Finite Group Databasebeta

← #11883988

Subgroups — #11883988

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 940 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
3#10595288C211yesmaximal, characteristic, complemented
4C2×#63934C211yesmaximal, characteristic, complemented
5#10592875C211yesmaximal, characteristic, complemented
6C3×#5170C211yesmaximal, characteristic, complemented
7C3×#5169C211yesmaximal, characteristic, complemented
8#10591589C211yesmaximal, characteristic, complemented
9#10591570C211yesmaximal, characteristic, complemented
10#10591449C211yesmaximal, characteristic, complemented
11#10591444C211yesmaximal, characteristic, complemented
12#10590967C211yesmaximal, characteristic, complemented
13#10590947C211yesmaximal, characteristic, complemented
14#10590743C211yesmaximal, characteristic, complemented
15#10590725C211yesmaximal, characteristic, complemented
16#80156—31nomaximal
17#80060—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3799C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic, complemented
24#64156C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26#64149C2211yescharacteristic
27C2×#3753C2211yescharacteristic, complemented
28C2×#3745C2211yescharacteristic, complemented
29C3×#946C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C3×#938C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic, complemented
33#63983—21no—
34#63977—21no—
35#63971—21no—
36D3×#215—24no—
37#63934—24no—
38#63909C2211yescharacteristic
39#63909C2211yescharacteristic, complemented
40#63907—21no—
41#63906—21no—
42#63904—21no—
43C4×#625C2211yescharacteristic
44#63898C2211yescharacteristic
45#63888—21no—
46#63843C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63642C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63576C2211yescharacteristic, complemented
60#63572C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#5817—31no—
64C22×#215—31no—
65D4×#67—31no—
66C2×#932—31no—
67C2×#914—31no—
68C2×D3×SD16—31no—
69#5633—31no—
70#5609—31no—
71C3×#450—31no—
72C3×#448—31no—
73#5176—31no—
74#5176—31no—
75#5176—61no—
76#5170D311yescharacteristic, complemented
77#5169D311yescharacteristic, complemented
78#5165—31no—
79#5163—31no—
80#5049—31no—
81#5038—31no—
82#4819—31no—
83#4817—31no—
84#4812—31no—
85#4810—31no—
86#4775—31no—
87#4773—31no—
88#4762—31no—
89#4757—31no—
90#4734—31no—
91#4732—31no—
92#4730—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C3×D3×Q8—22no—
105C3×D3×Q8—41no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2311yescharacteristic
114D3×#67—44no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#625D411yescharacteristic
120C2×#624—21no—
121C2×D3×Dic3—21no—
122D3×D12—22no—
123D3×D12—41no—
124#3799—22no—
125#3799—41no—
126C32×SD16—41no—
127C2×C32×C8C2311yescharacteristic
128#3755—22no—
129#3753—22no—
130#3752—21no—
131#3752—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3745—41no—
135C3×#217—21no—
136C3×#215—22no—
137C3×#214—22no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3724D411yescharacteristic
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151Dic32—21no—
152#3717—22no—
153#3715D414yescomplemented
154#3714—22no—
155#3711—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×#239—31no—
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×D3×D4C2×D311yescharacteristic
166C2×#235—31no—
167C22×D12—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16C2×D311yescharacteristic, complemented
172C2×C3×SD16C2×D311yescharacteristic, complemented
173C3×C22⋊Q8—31no—
174C3×#121—31no—
175#953—61no—
176#947—31no—
177#947—31no—
178#947—61no—
179#947—61no—
180#946—61no—
181#946C2×D311yescharacteristic, complemented
182Q8×Dic3—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—61no—
188C2×#215—64no—
189C2×#215C2×D311yescharacteristic
190#940—31no—
191#940—31no—
192#940—61no—
193#939—61no—
194#938C2×D311yescharacteristic
195#937—61no—
196#937—61no—
197D4×Dic3—31no—
198C2×#214—31no—
199C2×#214C2×D311yescharacteristic, complemented
