Finite Group Databasebeta

← #11895691

Subgroups — #11895691

Order 1152.

755 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595210C211yesmaximal, characteristic
2#10594322C211yesmaximal, characteristic, complemented
3#10592459C211yesmaximal, characteristic
4C3×#4768C211yesmaximal, characteristic, complemented
5C3×#4758C211yesmaximal, characteristic, complemented
6#10591444C211yesmaximal, characteristic
7#10591442C211yesmaximal, characteristic, complemented
8#10591409C211yesmaximal, characteristic, complemented
9#10590872C211yesmaximal, characteristic, complemented
10#10590792C211yesmaximal, characteristic, complemented
11#10590790C211yesmaximal, characteristic, complemented
12C8×#627C211yesmaximal, characteristic, complemented
13#10590536C211yesmaximal, characteristic, complemented
14#10590497C211yesmaximal, characteristic, complemented
15#10590470C211yesmaximal, characteristic, complemented
16#81635—31nomaximal
17#79624—31nomaximal
18#64149C2211yescharacteristic
19#64097C2211yescharacteristic
20C3×#936C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C3×#890C2211yescharacteristic
24C3×#887C2211yescharacteristic
25#63975—21no—
26#63966—21no—
27#63953—21no—
28#63952—21no—
29C4×#627C2211yescharacteristic
30#63894C2211yescharacteristic
31#63869C2211yescharacteristic
32#63867—21no—
33#63864C2211yescharacteristic
34#63846—21no—
35#63844—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63840—21no—
40C2×#3718C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C32×#102C2211yescharacteristic
43#63659C2211yescharacteristic
44#63648C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63576C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63564C2211yescharacteristic
61#5685—31no—
62#5681—31no—
63#5569—31no—
64#5559—31no—
65C3×#488—31no—
66C3×C4×SD16—31no—
67#5166—31no—
68#5163—31no—
69#5066—31no—
70#5054—31no—
71#5028—31no—
72#5009—31no—
73#4871—31no—
74#4854—31no—
75#4800—31no—
76#4798—31no—
77#4791—31no—
78#4790—31no—
79#4790—31no—
80#4788—31no—
81#4768D311yescharacteristic, complemented
82#4763—31no—
83#4762—31no—
84#4760—31no—
85#4760—31no—
86#4760—61no—
87#4758D311yescharacteristic, complemented
88#4697—31no—
89C4×#204—31no—
90C8×Dic6—31no—
91C8×Dic6—31no—
92C2×C32×D4C2311yescharacteristic
93C2×#638—21no—
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634—21no—
97C22×C3×Dic3—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627D411yescharacteristic
101C2×#624—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105#3750—21no—
106C4×C3⋊Dic3C2311yescharacteristic
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C3×#217—21no—
109C3×#217—21no—
110C3×#217—21no—
111C3×#214—22no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3C2311yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122#3724—21no—
123#3724D411yescharacteristic
124Dic3⋊Dic3—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130#3722—21no—
131#3722—21no—
132#3722—21no—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136#3718—22no—
137#3717—22no—
138#3365—91noSylow
139C2×C3×SD16—31no—
140C3×#125—31no—
141C3×#124—31no—
142C3×C4×Q8—31no—
143C3×C4×D4—31no—
144#947—31no—
145Q8×Dic3—31no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148C2×#216—31no—
149C2×#216—31no—
150C2×#215—31no—
151#940—31no—
152#940—31no—
153#940—61no—
154#936C2×D311yescharacteristic
155D4×Dic3C2×D311yescharacteristic
156C2×#214C2×D311yescharacteristic
157#929—61no—
158C4×#67—61no—
159C2×#204—31no—
160#893—31no—
161#890—31no—
162#890—61no—
163#890C2×D311yescharacteristic
164#889—61no—
165#889—61no—
166#888—31no—
167#888—31no—
168#888—61no—
169#888—61no—
170#888—61no—
171#887—31no—
172#887—31no—
173#887—61no—
174#887C2×D311yescharacteristic
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—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#106—31no—
190C3×#103—31no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#102—21no—
194C3×#102—31no—
195C3×#102C2×D311yescharacteristic
196C3×#102C2×D311yescharacteristic
197C3×C4×C8—31no—
198C3×C4×C8—31no—
199#835—31no—
