Finite Group Databasebeta

← #11884028

Subgroups — #11884028

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3C2×#63796C211yesmaximal, characteristic, complemented
4#10594329C211yesmaximal, characteristic, complemented
5#10592474C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4762C211yesmaximal, characteristic, complemented
8#10591518C211yesmaximal, characteristic, complemented
9#10591472C211yesmaximal, characteristic, complemented
10#10590823C211yesmaximal, characteristic, complemented
11#10590754C211yesmaximal, characteristic, complemented
12#10590737C211yesmaximal, characteristic, complemented
13#10590598C211yesmaximal, characteristic, complemented
14#10590503C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#80404—31nomaximal
17#80156—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×#3797C2211yescharacteristic, complemented
23#64147C2211yescharacteristic
24C2×#3753C2211yescharacteristic, complemented
25C2×C8×C3⋊D3C2211yescharacteristic, complemented
26#64104C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic, complemented
29C2×C3×#214C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic, complemented
32C3×#897C2211yescharacteristic, complemented
33C3×#887C2211yescharacteristic, complemented
34#63983—21no—
35#63976—21no—
36#63970—21no—
37#63934—24no—
38#63910—21no—
39#63908C2211yescharacteristic
40C4×#626C2211yescharacteristic
41#63895—21no—
42#63894—21no—
43Dic3×D12C2211yescharacteristic
44#63864C2211yescharacteristic, complemented
45#63852—21no—
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic, complemented
51#63796—24no—
52C32×#102C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63D4×#67—31no—
64C2×#932—31no—
65C2×#914—31no—
66C2×D3×SD16—31no—
67C2×D3×SD16—31no—
68#5717—31no—
69#5633—31no—
70#5576—31no—
71C3×#460—31no—
72C3×#450—31no—
73#5176—31no—
74#5172—31no—
75#5170—31no—
76#5170—31no—
77#5165—31no—
78#5074—31no—
79#5049—31no—
80#5026—31no—
81#4844—31no—
82#4836—31no—
83#4780—31no—
84#4776D311yescharacteristic, complemented
85#4775—31no—
86#4775—31no—
87#4775—61no—
88#4773—31no—
89#4773—31no—
90#4762D311yescharacteristic, complemented
91#4757—31no—
92#4734—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111D3×#67—44no—
112C2×#627—21no—
113C2×#626—21no—
114C2×#626D411yescharacteristic
115C2×#625—21no—
116C2×#625—21no—
117C2×#624—21no—
118C2×#624—21no—
119C2×D3×Dic3—21no—
120#3802—22no—
121#3802—41no—
122#3799—22no—
123#3799—41no—
124#3797—22no—
125#3797—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3757—21no—
129#3753—22no—
130#3752—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C8×C3⋊D3—22no—
134C3×#214—22no—
135C3×#214—41no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×#204—22no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152#3715—22no—
153#3715D414yescomplemented
154#3714—22no—
155#3714—41no—
156#3711—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—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C3×#127—31no—
173C3×C22⋊Q8—31no—
174C3×C4×Q8—31no—
175#953—61no—
176#947—31no—
177C2×#215—31no—
178C2×#215—31no—
179#940C2×D311yescharacteristic
180#939—61no—
181#938—31no—
182#938—31no—
183#938—31no—
184#938—61no—
185#938—61no—
186#937—61no—
187#937—61no—
188#937—61no—
189D4×Dic3—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214C2×D311yescharacteristic, complemented
193C2×#214C2×D311yescharacteristic, complemented
194#932—64no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—61no—
200#930—31no—
201C4×#67—31no—
202C2×#208—31no—
203#914—64no—
204D3×SD16—64no—
205D3×SD16—64no—
206C2×D24—31no—
207C2×D24—31no—
208C2×#204C2×D311yescharacteristic
209C2×#204C2×D311yescharacteristic, complemented
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212C2×D3×C8—31no—
