Finite Group Databasebeta

← #11896258

Subgroups — #11896258

Order 1152.

764 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595198C211yesmaximal, characteristic, complemented
2#10594452C211yesmaximal, characteristic, complemented
3#10592467C211yesmaximal, characteristic, complemented
4C3×#4785C211yesmaximal, characteristic, complemented
5C3×#4764C211yesmaximal, characteristic, complemented
6#10591434C211yesmaximal, characteristic, complemented
7#10591428C211yesmaximal, characteristic
8#10591410C211yesmaximal, characteristic, complemented
9#10590895C211yesmaximal, characteristic, complemented
10#10590787C211yesmaximal, characteristic, complemented
11#10590747C211yesmaximal, characteristic, complemented
12#10590740C211yesmaximal, characteristic, complemented
13#10590530C211yesmaximal, characteristic, complemented
14#10590490C211yesmaximal, characteristic, complemented
15#10590474C211yesmaximal, characteristic, complemented
16#81710—31nomaximal
17#79852—31nomaximal
18#64145C2211yescharacteristic
19#64099C2211yescharacteristic
20C3×#940C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#890C2211yescharacteristic
25Dic3×#67—21no—
26#63969—21no—
27#63961—21no—
28#63959—21no—
29#63918C2211yescharacteristic
30C4×#627C2211yescharacteristic
31#63899—21no—
32#63898C2211yescharacteristic
33#63898C2211yescharacteristic
34#63893—21no—
35Dic3×D12C2211yescharacteristic
36D3×C4⋊Dic3—21no—
37#63860C2211yescharacteristic
38#63851—21no—
39#63844C2211yescharacteristic
40C2×#3716C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C32×#102C2211yescharacteristic
43#63659C2211yescharacteristic
44#63643C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63576C2211yescharacteristic
55#63575C2211yescharacteristic
56#63572C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63567C2211yescharacteristic
60#63563C2211yescharacteristic
61#5713—31no—
62#5690—31no—
63#5559—31no—
64#5543—31no—
65C3×#490—31no—
66C3×#442—31no—
67#5153—31no—
68#5150—31no—
69#5072—31no—
70#5063—31no—
71#5016—31no—
72#5007—31no—
73#4871—31no—
74#4857—31no—
75#4787—31no—
76#4787—31no—
77#4785D311yescharacteristic, complemented
78#4768—31no—
79#4768—31no—
80#4768—61no—
81#4766—31no—
82#4765—31no—
83#4764D311yescharacteristic, complemented
84#4759—31no—
85#4757—31no—
86#4756—31no—
87#4756—31no—
88#4714—31no—
89#4710—31no—
90#4701—31no—
91#4701—31no—
92C2×C32×D4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×#627—21no—
101C2×#627D411yescharacteristic
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3757—21no—
108#3757—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111#3750—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#213—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724D411yescharacteristic
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—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136#3716—22no—
137#3713—22no—
138#3370—91noSylow
139C2×C3×D8—31no—
140C3×#127—31no—
141C3×#125—31no—
142C3×C4×D4—31no—
143C3×C4×D4—31no—
144#940C2×D311yescharacteristic
145#936—31no—
146#936—31no—
147#936—31no—
148#936—61no—
149#936—61no—
150#935—61no—
151#935—61no—
152D4×Dic3—31no—
153D4×Dic3—31no—
154D4×Dic3—31no—
155D4×Dic3—61no—
156D4×Dic3C2×D311yescharacteristic
157C2×#214—31no—
158C2×#213—31no—
159C2×#213—31no—
160C2×#213C2×D311yescharacteristic
161#929—61no—
162C4×#67—61no—
163C2×C4⋊Dic3—61no—
164#924—61no—
165C2×#204—31no—
166#897—61no—
167#896—61no—
168#896—61no—
169#893—31no—
170#893—31no—
171#893C2×D311yescharacteristic
172D3×C4⋊C4—61no—
173#890—31no—
174#890—31no—
175#890—61no—
176#890C2×D311yescharacteristic
177#888—31no—
178#887—31no—
179#885—61no—
180#883—61no—
181#878—61no—
182#878—61no—
183#875—31no—
184C4×D12—31no—
185#869—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C3×#106—31no—
190C3×#102—21no—
191C3×#102—31no—
192C3×#102—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#102C2×D311yescharacteristic
196C3×#102C2×D311yescharacteristic
197C3×#97—31no—
198C3×#97—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—61no—
203#832C2×D311yescharacteristic
204#821—31no—
205#821C2×D311yescharacteristic
206#821C2×D311yescharacteristic
207#818—31no—
208#816—31no—
209#816—31no—
210#816—31no—
211#816—61no—
212#815C2×D311yescharacteristic
213#815C2×D311yescharacteristic
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218C8×Dic3—31no—
