Finite Group Databasebeta

← #11883984

Subgroups — #11883984

Order 1152.

1191 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#626C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3C2×#63930C211yesmaximal, characteristic, complemented
4#10594329C211yesmaximal, characteristic, complemented
5#10592472C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4757C211yesmaximal, characteristic, complemented
8#10591471C211yesmaximal, characteristic, complemented
9#10590967C211yesmaximal, characteristic, complemented
10#10590881C211yesmaximal, characteristic, complemented
11#10590824C211yesmaximal, characteristic, complemented
12#10590739C211yesmaximal, characteristic, complemented
13#10590585C211yesmaximal, characteristic, complemented
14#10590549C211yesmaximal, characteristic, complemented
15#10590509C211yesmaximal, characteristic, complemented
16#80156—31nomaximal
17#79794—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#626—21no—
21C2×#3799C2211yescharacteristic, complemented
22C2×#3797C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24C2×#3745C2211yescharacteristic, complemented
25#64104C2211yescharacteristic, complemented
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic, complemented
31C3×#887C2211yescharacteristic, complemented
32#63981—21no—
33#63978—21no—
34#63977—21no—
35#63934—24no—
36#63930—24no—
37#63916C2211yescharacteristic
38#63911C2211yescharacteristic
39#63910—21no—
40#63909C2211yescharacteristic
41C4×#626C2211yescharacteristic
42#63895—21no—
43#63894—21no—
44#63864C2211yescharacteristic, complemented
45#63852—21no—
46C2×#3717C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic
53#63647C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63D4×#67—31no—
64C2×#932—31no—
65C2×#914—31no—
66C2×D3×SD16—31no—
67C2×D3×SD16—31no—
68#5633—31no—
69#5576—31no—
70D4×D12—31no—
71C3×#450—31no—
72C3×#440—31no—
73#5176—31no—
74#5170—31no—
75#5165—31no—
76#5049—31no—
77#5027—31no—
78#5016—31no—
79#4886—31no—
80#4883—31no—
81#4810—31no—
82#4806—31no—
83#4776D311yescharacteristic, complemented
84#4775—31no—
85#4773—31no—
86#4773—31no—
87#4773—61no—
88#4762—31no—
89#4757D311yescharacteristic, complemented
90#4734—31no—
91#4728—31no—
92#4712—31no—
93#4706—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3—41no—
100C2×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C3×#67—21no—
105C22×C3×Dic3—21no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—44no—
119C2×#626D411yescharacteristic
120C2×#624—21no—
121C2×#624—21no—
122#3799—22no—
123#3799—41no—
124#3797—22no—
125#3797—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3753—22no—
129#3752—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3745—41no—
132C3×#217—21no—
133C3×#214—22no—
134C3×#214D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—41no—
144Dic3⋊Dic3D411yescharacteristic
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151#3717—22no—
152#3717—22no—
153#3715—22no—
154#3714—22no—
155#3711—22no—
156#3710—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×#67—61no—
160C2×#239—31no—
161C2×D3×Q8—31no—
162C2×D3×Q8—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C2×D3×D4C2×D311yescharacteristic
167C2×#235—31no—
168C22×D12—61no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C3×C22⋊Q8—31no—
173C3×C4×Q8—31no—
174C3×C4×D4—31no—
175#953—61no—
176#947—31no—
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—31no—
180#940—31no—
181#939—61no—
182#938—31no—
183#937—61no—
184D4×Dic3C2×D311yescharacteristic
185C2×#214—31no—
186C2×#214C2×D311yescharacteristic
187C2×#214C2×D311yescharacteristic
188#932—64no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—61no—
193#930—31no—
194#930—61no—
195C4×#67—31no—
196C2×#208—31no—
197#914—64no—
198D3×SD16—64no—
199D3×SD16—64no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—61no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204C2×D311yescharacteristic, complemented
207C2×ΓL(1,𝔽25)—31no—
208C2×D3×C8—31no—
209C2×D3×C8—31no—
210#897—61no—
211#897C2×D311yescharacteristic, complemented
