Finite Group Databasebeta

← #11887324

Subgroups — #11887324

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595344C211yesmaximal, characteristic, complemented
2#10594630C211yesmaximal, characteristic
3#10592512C211yesmaximal, characteristic, complemented
4C3×#4807C211yesmaximal, characteristic, complemented
5C3×#4788C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic, complemented
7#10591652C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590940C211yesmaximal, characteristic, complemented
11#10590863C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590545C211yesmaximal, characteristic, complemented
14#10590449C211yesmaximal, characteristic, complemented
15#10590443C211yesmaximal, characteristic, complemented
16#80671—31nomaximal
17#79677—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64155C2211yescharacteristic
21C2×#3756C2211yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic
23#64106C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic, complemented
29C3×#895C2211yescharacteristic
30C3×#893C2211yescharacteristic
31#63922—21no—
32D3×(C2×D3)⋊C4—21no—
33#63908—21no—
34C4×#626C2211yescharacteristic
35#63900C2211yescharacteristic
36#63891—21no—
37#63869C2211yescharacteristic, complemented
38#63860C2211yescharacteristic
39#63859—21no—
40#63854—21no—
41#63847—21no—
42#63841C2211yescharacteristic, complemented
43#63836—21no—
44C32×#103C2211yescharacteristic, complemented
45#63643C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5639—31no—
62#5612—31no—
63#5581—31no—
64#5554—31no—
65C3×#465—31no—
66C3×C4×SD16—31no—
67#5173—31no—
68#5169—31no—
69#5169—31no—
70#5166—31no—
71#5113—31no—
72C8×#67—31no—
73#5047—31no—
74#5035—31no—
75#5028—31no—
76#5009—31no—
77#4871—31no—
78#4866—31no—
79#4862—31no—
80#4862—31no—
81#4813—31no—
82#4813—31no—
83#4813—61no—
84#4807D311yescharacteristic, complemented
85#4788D311yescharacteristic, complemented
86#4772—31no—
87D3×#102—31no—
88D3×#102—31no—
89#4768—31no—
90#4697—31no—
91C8×D12—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×#626D411yescharacteristic
102C2×#625—21no—
103C2×#625—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802—41no—
108#3795—22no—
109#3795—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3756—41no—
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#215—22no—
121C3×#215—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D3×C8—41no—
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143Dic32—21no—
144#3296—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×#235—31no—
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156#946—31no—
157#946—31no—
158#946—61no—
159#946C2×D311yescharacteristic, complemented
160Q8×Dic3C2×D311yescharacteristic, complemented
161C2×#216—31no—
162C2×#216—31no—
163C2×#216—61no—
164C2×#215C2×D311yescharacteristic
165C2×#215C2×D311yescharacteristic
166#938—61no—
167#937—61no—
168#936—31no—
169#930—61no—
170C4×#67—31no—
171C2×(C2×D3)⋊C4—61no—
172#926—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—61no—
176C2×D3×C8C2×D311yescharacteristic, complemented
177#897—31no—
178#897—31no—
179#897—61no—
180#895C2×D311yescharacteristic
181#894—61no—
182#893C2×D311yescharacteristic
183#892—31no—
184#892—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187#890—31no—
188#889—61no—
189#889—61no—
190#886—61no—
191#883—61no—
192#883—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#876—61no—
197#875—31no—
198C4×D12—31no—
199#872—61no—
200#870—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×#103—21no—
204C3×#103C2×D311yescharacteristic, complemented
205C3×#103C2×D311yescharacteristic, complemented
206C3×#102—31no—
207C3×#102—31no—
208C3×C4×C8—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#830—31no—
214#821—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#810—31no—
229#810—31no—
230#809—31no—
231#809—31no—
232#808C2×D311yescharacteristic, complemented
233#808C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236#807—61no—
237C4⋊(C3⋊C8)—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—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
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—
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—
270#626—22no—
271#625—42no—
272#625—42no—
273#624—42no—
274D3×Dic3—42no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—31no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—31no—
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—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C2×#67—31no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C22×Dic3—61no—
310#237—62no—
311#237—121no—
312D3×D4—62no—
313D3×D4—62no—
314D3×D4—121no—
315D3×D4—121no—
316#235—62no—
317#235—121no—
318C2×D12—21no—
319C2×D12—31no—
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C3×SD16—62no—
334C3×SD16—121no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—121no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—31no—
352C3×C42—61no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#216—121no—
358#216—121no—
359#216—122no—
360#215—22no—
361#215—41no—
362(C2×D3)⋊C4—21no—
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—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—121no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—21no—
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
407D3×C8—41no—
408D3×C8—121no—
409D3×C8—121no—
