Finite Group Databasebeta

← #11895681

Subgroups — #11895681

Order 1152.

752 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595388C211yesmaximal, characteristic
2#10594318C211yesmaximal, characteristic, complemented
3#10592497C211yesmaximal, characteristic, complemented
4C3×#4800C211yesmaximal, characteristic, complemented
5C3×#4791C211yesmaximal, characteristic, complemented
6#10591577C211yesmaximal, characteristic, complemented
7#10591539C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10590879C211yesmaximal, characteristic
10#10590782C211yesmaximal, characteristic, complemented
11#10590758C211yesmaximal, characteristic, complemented
12#10590644C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic
14#10590470C211yesmaximal, characteristic, complemented
15#10590460C211yesmaximal, characteristic, complemented
16#81635—31nomaximal
17#81041—31nomaximal
18#64156C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21#64096C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#888C2211yescharacteristic
26C4×#627C2211yescharacteristic
27#63911C2211yescharacteristic
28#63898C2211yescharacteristic
29#63894C2211yescharacteristic
30#63890—21no—
31#63880—21no—
32#63872C2211yescharacteristic
33#63870—21no—
34#63854—21no—
35#63852—21no—
36#63847—21no—
37#63844C2211yescharacteristic
38#63844C2211yescharacteristic
39#63843—21no—
40#63839—21no—
41C2×#3716C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63641C2211yescharacteristic
44#63636C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63576C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5721—31no—
62#5685—31no—
63#5681—31no—
64#5585—31no—
65C3×#488—31no—
66C3×#475—31no—
67#5088—31no—
68#5066—31no—
69#5054—31no—
70C4×#216—31no—
71#4871—31no—
72#4871—31no—
73#4852—31no—
74#4852—31no—
75#4848—31no—
76#4830—31no—
77#4800—31no—
78#4800—31no—
79#4800D311yescharacteristic, complemented
80#4798—31no—
81#4798—31no—
82#4798—31no—
83#4798—61no—
84#4791D311yescharacteristic, complemented
85#4790—31no—
86#4763—31no—
87#4762—31no—
88#4760—31no—
89#4758—31no—
90C4×#204—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×Dic6—21no—
97C2×#627D411yescharacteristic
98C2×#626—21no—
99C2×#626—21no—
100C2×#624—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3756—22no—
105#3752—21no—
106#3752—21no—
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111#3744—22no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126#3724—21no—
127#3724—21no—
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3D411yescharacteristic
132Dic3⋊Dic3D411yescharacteristic
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137#3716—22no—
138#3365—91noSylow
139C3×C4⋊Q8—31no—
140C3×#125—31no—
141C3×#124—31no—
142C3×C4×Q8—31no—
143#947—31no—
144#947—31no—
145#947—61no—
146#947C2×D311yescharacteristic
147Q8×Dic3—61no—
148Q8×Dic3C2×D311yescharacteristic
149#944—61no—
150C2×#216—31no—
151C2×#216—31no—
152C2×#216—61no—
153#940—31no—
154D4×Dic3—31no—
155C2×#214—31no—
156C2×#204—31no—
157C2×#204—31no—
158C2×#204—31no—
159C2×#204—61no—
160#894—61no—
161#894—61no—
162#893—31no—
163#893—31no—
164#890—31no—
165#890—31no—
166#890C2×D311yescharacteristic
167#889—61no—
168#889—61no—
169#889—61no—
170#889—61no—
171#888—61no—
172#888C2×D311yescharacteristic
173#887—31no—
174#887—31no—
175#887—31no—
176#887—31no—
177#887—61no—
178#887—61no—
179#886—61no—
180#885—61no—
181#883—61no—
182#67⋊C4—61no—
183#875—61no—
184#874—31no—
185C4×D12—31no—
186C4×D12—61no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C3×#106—31no—
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×#103—21no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103C2×D311yescharacteristic
198C3×#103C2×D311yescharacteristic