212#896—61no—
213#895—31no—
214#895—31no—
215#895—31no—
216#895—31no—
217#895—61no—
218#895—61no—
219#893—61no—
220#887C2×D311yescharacteristic, complemented
221#885—61no—
222#884—61no—
223#882—61no—
224#882—61no—
225#875—31no—
226#875—61no—
227#874—31no—
228C4×D12—31no—
229C4×D12—61no—
230C3×#107—31no—
231C3×#103—31no—
232C3×#102—21no—
233C3×#102—31no—
234C3×#102C2×D311yescharacteristic
235C3×#102C2×D311yescharacteristic
236C3×C22⋊C8—31no—
237C3×#97—31no—
238#835—31no—
239#821—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—61no—
243(C2×D3)⋊C8C2×D311yescharacteristic, complemented
244#816C2×D311yescharacteristic, complemented
245#815C2×D311yescharacteristic, complemented
246Dic3⋊C8—31no—
247#810—31no—
248#809—31no—
249#809—31no—
250#809—31no—
251#809—61no—
252#809C2×D311yescharacteristic, complemented
253#807C2×D311yescharacteristic, complemented
254C4⋊(C3⋊C8)—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—81no—
261C22×C3⋊D3C2×D411yescharacteristic
262C22×C3×D3—21no—
263C22×C3×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—81no—
266C22×C3×D3C2×D411yescharacteristic
267C32×D4—21no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—42no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—21no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6C2×D412yescomplemented
296#627—42no—
297#626—22no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—42no—
302#626—81no—
303#624—42no—
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—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—31no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—31no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—121no—
329C2×C3×Q8—31no—
330C2×C3×Q8—31no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—62no—
335C2×C3×D4—121no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C2×#67—21no—
341C2×#67—31no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—121no—
350C2×#67—124no—
351C22×Dic3—21no—
352#239—62no—
353#239—121no—
354D3×Q8—62no—
355D3×Q8—62no—
356D3×Q8—121no—
357D3×Q8—121no—
358D3×D4—22no—
359D3×D4—41no—
360D3×D4—62no—
361D3×D4—62no—
362D3×D4—122no—
363D3×D4—121no—
364D3×D4—121no—
365D3×D4—122no—
366#235—62no—
367#235—121no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—121no—
383C2×D12—124no—
384C2×D12C22×D311yescharacteristic
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3C22×D311yescharacteristic
393C2×Dic6—61no—
394C2×Dic6—61no—
395C2×Dic6C22×D311yescharacteristic
396C2×Dic6C22×D311yescharacteristic
397C3×SD16—34no—
398C3×SD16—62no—
399C3×SD16—121no—
400C2×C3×C8—21no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—21no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4C22×D311yescharacteristic
410C3×C4⋊C4C22×D311yescharacteristic
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C42—31no—
414C3×C42—61no—
415#217—21no—
416#217—31no—
417#217—61no—
418#215—62no—
419#215—62no—
420#215—62no—
421#214—22no—
422#214—62no—
423#214D1214yescomplemented
424#213—62no—
425#213—62no—
426#213—62no—
427#213—122no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—121no—
442C4⋊Dic3—21no—
443C4⋊Dic3—31no—
444C4⋊Dic3C22×D311yescharacteristic
445Dic3⋊C4—21no—
446Dic3⋊C4—31no—
447C4×Dic3—21no—
448C4×Dic3C22×D311yescharacteristic
449#208—62no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455D24—62no—
456D24—121no—
457D24—121no—
458D24—122no—
459#204—41no—
460#204—62no—
461#204—62no—
462ΓL(1,𝔽25)—62no—
463D3×C8—62no—
464D3×C8—62no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—84no—
478C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
479C2×C3×D3—21no—
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—84no—
486C32×C4—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—91no—
498C22×D4—31no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—184no—
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—91no—
514#127—91no—
515#124—91no—
516#124—181no—
517C22⋊Q8—31no—
518C22⋊Q8—181no—
519#121—91no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—31no—
