Finite Group Databasebeta

← #11895903

Subgroups — #11895903

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594376C211yesmaximal, characteristic, complemented
2#10594335C211yesmaximal, characteristic, complemented
3#10592574C211yesmaximal, characteristic, complemented
4C3×#4875C211yesmaximal, characteristic, complemented
5C3×#4872C211yesmaximal, characteristic
6#10590890C211yesmaximal, characteristic, complemented
7#10590785C211yesmaximal, characteristic, complemented
8#10590755C211yesmaximal, characteristic
9#10590751C211yesmaximal, characteristic
10#10590559C211yesmaximal, characteristic, complemented
11#10590555C211yesmaximal, characteristic, complemented
12#10590541C211yesmaximal, characteristic, complemented
13#10590531C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#81100—31nomaximal
17#79571—31nomaximal
18C2×D3×Dic6—21no—
19#64097C2211yescharacteristic
20#64096C2211yescharacteristic
21C2×C3×D24C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63918C2211yescharacteristic
27C4×#627C2211yescharacteristic
28#63898C2211yescharacteristic
29#63896—21no—
30Dic3×D12C2211yescharacteristic
31#63887—21no—
32#63866C2211yescharacteristic
33#63863C2211yescharacteristic
34#63862—21no—
35#63860C2211yescharacteristic
36#63859—21no—
37#63855—21no—
38#63851—21no—
39#63851—21no—
40C2×#3716C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C32×#107C2211yescharacteristic
43#63643C2211yescharacteristic
44#63641C2211yescharacteristic
45#63637C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63555C2211yescharacteristic
60#63554C2211yescharacteristic
61#5727—31no—
62#5568—31no—
63#5542—31no—
64D4×Dic6—31no—
65C3×#477—31no—
66C3×C4×D8—31no—
67#5153—31no—
68#5153—31no—
69#5089—31no—
70#5026—31no—
71#5019—31no—
72#5007—31no—
73#4890—31no—
74#4889—31no—
75#4875—31no—
76#4875—31no—
77#4875—61no—
78#4875D311yescharacteristic, complemented
79#4872D311yescharacteristic
80#4844—31no—
81#4828—31no—
82#4819—31no—
83#4818—31no—
84#4794—31no—
85#4792—31no—
86#4765—31no—
87#4765—31no—
88#4757—31no—
89#4757—31no—
90#4681—31no—
91#4679—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#627D411yescharacteristic
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×Dic6—44no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×D24—22no—
125#3724D411yescharacteristic
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3D411yescharacteristic
130Dic3⋊Dic3D411yescharacteristic
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137#3716—22no—
138#3715—22no—
139#3367—91noSylow
140C2×D3×Q8—61no—
141C22×Dic6—61no—
142C2×C3×D8—31no—
143C3×C4⋊Q8—31no—
144C3×C4×Q8—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147#947—31no—
148#946—61no—
149#944—31no—
150C2×#215—31no—
151#936—31no—
152#936—31no—
153D4×Dic3—31no—
154D4×Dic3—31no—
155C2×#214—31no—
156C2×#214—31no—
157#926—61no—
158#924—61no—
159#924—61no—
160C2×D24C2×D311yescharacteristic
161C2×#204—31no—
162#898—61no—
163#896—61no—
164#896—61no—
165#896—61no—
166#893—31no—
167#893C2×D311yescharacteristic
168#893C2×D311yescharacteristic
169#888—31no—
170#888—31no—
171#888—31no—
172#888—61no—
173#888C2×D311yescharacteristic
174#887—31no—
175#887—31no—
176#887—61no—
177#887C2×D311yescharacteristic
178#879—61no—
179#879—61no—
180#878—61no—
181#878—61no—
182#876—61no—
183#875—31no—
184C4×D12—31no—
185#872—61no—
186#869—31no—
187#869—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C3×#107—21no—
191C3×#107—31no—
192C3×#107C2×D311yescharacteristic
193C3×#107C2×D311yescharacteristic
194C3×C4⋊C8—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×C4×C8—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#821—31no—
204#816—31no—
205#816—31no—
206#816—31no—
207#816—31no—
208#816—61no—
209#816C2×D311yescharacteristic
210#815—31no—
211#815—31no—
212#815—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—61no—
217Dic3⋊C8C2×D311yescharacteristic
218C8×Dic3C2×D311yescharacteristic
219#810—31no—