199C3×#102—31no—
200C3×#102—31no—
201C3×C4×C8—31no—
202#835C2×D311yescharacteristic
203#835C2×D311yescharacteristic
204#832—31no—
205#821—31no—
206#821—31no—
207#821C2×D311yescharacteristic
208#817C2×D311yescharacteristic
209#816—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—61no—
214Dic3⋊C8C2×D311yescharacteristic
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3C2×D311yescharacteristic
219#810—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#809C2×D311yescharacteristic
227#808C2×D311yescharacteristic
228#807—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)—21no—
244#634—21no—
245#634#4112yes—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—21no—
254C3×D12—21no—
255C3×Dic6—42no—
256#627—22no—
257#626—42no—
258#626—81no—
259#624—81no—
260D3×Dic3—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—91no—
266#557—91no—
267#488—31no—
268#488—91no—
269#486—91no—
270#478—91no—
271#478—91no—
272#475—31no—
273#464—91no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8—61no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×D4—31no—
285C2×#67—61no—
286C2×#67—61no—
287C22×Dic3—61no—
288C2×D12—31no—
289C2×D12—31no—
290C2×D12—61no—
291C2×D12—61no—
292C2×D12—61no—
293C2×D12C22×D311yescharacteristic
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×Dic6—21no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—31no—
302C2×Dic6—61no—
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C3×C4⋊C4—21no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C22⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C42—31no—
321C3×C42—31no—
322C3×C42—61no—
323#217—61no—
324#216—62no—
325#216—62no—
326#216—122no—
327#214—62no—
328(C2×D3)⋊C4—21no—
329(C2×D3)⋊C4—21no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—121no—
338(C2×D3)⋊C4—121no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—121no—
363C4×Dic3—21no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—121no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381#204—62no—
382#204—62no—
383#204—62no—
384#204—122no—
385C22×C32C22×D411yescharacteristic
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C2×C3⋊D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C32×C4—41no—
393C32×C4—41no—
394C32×C4C2×#4111yescharacteristic
395C32×C42−1+411yescharacteristic
396C3⋊Dic3—22no—
397C3⋊Dic3—21no—
398C3⋊Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3#13512yes—
406C2×Q16—91no—
407C2×SD16—91no—
408C2×SD16—91no—
409C4⋊Q8—31no—
410C4⋊Q8—181no—
411#127—91no—
412#125—31no—
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—91no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—181no—
427C4×D4—91no—
428C4×D4—91no—
429C4×D4—181no—
430#107—91no—
431#106—31no—
432#106—31no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#103—31no—
437#103—31no—
438#103—91no—
439#103D3211yescharacteristic
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—61no—
450C22×D3—21no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—121no—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—41no—
459C3×Q8—41no—
460C3×Q8—122no—
461C3×D4—61no—
462C3×D4—61no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4C23×D311yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479#67—122no—
480#67—241no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—121no—
493C2×Dic3—241no—
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497C2×Dic3D3×D411yescharacteristic
498D12—21no—
499D12—21no—
500D12—61no—
501D12—61no—
502D12—61no—
503D12—61no—
504D12—121no—
505D12—121no—
506D12—122no—
507D12—241no—
508C4×D3—241no—
509C4×D3—241no—
510C4×D3—241no—
511Dic6—32no—
512Dic6—32no—
513Dic6—42no—
514Dic6—62no—
515Dic6—62no—
516Dic6—61no—
517Dic6—61no—