410D3×C8—122no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3#13512yes—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—91no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—31no—
442C22×C8—31no—
443C22×C8—91no—
444#126—181no—
445#125—91no—
446#125—181no—
447#124—91no—
448#123—181no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—31no—
454#121—181no—
455#120—181no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—91no—
459#117—91no—
460#117—181no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—31no—
465#106—31no—
466C4⋊C8—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103D3211yescharacteristic, complemented
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479C4×C8—31no—
480C23×C3—31no—
481C23×C3—61no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3D3×D411yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×D4—32no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—241no—
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—241no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—62no—
524#67—122no—
525#67—122no—
526#67—122no—
527#67—122no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—122no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543D12—21no—
544D12—21no—
545D12—21no—
546D12—62no—
547D12—81no—
548D12#23512yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—81no—
556C4×D3—121no—
557C4×D3—121no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—122no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—62no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C2×C32#54611yescharacteristic
578C2×C32C2×#13511yescharacteristic
579C2×C32#57711yescharacteristic
580C3⋊D3—22no—
581C3×D3—42no—
582C3×D3—41no—
583C3×D3—81no—
584C24—181no—
585#41—182no—
586#41—361no—
587C2×Q8—91no—
588C2×Q8C2×D3211yescharacteristic
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—182no—
595C2×D4—181no—
596C2×D4—361no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—91no—
600C22×C4—181no—
601C22×C4—181no—
602Q16—361no—
603SD16—62no—
604SD16—121no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—91no—
608C2×C8—121no—
609C2×C8—361no—
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4C2×D3211yescharacteristic
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—31no—
634C42—61no—
635C42—181no—
636C22×C3—21no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—62no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—22no—
651C2×D3—21no—
652C2×D3—32no—
653C2×D3—32no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—244no—
667C2×D3—244no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4C2×#23511yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690Dic3—61no—
691Dic3—61no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699C32#329611yescharacteristic, complemented, Sylow
700C23—31no—
701C23—61no—
702C23—61no—
703C23—91no—
704C23—362no—
705C23—362no—
706C23—721no—
707Q8—21no—
708Q8—21no—
709Q8—181no—
710Q8—181no—
711D4—32no—
712D4—61no—
713D4—61no—
714D4—61no—
715D4—182no—
716D4—241no—
717D4—362no—
718D4—362no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—241no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—61no—
739C8—61no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—122no—
745C2×C3—121no—
746C2×C3—241no—
747C2×C3#555011yescharacteristic
748C2×C3#561011yescharacteristic
749C2×C3#576211yescharacteristic
750C2×C3#576211yescharacteristic
751C2×C3D3×#13511yescharacteristic
752C2×C3D3×#13511yescharacteristic
753D3—41no—
754D3—42no—
755D3—62no—
756D3—62no—
757D3—81no—
758D3—122no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—62no—
763C22—92no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—181no—
770C22—181no—
771C22—724no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—121no—
779C4—121no—
780C4—181no—
781C4—361no—
782C4—361no—
783C4D3×#23511yescharacteristic
784C4#6431411yescharacteristic
785C3—21no—
786C3#7967711yescharacteristic, complemented
787C3#8067111yescharacteristic, complemented
788C2—121no—
789C2—122no—
790C2—182no—
791C2—241no—
792C2#1059428311yescharacteristic
793C2#1059474811yescharacteristic
794C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594630C2
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
1. #10595344C2semidirect
3. #10592512C2semidirect
4. C3×#4807C2semidirect
5. C3×#4788C2semidirect
6. #10591655C2semidirect
7. #10591652C2semidirect
8. #10591604C2semidirect
9. #10590954C2semidirect
10. #10590940C2semidirect
11. #10590863C2semidirect
12. C8×#626C2semidirect
13. #10590545C2semidirect
14. #10590449C2semidirect
15. #10590443C2semidirect
21. C2×#3756C22semidirect
24. C3×#946C22semidirect
25. C3×Q8×Dic3C22semidirect
28. C2×C3×D3×C8C22semidirect
37. #63869C22semidirect
42. #63841C22semidirect
44. C32×#103C22semidirect
45. #63643C22semidirect
46. #63634C22semidirect
49. C3×C8×Dic3C22semidirect
50. C3×#808C22semidirect
51. C3×#808C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4807D3semidirect
85. #4788D3semidirect
159. #946C2×D3semidirect
160. Q8×Dic3C2×D3semidirect
176. C2×D3×C8C2×D3semidirect
204. C3×#103C2×D3semidirect
205. C3×#103C2×D3semidirect
227. C8×Dic3C2×D3semidirect
232. #808C2×D3semidirect
233. #808C2×D3semidirect
470. #103D32semidirect
699. C32#3296semidirect
786. C3#79677semidirect
787. C3#80671semidirect

Maximal subgroups

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

subgroupindex
#105953442
#105946302
#105925122
C3×#48072
C3×#47882
#105916552
#105916522
#105916042
#105909542
#105909402
#105908632
C8×#6262
#105905452
#105904492
#105904432
#806713
#796773