213C2×D3×C8—61no—
214#897—61no—
215#897C2×D311yescharacteristic, complemented
216#896—61no—
217#895—31no—
218#895—31no—
219#895—61no—
220#895—61no—
221#893—61no—
222#887C2×D311yescharacteristic, complemented
223#885—61no—
224#884—61no—
225#875—31no—
226#875—61no—
227C4×D12—31no—
228C4×D12—31no—
229C4×D12—61no—
230C3×C4⋊C8—31no—
231C3×#102—21no—
232C3×#102—31no—
233C3×#102—31no—
234C3×#102C2×D311yescharacteristic, complemented
235C3×#102C2×D311yescharacteristic, complemented
236C3×C22⋊C8—31no—
237#835—31no—
238#835—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8C2×D311yescharacteristic, complemented
245#816—31no—
246#816—31no—
247#815—31no—
248Dic3⋊C8C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic
250#809C2×D311yescharacteristic, complemented
251#807—31no—
252#807—31no—
253#807—61no—
254#803—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×D4—21no—
268C32×D4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—42no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C3×#67—42no—
280C3×#67—42no—
281C3×#67—81no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12C2×D412yes—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6C2×D412yescomplemented
297#627—42no—
298#626—22no—
299#626—42no—
300#625—42no—
301#625—42no—
302#624—42no—
303#624—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
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—31no—
318#450—31no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×Q8—31no—
330C2×C3×D4—21no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—62no—
337C2×C3×D4—121no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—31no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—31no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—121no—
353C2×#67—124no—
354C22×Dic3—61no—
355#239—62no—
356#239—121no—
357D3×Q8—62no—
358D3×Q8—62no—
359D3×Q8—121no—
360D3×Q8—121no—
361D3×D4—22no—
362D3×D4—41no—
363D3×D4—62no—
364D3×D4—62no—
365D3×D4—121no—
366D3×D4—121no—
367D3×D4—124no—
368#235—62no—
369#235—121no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3C22×D311yescharacteristic
389C2×Dic6—61no—
390C2×Dic6—61no—
391C2×Dic6C22×D311yescharacteristic
392C2×Dic6C22×D311yescharacteristic
393C3×SD16—62no—
394C3×SD16—62no—
395C3×SD16—62no—
396C3×SD16—121no—
397C2×C3×C8—21no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C3×C4⋊C4—21no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C22⋊C4—61no—
408C3×C42—31no—
409C3×C42—61no—
410#217—31no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—61no—
415#217—121no—
416#215—34no—
417#215—62no—
418#214—22no—
419#214—34no—
420#214—41no—
421#214—62no—
422#213—62no—
423#213—62no—
424#213—62no—
425#213—122no—
426#213—121no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—61no—
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—121no—
440C4⋊Dic3—21no—
441C4⋊Dic3—31no—
442C4⋊Dic3—31no—
443C4⋊Dic3—31no—
444C4⋊Dic3—61no—
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—
457#204—22no—
458#204—22no—
459ΓL(1,𝔽25)—62no—
460D3×C8—62no—
461D3×C8—62no—
462D3×C8—122no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—84no—
483D32—84no—
484C32×C4—41no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—21no—
488C3⋊Dic3—41no—
489C3×Dic3—22no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—91no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127—31no—
513#124—91no—
514#124—181no—
515C22⋊Q8—31no—
516C22⋊Q8—181no—
517#121—91no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—31no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—31no—
530#103—91no—
531#103—91no—
532#102—31no—
533#102—31no—
534#102—91no—
535#102D3211yescharacteristic, complemented
