Finite Group Databasebeta

← #11895643

Subgroups — #11895643

Order 1152.

747 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593939C211yesmaximal, characteristic
2#10593851C211yesmaximal, characteristic, complemented
3#10592546C211yesmaximal, characteristic, complemented
4C3×#4845C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590878C211yesmaximal, characteristic
7#10590872C211yesmaximal, characteristic, complemented
8Dic3×Dic12C211yesmaximal, characteristic, complemented
9#10590803C211yesmaximal, characteristic, complemented
10#10590801C211yesmaximal, characteristic, complemented
11#10590799C211yesmaximal, characteristic
12#10590767C211yesmaximal, characteristic, complemented
13Dic3×#204C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15#10590274C211yesmaximal, characteristic, complemented
16#80581—31nomaximal
17#79935—31nomaximal
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19#64079C2211yescharacteristic
20C2×C3×Dic12C2211yescharacteristic
21C2×C3×#204C2211yescharacteristic
22C3×#875C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918C2211yescharacteristic
26#63911C2211yescharacteristic
27#63907—21no—
28Dic3×D12C2211yescharacteristic
29#63890—21no—
30#63881—21no—
31#63869C2211yescharacteristic
32#63867—21no—
33#63864C2211yescharacteristic
34#63853—21no—
35#63846—21no—
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63839—21no—
40#63837—21no—
41C2×#3717C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43#63648C2211yescharacteristic
44#63648C2211yescharacteristic
45#63645C2211yescharacteristic
46#63644C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5681—31no—
62#5585—31no—
63#5569—31no—
64#5567—31no—
65C3×#464—31no—
66C3×C8×Q8—31no—
67#5185—31no—
68Dic3×Q16—31no—
69#5163—31no—
70Dic3×SD16—31no—
71#5056—31no—
72C4×#215—31no—
73#4851—31no—
74#4848—31no—
75#4847—31no—
76#4847—31no—
77#4847—31no—
78#4847—61no—
79#4845—31no—
80#4845D311yescharacteristic, complemented
81#4830D311yescharacteristic, complemented
82#4800—31no—
83#4791—31no—
84#4766—31no—
85#4760—31no—
86C4×Dic12—31no—
87#4697—31no—
88#4697—31no—
89#4694—31no—
90C4×#204—31no—
91C4×#204—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C3×D12C2311yescharacteristic
95C2×C3×Dic6D411yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#626—21no—
100C2×#626—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105#3752—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110#3750—21no—
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3D411yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4D411yescharacteristic
117C3×Dic3⋊C4D411yescharacteristic
118C3×C4×Dic3—21no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×Dic12—22no—
124C3×#204—22no—
125#3724—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3717—22no—
138#3365—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×#124—31no—
142C3×C4×Q8—31no—
143C3×C4×Q8—31no—
144#947—31no—
145#947—61no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149#944—61no—
150C2×#215—31no—
151#940—31no—
152D4×Dic3—31no—
153C2×Dic12C2×D311yescharacteristic
154C2×#204—31no—
155C2×#204C2×D311yescharacteristic
156#894—61no—
157#894—61no—
158#893—61no—
159#890—31no—
160#890—61no—
161#889—61no—
162#889—61no—
163#888—31no—
164#888—61no—
165#887—61no—
166#886—61no—
167#885—61no—
168#883—61no—
169#67⋊C4—61no—
170#875—31no—
171#875C2×D311yescharacteristic
172#874—31no—
173C4×D12—31no—
174C4×D12—31no—
175C4×D12—31no—
176C4×D12—61no—
177#870—31no—
178#870—31no—
179#870—31no—
180#870—61no—
181#870—61no—
182#869—31no—
183C4×Dic6—31no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C4×Dic6C2×D311yescharacteristic
189C3×C4⋊C8—21no—
190C3×C4⋊C8—31no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8C2×D311yescharacteristic
193C3×C4⋊C8C2×D311yescharacteristic
194C3×#103—31no—
195C3×#102—31no—
196C3×C4×C8—31no—
197C3×C4×C8—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—61no—
212#821—61no—
213#821C2×D311yescharacteristic
214#818—31no—
215#818—31no—
216#818—61no—
217#817—31no—
218#817—31no—
