Finite Group Databasebeta

← #11883990

Subgroups — #11883990

Order 1152.

1154 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595402C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4#10594618C211yesmaximal, characteristic, complemented
5#10592518C211yesmaximal, characteristic, complemented
6C3×#4812C211yesmaximal, characteristic, complemented
7C3×#4806C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591621C211yesmaximal, characteristic, complemented
10#10590947C211yesmaximal, characteristic, complemented
11#10590876C211yesmaximal, characteristic, complemented
12#10590724C211yesmaximal, characteristic, complemented
13#10590615C211yesmaximal, characteristic, complemented
14#10590576C211yesmaximal, characteristic, complemented
15#10590484C211yesmaximal, characteristic, complemented
16#80834—31nomaximal
17#80060—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C2×#3802—21no—
20C2×D3×D12C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×#3799C2211yescharacteristic, complemented
23#64156C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25C2×#3745C2211yescharacteristic
26#64102C2211yescharacteristic
27C3×#946C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic, complemented
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×#895C2211yescharacteristic
34D3×#215—24no—
35#63922—21no—
36#63922—21no—
37#63914C2211yescharacteristic
38#63912—21no—
39#63909C2211yescharacteristic, complemented
40#63907—21no—
41#63906—21no—
42#63904—21no—
43C4×#625C2211yescharacteristic
44#63888—21no—
45#63843C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×D3×C3⋊C8C2211yescharacteristic, complemented
51#63794—24no—
52C32×#103C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63#5817—31no—
64C22×#215—31no—
65C2×#914—31no—
66C2×D3×SD16—31no—
67C2×#908—31no—
68#5633—31no—
69#5609—31no—
70#5609—31no—
71C3×#468—31no—
72C3×#448—31no—
73#5176—31no—
74#5176—31no—
75#5169—31no—
76#5163—31no—
77#5127—31no—
78#5046—31no—
79#5038—31no—
80#5037—31no—
81#4889—31no—
82#4883—31no—
83#4819—31no—
84#4819—31no—
85#4819—61no—
86#4817—31no—
87#4812D311yescharacteristic, complemented
88#4810—31no—
89#4806D311yescharacteristic, complemented
90#4773—31no—
91#4762—31no—
92#4732—31no—
93#4730—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C3×D3×Q8—22no—
101C3×D3×Q8—41no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×#625—21no—
117C2×#625D411yescharacteristic
118C2×#624—21no—
119#3802—44no—
120D3×D12—22no—
121D3×D12—22no—
122D3×D12—41no—
123D3×D12—41no—
124#3799—22no—
125#3799—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3755—22no—
129#3752—21no—
130#3752—21no—
131#3752—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3745—22no—
135C3×#215—22no—
136C3×#215—41no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×#204—22no—
145C3×ΓL(1,𝔽25)—22no—
146#3724D411yescharacteristic
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151Dic32—21no—
152#3717D414yescomplemented
153#3715—22no—
154#3714—22no—
155#3714—41no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C2×#239—31no—
160C2×D3×Q8C2×D311yescharacteristic, complemented
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—61no—
164C2×D3×D4—61no—
165C2×#235—31no—
166C22×D12—31no—
167C22×D12—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×M16—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C3×#121—31no—
175#947—31no—
176#947—31no—
177#947—61no—
178#947—61no—
179#946—61no—
180#946C2×D311yescharacteristic, complemented
181Q8×Dic3—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—61no—
187C2×#215—64no—
188C2×#215C2×D311yescharacteristic, complemented
189C2×#215C2×D311yescharacteristic, complemented
190#940—31no—
191#940—31no—
192#937—61no—
193#937—61no—
194C2×#214—31no—
195C2×#213—31no—
196C2×#213—31no—
197#930—31no—
198#930—61no—
199C4×#67—31no—
200C4×#67—31no—
201C4×#67—61no—
202C22×C3⋊C8—31no—
203#914—64no—
204D3×SD16—64no—
205#908—64no—
206C2×D24—31no—
207C2×D24—31no—
208C2×D24—31no—
209C2×D24—31no—
210C2×D24—61no—
211C2×#204—31no—
212C2×#204C2×D311yescharacteristic, complemented
213C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
214C2×D3×C8—31no—
215#896—61no—
216#895—31no—
217#895C2×D311yescharacteristic
218#895C2×D311yescharacteristic
219#893—31no—
220#893—31no—
221#893—61no—
222#893—61no—
223#887—31no—
224#885—61no—
225#884—61no—
226#884—61no—
227#884—61no—
228#882—61no—
229#882—61no—
230C3×#107—31no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103C2×D311yescharacteristic, complemented
234C3×#103C2×D311yescharacteristic, complemented
235C3×#102—31no—
236C3×C22⋊C8—31no—
237#832—31no—
238#830—31no—
239#821—31no—
240#821C2×D311yescharacteristic, complemented
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#815—31no—
244#815—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—31no—
247Dic3⋊C8—61no—
248#810C2×D311yescharacteristic, complemented
249#809—31no—
250#809—31no—
251#809—31no—
252#809—31no—
253#809—61no—
254#807C2×D311yescharacteristic, complemented