527C4×D4—31no—
528C4×D4—91no—
529C4×D4—181no—
530#107—31no—
531C4⋊C8—91no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102D3211yescharacteristic
538C22⋊C8—31no—
539C22⋊C8—91no—
540#97—31no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—41no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C22×D3—21no—
550C22×D3—31no—
551C22×D3—31no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—81no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—122no—
566C22×D3—124no—
567C22×D3—242no—
568C22×D3—241no—
569C22×D3—241no—
570C22×D3—242no—
571C22×D3D3×D411yescharacteristic
572C3×Q8—32no—
573C3×Q8—61no—
574C3×Q8—61no—
575C3×Q8—61no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—22no—
579C3×D4—41no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—122no—
583C3×D4C2×D1212yes—
584C3×D4D3×D412yes—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—41no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—122no—
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600#67—42no—
601#67—62no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—124no—
609#67—241no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—42no—
616C2×Dic3—61no—
617C2×Dic3D3×D411yescharacteristic
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620D12—21no—
621D12—21no—
622D12—62no—
623D12—62no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—121no—
633D12—121no—
634D12—121no—
635D12—122no—
636D12—122no—
637D12—122no—
638D12—122no—
639D12—122no—
640D12—122no—
641D12—242no—
642D12—241no—
643C4×D3—21no—
644C4×D3—21no—
645C4×D3—61no—
646C4×D3—61no—
647C4×D3—61no—
648C4×D3—61no—
649C4×D3—121no—
650C4×D3—121no—
651C4×D3—122no—
652C4×D3—122no—
653C4×D3—122no—
654C4×D3—122no—
655Dic6—21no—
656Dic6—21no—
657Dic6—21no—
658Dic6—122no—
659Dic6—122no—
660Dic6C2×D1212yescomplemented
661C3×C8—21no—
662C3×C8—21no—
663C3×C8—32no—
664C3×C8—41no—
665C3×C8—61no—
666C3⋊C8—21no—
667C3⋊C8—61no—
668C3⋊C8—61no—
669C3⋊C8—121no—
670C3⋊C8C2×D1212yescomplemented
671C2×C32—42no—
672C2×C32D4211yescharacteristic
673C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
674C2×C32#57711yescharacteristic
675C3⋊D3—22no—
676C3⋊D3—81no—
677C3⋊D3—81no—
678C3×D3—41no—
679C3×D3—81no—
680C24—61no—
681C24—181no—
682#41—182no—
683#41—361no—
684C2×Q8—31no—
685C2×Q8—31no—
686C2×Q8—181no—
687C2×Q8—182no—
688C2×Q8—361no—
689C2×D4—31no—
690C2×D4—61no—
691C2×D4—62no—
692C2×D4—91no—
693C2×D4—91no—
694C2×D4—91no—
695C2×D4—121no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4—181no—
703C2×D4—182no—
704C2×D4—364no—
705C2×D4—361no—
706C2×D4C2×D3211yescharacteristic
707C22×C4—31no—
708C22×C4—61no—
709C22×C4—91no—
710C22×C4—181no—
711C22×C4—181no—
712SD16—34no—
713SD16—62no—
714SD16—121no—
715SD16—182no—
716SD16—182no—
717SD16—182no—
718D8—182no—
719D8—182no—
720D8—361no—
721M16—182no—
722C2×C8—31no—
723C2×C8—31no—
724C2×C8—91no—
725C2×C8—182no—
726C2×C8C2×D3211yescharacteristic
727C4⋊C4—31no—
728C4⋊C4—61no—
729C4⋊C4—61no—
730C4⋊C4—91no—
731C4⋊C4C2×D3211yescharacteristic
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—91no—
735C22⋊C4—91no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C22⋊C4—181no—
741C42—31no—
742C42—61no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—21no—
746C22×C3—42no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—81no—
755C22×C3—81no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—244no—
760C22×C3C2×D3×D411yescharacteristic
761C22×C3C2×D3×D411yescharacteristic
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—32no—
766C2×D3—32no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—62no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—84no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—122no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—241no—
792C2×D3—241no—
793C2×D3—241no—
794C2×D3—241no—
795C2×D3—241no—
796C2×D3—244no—
797C2×D3—244no—
798C2×D3—248no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—61no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4—62no—
807C3×C4—81no—
808C3×C4—121no—
809C3×C4—121no—
