Finite Group Databasebeta

← #11887272

Subgroups — #11887272

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic
2#10594553C211yesmaximal, characteristic, complemented
3#10592507C211yesmaximal, characteristic, complemented
4C3×#4805C211yesmaximal, characteristic, complemented
5C3×#4800C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591577C211yesmaximal, characteristic, complemented
8#10591560C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590758C211yesmaximal, characteristic, complemented
11#10590721C211yesmaximal, characteristic, complemented
12#10590652C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590507C211yesmaximal, characteristic, complemented
15#10590470C211yesmaximal, characteristic, complemented
16#81652—31nomaximal
17#81445—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3756C2211yescharacteristic, complemented
21C2×#3744C2211yescharacteristic
22#64106C2211yescharacteristic, complemented
23C3×#947C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#890C2211yescharacteristic, complemented
27#63923—21no—
28#63921—21no—
29#63916C2211yescharacteristic
30#63910—21no—
31C4×#626C2211yescharacteristic
32#63894C2211yescharacteristic
33#63857C2211yescharacteristic
34#63853—21no—
35#63850—21no—
36#63849C2211yescharacteristic, complemented
37#63848—21no—
38#63845—21no—
39#63844C2211yescharacteristic, complemented
40#63841—21no—
41C2×#3716C2211yescharacteristic
42C2×#3710C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63647C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61#5694—31no—
62#5676—31no—
63#5630—31no—
64#5513—31no—
65C3×#488—31no—
66C3×#483—31no—
67#5066—31no—
68#5054—31no—
69#5051—31no—
70C2×#809—31no—
71#4871—31no—
72#4866—31no—
73#4864—31no—
74#4852—31no—
75#4813—31no—
76#4808—31no—
77#4808—31no—
78#4808—61no—
79#4805D311yescharacteristic, complemented
80#4804—31no—
81#4804—31no—
82#4800D311yescharacteristic, complemented
83#4798—31no—
84#4779—31no—
85#4778—31no—
86#4776—31no—
87D3×#102—31no—
88#4731—31no—
89#67⋊C8—31no—
90C4×#204—31no—
91C8×D12—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832—41no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#624—21no—
108D3×D12—22no—
109D3×D12—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3756—41no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3744—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133#3722—21no—
134#3722—21no—
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140Dic32—21no—
141#3716—41no—
142#3710—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C3×#125—31no—
151C3×#124—31no—
152C3×C22⋊Q8—31no—
153C2×C3×C4⋊C4—31no—
154#947C2×D311yescharacteristic
155#946C2×D311yescharacteristic
156C2×#216—31no—
157C2×#216—31no—
158C2×#216—61no—
159#938—31no—
160C2×#214—31no—
161#929—61no—
162C4×#67—31no—
163#926—61no—
164#924—31no—
165C22×C3⋊C8—31no—
166C2×#204—31no—
167C2×#204—31no—
168C2×#204—31no—
169C2×#204—61no—
170C2×D3×C8—31no—
171C2×D3×C8—31no—
172C2×D3×C8—31no—
173#898—61no—
174#898—61no—
175#897—31no—
176#897—31no—
177#897—31no—
178#897—61no—
179#895—31no—
180#895—61no—
181#894—61no—
182#894—61no—
183#893—31no—
184#892—31no—
185#892—31no—
186#892—61no—
187D3×C4⋊C4C2×D311yescharacteristic
188#890—61no—
189#890C2×D311yescharacteristic, complemented
190#889—61no—
191#887—31no—
192#884—61no—
193#883—61no—
194#882—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic, complemented
207C3×#103C2×D311yescharacteristic, complemented
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211C3×C4×C8—31no—
212#835C2×D311yescharacteristic, complemented
213#835C2×D311yescharacteristic, complemented
214#832—31no—
215#821—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—61no—
221(C2×D3)⋊C8C2×D311yescharacteristic
222#817C2×D311yescharacteristic, complemented
223#816—31no—
224Dic3⋊C8—31no—
225C8×Dic3C2×D311yescharacteristic, complemented
226#810—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237C4⋊(C3⋊C8)—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—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—42no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—42no—
258#634—21no—
259#634—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271#626—22no—
272#626—42no—
273#626—81no—
274#624—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—31no—
282#483—31no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—21no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C2×#67—31no—
303C2×#67—61no—
304C2×#67—61no—
305#239—62no—
306#239—62no—
307#239—122no—
308#239—121no—
309#239—121no—
310#239—122no—
311D3×D4—62no—
312D3×D4—121no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—121no—
323C2×D12—121no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—121no—
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
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×C22⋊C4—61no—
356C3×C42—31no—
357#217—31no—
358#217—61no—
359#217—61no—
360#216—121no—
361#216—121no—
362#216—122no—
363#214—121no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
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—61no—
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
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—62no—
407#204—62no—
408#204—122no—
409#204—121no—
410D3×C8—121no—
411D3×C8—121no—
412D3×C8—121no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13512yes—
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—
444C22×C8—91no—
445C22×C8—91no—
446#126—181no—
447#125—31no—
448#125—181no—
449#124—31no—