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)C2×D412yes—
278C4×C3⋊D3—42no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—42no—
288C3×D12—42no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C3×Dic6C2×D412yescomplemented
297#626—42no—
298#626—42no—
299#626—42no—
300#626—42no—
301#625—22no—
302#625—42no—
303#625—81no—
304#624—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—31no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—31no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—21no—
329C2×C3×Q8—31no—
330C2×C3×Q8—61no—
331C2×C3×Q8—62no—
332C2×C3×Q8—121no—
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—61no—
342C2×#67—31no—
343C2×#67—31no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352#239—62no—
353#239—121no—
354D3×Q8—22no—
355D3×Q8—41no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4—121no—
359D3×D4—121no—
360D3×D4—124no—
361D3×D4—124no—
362#235—62no—
363#235—121no—
364C2×D12—21no—
365C2×D12—21no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—62no—
373C2×D12—62no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—121no—
379C2×D12—121no—
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—121no—
388C2×C4×D3C22×D311yescharacteristic
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6—21no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—62no—
393C3×SD16—62no—
394C3×SD16—121no—
395C3×M16—62no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409#217—31no—
410#217—31no—
411#215—22no—
412#215—34no—
413#215—41no—
414#215—62no—
415#215—62no—
416#215—62no—
417#215—122no—
418#214—62no—
419#213—62no—
420#213—121no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—121no—
435(C2×D3)⋊C4—121no—
436(C2×D3)⋊C4—121no—
437C4⋊Dic3—61no—
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—21no—
440Dic3⋊C4—31no—
441Dic3⋊C4—31no—
442Dic3⋊C4—61no—
443C4×Dic3—31no—
444C4×Dic3—31no—
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3—61no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—62no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454D24—62no—
455D24—62no—
456D24—62no—
457D24—122no—
458D24—121no—
459#204—22no—
460#204—34no—
461ΓL(1,𝔽25)—22no—
462D3×C8—62no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—22no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3AGL(1,ℤ/8)12yescomplemented
482D32—84no—
483D32—84no—
484C32×C4—41no—
485C32×C4—41no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3×Dic3—21no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—31no—
496C22×D4—91no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—31no—
511C22×C8—91no—
512#127—91no—
513#124—91no—
514#124—181no—
515C22⋊Q8—31no—
516C22⋊Q8—181no—
517#121—31no—
518#121—31no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—181no—
528#107—31no—
529C4⋊C8—91no—
530#103—31no—
531#103D3211yescharacteristic, complemented
532#102—31no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—121no—
550C22×D3—121no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3D3×D411yescharacteristic
564C22×D3D3×D411yescharacteristic
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—32no—
570C3×Q8—41no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—122no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—122no—
579C3×D4—122no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—122no—
596C2×C3×C4C23×D311yescharacteristic
597C2×C3×C4C23×D311yescharacteristic
598#67—62no—
599#67—62no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—241no—
607#67—241no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3D3×D411yescharacteristic
617C2×Dic3D3×D411yescharacteristic
618D12—21no—
619D12—21no—
620D12—21no—
621D12—21no—
622D12—32no—
623D12—32no—
624D12—42no—
625D12—42no—
626D12—62no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—121no—
634D12—121no—
635D12—121no—
636D12—122no—
637D12—122no—
638D12—122no—
639D12—122no—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—21no—
643C4×D3—21no—
644C4×D3—42no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—122no—
648C4×D3—122no—
649C4×D3—242no—
650Dic6—21no—
651Dic6—42no—
652Dic6D3×D412yescomplemented
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—32no—
656C3×C8—41no—
657C3×C8—61no—
658C3⋊C8—21no—
659C3⋊C8—61no—
660C3⋊C8—61no—
661C3⋊C8—121no—
662C3⋊C8D3×D412yescomplemented
663C2×C32D4211yescharacteristic
664C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
665C2×C32#57711yescharacteristic
666C3⋊D3—42no—
667C3⋊D3—81no—
668C3×D3—22no—
669C3×D3—41no—
670C3×D3—81no—
671C3×D3—81no—
672C24—181no—
673C24—181no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8—61no—
678C2×Q8—62no—
679C2×Q8—121no—
680C2×Q8C2×D3211yescharacteristic
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—91no—
686C2×D4—91no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—182no—
691C2×D4—182no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—361no—
697C2×D4—361no—
698C2×D4—364no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—61no—
702C22×C4—181no—
