Finite Group Databasebeta

← #11895656

Subgroups — #11895656

Order 1152.

760 conjugacy classes of subgroups.

The subgroup lattice has 717 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595351C211yesmaximal, characteristic, complemented
2#10595210C211yesmaximal, characteristic
3#10592862C211yesmaximal, characteristic
4C3×#5166C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591607C211yesmaximal, characteristic, complemented
7#10591581C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10591478C211yesmaximal, characteristic, complemented
10#10591411C211yesmaximal, characteristic, complemented
11#10591402C211yesmaximal, characteristic
12#10590872C211yesmaximal, characteristic, complemented
13#10590816C211yesmaximal, characteristic, complemented
14#10590769C211yesmaximal, characteristic, complemented
15#10590644C211yesmaximal, characteristic, complemented
16#80581—31nomaximal
17#79624—31nomaximal
18C2×C32×SD16C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21#64149C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#936C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27#63975—21no—
28#63966—21no—
29#63953—21no—
30#63952—21no—
31#63919—21no—
32#63919C2211yescharacteristic
33C4×#627—21no—
34C4×#627C2211yescharacteristic
35#63894C2211yescharacteristic
36#63869—21no—
37#63869—21no—
38#63869C2211yescharacteristic
39#63869C2211yescharacteristic
40#63864C2211yescharacteristic
41#63843C2211yescharacteristic
42#63659C2211yescharacteristic
43#63648C2211yescharacteristic
44#63641C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52#63575C2211yescharacteristic
53#63574C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5681—31no—
62#5569—31no—
63#5569—31no—
64#5559—31no—
65C3×#464—31no—
66C3×C4×SD16—31no—
67#5185—31no—
68Dic3×Q16—31no—
69#5166D311yescharacteristic, complemented
70#5163—31no—
71#5163—31no—
72#5163—61no—
73Dic3×SD16D311yescharacteristic, complemented
74#5056—31no—
75#5028—31no—
76C4×#215—31no—
77#5009—31no—
78#4871—31no—
79#4854—31no—
80#4847—31no—
81#4830—31no—
82#4800—31no—
83#4791—31no—
84#4790—31no—
85#4788—31no—
86#4768—31no—
87#4766—31no—
88#4760—31no—
89#4760—31no—
90#4697—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C22×C3×Dic3—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×#624—21no—
102C32×SD16—22no—
103C2×C32×C8C2311yescharacteristic
104#3755—22no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4×C3⋊Dic3—21no—
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×#217—21no—
111C3×#217—21no—
112C3×#217—21no—
113C3×#216—22no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724—21no—
127#3724—21no—
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136#3722—21no—
137Dic32—21no—
138#3365—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—21no—
141C2×C3×SD16C2×D311yescharacteristic
142C2×C3×SD16C2×D311yescharacteristic
143C3×#124—31no—
144C3×C4×Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—31no—
147#947—31no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3—61no—
152Q8×Dic3C2×D311yescharacteristic
153Q8×Dic3C2×D311yescharacteristic
154C2×#216C2×D311yescharacteristic
155C2×#215—31no—
156C2×#215—31no—
157C2×#215—61no—
158#940—31no—
159#940—31no—
160#940—61no—
161#936C2×D311yescharacteristic
162D4×Dic3C2×D311yescharacteristic
163#929—61no—
164C4×#67—61no—
165#893—31no—
166#890—31no—
167#890—31no—
168#890—61no—
169#890—61no—
170#888—31no—
171#888—31no—
172#888—61no—
173#888—61no—
174#887—31no—
175#886—61no—
176#885—61no—
177#885—61no—
178#883—61no—
179#883—61no—
180#67⋊C4—61no—
181#875—31no—
182C4×D12—31no—
183#870—31no—
184#870—31no—
185#870—61no—
186#870—61no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—61no—
190C4×Dic6—61no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×C4×C8—31no—
198#835—31no—
199#835—31no—
200#835C2×D311yescharacteristic
201#832—31no—
202#832—31no—
203#832—61no—
204#832C2×D311yescharacteristic
205#832C2×D311yescharacteristic
206#821—31no—
207#821—31no—
208#821—31no—
209#821—31no—
210#821—61no—
211#818—31no—
212#817C2×D311yescharacteristic
213#816—31no—