450#123—181no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461#117—91no—
462#117—181no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—181no—
465#107—91no—
466#106—31no—
467#106—31no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103D3211yescharacteristic, complemented
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481C4×C8—31no—
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—22no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—41no—
504C3×D4—61no—
505C3×D4—61no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—122no—
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—62no—
525#67—122no—
526#67—241no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538C2×Dic3D3×D411yescharacteristic
539D12—21no—
540D12—21no—
541D12—32no—
542D12—32no—
543D12—62no—
544D12—62no—
545D12—61no—
546D12—61no—
547D12—121no—
548D12—122no—
549D12—122no—
550D12—124no—
551D12—122no—
552D12—241no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—42no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—61no—
560C4×D3—121no—
561C4×D3—121no—
562C4×D3—122no—
563C4×D3—122no—
564C4×D3—124no—
565C4×D3—241no—
566C4×D3—241no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—121no—
572Dic6—121no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
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×#13511yescharacteristic
585C2×C32#57711yescharacteristic
586C3⋊D3—42no—
587C3⋊D3—41no—
588C3×D3—22no—
589C3×D3—81no—
590C24—181no—
591#41—182no—
592#41—361no—
593C2×Q8—91no—
594C2×Q8C2×D3211yescharacteristic
595C2×D4—31no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—181no—
599C2×D4—181no—
600C2×D4—182no—
601C2×D4—181no—
602C2×D4—361no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—91no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—361no—
609SD16—182no—
610SD16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—361no—
615C2×C8—361no—
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—181no—
641C42—181no—
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—61no—
657C2×D3—62no—
658C2×D3—61no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—122no—
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—244no—
675C2×D3—244no—
676C2×D3#91612yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—42no—
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—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4D3×#4111yescharacteristic
692C3×C4D3×#4111yescharacteristic
693C3×C4#100911yescharacteristic
694C3×C4#100911yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—21no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—61no—
702Dic3—61no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707C32#329611yescharacteristic, complemented, Sylow
708C23—31no—
709C23—61no—
710C23—91no—
711C23—181no—
712C23—362no—
713C23—362no—
714C23—721no—
715Q8—21no—
716Q8—21no—
717Q8—181no—
718Q8—181no—
719D4—61no—
720D4—61no—
721D4—92no—
722D4—182no—
723D4—181no—
724D4—362no—
725D4—362no—
726D4—721no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—91no—
738C2×C4—122no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
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—62no—
753C2×C3—241no—
754C2×C3#565411yescharacteristic
755C2×C3#567611yescharacteristic
756C2×C3C2×#91611yescharacteristic
757C2×C3D3×#13511yescharacteristic
758C2×C3#577011yescharacteristic
759C2×C3#577811yescharacteristic
760D3—22no—
761D3—81no—
762D3—121no—
763D3—122no—
764D3—121no—
765D3—122no—
766D3—241no—
767D3—242no—
768C22—32no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—181no—
775C22—181no—
776C22—181no—
777C22—182no—
778C22—361no—
779C22—361no—
780C22—724no—
781C22D32×D411yescharacteristic
782C4—41no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—181no—
791C4—361no—
792C4#6430811yescharacteristic
793C4#6431211yescharacteristic
794C3—21no—
795C3#8144511yescharacteristic, complemented
796C3#8165211yescharacteristic, complemented
797C2—62no—
798C2—241no—
799C2—361no—
800C2—362no—
801C2#1059428211yescharacteristic
802C2D3×#91611yescharacteristic
803C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595431C2
hypercenter#103D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594553C2semidirect
3. #10592507C2semidirect
4. C3×#4805C2semidirect
5. C3×#4800C2semidirect
6. #10591596C2semidirect
7. #10591577C2semidirect
8. #10591560C2semidirect
9. #10590946C2semidirect
10. #10590758C2semidirect
11. #10590721C2semidirect
12. #10590652C2semidirect
13. D3×#809C2semidirect
14. #10590507C2semidirect
15. #10590470C2semidirect
20. C2×#3756C22semidirect
22. #64106C22semidirect
26. C3×#890C22semidirect
36. #63849C22semidirect
39. #63844C22semidirect
42. C2×#3710C22semidirect
44. C32×#103C22semidirect
45. #63647C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×#817C22semidirect
52. C3×C8×Dic3C22semidirect
54. C3×#808C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
79. #4805D3semidirect
82. #4800D3semidirect
189. #890C2×D3semidirect
206. C3×#103C2×D3semidirect
207. C3×#103C2×D3semidirect
212. #835C2×D3semidirect
213. #835C2×D3semidirect
222. #817C2×D3semidirect
225. C8×Dic3C2×D3semidirect
234. #808C2×D3semidirect
472. #103D32semidirect
707. C32#3296semidirect
795. C3#81445semidirect
796. C3#81652semidirect

Maximal subgroups

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

subgroupindex
#105954312
#105945532
#105925072
C3×#48052
C3×#48002
#105915962
#105915772
#105915602
#105909462
#105907582
#105907212
#105906522
D3×#8092
#105905072
#105904702
#816523
#814453