Finite Group Databasebeta

← #11895276

Subgroups — #11895276

Order 1152.

754 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594485C211yesmaximal, characteristic, complemented
2#10594350C211yesmaximal, characteristic, complemented
3#10592569C211yesmaximal, characteristic, complemented
4C3×#4857C211yesmaximal, characteristic, complemented
5C3×#4852C211yesmaximal, characteristic, complemented
6#10590872C211yesmaximal, characteristic, complemented
7#10590754C211yesmaximal, characteristic
8#10590748C211yesmaximal, characteristic, complemented
9#10590644C211yesmaximal, characteristic, complemented
10#10590567C211yesmaximal, characteristic, complemented
11#10590544C211yesmaximal, characteristic, complemented
12#10590537C211yesmaximal, characteristic, complemented
13#10590534C211yesmaximal, characteristic
14#10590459C211yesmaximal, characteristic
15#10590453C211yesmaximal, characteristic, complemented
16#81215—31nomaximal
17#79620—31nomaximal
18#64102C2211yescharacteristic
19#64097C2211yescharacteristic
20C2×C3×#204C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#890C2211yescharacteristic
23C3×#887C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C4×#627C2211yescharacteristic
26#63899—21no—
27#63898C2211yescharacteristic
28#63896—21no—
29Dic3×D12C2211yescharacteristic
30D3×Dic3⋊C4—21no—
31#63874—21no—
32#63873C2211yescharacteristic
33#63869C2211yescharacteristic
34#63868—21no—
35#63868—21no—
36#63865—21no—
37#63864C2211yescharacteristic
38#63864C2211yescharacteristic
39#63857—21no—
40C2×#3715C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C32×#106C2211yescharacteristic
43#63648C2211yescharacteristic
44#63641C2211yescharacteristic
45#63636C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5690—31no—
62#5568—31no—
63#5568—31no—
64#5539—31no—
65C3×#479—31no—
66C3×C4×SD16—31no—
67#5165—31no—
68#5162—31no—
69#5068—31no—
70C4×#215—31no—
71#5022—31no—
72#5016—31no—
73#4877—31no—
74#4872—31no—
75#4870—31no—
76#4870—31no—
77#4870—61no—
78#4857D311yescharacteristic, complemented
79#4852D311yescharacteristic, complemented
80#4844—31no—
81#4830—31no—
82#4819—31no—
83#4818—31no—
84#4800—31no—
85#4800—31no—
86#4792—31no—
87#4792—31no—
88#4758—31no—
89#4756—31no—
90#4697—31no—
91C8×Dic6—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627D411yescharacteristic
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105#3752—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×(C2×D3)⋊C4—21no—
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3C2311yescharacteristic
113C3×Dic3⋊C4—21no—
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
116C3×C4×Dic3—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#3724—21no—
125#3724—21no—
126#3724D411yescharacteristic
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130#3722—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136#3715—22no—
137#3714—22no—
138#3360—91noSylow
139C2×C3×SD16—31no—
140C3×#125—31no—
141C3×C4×Q8—31no—
142C3×C4×Q8—31no—
143C3×C4×D4—31no—
144#947—31no—
145#947—31no—
146#944—31no—
147#944—31no—
148C2×#215—31no—
149D4×Dic3—31no—
150D4×Dic3—31no—
151C2×#214—31no—
152C2×#213—31no—
153#924—61no—
154C2×Dic3⋊C4—61no—
155C2×D24—31no—
156C2×#204C2×D311yescharacteristic
157#898—61no—
158#898—61no—
159#897—61no—
160#896—61no—
161#896—61no—
162#896—61no—
163#896—61no—
164#893—31no—
165#893—31no—
166#893—31no—
167#893—61no—
168#893C2×D311yescharacteristic
169D3×C4⋊C4—61no—
170#890—31no—
171#890C2×D311yescharacteristic
172#888—31no—
173#888—31no—
174#888—61no—
175#887C2×D311yescharacteristic
176#887C2×D311yescharacteristic
177#878—61no—
178#878—61no—
179#876—61no—
180#876—61no—
181#875—31no—
182#875—31no—
183C4×D12—31no—
184#872—61no—
185#872—61no—
186#870—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C3×#107—31no—
190C3×#106—21no—
191C3×#106C2×D311yescharacteristic
192C3×#106C2×D311yescharacteristic