214#816C2×D311yescharacteristic
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—61no—
219Dic3⋊C8C2×D311yescharacteristic
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3C2×D311yescharacteristic
224#810—31no—
225#809—31no—
226#809—31no—
227#808—31no—
228#808—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C23×C32—21no—
233C22×C3⋊D3—21no—
234C32×Q8—21no—
235C32×Q8#4112yes—
236C32×D4—21no—
237C32×D4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240#638—42no—
241#638—81no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D411yescharacteristic
244C2×C3⋊Dic3C2×D411yescharacteristic
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—81no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×Dic6—21no—
257C3×Dic6—21no—
258#627—22no—
259#627—42no—
260#624—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—91no—
266#557—91no—
267#488—91no—
268#488—91no—
269#486—91no—
270#478—91no—
271#478—91no—
272#475—91no—
273#464—31no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—31no—
279C4×SD16—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×D4—21no—
285C2×C3×D4C22×D311yescharacteristic
286C2×C3×D4C22×D311yescharacteristic
287C22×C3×C4—61no—
288C2×#67—61no—
289C2×#67—61no—
290C2×#67—61no—
291C2×#67—61no—
292C2×#67—121no—
293C2×#67—121no—
294C22×Dic3—21no—
295C2×D12—31no—
296C2×D12—31no—
297C2×D12—61no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×Dic6—31no—
301C2×Dic6—31no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6C22×D311yescharacteristic
305C3×Q16—62no—
306C3×SD16—22no—
307C3×SD16—22no—
308C3×SD16—42no—
309C2×C3×C8—21no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8C22×D311yescharacteristic
313C2×C3×C8C22×D311yescharacteristic
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C22⋊C4—61no—
321C3×C22⋊C4—61no—
322C3×C42—31no—
323C3×C42—31no—
324C3×C42—61no—
325C3×C42—61no—
326#217—21no—
327#217—21no—
328#217—21no—
329#216—22no—
330#215—62no—
331#215—62no—
332#215—122no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—121no—
352C4⋊Dic3C22×D311yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368C4×Dic3—21no—
369C4×Dic3—21no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—121no—
378C4×Dic3C22×D311yescharacteristic
379C4×Dic3C22×D311yescharacteristic
380C2×C3⋊C8—31no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—61no—
383C2×C3⋊C8C22×D311yescharacteristic
384C2×C3⋊C8C22×D311yescharacteristic
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32C22×D411yescharacteristic
389C2×C3⋊D3—41no—
390C2×C3⋊D3—41no—
391C2×C3⋊D3—41no—
392C32×C4—22no—
393C32×C4C2×#4111yescharacteristic
394C32×C42−1+411yescharacteristic
395C3⋊Dic3—21no—
396C3⋊Dic3—41no—
397C3⋊Dic3#13512yes—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C2×Q16—31no—
407C2×SD16—91no—
408C2×SD16D3211yescharacteristic
409C4⋊Q8—91no—
410C4⋊Q8—181no—
411#127—91no—
412#125—91no—
413#125—91no—
414#125—181no—
415#125—181no—
416#124—31no—
417#124—91no—
418#124—181no—
419#123—181no—
420#123—181no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—181no—
427C4×D4—31no—
428C4×D4—91no—
429C4×D4—181no—
430#107—91no—
431#106—31no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#103—31no—
437#103—31no—
438#103—91no—
439#103—91no—
440#102—31no—
441#102—31no—
442#102—91no—
443#102—91no—
444#102—91no—
445#102—91no—
446C4×C8—31no—
447C4×C8—91no—
448C4×C8—91no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—41no—
452C22×D3—61no—
453C22×D3—61no—
454C22×D3—121no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—22no—
458C3×Q8—41no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×Q8#23512yes—
462C3×Q8#23712yes—
463C3×D4—21no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—41no—
468C3×D4—41no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—241no—
482C2×C3×C4C23×D311yescharacteristic
483C2×C3×C4C23×D311yescharacteristic
484#67—122no—
485#67—122no—
486#67—242no—
487#67—241no—
488#67—241no—
489#67—242no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—81no—
503C2×Dic3—121no—
504C2×Dic3D3×D411yescharacteristic
505C2×Dic3D3×D411yescharacteristic