200#832—31no—
201#832—31no—
202#832—61no—
203#832C2×D311yescharacteristic
204#821—31no—
205#821—31no—
206#821—31no—
207#821—61no—
208#817—31no—
209#816—31no—
210#816C2×D311yescharacteristic
211#816C2×D311yescharacteristic
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3—61no—
219C8×Dic3C2×D311yescharacteristic
220C8×Dic3C2×D311yescharacteristic
221#810C2×D311yescharacteristic
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#808—31no—
227#808C2×D311yescharacteristic
228#807—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C23×C32—21no—
233C22×C3⋊D3—21no—
234C32×D4—21no—
235C32×D4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238#638—42no—
239#638—81no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—21no—
245#634—42no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—81no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6#4112yes—
259#627—22no—
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—31no—
268#488—91no—
269#486—91no—
270#478—91no—
271#478—91no—
272#475—91no—
273#464—91no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—31no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×D4—21no—
283C2×C3×D4C22×D311yescharacteristic
284C2×C3×D4C22×D311yescharacteristic
285C22×C3×C4—61no—
286C2×#67—61no—
287C2×#67—61no—
288C2×#67—61no—
289C2×#67—61no—
290C2×#67—121no—
291C2×#67—121no—
292C22×Dic3—21no—
293C2×D12—31no—
294C2×D12—31no—
295C2×D12—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6—121no—
303C2×Dic6C22×D311yescharacteristic
304C2×Dic6C22×D311yescharacteristic
305C3×SD16—62no—
306C2×C3×C8—21no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C3×C4⋊C4—21no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C4⋊C4C22×D311yescharacteristic
319C3×C22⋊C4—61no—
320C3×C22⋊C4—61no—
321C3×C22⋊C4—61no—
322C3×C42—31no—
323C3×C42—31no—
324C3×C42—61no—
325#217—21no—
326#217—21no—
327#217—21no—
328#216—62no—
329#216—62no—
330#215—62no—
331#214—22no—
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—61no—
338C4⋊Dic3—21no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3C22×D311yescharacteristic
349C4⋊Dic3C22×D311yescharacteristic
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—121no—
365C4×Dic3—21no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382#204—62no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32C22×D411yescharacteristic
387C2×C3⋊D3—41no—
388C2×C3⋊D3—41no—
389C2×C3⋊D3—41no—
390C32×C4—41no—
391C32×C4C2×#4111yescharacteristic
392C32×C42−1+411yescharacteristic
393C3⋊Dic3—21no—
394C3⋊Dic3—41no—
395C3⋊Dic3#13512yes—
396C3×Dic3—22no—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C2×Q16—91no—
405C2×SD16—31no—
406C2×SD16—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409#127—91no—
410#125—31no—
411#125—91no—
412#125—181no—
413#125—181no—
414#124—31no—
415#124—91no—
416#124—181no—
417#123—181no—
418#123—181no—
419C4×Q8—31no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—181no—
425C4×D4—31no—
426C4×D4—91no—
427C4×D4—181no—
428#107—91no—
429#106—31no—
430#106—91no—
431C4⋊C8—91no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#103—31no—
435#103—31no—
436#103—31no—
437#103—91no—
438#102—31no—
439#102—91no—
440#102—91no—
441#102—91no—
442#102—91no—
443#102D3211yescharacteristic
444C4×C8—31no—
445C4×C8—31no—
446C4×C8—91no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—41no—
450C22×D3—61no—
451C22×D3—61no—
452C22×D3—121no—
453C3×Q8—32no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—41no—
462C3×D4—41no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—41no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—241no—
476C2×C3×C4C23×D311yescharacteristic
477C2×C3×C4C23×D311yescharacteristic
478#67—122no—
479#67—122no—
480#67—242no—
481#67—241no—
482#67—241no—
483#67—242no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—81no—
497C2×Dic3—121no—
498C2×Dic3D3×D411yescharacteristic
499C2×Dic3D3×D411yescharacteristic
500C2×Dic3D3×D411yescharacteristic
501C2×Dic3D3×D411yescharacteristic
502D12—61no—
503D12—61no—
504D12—61no—
505D12—61no—
506D12—121no—