200#932—64no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—61no—
205#930—31no—
206#930—31no—
207#930—61no—
208C4×#67—31no—
209C4×#67—31no—
210C4×#67—61no—
211C2×#208—31no—
212C22×C3⋊C8—31no—
213#914—64no—
214D3×SD16—64no—
215C2×D24—31no—
216C2×D24—31no—
217C2×D24—31no—
218C2×D24—61no—
219C2×#204—31no—
220C2×ΓL(1,𝔽25)—31no—
221C2×D3×C8—31no—
222#896—61no—
223#895—31no—
224#895—31no—
225#893—31no—
226#893—61no—
227#887—31no—
228#885—61no—
229#884—61no—
230#884—61no—
231#882—61no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×#102—31no—
236C3×C22⋊C8—31no—
237C3×C22⋊C8—31no—
238#835C2×D311yescharacteristic, complemented
239#832C2×D311yescharacteristic, complemented
240#821—31no—
241#821—31no—
242#821C2×D311yescharacteristic
243(C2×D3)⋊C8C2×D311yescharacteristic, complemented
244(C2×D3)⋊C8C2×D311yescharacteristic, complemented
245#816C2×D311yescharacteristic, complemented
246#815—31no—
247#815—31no—
248#815—61no—
249Dic3⋊C8—31no—
250Dic3⋊C8—31no—
251#809—31no—
252#809—31no—
253#807—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—81no—
262C22×C3×D3C2×D411yescharacteristic
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8—21no—
269C32×D4—21no—
270C32×D4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273#638—42no—
274#638—81no—
275C2×C3⋊Dic3C2×D411yescharacteristic
276C2×C3⋊Dic3C2×D411yescharacteristic
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)—21no—
281C3×#67—42no—
282C3×#67—42no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yescomplemented
298#626—42no—
299#626—42no—
300#626—42no—
301#626—42no—
302#625—22no—
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—91no—
318#450—31no—
319#449—91no—
320#448—31no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
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—21no—
336C2×C3×D4—31no—
337C2×C3×D4—61no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—121no—
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—31no—
349C2×#67—31no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—121no—
359C2×#67—121no—
360C2×#67—124no—
361C22×Dic3—61no—
362#239—62no—
363#239—121no—
364D3×Q8—22no—
365D3×Q8—41no—
366D3×D4—22no—
367D3×D4—41no—
368D3×D4—62no—
369D3×D4—121no—
370D3×D4—124no—
371#235—62no—
372#235—121no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—61no—
384C2×D12—121no—
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3C22×D311yescharacteristic
391C2×C4×D3C22×D311yescharacteristic
392C2×Dic6—21no—
393C2×Dic6C22×D311yescharacteristic
394C3×SD16—41no—
395C3×SD16—41no—
396C3×SD16—42no—
397C3×SD16—62no—
398C3×SD16—62no—
399C2×C3×C8—21no—
400C2×C3×C8—31no—
401C2×C3×C8—31no—
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C3×C4⋊C4—31no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409#217—21no—
410#217—31no—
411#217—31no—
412#217—61no—
413#215—22no—
414#215—34no—
415#215—62no—
416#215—62no—
417#215—62no—
418#215—122no—
419#214—22no—
420#214—34no—
421#213—62no—
422#213—62no—
423#213—62no—
424#213—122no—
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—61no—
437(C2×D3)⋊C4—121no—
438(C2×D3)⋊C4—121no—
439C4⋊Dic3—61no—
440C4⋊Dic3C22×D311yescharacteristic
441C4⋊Dic3C22×D311yescharacteristic
442Dic3⋊C4—21no—
443Dic3⋊C4—31no—
444Dic3⋊C4—31no—
445Dic3⋊C4—61no—
446C4×Dic3—31no—
447C4×Dic3—31no—
448C4×Dic3—61no—
449C4×Dic3—61no—
450C4×Dic3—61no—
451#208—62no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—62no—
456C2×C3⋊C8C22×D311yescharacteristic
457C2×C3⋊C8C22×D311yescharacteristic
458D24—62no—
459D24—121no—
460D24—121no—
461D24—122no—
462#204—62no—
463ΓL(1,𝔽25)—62no—
464D3×C8—62no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—22no—
479C2×C3×D3—21no—
480C2×C3×D3—21no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—84no—
484C2×C3×D3AGL(1,ℤ/8)12yescomplemented
485D32—84no—
486C32×C4—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3⋊Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—22no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—31no—
498C22×D4—31no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×SD16—184no—
