Finite Group Databasebeta

← #11895860

Subgroups — #11895860

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#627C211yesmaximal, characteristic, complemented
2#10594335C211yesmaximal, characteristic, complemented
3#10592456C211yesmaximal, characteristic, complemented
4C3×#4757C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic
6#10591489C211yesmaximal, characteristic, complemented
7#10591476C211yesmaximal, characteristic
8#10591468C211yesmaximal, characteristic
9#10590895C211yesmaximal, characteristic, complemented
10#10590890C211yesmaximal, characteristic, complemented
11#10590866C211yesmaximal, characteristic, complemented
12#10590784C211yesmaximal, characteristic, complemented
13#10590557C211yesmaximal, characteristic, complemented
14#10590555C211yesmaximal, characteristic, complemented
15#10590432C211yesmaximal, characteristic, complemented
16#79751—31nomaximal
17#79571—31nomaximal
18C22×#627—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21#64096C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63982—21no—
29#63964—21no—
30#63964—21no—
31#63919C2211yescharacteristic
32#63918C2211yescharacteristic
33#63918C2211yescharacteristic
34C4×#627C2211yescharacteristic
35#63866C2211yescharacteristic
36#63863C2211yescharacteristic
37#63862—21no—
38#63860C2211yescharacteristic
39#63859—21no—
40#63855—21no—
41#63851—21no—
42C32×#102C2211yescharacteristic
43#63643C2211yescharacteristic
44#63642C2211yescharacteristic
45#63634C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×#815C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×#807C2211yescharacteristic
52#63572C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5568—31no—
62#5542—31no—
63D4×Dic6—31no—
64D4×Dic6—31no—
65C3×#440—31no—
66C3×C4×D8—31no—
67#5165—31no—
68#5162—31no—
69#5153—31no—
70#5153—31no—
71#5021—31no—
72#5019—31no—
73#5016—31no—
74#5007—31no—
75#4890—31no—
76#4875—31no—
77#4875—31no—
78#4875—31no—
79#4794—31no—
80#4792—31no—
81#4765—31no—
82#4765—31no—
83#4757—31no—
84#4757—31no—
85#4757—61no—
86#4757D311yescharacteristic, complemented
87#4756D311yescharacteristic
88#4714—31no—
89#4701—31no—
90#4681—31no—
91#4679—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634C2311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#627—21no—
102C2×#627—21no—
103C2×#627—44no—
104C2×#627D411yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3757—21no—
108#3754—22no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#214—22no—
117C3×#213—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134Dic3⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3367—91noSylow
140C22×Dic6—61no—
141C22×Dic6—61no—
142C2×C3×SD16—31no—
143C2×C3×D8—31no—
144C3×C4×Q8—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148#947—31no—
149#944—31no—
150#936—31no—
151#936—31no—
152D4×Dic3—31no—
153D4×Dic3—31no—
154D4×Dic3—61no—
155D4×Dic3C2×D311yescharacteristic
156D4×Dic3C2×D311yescharacteristic
157C2×#214—31no—
158C2×#214—31no—
159C2×#214—61no—
160C2×#214C2×D311yescharacteristic
161C2×#213C2×D311yescharacteristic
162#926—61no—
163#924—61no—
164#924—61no—
165#924—61no—
166#898—61no—
167#896—61no—
168#893C2×D311yescharacteristic
169#888—31no—
170#888—31no—
171#888—31no—
172#888—31no—
173#887—31no—
174#887—31no—
175#887—61no—
176#887C2×D311yescharacteristic
177#879—61no—
178#879—61no—
179#878—61no—
180#878—61no—
181#878—61no—
182#878—61no—
183#876—61no—
184#875—31no—
185#872—61no—
186#869—31no—
187#869—31no—
188#869—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#103—31no—
194C3×#102—21no—
195C3×#102—31no—
196C3×#102C2×D311yescharacteristic
197C3×#102C2×D311yescharacteristic
198C3×#97—31no—
199C3×C4×C8—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#821—31no—
205#821C2×D311yescharacteristic
206#816—31no—
207#816—31no—
208#816—31no—
209#816—31no—
210#816—31no—
211#816—61no—
212#816C2×D311yescharacteristic
213#815—31no—
214#815—31no—
215#815—61no—
216#815C2×D311yescharacteristic
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221C8×Dic3C2×D311yescharacteristic
222#810—31no—
223#810—31no—
224#810—31no—
225#809—31no—
226#807—31no—