810C3×C4C22×D1211yescharacteristic
811C3×C4C2×D3×D411yescharacteristic
812C3×C4#100411yescharacteristic
813C3×C4#100911yescharacteristic
814Dic3—21no—
815Dic3—21no—
816Dic3—22no—
817Dic3—21no—
818Dic3—41no—
819Dic3—41no—
820Dic3—61no—
821Dic3—61no—
822Dic3—121no—
823C32#326511yescharacteristic, complemented, Sylow
824C23—21no—
825C23—31no—
826C23—61no—
827C23—91no—
828C23—122no—
829C23—122no—
830C23—181no—
831C23—181no—
832C23—241no—
833C23—362no—
834C23—362no—
835C23—721no—
836Q8—32no—
837Q8—61no—
838Q8—61no—
839Q8—61no—
840Q8—362no—
841D4—21no—
842D4—61no—
843D4—61no—
844D4—122no—
845D4—182no—
846D4—181no—
847D4—181no—
848D4—181no—
849D4—181no—
850D4—362no—
851D4—362no—
852D4—362no—
853D4—362no—
854D4—362no—
855D4—362no—
856D4—721no—
857D4D3×D1212yes—
858C2×C4—21no—
859C2×C4—31no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—91no—
868C2×C4—122no—
869C2×C4—181no—
870C2×C4—181no—
871C2×C4—362no—
872C2×C4—362no—
873C2×C4C22×D3211yescharacteristic
874C8—21no—
875C8—32no—
876C8—61no—
877C8—181no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—42no—
882C2×C3—42no—
883C2×C3—82no—
884C2×C3—121no—
885C2×C3—241no—
886C2×C3D4×D1211yescharacteristic
887C2×C3#559011yescharacteristic
888C2×C3#576211yescharacteristic
889C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
890C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
891C2×C3#577811yescharacteristic
892D3—41no—
893D3—62no—
894D3—62no—
895D3—81no—
896D3—122no—
897D3—242no—
898D3—241no—
899D3—241no—
900D3—241no—
901D3—241no—
902D3—481no—
903C22—22no—
904C22—41no—
905C22—41no—
906C22—61no—
907C22—61no—
908C22—61no—
909C22—92no—
910C22—121no—
911C22—121no—
912C22—121no—
913C22—181no—
914C22—181no—
915C22—244no—
916C22—361no—
917C22—361no—
918C22—361no—
919C22—361no—
920C22—361no—
921C22—361no—
922C22—724no—
923C22D32×D411yescharacteristic
924C4—41no—
925C4—61no—
926C4—61no—
927C4—61no—
928C4—62no—
929C4—121no—
930C4—121no—
931C4—181no—
932C4C2×D3×D1211yescharacteristic
933C4#6431411yescharacteristic
934C3—21no—
935C3#7979411yescharacteristic, complemented
936C3#8015611yescharacteristic, complemented
937C2—42no—
938C2—121no—
939C2—182no—
940C2—241no—
941C2—721no—
942C2—721no—
943C2#1059427711yescharacteristic
944C2#1059472611yescharacteristic
945C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D4×#626C2semidirect
2. C2×#63934C2semidirect
3. C2×#63930C2semidirect
4. #10594329C2semidirect
5. #10592472C2semidirect
6. C3×#4776C2semidirect
7. C3×#4757C2semidirect
8. #10591471C2semidirect
9. #10590967C2semidirect
10. #10590881C2semidirect
11. #10590824C2semidirect
12. #10590739C2semidirect
13. #10590585C2semidirect
14. #10590549C2semidirect
15. #10590509C2semidirect
21. C2×#3799C22semidirect
22. C2×#3797C22semidirect
24. C2×#3745C22semidirect
25. #64104C22semidirect
29. C2×C3×#204C22semidirect
30. C3×#897C22semidirect
31. C3×#887C22semidirect
44. #63864C22semidirect
46. C2×#3717C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3711C22semidirect
51. C2×#3710C22semidirect
53. #63647C22semidirect
54. #63636C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×#816C22semidirect
57. C3×#815C22semidirect
58. C3×#809C22semidirect
59. C3×#807C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
83. #4776D3semidirect
89. #4757D3semidirect
134. C3×#214D4semidirect
206. C2×#204C2×D3semidirect
211. #897C2×D3semidirect
220. #887C2×D3semidirect
243. (C2×D3)⋊C8C2×D3semidirect
244. #816C2×D3semidirect
245. #815C2×D3semidirect
252. #809C2×D3semidirect
253. #807C2×D3semidirect
295. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
423. #214D12semidirect
478. C2×C3⋊D3AGL(1,ℤ/8)semidirect
660. Dic6C2×D12semidirect
670. C3⋊C8C2×D12semidirect
823. C32#3265semidirect
935. C3#79794semidirect
936. C3#80156semidirect

Maximal subgroups

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

subgroupindex
D4×#6262
C2×#639342
C2×#639302
#105943292
#105924722
C3×#47762
C3×#47572
#105914712
#105909672
#105908812
#105908242
#105907392
#105905852
#105905492
#105905092
#801563
#797943