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—41no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—122no—
546C23×C3—122no—
547C23×C3—241no—
548C22×D3—21no—
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—81no—
558C22×D3—121no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—241no—
564C22×D3—241no—
565C22×D3D3×D411yescharacteristic
566C3×Q8—32no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—32no—
575C3×D4—41no—
576C3×D4—41no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4—241no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—41no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—42no—
597#67—42no—
598#67—62no—
599#67—81no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—242no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3D3×D411yescharacteristic
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620D12—21no—
621D12—21no—
622D12—21no—
623D12—62no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—121no—
629D12—121no—
630D12—122no—
631D12—122no—
632D12—122no—
633D12—242no—
634D12D3×D412yes—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—61no—
638C4×D3—61no—
639C4×D3—61no—
640C4×D3—61no—
641C4×D3—121no—
642C4×D3—121no—
643C4×D3—122no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—122no—
648Dic6—21no—
649Dic6—21no—
650Dic6—21no—
651Dic6—122no—
652Dic6—122no—
653Dic6D3×D412yescomplemented
654C3×C8—21no—
655C3×C8—21no—
656C3×C8—41no—
657C3×C8—61no—
658C3×C8—61no—
659C3⋊C8—21no—
660C3⋊C8—21no—
661C3⋊C8—32no—
662C3⋊C8—32no—
663C3⋊C8—62no—
664C2×C32—81no—
665C2×C32D4211yescharacteristic
666C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
667C2×C32#57711yescharacteristic
668C3⋊D3—22no—
669C3⋊D3—81no—
670C3×D3—42no—
671C3×D3—41no—
672C3×D3—81no—
673C24—61no—
674C24—181no—
675#41—182no—
676#41—361no—
677C2×Q8—31no—
678C2×Q8—31no—
679C2×Q8—181no—
680C2×Q8—182no—
681C2×Q8—361no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—62no—
688C2×D4—91no—
689C2×D4—91no—
690C2×D4—121no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—182no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—361no—
698C2×D4—364no—
699C2×D4C2×D3211yescharacteristic
700C22×C4—31no—
701C22×C4—91no—
702C22×C4—181no—
703C22×C4—181no—
704C22×C4—181no—
705SD16—62no—
706SD16—62no—
707SD16—62no—
708SD16—94no—
709SD16—121no—
710SD16—182no—
711D8—182no—
712D8—182no—
713D8—361no—
714M16—182no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—91no—
718C2×C8—182no—
719C2×C8C2×D3211yescharacteristic
720C4⋊C4—61no—
721C4⋊C4—61no—
722C4⋊C4—91no—
723C4⋊C4—91no—
724C4⋊C4C2×D3211yescharacteristic
725C22⋊C4—61no—
726C22⋊C4—91no—
727C22⋊C4—91no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—31no—
735C42—61no—
736C22×C3—21no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—62no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—244no—
756C22×C3C2×D3×D411yescharacteristic
757C22×C3C2×D3×D411yescharacteristic
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—22no—
762C2×D3—32no—
763C2×D3—32no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—62no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—84no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—244no—
787C2×D3—244no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—61no—
793C3×C4—61no—
794C3×C4—62no—
795C3×C4—61no—
796C3×C4—81no—
797C3×C4—121no—
798C3×C4C2×D3×D411yescharacteristic
799C3×C4C2×D3×D411yescharacteristic
800C3×C4#100411yescharacteristic
801C3×C4#100911yescharacteristic
802Dic3—21no—
803Dic3—21no—
804Dic3—21no—
805Dic3—22no—
806Dic3—41no—
807Dic3—61no—
808Dic3—61no—
809Dic3—121no—
810Dic3—121no—
811Dic3—121no—
812Dic3—241no—
813C32#326511yescharacteristic, complemented, Sylow
814C23—21no—
815C23—31no—
816C23—61no—
817C23—61no—
818C23—91no—