227#807—31no—
228#807—61no—
229#807C2×D311yescharacteristic
230#807C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233C23×C32—21no—
234C22×C3×D3—21no—
235C32×D4—21no—
236C32×D4#4112yes—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—42no—
242C2×C3⋊Dic3C2×D411yescharacteristic
243C2×C3⋊Dic3C2×D411yescharacteristic
244#634—21no—
245#634—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—42no—
250C2×C3×Dic3—42no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12—21no—
257C3×C4×D3—42no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260#627—22no—
261#627—42no—
262#627—42no—
263#627—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—91no—
274#477—91no—
275#474—91no—
276#463—91no—
277#463—91no—
278#461—91no—
279#446—91no—
280#440—31no—
281#440—91no—
282C4×D8—31no—
283C2×C3×Q8—31no—
284C2×C3×D4—21no—
285C2×C3×D4—31no—
286C2×C3×D4C22×D311yescharacteristic
287C2×C3×D4C22×D311yescharacteristic
288C22×C3×C4—61no—
289C22×C3×C4—61no—
290C22×C3×C4—61no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295C22×Dic3—121no—
296C2×D12C22×D311yescharacteristic
297C2×C4×D3—21no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—31no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—61no—
309C2×Dic6—124no—
310C2×Dic6—124no—
311C2×Dic6C22×D311yescharacteristic
312C3×SD16—62no—
313C3×D8—62no—
314C2×C3×C8—21no—
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319C3×C4⋊C4—21no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C22⋊C4—61no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—31no—
330C3×C42—61no—
331#217—21no—
332#217—21no—
333#217—61no—
334#217—61no—
335#217—61no—
336#217—61no—
337#217—61no—
338#217—61no—
339#217—121no—
340#214—22no—
341#214—64no—
342#214—62no—
343#214—62no—
344#213—22no—
345(C2×D3)⋊C4—21no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3C22×D311yescharacteristic
360C4⋊Dic3C22×D311yescharacteristic
361Dic3⋊C4—21no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—121no—
375C4×Dic3—21no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—121no—
382C4×Dic3C22×D311yescharacteristic
383C4×Dic3C22×D311yescharacteristic
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389C22×C32—22no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32C22×D411yescharacteristic
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C2×C3×D3—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×Dic3—41no—
409C3×Dic3AGL(1,ℤ/8)12yes—
410C22×Q8—181no—
411C2×SD16—31no—
412C2×SD16—91no—
413C2×D8—31no—
414C4⋊Q8—91no—
415C4⋊Q8—91no—
416C4⋊Q8—91no—
417C4⋊Q8—91no—
418#126—181no—
419#126—181no—
420#124—91no—
421#124—91no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C22⋊Q8—181no—
425C22⋊Q8—181no—
426C4×Q8—31no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×D4—31no—
430C4×D4—31no—
431C4×D4—31no—
432C4×D4—91no—
433#117—181no—
434#107—31no—
435#107—31no—
436#107—91no—
437C4⋊C8—91no—
438C4⋊C8—91no—
439C4⋊C8—91no—
440#103—31no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#102—31no—
447#102—91no—
448#102—91no—
449#102D3211yescharacteristic
450#97—31no—
451#97—91no—
452C4×C8—31no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—41no—
456C23×C3—61no—
457C22×D3—21no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—22no—
463C3×D4—41no—
464C3×D4—61no—
465C3×D4—61no—
466C3×D4#23512yes—
467C3×D4#23512yes—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—41no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—122no—
480C2×C3×C4—122no—
481C2×C3×C4—122no—
482C2×C3×C4C23×D311yescharacteristic
483C2×C3×C4C23×D311yescharacteristic
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—42no—
492C2×Dic3—42no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3—122no—
502C2×Dic3—122no—
503C2×Dic3—242no—
504C2×Dic3D3×D411yescharacteristic
505C2×Dic3D3×D411yescharacteristic
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508D12—21no—
509D12—21no—
510C4×D3—42no—
511Dic6—21no—
512Dic6—21no—
513Dic6—62no—
514Dic6—62no—
515Dic6—62no—
516Dic6—61no—
517Dic6—61no—
518Dic6—61no—
519Dic6—61no—
520Dic6—121no—
521Dic6—122no—
522Dic6—122no—
523Dic6—122no—
524Dic6—122no—
525Dic6—122no—
