Finite Group Databasebeta

← #11883982

Subgroups — #11883982

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
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2#10595402C211yesmaximal, characteristic, complemented
3D4×#625C211yesmaximal, characteristic, complemented
4C2×#63934C211yesmaximal, characteristic, complemented
5#10592864C211yesmaximal, characteristic, complemented
6C3×#5169C211yesmaximal, characteristic, complemented
7#10591621C211yesmaximal, characteristic, complemented
8#10591587C211yesmaximal, characteristic, complemented
9#10591583C211yesmaximal, characteristic, complemented
10#10591448C211yesmaximal, characteristic, complemented
11#10591446C211yesmaximal, characteristic, complemented
12#10590876C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590823C211yesmaximal, characteristic, complemented
15#10590723C211yesmaximal, characteristic, complemented
16#83864—31nomaximal
17#80156—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C22×#625—21no—
22C2×#3799C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic
24#64156C2211yescharacteristic, complemented
25D4×C3⋊Dic3C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C3×#946C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C2×C3×#214C2211yescharacteristic
31C3×D3×SD16—24no—
32C2×C3×#204C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63980—21no—
35#63976—21no—
36#63976—21no—
37#63934—24no—
38#63914C2211yescharacteristic
39#63909C2211yescharacteristic, complemented
40#63908C2211yescharacteristic
41#63908C2211yescharacteristic
42#63907—21no—
43#63906—21no—
44#63904—21no—
45C4×#625C2211yescharacteristic
46#63888—21no—
47#63843C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64#5817—31no—
65D4×#67—31no—
66D4×#67—31no—
67C2×#932—31no—
68C2×#914—31no—
69C2×D3×SD16D311yescharacteristic, complemented
70#5633—31no—
71C3×#450—31no—
72#5227—31no—
73#5217—31no—
74#5176—31no—
75#5176—31no—
76#5174—31no—
77#5172—31no—
78#5170—31no—
79#5169D311yescharacteristic, complemented
80#5165—31no—
81#5165—31no—
82#5165—61no—
83#5164—31no—
84#5163—31no—
85#5115—31no—
86#5111—31no—
87#5049—31no—
88#4775—31no—
89#4773—31no—
90#4762—31no—
91#4757—31no—
92#4734—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C3⋊Dic3—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C3×D3×D4—22no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C3×D3×D4—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6—21no—
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#625—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×#625—21no—
121C2×#625—44no—
122C2×#625D411yescharacteristic
123C2×#624—21no—
124#3799—22no—
125#3799—41no—
126C32×SD16—22no—
127C2×C32×C8C2311yescharacteristic
128#3757—21no—
129#3753—22no—
130#3752—21no—
131#3752—21no—
132C4⋊(C3⋊Dic3)C2311yescharacteristic
133C4×C3⋊Dic3C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#215—22no—
136C3×#215—41no—
137C3×#214D414yescomplemented
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×D3×C8—22no—
145#3724D411yescharacteristic
146Dic3⋊Dic3—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151(C2×D3)⋊Dic3D411yescharacteristic
152Dic32—21no—
153#3715—22no—
154#3714—22no—
155#3714—41no—
156#3711—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×#67—61no—
162C22×#67—61no—
163C2×#239—31no—
164C2×D3×Q8C2×D311yescharacteristic, complemented
165C2×D3×D4C2×D311yescharacteristic
166C2×D3×D4C2×D311yescharacteristic
167C2×#235—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—64no—
174C2×C3×SD16C2×D311yescharacteristic
175C2×C3×SD16C2×D311yescharacteristic
176C22×C3×C8—31no—
177C3×C22⋊Q8—31no—
178#953—61no—
179#953—61no—
180#947—31no—
181#947—31no—
182#947—61no—
183#947—61no—
184#946—61no—
185#946C2×D311yescharacteristic, complemented
186Q8×Dic3—31no—
187C2×#215—31no—
188C2×#215C2×D311yescharacteristic, complemented
189C2×#215C2×D311yescharacteristic, complemented
190#940—31no—
191#940—31no—
192#939—61no—
193#939—61no—
194#938—31no—
195#938—31no—
196#937—61no—
197#937—61no—
198D4×Dic3—31no—
199D4×Dic3—31no—
200D4×Dic3—61no—
201C2×#214—31no—
202C2×#214C2×D311yescharacteristic
203#932—64no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—61no—
209#930—31no—
210#930—31no—
211#930—31no—
212#930—61no—
213C4×#67—31no—
214C4×#67—31no—
215C4×#67—61no—
216C2×#208—31no—
217#914—64no—
218D3×SD16—24no—
219C2×D24—31no—
220C2×D24—31no—
221C2×#204C2×D311yescharacteristic, complemented
222C2×ΓL(1,𝔽25)—31no—
223C2×D3×C8C2×D311yescharacteristic, complemented
224#896—61no—
225#895—31no—
226#893—61no—
227#887—31no—
228#885—61no—
229#884—61no—
230C3×#102—31no—
231C3×#102—31no—
232C3×C22⋊C8—31no—
233#835—31no—
234#835—31no—
235#835—31no—
236#835—61no—
237#832—31no—
238#832C2×D311yescharacteristic
239#830—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243#821C2×D311yescharacteristic, complemented
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246#818—31no—
247#816—31no—
248#815—31no—
249#815—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—31no—
252Dic3⋊C8—61no—
253#809—31no—