219C8×Dic3—31no—
220C8×Dic3—61no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#809C2×D311yescharacteristic
226#808C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C23×C32—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C32×D4—21no—
236C32×D4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243#634—21no—
244#634—21no—
245C3×#67—42no—
246C3×#67—81no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—81no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12#4112yes—
258C3×C4×D3—42no—
259#627—41no—
260#627—81no—
261D3×Dic3—81no—
262D3×Dic3—81no—
263D3×Dic3—81no—
264C32×C8—21no—
265C3⋊(C3⋊C8)—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#559—91no—
269#554—91no—
270#490—31no—
271#489—91no—
272#488—91no—
273#479—91no—
274#478—91no—
275#474—91no—
276#463—91no—
277#463—91no—
278#459—91no—
279#446—91no—
280#442—31no—
281#440—91no—
282C4×D8—91no—
283C2×C3×D4—21no—
284C2×C3×D4—31no—
285C2×C3×D4—31no—
286C2×C3×D4—61no—
287C2×C3×D4—61no—
288C2×C3×D4C22×D311yescharacteristic
289C2×C3×D4C22×D311yescharacteristic
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C2×#67—21no—
293C2×#67—21no—
294C22×Dic3—21no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298C2×D12C22×D311yescharacteristic
299C2×D12C22×D311yescharacteristic
300C2×C4×D3—21no—
301C2×C4×D3—61no—
302C2×C4×D3—61no—
303C2×C4×D3—61no—
304C2×Dic6—31no—
305C2×Dic6—31no—
306C2×Dic6—31no—
307C2×Dic6—31no—
308C2×Dic6—61no—
309C2×Dic6—61no—
310C2×Dic6—61no—
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—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C22⋊C4—61no—
325C3×C22⋊C4—61no—
326C3×C42—31no—
327C3×C42—31no—
328#217—21no—
329#217—61no—
330#217—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—61no—
335#217—61no—
336#217—61no—
337#217—61no—
338#217—121no—
339#217—121no—
340#214—62no—
341#213—22no—
342#213—62no—
343#213—62no—
344(C2×D3)⋊C4—21no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350C4⋊Dic3—21no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—121no—
360C4⋊Dic3C22×D311yescharacteristic
361C4⋊Dic3C22×D311yescharacteristic
362Dic3⋊C4—21no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—31no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—121no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3C22×D311yescharacteristic
379C4×Dic3C22×D311yescharacteristic
380C2×C3⋊C8—31no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—61no—
383C2×C3⋊C8C22×D311yescharacteristic
384C2×C3⋊C8C22×D311yescharacteristic
385#204—62no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32C22×D411yescharacteristic
390C2×C3×D3—22no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
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—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C2×SD16—91no—
410C2×D8—31no—
411C2×D8—91no—
412C4⋊Q8—91no—
413#127—31no—
414#125—31no—
415#125—91no—
416#124—91no—
417#124—91no—
418#124—181no—
419#123—181no—
420#123—181no—
421C22⋊Q8—181no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×D4—31no—
427C4×D4—31no—
428C4×D4—91no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—181no—
432C2×C4⋊C4—181no—
433#107—91no—
434#107—91no—
435#106—31no—
436C4⋊C8—91no—
437C4⋊C8—91no—
438C4⋊C8—91no—
439#103—91no—
440#103—91no—
441#103—91no—
442#102—31no—
443#102—31no—
444#102—31no—
445#102—31no—
446#102—91no—
447#102—91no—
448#102D3211yescharacteristic
449#97—31no—
450#97—31no—
451C4×C8—91no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—41no—
455C23×C3—61no—
456C23×C3—61no—
457C22×D3—21no—
458C22×D3—21no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—21no—
463C3×D4—32no—
464C3×D4—41no—
465C3×D4—41no—
466C3×D4—61no—
467C3×D4—61no—
468C3×D4—61no—
469C3×D4—122no—
470C3×D4—241no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—41no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—122no—
482C2×C3×C4—241no—
483C2×C3×C4C23×D311yescharacteristic
484C2×C3×C4C23×D311yescharacteristic
485#67—42no—
486#67—81no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—81no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×Dic3—241no—
503C2×Dic3—241no—
504C2×Dic3—241no—
505C2×Dic3D3×D411yescharacteristic
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508C2×Dic3D3×D411yescharacteristic
509D12—21no—
510D12—21no—
511D12—21no—
512D12#23512yes—
513C4×D3—42no—
514C4×D3—241no—
