Finite Group Databasebeta

← #11895688

Subgroups — #11895688

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594582C211yesmaximal, characteristic
2#10594322C211yesmaximal, characteristic, complemented
3#10592553C211yesmaximal, characteristic, complemented
4C3×#4871C211yesmaximal, characteristic, complemented
5C3×#4852C211yesmaximal, characteristic, complemented
6#10590876C211yesmaximal, characteristic
7#10590863C211yesmaximal, characteristic, complemented
8#10590859C211yesmaximal, characteristic, complemented
9#10590644C211yesmaximal, characteristic, complemented
10#10590552C211yesmaximal, characteristic
11#10590542C211yesmaximal, characteristic, complemented
12#10590533C211yesmaximal, characteristic, complemented
13#10590532C211yesmaximal, characteristic, complemented
14#10590482C211yesmaximal, characteristic, complemented
15#10590475C211yesmaximal, characteristic, complemented
16#81151—31nomaximal
17#79624—31nomaximal
18#64097C2211yescharacteristic
19#64096C2211yescharacteristic
20C2×C3×#204C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#890C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C4×#627C2211yescharacteristic
26#63915—21no—
27#63914C2211yescharacteristic
28#63905—21no—
29#63905—21no—
30C4×#625—21no—
31#63869C2211yescharacteristic
32#63867—21no—
33#63860C2211yescharacteristic
34#63860C2211yescharacteristic
35#63846—21no—
36#63844—21no—
37#63843C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63840—21no—
40C2×#3719C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C32×#106C2211yescharacteristic
43#63643C2211yescharacteristic
44#63641C2211yescharacteristic
45#63637C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5685—31no—
62#5569—31no—
63#5559—31no—
64#5559—31no—
65C3×#478—31no—
66C3×C4×SD16—31no—
67#5166—31no—
68#5163—31no—
69#5068—31no—
70#5028—31no—
71C4×#214—31no—
72#5009—31no—
73#4891—31no—
74#4873—31no—
75#4871D311yescharacteristic, complemented
76#4854—31no—
77#4854—31no—
78#4854—61no—
79#4852D311yescharacteristic, complemented
80#4845—31no—
81#4830—31no—
82#4790—31no—
83#4788—31no—
84#4768—31no—
85#4768—31no—
86#4767—31no—
87#4762—31no—
88#4760—31no—
89#4760—31no—
90#4697—31no—
91C8×Dic6—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627D411yescharacteristic
100C2×#625—21no—
101C2×#625—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3—21no—
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
122C3×#204—22no—
123#3724—21no—
124#3724D411yescharacteristic
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3719—22no—
137#3715—22no—
138#3365—91noSylow
139C2×C3×SD16—31no—
140C3×#125—31no—
141C3×C4×Q8—31no—
142C3×C4×D4—31no—
143C3×C4×D4—31no—
144Q8×Dic3—31no—
145Q8×Dic3—31no—
146C2×#216—31no—
147C2×#215—31no—
148#940—31no—
149#940—31no—
150#936—31no—
151#936—31no—
152C2×#214—31no—
153#929—61no—
154#929—61no—
155C4×#67—61no—
156C4×#67—61no—
157C2×Dic12—31no—
158C2×#204C2×D311yescharacteristic
159#893C2×D311yescharacteristic
160#893C2×D311yescharacteristic
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—31no—
174#887—61no—
175#887—61no—
176#887C2×D311yescharacteristic
177#885—61no—
178#885—61no—
179#883—61no—
180#883—61no—
181#875—31no—
182#875—31no—
183#870—31no—
184#870—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#107—31no—
190C3×#106—21no—
191C3×#106C2×D311yescharacteristic
192C3×#106C2×D311yescharacteristic
193C3×C4⋊C8—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#821—31no—
203#821—31no—
204#821C2×D311yescharacteristic
205#816—31no—
206#816—31no—
207#816—31no—
208#816—61no—
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—61no—
213Dic3⋊C8C2×D311yescharacteristic
214C8×Dic3—31no—
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3C2×D311yescharacteristic
218#810—31no—
219#810—31no—
220#810—31no—
221#810—61no—
222#810C2×D311yescharacteristic
223#809—31no—
224#809C2×D311yescharacteristic
225#809C2×D311yescharacteristic
226#808—31no—
227#808—31no—
228#808—61no—
229#807C2×D311yescharacteristic
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241#634—21no—
242#634—21no—
243#634—42no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×D12—21no—
251C3×D12—21no—
252C3×D12—21no—
253C3×D12—21no—
254C3×C4×D3—81no—
255C3×C4×D3—81no—
256C3×Dic6—21no—
257C3×Dic6#4112yes—
258#627—22no—
259#625—42no—
260#625—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—31no—
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×D4—31no—
282C2×C3×D4—31no—
283C22×C3×C4—61no—
284C22×C3×C4—61no—
285C2×#67—61no—
286C2×#67—61no—
287C2×#67—61no—
288C2×#67—61no—
289C2×D12C22×D311yescharacteristic
290C2×D12C22×D311yescharacteristic
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×Dic6—31no—
294C2×Dic6—31no—
295C2×Dic6—31no—
296C2×Dic6—31no—
297C2×Dic6—61no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—121no—
301C2×Dic6C22×D311yescharacteristic
302C3×SD16—62no—
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—21no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
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#217—61no—
325#217—61no—
326#217—61no—
327#216—62no—
328#215—62no—
329#214—62no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336C4⋊Dic3—21no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3C22×D311yescharacteristic