508C2×SD16D3211yescharacteristic, complemented
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—31no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—91no—
527C4×D4—91no—
528C4×D4—91no—
529C4×D4—181no—
530#107—91no—
531C4⋊C8—91no—
532#103—31no—
533#103—31no—
534#102—31no—
535#102—31no—
536#102—91no—
537#102—91no—
538C22⋊C8—31no—
539C22⋊C8—31no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—31no—
545C23×C3—41no—
546C23×C3—61no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—241no—
550C22×D3—21no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—81no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—241no—
565C22×D3—241no—
566C22×D3D3×D411yescharacteristic
567C22×D3D3×D411yescharacteristic
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—21no—
572C3×Q8—32no—
573C3×Q8—41no—
574C3×Q8—41no—
575C3×Q8—61no—
576C3×Q8—122no—
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—32no—
582C3×D4—41no—
583C3×D4—41no—
584C3×D4—61no—
585C3×D4—122no—
586C3×D4—122no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—41no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—122no—
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603#67—42no—
604#67—42no—
605#67—62no—
606#67—62no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—122no—
613#67—242no—
614#67—241no—
615#67—241no—
616#67—242no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—122no—
627C2×Dic3D3×D411yescharacteristic
628C2×Dic3D3×D411yescharacteristic
629D12—21no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—121no—
639D12—121no—
640D12—121no—
641D12—121no—
642D12—122no—
643D12—122no—
644D12—122no—
645D12—122no—
646D12D3×D412yes—
647C4×D3—21no—
648C4×D3—21no—
649C4×D3—21no—
650C4×D3—21no—
651C4×D3—42no—
652C4×D3—122no—
653C4×D3—122no—
654C4×D3—122no—
655Dic6—21no—
656Dic6—42no—
657Dic6D3×D412yescomplemented
658C3×C8—22no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—61no—
662C3×C8—61no—
663C3⋊C8—21no—
664C3⋊C8—21no—
665C3⋊C8—32no—
666C3⋊C8—32no—
667C3⋊C8—62no—
668C2×C32—81no—
669C2×C32D4211yescharacteristic
670C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
671C2×C32#57711yescharacteristic
672C3⋊D3—81no—
673C3⋊D3—81no—
674C3×D3—22no—
675C3×D3—42no—
676C3×D3—41no—
677C24—61no—
678C24—181no—
679#41—182no—
680#41—361no—
681C2×Q8—31no—
682C2×Q8—61no—
683C2×Q8—62no—
684C2×Q8—121no—
685C2×Q8C2×D3211yescharacteristic
686C2×D4—31no—
687C2×D4—61no—
688C2×D4—62no—
689C2×D4—61no—
690C2×D4—91no—
691C2×D4—91no—
692C2×D4—91no—
693C2×D4—121no—
694C2×D4—181no—
695C2×D4—182no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—361no—
702C2×D4—364no—
703C2×D4C2×D3211yescharacteristic
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—181no—
708C22×C4—181no—
709SD16—41no—
710SD16—62no—
711SD16—62no—
712SD16—94no—
713SD16—182no—
714SD16—182no—
715D8—182no—
716D8—182no—
717D8—361no—
718M16—182no—
719C2×C8—31no—
720C2×C8—31no—
721C2×C8—91no—
722C2×C8—182no—
723C2×C8C2×D3211yescharacteristic
724C4⋊C4—31no—
725C4⋊C4—31no—
726C4⋊C4—61no—
727C4⋊C4—91no—
728C4⋊C4—181no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4—91no—
732C22⋊C4—91no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C42—91no—
739C42—181no—
740C22×C3—21no—
741C22×C3—32no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—61no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—62no—
754C22×C3—81no—
755C22×C3—81no—
756C22×C3—81no—
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—21no—
766C2×D3—21no—
767C2×D3—22no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—84no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
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—241no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3#91412yescomplemented
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4—61no—
797C3×C4—62no—
798C3×C4—61no—
799C3×C4—81no—
800C3×C4—121no—
801C3×C4—121no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4C2×D3×D411yescharacteristic
804C3×C4#100411yescharacteristic
805C3×C4#100411yescharacteristic
