Finite Group Databasebeta

← #11889775

Subgroups — #11889775

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594633C211yesmaximal, characteristic
2#10594531C211yesmaximal, characteristic, complemented
3#10592588C211yesmaximal, characteristic, complemented
4C3×#4884C211yesmaximal, characteristic, complemented
5C3×#4882C211yesmaximal, characteristic, complemented
6#10590970C211yesmaximal, characteristic, complemented
7#10590946C211yesmaximal, characteristic, complemented
8#10590866C211yesmaximal, characteristic, complemented
9#10590725C211yesmaximal, characteristic, complemented
10#10590609C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590588C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590538C211yesmaximal, characteristic, complemented
15#10590430C211yesmaximal, characteristic, complemented
16#81486—31nomaximal
17#81289—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21#64102C2211yescharacteristic
22#64096C2211yescharacteristic, complemented
23C3×#897C2211yescharacteristic
24C3×#895C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic, complemented
27#63922—21no—
28#63921—21no—
29#63919C2211yescharacteristic, complemented
30#63916—21no—
31C4×#625—21no—
32C4×#625C2211yescharacteristic
33#63870—21no—
34#63863C2211yescharacteristic
35#63857C2211yescharacteristic
36#63857C2211yescharacteristic, complemented
37#63854—21no—
38#63851—21no—
39#63851—21no—
40C2×#3719C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#107C2211yescharacteristic, complemented
45#63642C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61#5630—31no—
62#5612—31no—
63#5511—31no—
64#5511—31no—
65C3×#484—31no—
66C3×#480—31no—
67#5051—31no—
68#5042—31no—
69#4966—31no—
70C2×#809—31no—
71#4890—31no—
72#4890—31no—
73#4889—31no—
74#4889—31no—
75#4889—61no—
76#4887—31no—
77#4886—31no—
78#4884D311yescharacteristic, complemented
79#4882D311yescharacteristic, complemented
80#4808—31no—
81#4803—31no—
82#4798—31no—
83#4794—31no—
84#4776—31no—
85D3×#102—31no—
86#4767—31no—
87#4765—31no—
88#4733—31no—
89#4731—31no—
90#4730—31no—
91#4728—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625D411yescharacteristic
107C2×#624—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3799—22no—
111#3799—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3744—22no—
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—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3724D411yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140#3719—41no—
141#3716—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C3×C22⋊Q8—31no—
150C3×#121—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153#947—31no—
154C2×#216—31no—
155#938—61no—
156#937—61no—
157#936—31no—
158C2×#214—31no—
159C4×#67—31no—
160C4×#67—31no—
161C4×#67—61no—
162C4×#67—61no—
163#924—31no—
164#924—31no—
165#924—61no—
166#924—61no—
167C2×#208—31no—
168C22×C3⋊C8—31no—
169C2×Dic12—31no—
170C2×#204—31no—
171C2×#204—31no—
172C2×#204—31no—
173C2×#204—61no—
174C2×ΓL(1,𝔽25)—31no—
175C2×D3×C8—31no—
176#897—31no—
177#897—31no—
178#897C2×D311yescharacteristic
179#896—61no—
180#896—61no—
181#895—61no—
182#895C2×D311yescharacteristic
183#894—61no—
184#893—31no—
185#893—31no—
186#893—61no—
187D3×C4⋊C4C2×D311yescharacteristic
188D3×C4⋊C4C2×D311yescharacteristic, complemented
189#889—61no—
190#889—61no—
191#888—31no—
192#888—31no—
193#887—31no—
194#887—31no—
195#887—61no—
196#883—61no—
197#882—61no—
198D3×C22⋊C4—61no—
199D3×C22⋊C4—61no—
200C3×#107—21no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#107C2×D311yescharacteristic, complemented
204C3×#107C2×D311yescharacteristic, complemented
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211#835—31no—
212#832—31no—
213#821—31no—
214#821—31no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic, complemented
218#816C2×D311yescharacteristic, complemented
219#815—31no—
220#815—31no—
221#815—61no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—61no—
228#810C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic
236#807C2×D311yescharacteristic, complemented
237#807C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
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
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—81no—
254#634—21no—
255#634—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—81no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#627—81no—
273#626—42no—
274#626—42no—
275#625—22no—
276#624—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—31no—
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—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—31no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C2×#67—31no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309#239—62no—
310#239—121no—
311D3×D4—62no—
312D3×D4—121no—
313#235—62no—
314#235—121no—
315C2×D12—21no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—121no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—121no—
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
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⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357#217—31no—
358#217—31no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#216—121no—
364#214—121no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
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—
376C4⋊Dic3—21no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—121no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398#208—121no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406#204—62no—
407#204—62no—
408#204—64no—
409#204—121no—
410ΓL(1,𝔽25)—121no—