515C4×D3—241no—
516C4×D3—241no—
517Dic6—61no—
518Dic6—61no—
519Dic6—61no—
520Dic6—61no—
521Dic6—121no—
522Dic6—121no—
523Dic6—121no—
524Dic6—121no—
525Dic6—241no—
526Dic6—241no—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—41no—
530C3×C8—61no—
531C3×C8—61no—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C3⋊C8—61no—
535C3⋊C8—61no—
536C3⋊C8—121no—
537C2×C32—81no—
538C2×C32#54811yescharacteristic
539C2×C32#57511yescharacteristic
540C2×C32#57611yescharacteristic
541C3×D3—42no—
542C3×D3—81no—
543C2×Q8—91no—
544C2×Q8—91no—
545C2×Q8—181no—
546C2×D4—31no—
547C2×D4—31no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4C2×D3211yescharacteristic
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—181no—
554C22×C4—181no—
555C22×C4—181no—
556SD16—182no—
557D8—62no—
558D8—182no—
559C2×C8—31no—
560C2×C8—31no—
561C2×C8—91no—
562C2×C8C2×D3211yescharacteristic
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4C2×D3211yescharacteristic
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22⋊C4—181no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C22⋊C4—181no—
582C22⋊C4—181no—
583C22⋊C4—181no—
584C22⋊C4—181no—
585C42—31no—
586C42—31no—
587C42—91no—
588C42—181no—
589C22×C3—21no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—62no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—121no—
601C22×C3—121no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3C2×D3×D411yescharacteristic
606C22×C3C2×D3×D411yescharacteristic
607C2×D3—22no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—61no—
620C3×C4—61no—
621C3×C4—81no—
622C3×C4—121no—
623C3×C4—121no—
624C3×C4C2×#23511yescharacteristic
625C3×C4D3×#4111yescharacteristic
626C3×C4#101011yescharacteristic
627C3×C4#101011yescharacteristic
628Dic3—21no—
629Dic3—21no—
630Dic3—21no—
631Dic3—21no—
632Dic3—41no—
633Dic3—41no—
634Dic3—61no—
635Dic3—61no—
636Dic3—61no—
637Dic3—61no—
638Dic3—121no—
639Dic3—121no—
640Dic3—121no—
641Dic3—121no—
642Dic3—121no—
643Dic3—121no—
644Dic3—241no—
645Dic3—241no—
646C32#337011yescharacteristic, complemented, Sylow
647C23—21no—
648C23—61no—
649C23—61no—
650Q8—181no—
651Q8—181no—
652Q8—361no—
653Q8—721no—
654D4—21no—
655D4—21no—
656D4—32no—
657D4—61no—
658D4—61no—
659D4—61no—
660D4—122no—
661D4—241no—
662C2×C4—21no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—122no—
672C2×C4—181no—
673C2×C4—181no—
674C2×C4—241no—
675C2×C4—721no—
676C2×C4—721no—
677C2×C4—721no—
678C2×C4C22×D3211yescharacteristic
679C8—21no—
680C8—61no—
681C8—61no—
682C8—181no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—81no—
687C2×C3—81no—
688C2×C3—122no—
689C2×C3—161no—
690C2×C3—241no—
691C2×C3#555211yescharacteristic
692C2×C3#567711yescharacteristic
693C2×C3#577311yescharacteristic
694C2×C3#577311yescharacteristic
695C2×C3#577411yescharacteristic
696C2×C3#577411yescharacteristic
697D3—42no—
698D3—81no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—62no—
703C22—121no—
704C22—121no—
705C22—121no—
706C22—121no—
707C22—121no—
708C22D32×D411yescharacteristic
709C4—41no—
710C4—61no—
711C4—61no—
712C4—61no—
713C4—61no—
714C4—121no—
715C4—121no—
716C4—181no—
717C4—181no—
718C4—361no—
719C4—361no—
720C4D3×#23511yescharacteristic
721C4#6430911yescharacteristic
722C3—21no—
723C3#7985211yescharacteristic, complemented
724C3#8171011yescharacteristic, complemented
725C2—81no—
726C2—122no—
727C2—241no—
728C2#1059407311yescharacteristic
729C2#1059472811yescharacteristic
730C2#1059475011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10591428C2
hypercenter#102D32
hypocenterC32#3370
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. #10595198C2semidirect
2. #10594452C2semidirect
3. #10592467C2semidirect
4. C3×#4785C2semidirect
5. C3×#4764C2semidirect
6. #10591434C2semidirect
8. #10591410C2semidirect
9. #10590895C2semidirect
10. #10590787C2semidirect
11. #10590747C2semidirect
12. #10590740C2semidirect
13. #10590530C2semidirect
14. #10590490C2semidirect
15. #10590474C2semidirect
77. #4785D3semidirect
83. #4764D3semidirect
646. C32#3370semidirect
723. C3#79852semidirect
724. C3#81710semidirect

Maximal subgroups

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

subgroupindex
#105951982
#105944522
#105924672
C3×#47852
C3×#47642
#105914342
#105914282
#105914102
#105908952
#105907872
#105907472
#105907402
#105905302
#105904902
#105904742
#817103
#798523