254#807—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—81no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C32×Q8—21no—
268C32×Q8—21no—
269C32×D4—21no—
270C32×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—42no—
275C2×C3⋊Dic3C2×D411yescharacteristic
276C2×C3⋊Dic3C2×D411yescharacteristic
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C3×#67—42no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
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#625—22no—
300#625—42no—
301#625—42no—
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—31no—
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—91no—
323#435—91no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
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—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—62no—
341C2×C3×D4—62no—
342C2×C3×D4—121no—
343C2×C3×D4—121no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—61no—
349C2×#67—21no—
350C2×#67—21no—
351C2×#67—31no—
352C2×#67—31no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—124no—
364C2×#67—124no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—121no—
368#239—62no—
369#239—121no—
370D3×Q8—22no—
371D3×Q8—41no—
372D3×D4—22no—
373D3×D4—22no—
374D3×D4—41no—
375D3×D4—41no—
376#235—62no—
377#235—121no—
378C2×D12—31no—
379C2×D12—31no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12C22×D311yescharacteristic
384C2×D12C22×D311yescharacteristic
385C2×C4×D3—21no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3C22×D311yescharacteristic
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6—21no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—22no—
393C3×SD16—22no—
394C3×SD16—34no—
395C3×SD16—42no—
396C3×SD16—62no—
397C3×SD16—62no—
398C3×SD16—121no—
399C2×C3×C8—21no—
400C2×C3×C8—31no—
401C2×C3×C8—31no—
402C2×C3×C8—62no—
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—31no—
406C3×C4⋊C4—61no—
407C3×C22⋊C4—61no—
408#217—31no—
409#217—31no—
410#217—61no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—121no—
415#215—22no—
416#215—41no—
417#215—62no—
418#214—62no—
419#214#6714yescomplemented
420#213—62no—
421#213—62no—
422#213—62no—
423#213—122no—
424#213—121no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—31no—
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—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—121no—
437(C2×D3)⋊C4—121no—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—61no—
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—31no—
445Dic3⋊C4—31no—
446Dic3⋊C4—61no—
447C4×Dic3—31no—
448C4×Dic3—31no—
449C4×Dic3—61no—
450C4×Dic3—61no—
451C4×Dic3—61no—
452#208—62no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8C22×D311yescharacteristic
457C2×C3⋊C8C22×D311yescharacteristic
458D24—62no—
459D24—121no—
460#204—22no—
461ΓL(1,𝔽25)—62no—
462D3×C8—22no—
463C22×C32—22no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
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×D3—84no—
482C2×C3×D3—84no—
483C2×C3×D3AGL(1,ℤ/8)12yescomplemented
484C32×C4—41no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—31no—
496C22×D4—31no—
497C22×D4—31no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—64no—
505C2×SD16—91no—
506C2×SD16D3211yescharacteristic
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—31no—
512#127—91no—
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—91no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—91no—
530#103—91no—
531#103—91no—
532#102—31no—
533#102—31no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—41no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—241no—
551C23×C3—241no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—42no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—81no—
561C22×D3—81no—
562C22×D3—121no—
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—21no—
575C3×D4—21no—
576C3×D4—22no—
577C3×D4—41no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—122no—
583C3×D4—122no—
584C3×D4D3×D412yes—
585C3×D4C2×#6712yes—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
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—61no—
598C2×C3×C4—122no—
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601#67—42no—
602#67—42no—
603#67—62no—
604#67—62no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—122no—
613#67—241no—
614#67—241no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—121no—
626C2×Dic3—122no—
627C2×Dic3—122no—
628C2×Dic3—242no—
629C2×Dic3D3×D411yescharacteristic
630C2×Dic3D3×D411yescharacteristic
631D12—21no—
632D12—21no—
633D12—21no—
634D12—21no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—121no—
640D12—121no—
641D12—122no—
642D12—122no—
643C4×D3—21no—
644C4×D3—21no—
645C4×D3—21no—
646C4×D3—21no—
647C4×D3—42no—
648C4×D3—122no—
649C4×D3—122no—
650Dic6—21no—
651Dic6—42no—
652Dic6C2×#6712yescomplemented
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⋊C8C2×#6712yescomplemented
663C2×C32—42no—
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—81no—
668C3×D3—22no—
669C3×D3—41no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—61no—