819C23—122no—
820C23—122no—
821C23—181no—
822C23—241no—
823C23—362no—
824C23—362no—
825C23—721no—
826Q8—32no—
827Q8—61no—
828Q8—61no—
829Q8—61no—
830Q8—362no—
831D4—21no—
832D4—21no—
833D4—32no—
834D4—61no—
835D4—61no—
836D4—61no—
837D4—122no—
838D4—122no—
839D4—182no—
840D4—181no—
841D4—181no—
842D4—241no—
843D4—362no—
844D4—362no—
845D4—362no—
846D4—362no—
847D4—362no—
848C2×C4—21no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—91no—
857C2×C4—181no—
858C2×C4—181no—
859C2×C4—181no—
860C2×C4—362no—
861C2×C4—362no—
862C2×C4—362no—
863C2×C4C22×D3211yescharacteristic
864C8—21no—
865C8—61no—
866C8—61no—
867C8—92no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—81no—
872C2×C3—81no—
873C2×C3—122no—
874C2×C3—121no—
875C2×C3—161no—
876C2×C3—241no—
877C2×C3#559011yescharacteristic
878C2×C3#560911yescharacteristic
879C2×C3#576211yescharacteristic
880C2×C3#576211yescharacteristic
881C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
882C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
883D3—41no—
884D3—42no—
885D3—62no—
886D3—62no—
887D3—81no—
888D3—122no—
889D3—241no—
890D3—241no—
891D3—481no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—61no—
896C22—61no—
897C22—61no—
898C22—62no—
899C22—92no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—181no—
906C22—181no—
907C22—244no—
908C22—361no—
909C22—361no—
910C22—361no—
911C22—724no—
912C22D32×D411yescharacteristic
913C4—41no—
914C4—61no—
915C4—61no—
916C4—61no—
917C4—62no—
918C4—121no—
919C4—181no—
920C4—361no—
921C4#6430711yescharacteristic
922C4D32×D411yescharacteristic
923C3—21no—
924C3#8015611yescharacteristic, complemented
925C3#8040411yescharacteristic, complemented
926C2—81no—
927C2—121no—
928C2—122no—
929C2—182no—
930C2—241no—
931C2—721no—
932C2#1059427511yescharacteristic
933C2#1059472611yescharacteristic
934C2#1059474811yescharacteristic
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. #10595293C2semidirect
2. C2×#63934C2semidirect
3. C2×#63796C2semidirect
4. #10594329C2semidirect
5. #10592474C2semidirect
6. C3×#4776C2semidirect
7. C3×#4762C2semidirect
8. #10591518C2semidirect
9. #10591472C2semidirect
10. #10590823C2semidirect
11. #10590754C2semidirect
12. #10590737C2semidirect
13. #10590598C2semidirect
14. #10590503C2semidirect
15. #10590454C2semidirect
21. C2×#3799C22semidirect
22. C2×#3797C22semidirect
24. C2×#3753C22semidirect
25. C2×C8×C3⋊D3C22semidirect
26. #64104C22semidirect
28. C2×C3×#214C22semidirect
29. C2×C3×#214C22semidirect
31. C2×C3×#204C22semidirect
32. C3×#897C22semidirect
33. C3×#887C22semidirect
44. #63864C22semidirect
47. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3711C22semidirect
52. C32×#102C22semidirect
53. #63648C22semidirect
54. #63634C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
58. C3×#809C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
61. #63557C22semidirect
62. #63554C22semidirect
84. #4776D3semidirect
90. #4762D3semidirect
153. #3715D4semidirect
192. C2×#214C2×D3semidirect
193. C2×#214C2×D3semidirect
209. C2×#204C2×D3semidirect
215. #897C2×D3semidirect
222. #887C2×D3semidirect
234. C3×#102C2×D3semidirect
235. C3×#102C2×D3semidirect
244. (C2×D3)⋊C8C2×D3semidirect
248. Dic3⋊C8C2×D3semidirect
250. #809C2×D3semidirect
296. C3×Dic6C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
472. C2×C3⋊D3AGL(1,ℤ/8)semidirect
535. #102D32semidirect
653. Dic6D3×D4semidirect
813. C32#3265semidirect
924. C3#80156semidirect
925. C3#80404semidirect

Maximal subgroups

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

subgroupindex
#105952932
C2×#639342
C2×#637962
#105943292
#105924742
C3×#47762
C3×#47622
#105915182
#105914722
#105908232
#105907542
#105907372
#105905982
#105905032
#105904542
#804043
#801563