193C3×C4⋊C8—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#821—31no—
203#821—31no—
204#821—31no—
205#821—61no—
206#816—31no—
207#816—31no—
208#816C2×D311yescharacteristic
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#810C2×D311yescharacteristic
220#810C2×D311yescharacteristic
221#809—31no—
222#809—31no—
223#809—31no—
224#809—61no—
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⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240C4⋊(C3⋊D3)—21no—
241C4⋊(C3⋊D3)—21no—
242C4×C3⋊D3—42no—
243#634—81no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12#4112yes—
253C3×C4×D3—81no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258#627—22no—
259D3×Dic3—42no—
260D3×Dic3—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#556—91no—
266#554—91no—
267#488—91no—
268#488—91no—
269#487—91no—
270#479—31no—
271#479—91no—
272#476—91no—
273#463—91no—
274#463—91no—
275#461—91no—
276C8×Q8—91no—
277C4×SD16—31no—
278C4×SD16—91no—
279C4×D8—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×D4—31no—
283C22×C3×C4—61no—
284C22×Dic3—61no—
285C22×Dic3—61no—
286C2×D12—31no—
287C2×D12—31no—
288C2×D12—61no—
289C2×D12C22×D311yescharacteristic
290C2×C4×D3—21no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—121no—
296C2×Dic6—31no—
297C2×Dic6—31no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—121no—
301C2×Dic6C22×D311yescharacteristic
302C2×Dic6C22×D311yescharacteristic
303C3×SD16—62no—
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
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×C4⋊C4C22×D311yescharacteristic
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C22⋊C4—61no—
321C3×C42—31no—
322C3×C42—31no—
323C3×C42—61no—
324C3×C42—61no—
325#217—61no—
326#217—61no—
327#215—62no—
328#214—62no—
329#213—62no—
330(C2×D3)⋊C4—21no—
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—61no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—121no—
344C4⋊Dic3—21no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
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—
368Dic3⋊C4—121no—
369C4×Dic3—21no—
370C4×Dic3—21no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—61no—
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
381D24—62no—
382#204—22no—
383C22×C32C22×D411yescharacteristic
384C2×C3⋊D3—41no—
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
387C2×C3×D3—22no—
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#13512yes—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C2×SD16—31no—
405C2×SD16—91no—
406C2×D8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—91no—
409#126—181no—
410#126—181no—
411#125—31no—
412#125—91no—
413#124—91no—
414#124—91no—
415C22⋊Q8—181no—
416C22⋊Q8—181no—
417C22⋊Q8—181no—
418C22⋊Q8—181no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—91no—
422C4×D4—31no—
423C4×D4—91no—
424C4×D4—91no—
425C4×D4—91no—
426#117—181no—
427C2×C4⋊C4—181no—
428#107—31no—
429#106—91no—
430#106D3211yescharacteristic
431C4⋊C8—31no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#103—31no—
435#103—31no—
436#103—31no—
437#103—91no—
438#103—91no—
439#103—91no—
440#102—31no—
441#102—91no—
442#102—91no—
443#102—91no—
444C4×C8—31no—
445C4×C8—91no—
446C4×C8—91no—
447C23×C3—61no—
448C22×D3—21no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—121no—
452C3×Q8—61no—
453C3×Q8—61no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×D4—32no—
457C3×D4—61no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—241no—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—31no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—121no—
487C2×Dic3—122no—
488C2×Dic3—241no—
489C2×Dic3D3×D411yescharacteristic
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493D12—21no—
494D12—62no—
495D12—61no—
496D12—61no—
497D12—61no—
498D12—61no—
499D12—121no—
500D12#23512yes—
501C4×D3—81no—
502C4×D3—122no—
503C4×D3—122no—
504C4×D3—122no—
505C4×D3—242no—
506C4×D3—241no—