220#810—31no—
221#810—31no—
222#810—61no—
223#810C2×D311yescharacteristic
224#809—31no—
225#809C2×D311yescharacteristic
226#809C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—61no—
230#807C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
232#803—31no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242#634—21no—
243#634—21no—
244#634—42no—
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—21no—
253C3×D12—21no—
254C3×D12#4112yes—
255C3×C4×D3—42no—
256C3×C4×D3—42no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—42no—
260#627—22no—
261#627—42no—
262D3×Dic3—42no—
263D3×Dic3—42no—
264C32×C8—21no—
265C3⋊(C3⋊C8)—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#556—91no—
269D4×Q8—91no—
270#489—91no—
271#489—91no—
272#487—91no—
273#477—31no—
274#477—91no—
275#474—91no—
276#463—91no—
277#463—91no—
278#461—91no—
279#446—91no—
280#440—91no—
281#440—91no—
282C4×D8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—61no—
285C2×C3×D4—31no—
286C2×C3×D4—31no—
287C22×C3×C4—61no—
288C22×C3×C4—61no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291D3×Q8—124no—
292C2×D12C22×D311yescharacteristic
293C2×D12C22×D311yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×Dic6—21no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—31no—
302C2×Dic6—31no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—121no—
309C2×Dic6—124no—
310C2×Dic6C22×D311yescharacteristic
311C3×D8—62no—
312C2×C3×C8—21no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—31no—
330C3×C42—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—61no—
335#217—61no—
336#217—61no—
337#215—62no—
338#214—62no—
339#214—62no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—121no—
371Dic3⋊C4—121no—
372C4×Dic3—21no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—121no—
379C4×Dic3C22×D311yescharacteristic
380C4×Dic3C22×D311yescharacteristic
381C2×C3⋊C8—31no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—61no—
384C2×C3⋊C8C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386D24—22no—
387#204—62no—
388C22×C32C22×D411yescharacteristic
389C2×C3×D3—22no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C42−1+411yescharacteristic
399C3⋊Dic3—21no—
400C3⋊Dic3—21no—
401C3⋊Dic3—41no—
402C3⋊Dic3—41no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3AGL(1,ℤ/8)12yes—
409C22×Q8—181no—
410C2×SD16—91no—
411C2×SD16—91no—
412C2×D8—31no—
413C4⋊Q8—31no—
414C4⋊Q8—91no—
415C4⋊Q8—91no—
416C4⋊Q8—91no—
417#126—181no—
418#126—181no—
419#124—91no—
420#124—91no—
421C22⋊Q8—181no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C22⋊Q8—181no—
425C4×Q8—31no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×D4—31no—
429C4×D4—31no—
430C4×D4—91no—
431C4×D4—91no—
432#117—181no—
433#107—31no—
434#107—91no—
435#107D3211yescharacteristic
436C4⋊C8—31no—
437C4⋊C8—91no—
438C4⋊C8—91no—
439#103—31no—
440#103—31no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103—91no—
445#102—31no—
446#102—31no—
447#102—91no—
448#102—91no—
449#97—91no—
450#97—91no—
451C4×C8—31no—
452C23×C3—61no—
453C23×C3—61no—
454C22×D3—21no—
455C22×D3—21no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—122no—
459C3×D4—32no—
460C3×D4—61no—
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—122no—
477C2×C3×C4—122no—
478C2×C3×C4C23×D311yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3—122no—
495C2×Dic3—122no—
496C2×Dic3D3×D411yescharacteristic
497C2×Dic3D3×D411yescharacteristic
498C2×Dic3D3×D411yescharacteristic
499C2×Dic3D3×D411yescharacteristic
500D12—21no—
501D12—21no—
502D12—21no—
503D12#23512yes—
504C4×D3—42no—
505C4×D3—42no—
506C4×D3—122no—
507C4×D3—122no—
508Dic6—21no—
509Dic6—21no—
510Dic6—42no—
511Dic6—62no—
512Dic6—62no—
513Dic6—62no—
514Dic6—61no—
515Dic6—61no—
516Dic6—61no—
517Dic6—61no—
518Dic6—121no—
519Dic6—122no—
520Dic6—122no—
521Dic6—122no—
522Dic6—122no—
523Dic6—242no—
524C3×C8—21no—
525C3×C8—21no—
526C3×C8—41no—
527C3×C8—61no—
528C3×C8—61no—
529C3⋊C8—21no—
530C3⋊C8—21no—