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—62no—
686C2×D4—62no—
687C2×D4—91no—
688C2×D4—91no—
689C2×D4—121no—
690C2×D4—121no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—364no—
698C2×D4C2×D3211yescharacteristic
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—61no—
702C22×C4—181no—
703C22×C4—181no—
704SD16—22no—
705SD16—34no—
706SD16—62no—
707SD16—62no—
708SD16—121no—
709SD16—182no—
710D8—182no—
711D8—182no—
712D8—361no—
713M16—182no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—62no—
717C2×C8—91no—
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—31no—
720C4⋊C4—61no—
721C4⋊C4—91no—
722C4⋊C4—91no—
723C4⋊C4—181no—
724C22⋊C4—61no—
725C22⋊C4—91no—
726C22⋊C4—91no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—91no—
734C42—181no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—21no—
738C22×C3—32no—
739C22×C3—42no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—244no—
758C22×C3—244no—
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—84no—
773C2×D3—84no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3#91412yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—61no—
789C3×C4—62no—
790C3×C4—61no—
791C3×C4—81no—
792C3×C4—121no—
793C3×C4C2×D3×D411yescharacteristic
794C3×C4#100411yescharacteristic
795C3×C4#100411yescharacteristic
796C3×C4C22×#6711yescharacteristic
797Dic3—22no—
798Dic3—21no—
799Dic3—21no—
800Dic3—41no—
801Dic3—61no—
802Dic3—61no—
803Dic3—61no—
804Dic3—61no—
805Dic3—121no—
806Dic3—121no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—21no—
812C23—31no—
813C23—31no—
814C23—61no—
815C23—61no—
816C23—122no—
817C23—122no—
818C23—122no—
819C23—122no—
820C23—181no—
821C23—241no—
822C23—241no—
823Q8—21no—
824Q8—21no—
825Q8—32no—
826Q8—61no—
827Q8—122no—
828D4—21no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—122no—
834D4—122no—
835D4—182no—
836D4—181no—
837D4—181no—
838D4—362no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—721no—
844D4D3×#6712yes—
845C2×C4—21no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—91no—
855C2×C4—91no—
856C2×C4—122no—
857C2×C4—181no—
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—42no—
869C2×C3—42no—
870C2×C3—62no—
871C2×C3—82no—
872C2×C3—121no—
873C2×C3—241no—
874C2×C3—241no—
875C2×C3#559011yescharacteristic
876C2×C3C2×#91411yescharacteristic
877C2×C3#576211yescharacteristic
878C2×C3#576211yescharacteristic
879C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
880C2×C3D4×#6711yescharacteristic
881D3—22no—
882D3—41no—
883D3—81no—
884D3—81no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—22no—
889C22—32no—
890C22—41no—
891C22—41no—
892C22—61no—
893C22—61no—
894C22—61no—
895C22—61no—
896C22—61no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—244no—
904C22—244no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22D32×D411yescharacteristic
909C4—41no—
910C4—61no—
911C4—61no—
912C4—62no—
913C4—121no—
914C4—181no—
915C4—181no—
916C4—361no—
917C4#6431311yescharacteristic
918C4C2×D3×#6711yescharacteristic
919C3—21no—
920C3#8015611yescharacteristic, complemented
921C3#8386411yescharacteristic, complemented
922C2—42no—
923C2—62no—
924C2—121no—
925C2—241no—
926C2—241no—
927C2—721no—
928C2D3×#91411yescharacteristic
929C2#1059474811yescharacteristic
930C2#1059528711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×SD16C2semidirect
2. #10595402C2semidirect
3. D4×#625C2semidirect
4. C2×#63934C2semidirect
5. #10592864C2semidirect
6. C3×#5169C2semidirect
7. #10591621C2semidirect
8. #10591587C2semidirect
9. #10591583C2semidirect
10. #10591448C2semidirect
11. #10591446C2semidirect
12. #10590876C2semidirect
13. #10590826C2semidirect
14. #10590823C2semidirect
15. #10590723C2semidirect
18. C2×C3×D3×Q8C22semidirect
22. C2×#3799C22semidirect
24. #64156C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#215C22semidirect
29. C2×C3×#215C22semidirect
32. C2×C3×#204C22semidirect
33. C2×C3×D3×C8C22semidirect
39. #63909C22semidirect
47. #63843C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
51. C2×#3711C22semidirect
52. #63662C22semidirect
53. #63648C22semidirect
54. #63641C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. #63575C22semidirect
59. #63566C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63555C22semidirect
69. C2×D3×SD16D3semidirect
79. #5169D3semidirect
137. C3×#214D4semidirect
164. C2×D3×Q8C2×D3semidirect
185. #946C2×D3semidirect
188. C2×#215C2×D3semidirect
189. C2×#215C2×D3semidirect
221. C2×#204C2×D3semidirect
223. C2×D3×C8C2×D3semidirect
243. #821C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
296. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
419. #214#67semidirect
483. C2×C3×D3AGL(1,ℤ/8)semidirect
652. Dic6C2×#67semidirect
662. C3⋊C8C2×#67semidirect
783. C2×D3#914semidirect
810. C32#3265semidirect
920. C3#80156semidirect
921. C3#83864semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
#105954022
D4×#6252
C2×#639342
#105928642
C3×#51692
#105916212
#105915872
#105915832
#105914482
#105914462
#105908762
#105908262
#105908232
#105907232
#838643
#801563