806Dic3—22no—
807Dic3—21no—
808Dic3—21no—
809Dic3—41no—
810Dic3—41no—
811Dic3—61no—
812Dic3—61no—
813Dic3—61no—
814Dic3—61no—
815Dic3—121no—
816Dic3—121no—
817C32#326511yescharacteristic, complemented, Sylow
818C23—21no—
819C23—31no—
820C23—31no—
821C23—61no—
822C23—122no—
823C23—122no—
824C23—181no—
825C23—181no—
826C23—241no—
827C23—362no—
828C23—362no—
829C23—721no—
830Q8—21no—
831Q8—21no—
832Q8—32no—
833Q8—61no—
834Q8—122no—
835D4—21no—
836D4—21no—
837D4—32no—
838D4—61no—
839D4—122no—
840D4—122no—
841D4—182no—
842D4—181no—
843D4—181no—
844D4—181no—
845D4—181no—
846D4—362no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—721no—
852C2×C4—21no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—91no—
863C2×C4—91no—
864C2×C4—122no—
865C2×C4—362no—
866C2×C4—362no—
867C2×C4C22×D3211yescharacteristic
868C8—21no—
869C8—61no—
870C8—61no—
871C8—92no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—62no—
876C2×C3—81no—
877C2×C3—81no—
878C2×C3—122no—
879C2×C3—121no—
880C2×C3—161no—
881C2×C3#559011yescharacteristic
882C2×C3#559011yescharacteristic
883C2×C3C2×#91411yescharacteristic
884C2×C3#576211yescharacteristic
885C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
886C2×C3#577811yescharacteristic
887D3—22no—
888D3—41no—
889D3—42no—
890D3—241no—
891D3—241no—
892D3—241no—
893D3—241no—
894D3—481no—
895D3—481no—
896C22—32no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—61no—
901C22—61no—
902C22—61no—
903C22—61no—
904C22—61no—
905C22—62no—
906C22—121no—
907C22—121no—
908C22—244no—
909C22—361no—
910C22—361no—
911C22—361no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22—724no—
916C22D32×D411yescharacteristic
917C4—41no—
918C4—61no—
919C4—61no—
920C4—62no—
921C4—121no—
922C4—121no—
923C4—181no—
924C4—181no—
925C4D32×D411yescharacteristic
926C4#6433011yescharacteristic
927C3—21no—
928C3#8006011yescharacteristic, complemented
929C3#8015611yescharacteristic, complemented
930C2—62no—
931C2—81no—
932C2—121no—
933C2—122no—
934C2—721no—
935C2—721no—
936C2D3×#91411yescharacteristic
937C2#1059475111yescharacteristic
938C2#1059528911yescharacteristic
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. #10595402C2semidirect
2. C2×D3×#215C2semidirect
3. #10595288C2semidirect
4. C2×#63934C2semidirect
5. #10592875C2semidirect
6. C3×#5170C2semidirect
7. C3×#5169C2semidirect
8. #10591589C2semidirect
9. #10591570C2semidirect
10. #10591449C2semidirect
11. #10591444C2semidirect
12. #10590967C2semidirect
13. #10590947C2semidirect
14. #10590743C2semidirect
15. #10590725C2semidirect
18. C2×C3×D3×Q8C22semidirect
22. C2×#3799C22semidirect
23. C2×C32×SD16C22semidirect
24. #64156C22semidirect
25. C2×#3755C22semidirect
27. C2×#3753C22semidirect
28. C2×#3745C22semidirect
29. C3×#946C22semidirect
32. C2×C3×#214C22semidirect
39. #63909C22semidirect
46. #63843C22semidirect
47. C2×#3717C22semidirect
50. C2×#3711C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63642C22semidirect
53. C3×#835C22semidirect
54. C3×#832C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63576C22semidirect
60. #63572C22semidirect
61. #63564C22semidirect
62. #63564C22semidirect
76. #5170D3semidirect
77. #5169D3semidirect
153. #3715D4semidirect
162. C2×D3×Q8C2×D3semidirect
171. C2×C3×SD16C2×D3semidirect
172. C2×C3×SD16C2×D3semidirect
181. #946C2×D3semidirect
199. C2×#214C2×D3semidirect
238. #835C2×D3semidirect
239. #832C2×D3semidirect
243. (C2×D3)⋊C8C2×D3semidirect
244. (C2×D3)⋊C8C2×D3semidirect
245. #816C2×D3semidirect
297. C3×Dic6C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
484. C2×C3×D3AGL(1,ℤ/8)semidirect
508. C2×SD16D32semidirect
657. Dic6D3×D4semidirect
791. C2×D3#914semidirect
817. C32#3265semidirect
928. C3#80060semidirect
929. C3#80156semidirect

Maximal subgroups

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

subgroupindex
#105954022
C2×D3×#2152
#105952882
C2×#639342
#105928752
C3×#51702
C3×#51692
#105915892
#105915702
#105914492
#105914442
#105909672
#105909472
#105907432
#105907252
#801563
#800603