531C3⋊C8—61no—
532C3⋊C8—61no—
533C3⋊C8—121no—
534C2×C32#54811yescharacteristic
535C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
536C2×C32#57811yescharacteristic
537C3×D3—42no—
538C3×D3—81no—
539C2×Q8—31no—
540C2×Q8—61no—
541C2×Q8—91no—
542C2×Q8—91no—
543C2×Q8—181no—
544C2×Q8—181no—
545C2×Q8—364no—
546C2×D4—31no—
547C2×D4—31no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—181no—
551C22×C4—181no—
552SD16—182no—
553SD16—182no—
554D8—62no—
555C2×C8—31no—
556C2×C8—31no—
557C2×C8—91no—
558C2×C8C2×D3211yescharacteristic
559C4⋊C4—31no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—91no—
563C4⋊C4—91no—
564C4⋊C4—91no—
565C4⋊C4—91no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4C2×D3211yescharacteristic
572C4⋊C4C2×D3211yescharacteristic
573C22⋊C4—61no—
574C22⋊C4—61no—
575C22⋊C4—181no—
576C22⋊C4—181no—
577C22⋊C4—181no—
578C22⋊C4—181no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C42—31no—
582C42—31no—
583C42—61no—
584C42—91no—
585C42—181no—
586C22×C3—21no—
587C22×C3—62no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3C2×D3×D411yescharacteristic
594C22×C3C2×D3×D411yescharacteristic
595C2×D3—22no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—41no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—32no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—81no—
612C3×C4—81no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4C2×#23511yescharacteristic
616C3×C4#100711yescharacteristic
617C3×C4D3×#4111yescharacteristic
618C3×C4#101011yescharacteristic
619Dic3—21no—
620Dic3—21no—
621Dic3—21no—
622Dic3—41no—
623Dic3—41no—
624Dic3—62no—
625Dic3—61no—
626Dic3—61no—
627Dic3—61no—
628Dic3—61no—
629Dic3—121no—
630Dic3—122no—
631Dic3—121no—
632Dic3—121no—
633Dic3—121no—
634Dic3—121no—
635Dic3—241no—
636Dic3#91112yes—
637C32#336711yescharacteristic, complemented, Sylow
638C23—61no—
639C23—61no—
640Q8—61no—
641Q8—61no—
642Q8—122no—
643Q8—182no—
644Q8—181no—
645Q8—181no—
646Q8—362no—
647Q8—362no—
648D4—32no—
649D4—61no—
650D4—61no—
651D4—61no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—91no—
661C2×C4—91no—
662C2×C4—122no—
663C2×C4—122no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—362no—
667C2×C4—362no—
668C2×C4C22×D3211yescharacteristic
669C8—21no—
670C8—61no—
671C8—61no—
672C8—181no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—122no—
677C2×C3—241no—
678C2×C3#555211yescharacteristic
679C2×C3#563311yescharacteristic
680C2×C3C2×#91111yescharacteristic
681C2×C3#576611yescharacteristic
682C2×C3#577111yescharacteristic
683C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
684D3—42no—
685D3—81no—
686C22—62no—
687C22—121no—
688C22—121no—
689C22—121no—
690C22—121no—
691C22—121no—
692C22D32×D411yescharacteristic
693C4—32no—
694C4—41no—
695C4—41no—
696C4—61no—
697C4—61no—
698C4—61no—
699C4—121no—
700C4—121no—
701C4—181no—
702C4—181no—
703C4—361no—
704C4—361no—
705C4D3×#23511yescharacteristic
706C4#6431511yescharacteristic
707C3—21no—
708C3#7957111yescharacteristic, complemented
709C3#8110011yescharacteristic, complemented
710C2—122no—
711C2—241no—
712C2#1059437511yescharacteristic
713C2D3×#91111yescharacteristic
714C2#1059476811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenter#107D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594376C2semidirect
2. #10594335C2semidirect
3. #10592574C2semidirect
4. C3×#4875C2semidirect
6. #10590890C2semidirect
7. #10590785C2semidirect
10. #10590559C2semidirect
11. #10590555C2semidirect
12. #10590541C2semidirect
13. #10590531C2semidirect
14. #10590461C2semidirect
15. #10590454C2semidirect
78. #4875D3semidirect
637. C32#3367semidirect
708. C3#79571semidirect
709. C3#81100semidirect

Maximal subgroups

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

subgroupindex
#105943762
#105943352
#105925742
C3×#48752
C3×#48722
#105908902
#105907852
#105907552
#105907512
#105905592
#105905552
#105905412
#105905312
#105904612
#105904542
#811003
#795713