518Dic6—62no—
519Dic6—121no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—41no—
523C3×C8—61no—
524C3×C8—61no—
525C3⋊C8—21no—
526C3⋊C8—21no—
527C3⋊C8—61no—
528C3⋊C8—61no—
529C3⋊C8—121no—
530C2×C32#54811yescharacteristic
531C2×C32C2×#13511yescharacteristic
532C2×C32#57711yescharacteristic
533C3⋊D3—81no—
534C3×D3—81no—
535C2×Q8—61no—
536C2×Q8—91no—
537C2×Q8—91no—
538C2×Q8C2×D3211yescharacteristic
539C2×D4—31no—
540C2×D4—91no—
541C2×D4—181no—
542C2×D4—181no—
543C22×C4—181no—
544C22×C4—181no—
545Q16—182no—
546SD16—182no—
547SD16—182no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—91no—
551C2×C8C2×D3211yescharacteristic
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4C2×D3211yescharacteristic
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C42—31no—
575C42—31no—
576C42—61no—
577C42—91no—
578C42—181no—
579C42—181no—
580C42—181no—
581C22×C3—21no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3—121no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—121no—
596C2×D3—241no—
597C2×D3—241no—
598C2×D3—241no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—32no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—81no—
610C3×C4—81no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4#100711yescharacteristic
615C3×C4D3×#4111yescharacteristic
616C3×C4D3×#4111yescharacteristic
617C3×C4#101011yescharacteristic
618Dic3—21no—
619Dic3—21no—
620Dic3—21no—
621Dic3—41no—
622Dic3—41no—
623Dic3—41no—
624Dic3—62no—
625Dic3—62no—
626Dic3—61no—
627Dic3—61no—
628Dic3—61no—
629Dic3—61no—
630Dic3—122no—
631Dic3—121no—
632Dic3—121no—
633Dic3#91612yes—
634C32#336511yescharacteristic, complemented, Sylow
635C23—61no—
636C23—181no—
637Q8—21no—
638Q8—21no—
639Q8—92no—
640Q8—122no—
641Q8—182no—
642Q8—181no—
643D4—61no—
644D4—61no—
645D4—181no—
646D4—181no—
647D4—362no—
648D4—721no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—91no—
659C2×C4—91no—
660C2×C4—181no—
661C2×C4—721no—
662C2×C4—721no—
663C2×C4C22×D3211yescharacteristic
664C8—21no—
665C8—61no—
666C8—61no—
667C8—181no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—241no—
672C2×C3#563311yescharacteristic
673C2×C3#567711yescharacteristic
674C2×C3C2×#91611yescharacteristic
675C2×C3D3×#13511yescharacteristic
676C2×C3#577011yescharacteristic
677C2×C3#577811yescharacteristic
678D3—81no—
679D3—241no—
680D3—241no—
681D3—481no—
682C22—121no—
683C22—121no—
684C22—121no—
685C22—361no—
686C22—361no—
687C22—361no—
688C22D32×D411yescharacteristic
689C4—32no—
690C4—41no—
691C4—41no—
692C4—61no—
693C4—61no—
694C4—61no—
695C4—121no—
696C4—121no—
697C4—121no—
698C4—182no—
699C4—181no—
700C4—181no—
701C4#6429711yescharacteristic
702C4#6431211yescharacteristic
703C3—21no—
704C3#8104111yescharacteristic, complemented
705C3#8163511yescharacteristic, complemented
706C2—241no—
707C2—721no—
708C2#1059407511yescharacteristic
709C2D3×#91611yescharacteristic
710C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#63911C22
hypercenter#103D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594318C2semidirect
3. #10592497C2semidirect
4. C3×#4800C2semidirect
5. C3×#4791C2semidirect
6. #10591577C2semidirect
7. #10591539C2semidirect
8. #10591537C2semidirect
10. #10590782C2semidirect
11. #10590758C2semidirect
12. #10590644C2semidirect
14. #10590470C2semidirect
15. #10590460C2semidirect
79. #4800D3semidirect
84. #4791D3semidirect
634. C32#3365semidirect
704. C3#81041semidirect
705. C3#81635semidirect

Maximal subgroups

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

subgroupindex
#105953882
#105943182
#105924972
C3×#48002
C3×#47912
#105915772
#105915392
#105915372
#105908792
#105907822
#105907582
#105906442
#105905482
#105904702
#105904602
#816353
#810413