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508D12—61no—
509D12—61no—
510D12—61no—
511D12—61no—
512D12—121no—
513D12—121no—
514C4×D3—241no—
515C4×D3—241no—
516Dic6—21no—
517Dic6—21no—
518Dic6—62no—
519Dic6—62no—
520Dic6—122no—
521Dic6—122no—
522C3×C8—21no—
523C3×C8—21no—
524C3×C8—41no—
525C3×C8—61no—
526C3×C8—61no—
527C3⋊C8—21no—
528C3⋊C8—21no—
529C3⋊C8—61no—
530C3⋊C8—61no—
531C3⋊C8—121no—
532C2×C32—81no—
533C2×C32#54811yescharacteristic
534C2×C32C2×#13511yescharacteristic
535C2×C32#57711yescharacteristic
536C3⋊D3—81no—
537C2×Q8—31no—
538C2×Q8—91no—
539C2×Q8—181no—
540C2×Q8C2×D3211yescharacteristic
541C2×D4—91no—
542C2×D4—181no—
543C2×D4—181no—
544C2×D4C2×D3211yescharacteristic
545C22×C4—61no—
546C22×C4—181no—
547Q16—62no—
548SD16—22no—
549SD16—182no—
550C2×C8—31no—
551C2×C8—31no—
552C2×C8—91no—
553C2×C8C2×D3211yescharacteristic
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—91no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—181no—
574C22⋊C4—181no—
575C22⋊C4—181no—
576C42—31no—
577C42—31no—
578C42—61no—
579C42—61no—
580C42—91no—
581C42—181no—
582C42—181no—
583C22×C3—21no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3C2×D3×D411yescharacteristic
594C22×C3C2×D3×D411yescharacteristic
595C2×D3—121no—
596C2×D3—121no—
597C2×D3—121no—
598C2×D3—121no—
599C2×D3—121no—
600C2×D3—121no—
601C2×D3—241no—
602C2×D3—241no—
603C2×D3—241no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—42no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4C2×#23511yescharacteristic
618C3×C4C2×#23711yescharacteristic
619C3×C4#101011yescharacteristic
620C3×C4#101011yescharacteristic
621Dic3—21no—
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—32no—
626Dic3—32no—
627Dic3—41no—
628Dic3—41no—
629Dic3—41no—
630Dic3—41no—
631Dic3—62no—
632Dic3—61no—
633Dic3—61no—
634Dic3—121no—
635Dic3—121no—
636Dic3—121no—
637Dic3—241no—
638C32#336511yescharacteristic, complemented, Sylow
639C23—21no—
640C23—181no—
641Q8—21no—
642Q8—61no—
643Q8—61no—
644Q8—182no—
645Q8—362no—
646Q8#380412yes—
647D4—21no—
648D4—21no—
649D4—181no—
650D4—181no—
651D4—362no—
652D4—721no—
653C2×C4—21no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—181no—
665C2×C4—241no—
666C2×C4—721no—
667C2×C4C22×D3211yescharacteristic
668C8—21no—
669C8—61no—
670C8—61no—
671C8—181no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—81no—
676C2×C3—81no—
677C2×C3—161no—
678C2×C3#555211yescharacteristic
679C2×C3#559811yescharacteristic
680C2×C3#576211yescharacteristic
681C2×C3D3×#13511yescharacteristic
682C2×C3D3×#13511yescharacteristic
683C2×C3#577811yescharacteristic
684D3—241no—
685D3—241no—
686D3—481no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—361no—
691C22—361no—
692C22—361no—
693C22D32×D411yescharacteristic
694C4—22no—
695C4—61no—
696C4—61no—
697C4—61no—
698C4—61no—
699C4—92no—
700C4—121no—
701C4—121no—
702C4—121no—
703C4—121no—
704C4—181no—
705C4—361no—
706C4#6430911yescharacteristic
707C4C2×#380411yescharacteristic
708C3—21no—
709C3#7962411yescharacteristic, complemented
710C3#8058111yescharacteristic, complemented
711C2—81no—
712C2—721no—
713C2#1059474711yescharacteristic
714C2#1059475111yescharacteristic
715C2#1059514111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#64149C22
hypercenterC2×SD16D32
hypocenterC32#3365
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. #10595351C2semidirect
4. C3×#5166C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591607C2semidirect
7. #10591581C2semidirect
8. #10591536C2semidirect
9. #10591478C2semidirect
10. #10591411C2semidirect
12. #10590872C2semidirect
13. #10590816C2semidirect
14. #10590769C2semidirect
15. #10590644C2semidirect
69. #5166D3semidirect
73. Dic3×SD16D3semidirect
638. C32#3365semidirect
709. C3#79624semidirect
710. C3#80581semidirect

Maximal subgroups

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

subgroupindex
#105953512
#105952102
#105928622
C3×#51662
C3×Dic3×SD162
#105916072
#105915812
#105915362
#105914782
#105914112
#105914022
#105908722
#105908162
#105907692
#105906442
#805813
#796243