703C22×C4—181no—
704SD16—62no—
705SD16—62no—
706SD16—94no—
707SD16—121no—
708SD16—182no—
709SD16—182no—
710D8—182no—
711D8—182no—
712D8—361no—
713M16—62no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—91no—
717C2×C8—182no—
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—31no—
720C4⋊C4—61no—
721C4⋊C4—91no—
722C4⋊C4—181no—
723C4⋊C4C2×D3211yescharacteristic
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—91no—
728C22⋊C4—91no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—91no—
734C42—181no—
735C22×C3—21no—
736C22×C3—32no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—122no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—244no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3#91412yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—61no—
791C3×C4—62no—
792C3×C4—61no—
793C3×C4—81no—
794C3×C4—81no—
795C3×C4—121no—
796C3×C4C2×D3×D411yescharacteristic
797C3×C4C2×D3×D411yescharacteristic
798C3×C4#100411yescharacteristic
799C3×C4#100911yescharacteristic
800Dic3—22no—
801Dic3—21no—
802Dic3—21no—
803Dic3—41no—
804Dic3—61no—
805Dic3—61no—
806Dic3—61no—
807Dic3—61no—
808Dic3—121no—
809Dic3—121no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—31no—
812C23—31no—
813C23—61no—
814C23—61no—
815C23—181no—
816C23—181no—
817C23—362no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23—721no—
823Q8—21no—
824Q8—21no—
825Q8—32no—
826Q8—61no—
827Q8—122no—
828D4—61no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—92no—
833D4—122no—
834D4—122no—
835D4—182no—
836D4—181no—
837D4—181no—
838D4—181no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—721no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—91no—
856C2×C4—91no—
857C2×C4—122no—
858C2×C4—362no—
859C2×C4—362no—
860C2×C4C22×D3211yescharacteristic
861C8—21no—
862C8—32no—
863C8—61no—
864C8—181no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—62no—
869C2×C3—121no—
870C2×C3—241no—
871C2×C3—241no—
872C2×C3#559011yescharacteristic
873C2×C3#560911yescharacteristic
874C2×C3C2×#91411yescharacteristic
875C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
876C2×C3#577811yescharacteristic
877C2×C3#577811yescharacteristic
878D3—22no—
879D3—41no—
880D3—81no—
881D3—81no—
882D3—122no—
883D3—122no—
884D3—242no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—32no—
889C22—61no—
890C22—61no—
891C22—61no—
892C22—61no—
893C22—61no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—182no—
901C22—361no—
902C22—361no—
903C22—361no—
904C22—361no—
905C22—361no—
906C22—724no—
907C22—724no—
908C22D32×D411yescharacteristic
909C4—41no—
910C4—41no—
911C4—61no—
912C4—61no—
913C4—62no—
914C4—121no—
915C4—181no—
916C4—181no—
917C4#6430711yescharacteristic
918C4D32×D411yescharacteristic
919C3—21no—
920C3#8006011yescharacteristic, complemented
921C3#8083411yescharacteristic, complemented
922C2—62no—
923C2—121no—
924C2—241no—
925C2—241no—
926C2—362no—
927C2—721no—
928C2#1059427511yescharacteristic
929C2D3×#91411yescharacteristic
930C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3265
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. #10595402C2semidirect
2. C2×D3×#215C2semidirect
3. C2×#63794C2semidirect
4. #10594618C2semidirect
5. #10592518C2semidirect
6. C3×#4812C2semidirect
7. C3×#4806C2semidirect
8. #10591651C2semidirect
9. #10591621C2semidirect
10. #10590947C2semidirect
11. #10590876C2semidirect
12. #10590724C2semidirect
13. #10590615C2semidirect
14. #10590576C2semidirect
15. #10590484C2semidirect
18. C2×C3×D3×Q8C22semidirect
22. C2×#3799C22semidirect
23. #64156C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#215C22semidirect
29. C2×C3×#215C22semidirect
30. C2×C3×#204C22semidirect
31. C2×C3×ΓL(1,𝔽25)C22semidirect
39. #63909C22semidirect
45. #63843C22semidirect
47. C2×#3715C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×D3×C3⋊C8C22semidirect
52. C32×#103C22semidirect
53. #63641C22semidirect
54. #63636C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#807C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63555C22semidirect
87. #4812D3semidirect
89. #4806D3semidirect
152. #3717D4semidirect
160. C2×D3×Q8C2×D3semidirect
180. #946C2×D3semidirect
188. C2×#215C2×D3semidirect
189. C2×#215C2×D3semidirect
212. C2×#204C2×D3semidirect
213. C2×ΓL(1,𝔽25)C2×D3semidirect
233. C3×#103C2×D3semidirect
234. C3×#103C2×D3semidirect
240. #821C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
248. #810C2×D3semidirect
254. #807C2×D3semidirect
296. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
481. C2×C3×D3AGL(1,ℤ/8)semidirect
531. #103D32semidirect
652. Dic6D3×D4semidirect
662. C3⋊C8D3×D4semidirect
783. C2×D3#914semidirect
810. C32#3265semidirect
920. C3#80060semidirect
921. C3#80834semidirect

Maximal subgroups

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

subgroupindex
#105954022
C2×D3×#2152
C2×#637942
#105946182
#105925182
C3×#48122
C3×#48062
#105916512
#105916212
#105909472
#105908762
#105907242
#105906152
#105905762
#105904842
#808343
#800603