411D3×C8—121no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—22no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
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#13712yes—
425D32—84no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—91no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×M16—91no—
444C22×C8—91no—
445C4⋊Q8—91no—
446#125—181no—
447#124—91no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—181no—
453C22⋊Q8—181no—
454#121—31no—
455#121—181no—
456#120—181no—
457C4×Q8—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—31no—
463C2×C22⋊C4—181no—
464#107—31no—
465#107—31no—
466#107D3211yescharacteristic, complemented
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—31no—
480#97—91no—
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3D3×D411yescharacteristic
495C22×D3D3×D411yescharacteristic
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—241no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
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—62no—
523#67—122no—
524#67—122no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—121no—
537C2×Dic3D3×D411yescharacteristic
538C2×Dic3D3×D411yescharacteristic
539D12—21no—
540D12—21no—
541D12—32no—
542D12—32no—
543D12—62no—
544D12—61no—
545D12—61no—
546D12—81no—
547D12—121no—
548D12—122no—
549D12—122no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—81no—
555C4×D3—81no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—242no—
561Dic6—21no—
562Dic6—21no—
563Dic6—62no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—121no—
569Dic6—241no—
570Dic6—241no—
571C3×C8—22no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32#54611yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C2×C32#57611yescharacteristic
584C3⋊D3—42no—
585C3×D3—22no—
586C3×D3—41no—
587C3×D3—81no—
588C24—181no—
589#41—182no—
590#41—361no—
591C2×Q8—31no—
592C2×Q8—91no—
593C2×Q8—181no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—181no—
599C2×D4—182no—
600C2×D4—181no—
601C2×D4—361no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—361no—
609SD16—182no—
610SD16—361no—
611M16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—361no—
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4C2×D3211yescharacteristic
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—91no—
639C42—181no—
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—122no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3#91812yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4D3×#4111yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4#100911yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—121no—
699Dic3—121no—
700Dic3—122no—
701Dic3—121no—
702Dic3—121no—
703C32#331411yescharacteristic, complemented, Sylow
704C23—31no—
705C23—31no—
706C23—61no—
707C23—181no—
708C23—362no—
709C23—362no—
710C23—721no—
711Q8—61no—
712Q8—61no—
713Q8—181no—
714Q8—181no—
715Q8—721no—
716D4—61no—
717D4—61no—
718D4—92no—
719D4—182no—
720D4—181no—
721D4—241no—
722D4—362no—
723D4—362no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—181no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—362no—
741C2×C4—721no—
742C2×C4C22×D3211yescharacteristic
743C8—21no—
744C8—61no—
745C8—61no—
746C8—181no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—62no—
751C2×C3—121no—
752C2×C3—241no—
753C2×C3#565411yescharacteristic
754C2×C3#565411yescharacteristic
755C2×C3#575711yescharacteristic
756C2×C3C2×#91811yescharacteristic
757C2×C3#577411yescharacteristic
758C2×C3D3×#13711yescharacteristic
759D3—22no—
760D3—41no—
761D3—81no—
762D3—122no—
763D3—122no—
764D3—242no—
765C22—32no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—182no—
775C22—361no—
776C22—361no—
777C22—724no—
778C22D32×D411yescharacteristic
779C4—41no—
780C4—41no—
781C4—61no—
782C4—61no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—181no—
787C4—181no—
788C4—361no—
789C4#6430611yescharacteristic
790C4#6432011yescharacteristic
791C3—21no—
792C3#8128911yescharacteristic, complemented
793C3#8148611yescharacteristic, complemented
794C2—62no—
795C2—121no—
796C2—241no—
797C2—362no—
798C2#1059461611yescharacteristic
799C2#1059473211yescharacteristic
800C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594633C2
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. #10594531C2semidirect
3. #10592588C2semidirect
4. C3×#4884C2semidirect
5. C3×#4882C2semidirect
6. #10590970C2semidirect
7. #10590946C2semidirect
8. #10590866C2semidirect
9. #10590725C2semidirect
10. #10590609C2semidirect
11. D3×#809C2semidirect
12. #10590588C2semidirect
13. #10590579C2semidirect
14. #10590538C2semidirect
15. #10590430C2semidirect
22. #64096C22semidirect
26. C3×D3×C4⋊C4C22semidirect
29. #63919C22semidirect
36. #63857C22semidirect
40. C2×#3719C22semidirect
42. C2×#3711C22semidirect
44. C32×#107C22semidirect
45. #63642C22semidirect
46. #63637C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#816C22semidirect
52. C3×#810C22semidirect
54. C3×#807C22semidirect
55. C3×#807C22semidirect
56. #63572C22semidirect
57. #63565C22semidirect
78. #4884D3semidirect
79. #4882D3semidirect
188. D3×C4⋊C4C2×D3semidirect
203. C3×#107C2×D3semidirect
204. C3×#107C2×D3semidirect
217. (C2×D3)⋊C8C2×D3semidirect
218. #816C2×D3semidirect
228. #810C2×D3semidirect
236. #807C2×D3semidirect
237. #807C2×D3semidirect
466. #107D32semidirect
703. C32#3314semidirect
792. C3#81289semidirect
793. C3#81486semidirect

Maximal subgroups

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

subgroupindex
#105946332
#105945312
#105925882
C3×#48842
C3×#48822
#105909702
#105909462
#105908662
#105907252
#105906092
D3×#8092
#105905882
#105905792
#105905382
#105904302
#814863
#812893