×D4—361no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—91no—
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—361no—
619C2×C8C2×D3211yescharacteristic
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
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—61no—
646C22×C3—61no—
647C22×C3—62no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—241no—
673C2×D3—241no—
674C2×D3—241no—
675C2×D3—244no—
676C2×D3—244no—
677C2×D3#91812yes—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—81no—
688C3×C4—81no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×#23911yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4#100911yescharacteristic
695C3×C4#100911yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—61no—
703Dic3—61no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—241no—
708C32#331411yescharacteristic, complemented, Sylow
709C23—31no—
710C23—61no—
711C23—91no—
712C23—181no—
713C23—362no—
714C23—362no—
715C23—721no—
716Q8—61no—
717Q8—61no—
718Q8—181no—
719Q8—181no—
720Q8—241no—
721D4—32no—
722D4—61no—
723D4—182no—
724D4—181no—
725D4—181no—
726D4—362no—
727D4—362no—
728D4—721no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—91no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—241no—
744C2×C4—241no—
745C2×C4—362no—
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—122no—
757C2×C3#563011yescharacteristic
758C2×C3#565411yescharacteristic
759C2×C3#575711yescharacteristic
760C2×C3C2×#91811yescharacteristic
761C2×C3#577411yescharacteristic
762C2×C3D3×#13711yescharacteristic
763D3—22no—
764D3—42no—
765D3—121no—
766D3—121no—
767D3—241no—
768D3—241no—
769D3—241no—
770D3—481no—
771C22—32no—
772C22—61no—
773C22—61no—
774C22—62no—
775C22—121no—
776C22—121no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—361no—
781C22—361no—
782C22—361no—
783C22—724no—
784C22D32×D411yescharacteristic
785C4—41no—
786C4—41no—
787C4—61no—
788C4—61no—
789C4—61no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—181no—
794C4—361no—
795C4#6430811yescharacteristic
796C4D3×#23911yescharacteristic
797C3—21no—
798C3#8098211yescharacteristic, complemented
799C3#8148611yescharacteristic, complemented
800C2—62no—
801C2—122no—
802C2—361no—
803C2—721no—
804C2#1059462011yescharacteristic
805C2#1059473211yescharacteristic
806C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594629C2
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. #10592585C2semidirect
4. C3×#4890C2semidirect
5. C3×#4884C2semidirect
6. #10590957C2semidirect
7. #10590946C2semidirect
8. #10590907C2semidirect
9. #10590813C2semidirect
10. #10590618C2semidirect
11. D3×#809C2semidirect
12. #10590590C2semidirect
13. #10590579C2semidirect
14. #10590535C2semidirect
15. #10590442C2semidirect
21. C2×#3743C22semidirect
22. #64106C22semidirect
27. C3×#888C22semidirect
33. #63900C22semidirect
40. #63844C22semidirect
41. C2×#3719C22semidirect
44. C32×#107C22semidirect
45. #63637C22semidirect
49. C3×#816C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
53. C3×#807C22semidirect
54. C3×#807C22semidirect
55. #63565C22semidirect
59. #63557C22semidirect
60. #63554C22semidirect
71. #4890D3semidirect
77. #4884D3semidirect
192. #888C2×D3semidirect
204. C3×#107C2×D3semidirect
205. C3×#107C2×D3semidirect
220. #816C2×D3semidirect
222. Dic3⋊C8C2×D3semidirect
227. #810C2×D3semidirect
235. #807C2×D3semidirect
236. #807C2×D3semidirect
467. #107D32semidirect
708. C32#3314semidirect
798. C3#80982semidirect
799. C3#81486semidirect

Maximal subgroups

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

subgroupindex
#105946292
#105945372
#105925852
C3×#48902
C3×#48842
#105909572
#105909462
#105909072
#105908132
#105906182
D3×#8092
#105905902
#105905792
#105905352
#105904422
#814863
#809823