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—121no—
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
381Dic12—62no—
382#204—22no—
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C32×C4—41no—
391C32×C4—41no—
392C32×C4C2×#4111yescharacteristic
393C32×C42−1+411yescharacteristic
394C3⋊Dic3—21no—
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
397C3⋊Dic3#13512yes—
398C3×Dic3—22no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—21no—
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—91no—
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—31no—
427C4×D4—181no—
428#107—31no—
429#106—91no—
430#106D3211yescharacteristic
431C4⋊C8—31no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#103—31no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—31no—
440#102—31no—
441#102—91no—
442#102—91no—
443#102—91no—
444C4×C8—31no—
445C4×C8—91no—
446C4×C8—91no—
447C23×C3—61no—
448C23×C3—61no—
449C22×D3—21no—
450C22×D3—21no—
451C3×Q8—32no—
452C3×Q8—61no—
453C3×D4—61no—
454C3×D4—61no—
455C3×D4—61no—
456C3×D4—61no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—241no—
471C2×C3×C4—241no—
472C2×C3×C4C23×D311yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474#67—122no—
475#67—122no—
476#67—241no—
477#67—241no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—121no—
491C2×Dic3—121no—
492C2×Dic3D3×D411yescharacteristic
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496D12—21no—
497D12—21no—
498D12—21no—
499D12—21no—
500C4×D3—81no—
501C4×D3—81no—
502Dic6—21no—
503Dic6—62no—
504Dic6—62no—
505Dic6—62no—
506Dic6—61no—
507Dic6—61no—
508Dic6—61no—
509Dic6—61no—
510Dic6—121no—
511Dic6—122no—
512Dic6—122no—
513Dic6—242no—
514Dic6#23512yes—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—41no—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C2×C32#54811yescharacteristic
526C2×C32C2×#13511yescharacteristic
527C2×C32#57711yescharacteristic
528C3×D3—81no—
529C3×D3—81no—
530C2×Q8—31no—
531C2×Q8—91no—
532C2×Q8—91no—
533C2×Q8—181no—
534C2×D4—31no—
535C2×D4—31no—
536C2×D4—181no—
537C2×D4—181no—
538C22×C4—61no—
539C22×C4—61no—
540Q16—182no—
541SD16—62no—
542SD16—182no—
543C2×C8—31no—
544C2×C8—31no—
545C2×C8—91no—
546C2×C8C2×D3211yescharacteristic
547C4⋊C4—31no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4C2×D3211yescharacteristic
562C4⋊C4C2×D3211yescharacteristic
563C22⋊C4—61no—
564C22⋊C4—61no—
565C22⋊C4—181no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C42—31no—
570C42—31no—
571C42—61no—
572C42—91no—
573C42—181no—
574C42—181no—
575C42—181no—
576C22×C3—21no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3—121no—
582C22×C3—121no—
583C22×C3C2×D3×D411yescharacteristic
584C22×C3C2×D3×D411yescharacteristic
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—62no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—81no—
603C3×C4—81no—
604C3×C4—121no—
605C3×C4C2×#23511yescharacteristic
606C3×C4#100711yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4#101011yescharacteristic
609Dic3—21no—
610Dic3—21no—
611Dic3—21no—
612Dic3—21no—
613Dic3—22no—
614Dic3—32no—
615Dic3—32no—
616Dic3—41no—
617Dic3—62no—
618Dic3—61no—
619Dic3—61no—
620Dic3—121no—
621Dic3—122no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—241no—
627C32#336511yescharacteristic, complemented, Sylow
628C23—61no—
629C23—61no—
630Q8—32no—
631Q8—61no—
632Q8—182no—
633Q8—181no—
634Q8—181no—
635Q8—362no—
636D4—61no—
637D4—61no—
638D4—61no—
639D4—61no—
640D4—362no—
641D4—721no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—241no—
655C2×C4—241no—
656C2×C4C22×D3211yescharacteristic
657C8—21no—
658C8—61no—
659C8—61no—
660C8—181no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—241no—
665C2×C3—241no—
666C2×C3#555211yescharacteristic
667C2×C3#563311yescharacteristic
668C2×C3#576211yescharacteristic
669C2×C3D3×#13511yescharacteristic
670C2×C3D3×#13511yescharacteristic
671C2×C3#577511yescharacteristic
672D3—81no—
673D3—81no—
674C22—121no—
675C22—121no—
676C22—121no—
677C22—121no—
678C22—121no—
679C22—121no—
680C22D32×D411yescharacteristic
681C4—41no—
682C4—41no—
683C4—62no—
684C4—61no—
685C4—61no—
686C4—61no—
687C4—61no—
688C4—92no—
689C4—121no—
690C4—181no—
691C4—361no—
692C4—361no—
693C4D3×#23511yescharacteristic
694C4#6431511yescharacteristic
695C3—21no—
696C3#7962411yescharacteristic, complemented
697C3#8115111yescharacteristic, complemented
698C2—241no—
699C2—241no—
700C2#1059437511yescharacteristic
701C2#1059474711yescharacteristic
702C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#63914C22
hypercenter#106D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594322C2semidirect
3. #10592553C2semidirect
4. C3×#4871C2semidirect
5. C3×#4852C2semidirect
7. #10590863C2semidirect
8. #10590859C2semidirect
9. #10590644C2semidirect
11. #10590542C2semidirect
12. #10590533C2semidirect
13. #10590532C2semidirect
14. #10590482C2semidirect
15. #10590475C2semidirect
75. #4871D3semidirect
79. #4852D3semidirect
627. C32#3365semidirect
696. C3#79624semidirect
697. C3#81151semidirect

Maximal subgroups

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

subgroupindex
#105945822
#105943222
#105925532
C3×#48712
C3×#48522
#105908762
#105908632
#105908592
#105906442
#105905522
#105905422
#105905332
#105905322
#105904822
#105904752
#811513
#796243