507Dic6—21no—
508Dic6—21no—
509Dic6—21no—
510Dic6—21no—
511Dic6—62no—
512Dic6—62no—
513Dic6—241no—
514Dic6—241no—
515Dic6—242no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—41no—
519C3×C8—61no—
520C3×C8—61no—
521C3⋊C8—21no—
522C3⋊C8—21no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—121no—
526C2×C32#54811yescharacteristic
527C2×C32C2×#13511yescharacteristic
528C2×C32#57711yescharacteristic
529C3⋊D3—81no—
530C3×D3—42no—
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—91no—
534C2×Q8—181no—
535C2×D4—31no—
536C2×D4—91no—
537C22×C4—61no—
538C22×C4—181no—
539C22×C4—181no—
540C22×C4—181no—
541SD16—62no—
542SD16—182no—
543D8—182no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8—91no—
547C2×C8C2×D3211yescharacteristic
548C4⋊C4—31no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4C2×D3211yescharacteristic
563C4⋊C4C2×D3211yescharacteristic
564C22⋊C4—61no—
565C22⋊C4—181no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—31no—
574C42—61no—
575C42—61no—
576C42—91no—
577C22×C3—21no—
578C22×C3—62no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3C2×D3×D411yescharacteristic
582C22×C3C2×D3×D411yescharacteristic
583C2×D3—22no—
584C2×D3—41no—
585C2×D3—41no—
586C2×D3—122no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—241no—
594C2×D3—241no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—81no—
606C3×C4—81no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4—121no—
610C3×C4C2×#23511yescharacteristic
611C3×C4#100711yescharacteristic
612C3×C4D3×#4111yescharacteristic
613C3×C4#101011yescharacteristic
614Dic3—21no—
615Dic3—21no—
616Dic3—21no—
617Dic3—21no—
618Dic3—32no—
619Dic3—32no—
620Dic3—41no—
621Dic3—41no—
622Dic3—41no—
623Dic3—62no—
624Dic3—61no—
625Dic3—61no—
626Dic3—121no—
627Dic3—121no—
628Dic3—121no—
629Dic3—241no—
630C32#336011yescharacteristic, complemented, Sylow
631C23—61no—
632C23—181no—
633Q8—61no—
634Q8—61no—
635Q8—61no—
636Q8—61no—
637Q8—182no—
638Q8—721no—
639D4—32no—
640D4—61no—
641D4—181no—
642D4—181no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—181no—
655C2×C4—241no—
656C2×C4—362no—
657C2×C4—362no—
658C2×C4—721no—
659C2×C4C22×D3211yescharacteristic
660C8—21no—
661C8—61no—
662C8—61no—
663C8—181no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—122no—
668C2×C3#555211yescharacteristic
669C2×C3#563311yescharacteristic
670C2×C3#576211yescharacteristic
671C2×C3D3×#13511yescharacteristic
672C2×C3D3×#13511yescharacteristic
673C2×C3#577811yescharacteristic
674D3—42no—
675D3—242no—
676D3—241no—
677D3—241no—
678C22—62no—
679C22—121no—
680C22—121no—
681C22—361no—
682C22—361no—
683C22—361no—
684C22D32×D411yescharacteristic
685C4—41no—
686C4—41no—
687C4—61no—
688C4—61no—
689C4—61no—
690C4—61no—
691C4—92no—
692C4—121no—
693C4—121no—
694C4—121no—
695C4—181no—
696C4—361no—
697C4D3×#23511yescharacteristic
698C4#6431511yescharacteristic
699C3—21no—
700C3#7962011yescharacteristic, complemented
701C3#8121511yescharacteristic, complemented
702C2—122no—
703C2—721no—
704C2#1059437511yescharacteristic
705C2#1059474711yescharacteristic
706C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenter#106D32
hypocenterC32#3360
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
1. #10594485C2semidirect
2. #10594350C2semidirect
3. #10592569C2semidirect
4. C3×#4857C2semidirect
5. C3×#4852C2semidirect
6. #10590872C2semidirect
8. #10590748C2semidirect
9. #10590644C2semidirect
10. #10590567C2semidirect
11. #10590544C2semidirect
12. #10590537C2semidirect
15. #10590453C2semidirect
78. #4857D3semidirect
79. #4852D3semidirect
630. C32#3360semidirect
700. C3#79620semidirect
701. C3#81215semidirect

Maximal subgroups

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

subgroupindex
#105944852
#105943502
#105925692
C3×#48572
C3×#48522
#105908722
#105907542
#105907482
#105906442
#105905672
#105905442
#105905372
#105905342
#105904592
#105904532
#812153
#796203