526Dic6—122no—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—41no—
530C3×C8—61no—
531C3×C8—61no—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C3⋊C8—62no—
535C3⋊C8—61no—
536C3⋊C8—61no—
537C2×C32—42no—
538C2×C32#54811yescharacteristic
539C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
540C2×C32#57811yescharacteristic
541C3×D3—81no—
542C2×Q8—31no—
543C2×Q8—91no—
544C2×Q8—91no—
545C2×Q8—181no—
546C2×Q8—181no—
547C2×Q8—181no—
548C2×Q8—364no—
549C2×D4—31no—
550C2×D4C2×D3211yescharacteristic
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—181no—
555SD16—62no—
556SD16—182no—
557D8—62no—
558C2×C8—31no—
559C2×C8—31no—
560C2×C8—91no—
561C2×C8C2×D3211yescharacteristic
562C4⋊C4—31no—
563C4⋊C4—31no—
564C4⋊C4—61no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4C2×D3211yescharacteristic
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22⋊C4—61no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C22⋊C4—181no—
582C22⋊C4—181no—
583C22⋊C4—181no—
584C42—31no—
585C42—31no—
586C42—61no—
587C42—91no—
588C42—181no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—21no—
592C22×C3—42no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—121no—
600C22×C3—121no—
601C22×C3—121no—
602C22×C3C2×D3×D411yescharacteristic
603C22×C3C2×D3×D411yescharacteristic
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—32no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—61no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—81no—
616C3×C4—121no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4C2×#23511yescharacteristic
620C3×C4C2×#23511yescharacteristic
621C3×C4#101011yescharacteristic
622C3×C4#101011yescharacteristic
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—41no—
627Dic3—41no—
628Dic3—41no—
629Dic3—61no—
630Dic3—61no—
631Dic3—61no—
632Dic3—61no—
633Dic3—121no—
634Dic3—121no—
635Dic3—122no—
636Dic3—121no—
637Dic3—121no—
638Dic3—121no—
639Dic3—121no—
640Dic3—241no—
641Dic3#91112yes—
642C32#336711yescharacteristic, complemented, Sylow
643C23—21no—
644C23—61no—
645Q8—61no—
646Q8—61no—
647Q8—182no—
648Q8—181no—
649Q8—181no—
650Q8—362no—
651Q8—362no—
652Q8—362no—
653D4—21no—
654D4—61no—
655D4—61no—
656D4#379812yes—
657C2×C4—21no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—122no—
668C2×C4—122no—
669C2×C4—122no—
670C2×C4—181no—
671C2×C4—181no—
672C2×C4—362no—
673C2×C4C22×D3211yescharacteristic
674C8—21no—
675C8—61no—
676C8—61no—
677C8—181no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—42no—
682C2×C3—42no—
683C2×C3—82no—
684C2×C3—241no—
685C2×C3#555211yescharacteristic
686C2×C3#555211yescharacteristic
687C2×C3C2×#91111yescharacteristic
688C2×C3#577111yescharacteristic
689C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
690C2×C3#577911yescharacteristic
691D3—81no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—121no—
696C22—121no—
697C22—121no—
698C22D32×D411yescharacteristic
699C4—32no—
700C4—41no—
701C4—61no—
702C4—61no—
703C4—61no—
704C4—121no—
705C4—121no—
706C4—121no—
707C4—181no—
708C4—181no—
709C4—361no—
710C4—361no—
711C4C2×#379811yescharacteristic
712C4#6430911yescharacteristic
713C3—21no—
714C3#7957111yescharacteristic, complemented
715C3#7975111yescharacteristic, complemented
716C2—42no—
717C2—241no—
718C2#1059418911yescharacteristic
719C2D3×#91111yescharacteristic
720C2#1059475611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenter#102D32
hypocenterC32#3367
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
1. D4×#627C2semidirect
2. #10594335C2semidirect
3. #10592456C2semidirect
4. C3×#4757C2semidirect
6. #10591489C2semidirect
9. #10590895C2semidirect
10. #10590890C2semidirect
11. #10590866C2semidirect
12. #10590784C2semidirect
13. #10590557C2semidirect
14. #10590555C2semidirect
15. #10590432C2semidirect
86. #4757D3semidirect
642. C32#3367semidirect
714. C3#79571semidirect
715. C3#79751semidirect

Maximal subgroups

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

subgroupindex
D4×#6272
#105943352
#105924562
C3×#47572
C3×#47562
#105914892
#105914762
#105914682
#105908952
#105908902
#105908662
#105907842
#105905572
#105905552
#105904322
#797513
#795713