507D12—121no—
508C4×D3—241no—
509C4×D3—241no—
510Dic6—21no—
511Dic6—21no—
512Dic6—21no—
513Dic6—62no—
514Dic6—62no—
515Dic6—122no—
516Dic6—122no—
517Dic6—242no—
518Dic6#23512yes—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—41no—
522C3×C8—61no—
523C3×C8—61no—
524C3⋊C8—21no—
525C3⋊C8—21no—
526C3⋊C8—61no—
527C3⋊C8—61no—
528C3⋊C8—121no—
529C2×C32—81no—
530C2×C32#54811yescharacteristic
531C2×C32C2×#13511yescharacteristic
532C2×C32#57711yescharacteristic
533C3⋊D3—81no—
534C2×Q8—31no—
535C2×Q8—31no—
536C2×Q8—91no—
537C2×Q8—181no—
538C2×D4—91no—
539C2×D4—181no—
540C2×D4—181no—
541C2×D4C2×D3211yescharacteristic
542C22×C4—61no—
543C22×C4—181no—
544Q16—182no—
545SD16—62no—
546SD16—182no—
547C2×C8—31no—
548C2×C8—31no—
549C2×C8—91no—
550C2×C8C2×D3211yescharacteristic
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4C2×D3211yescharacteristic
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C22⋊C4—181no—
573C42—31no—
574C42—31no—
575C42—61no—
576C42—91no—
577C42—181no—
578C42—181no—
579C42—181no—
580C22×C3—21no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3—81no—
590C22×C3C2×D3×D411yescharacteristic
591C22×C3C2×D3×D411yescharacteristic
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—121no—
596C2×D3—121no—
597C2×D3—121no—
598C2×D3—241no—
599C2×D3—241no—
600C2×D3—241no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—62no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—81no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4C2×#23511yescharacteristic
615C3×C4D3×#4111yescharacteristic
616C3×C4#101011yescharacteristic
617C3×C4#101011yescharacteristic
618Dic3—21no—
619Dic3—21no—
620Dic3—21no—
621Dic3—21no—
622Dic3—22no—
623Dic3—32no—
624Dic3—32no—
625Dic3—41no—
626Dic3—41no—
627Dic3—41no—
628Dic3—62no—
629Dic3—62no—
630Dic3—61no—
631Dic3—61no—
632Dic3—121no—
633Dic3—121no—
634Dic3—241no—
635C32#336511yescharacteristic, complemented, Sylow
636C23—21no—
637C23—181no—
638Q8—32no—
639Q8—61no—
640Q8—61no—
641Q8—61no—
642Q8—182no—
643Q8—362no—
644D4—21no—
645D4—21no—
646D4—181no—
647D4—181no—
648D4—362no—
649D4—721no—
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—61no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—181no—
662C2×C4—241no—
663C2×C4—721no—
664C2×C4C22×D3211yescharacteristic
665C8—21no—
666C8—61no—
667C8—61no—
668C8—181no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—81no—
673C2×C3—81no—
674C2×C3—161no—
675C2×C3#555211yescharacteristic
676C2×C3#567711yescharacteristic
677C2×C3#576211yescharacteristic
678C2×C3D3×#13511yescharacteristic
679C2×C3D3×#13511yescharacteristic
680C2×C3#577011yescharacteristic
681D3—241no—
682D3—241no—
683D3—481no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—361no—
688C22—361no—
689C22—361no—
690C22D32×D411yescharacteristic
691C4—41no—
692C4—62no—
693C4—61no—
694C4—61no—
695C4—61no—
696C4—61no—
697C4—92no—
698C4—121no—
699C4—121no—
700C4—121no—
701C4—181no—
702C4—361no—
703C4D3×#23511yescharacteristic
704C4#6430911yescharacteristic
705C3—21no—
706C3#7962411yescharacteristic, complemented
707C3#8163511yescharacteristic, complemented
708C2—81no—
709C2—721no—
710C2#1059407311yescharacteristic
711C2#1059473011yescharacteristic
712C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#64149C22
hypercenter#102D32
hypocenterC32#3365
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
2. #10594322C2semidirect
4. C3×#4768C2semidirect
5. C3×#4758C2semidirect
7. #10591442C2semidirect
8. #10591409C2semidirect
9. #10590872C2semidirect
10. #10590792C2semidirect
11. #10590790C2semidirect
12. C8×#627C2semidirect
13. #10590536C2semidirect
14. #10590497C2semidirect
15. #10590470C2semidirect
81. #4768D3semidirect
87. #4758D3semidirect
635. C32#3365semidirect
706. C3#79624semidirect
707. C3#81635semidirect

Maximal subgroups

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

subgroupindex
#105952102
#105943222
#105924592
C3×#47682
C3×#47582
#105914442
#105914422
#105914092
#105908722
#105907922
#105907902
C8×#6272
#105905362
#105904972
#105904702
#816353
#796243