219#817—31no—
220#817—61no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816C2×D311yescharacteristic
225Dic3⋊C8C2×D311yescharacteristic
226Dic3⋊C8C2×D311yescharacteristic
227C8×Dic3C2×D311yescharacteristic
228C8×Dic3C2×D311yescharacteristic
229#809—31no—
230#808—31no—
231C4×C3⋊C8C2×D311yescharacteristic
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C4⋊(C3⋊D3)—21no—
241C4⋊(C3⋊D3)—21no—
242C4×C3⋊D3—81no—
243C2×C3×Dic3—21no—
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×Dic6—21no—
253C3×Dic6—22no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6#4112yes—
257#627—42no—
258#626—42no—
259#626—81no—
260D3×Dic3—81no—
261C32×C8—21no—
262C32×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—91no—
271#478—91no—
272#475—91no—
273#464—31no—
274#464—91no—
275#460—91no—
276C8×Q8—31no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×D4—31no—
284C2×#67—61no—
285C2×#67—61no—
286C22×Dic3—61no—
287C2×D12—31no—
288C2×D12—31no—
289C2×D12—61no—
290C2×D12—61no—
291C2×D12—61no—
292C2×D12C22×D311yescharacteristic
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—121no—
297C2×Dic6—61no—
298C2×Dic6—61no—
299C2×Dic6D1211yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C2×Dic6C22×D311yescharacteristic
302C3×Q16—62no—
303C3×SD16—62no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C2×C3×C8C22×D311yescharacteristic
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C42—21no—
320C3×C42—31no—
321C3×C42—31no—
322C3×C42—61no—
323C3×C42C22×D311yescharacteristic
324C3×C42C22×D311yescharacteristic
325#217—61no—
326#215—62no—
327(C2×D3)⋊C4—21no—
328(C2×D3)⋊C4—21no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
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—121no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3D1211yescharacteristic
352C4⋊Dic3C22×D311yescharacteristic
353Dic3⋊C4—21no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—121no—
366Dic3⋊C4—121no—
367Dic3⋊C4D1211yescharacteristic
368Dic3⋊C4D1211yescharacteristic
369C4×Dic3—21no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3C22×D311yescharacteristic
377C4×Dic3C22×D311yescharacteristic
378C2×C3⋊C8C22×D311yescharacteristic
379C2×C3⋊C8C22×D311yescharacteristic
380Dic12—22no—
381#204—22no—
382#204—62no—
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—21no—
391C32×C4—21no—
392C32×C4C2×#4111yescharacteristic
393C32×C42−1+411yescharacteristic
394C3⋊Dic3—41no—
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3#13512yes—
404C2×Q16—31no—
405C2×SD16—31no—
406C2×SD16—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409#127—91no—
410#125—91no—
411#125—91no—
412#125—181no—
413#125—181no—
414#124—31no—
415#124—91no—
416#124—181no—
417#123—181no—
418#123—181no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—181no—
425C4×D4—91no—
426C4×D4—91no—
427C4×D4—181no—
428#107—91no—
429#106—91no—
430#106—91no—
431C4⋊C8—31no—
432C4⋊C8—31no—
433C4⋊C8D3211yescharacteristic
434#103—31no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—91no—
440#102—91no—
441#102—91no—
442#102—91no—
443#102—91no—
444C4×C8—31no—
445C4×C8—31no—
446C4×C8—31no—
447C23×C3—61no—
448C22×D3—21no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—121no—
452C3×Q8—32no—
453C3×Q8—62no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×D4—61no—
458C3×D4—61no—
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—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4C2×D1211yescharacteristic
470C2×C3×C4C2×D1211yescharacteristic
471C2×C3×C4D3×D411yescharacteristic
472C2×C3×C4D3×D411yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475#67—122no—
476#67—241no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—121no—
487C2×Dic3—121no—
488C2×Dic3—121no—
489C2×Dic3—241no—
490C2×Dic3C2×D1211yescharacteristic
491C2×Dic3C2×D1211yescharacteristic
492C2×Dic3C2×D1211yescharacteristic
493C2×Dic3C2×D1211yescharacteristic
494D12—21no—
495D12—21no—
496D12—62no—
497D12—61no—
498D12—61no—
499D12—61no—
500D12—61no—
501D12—121no—
502D12—122no—
503D12—241no—
504C4×D3—241no—
505C4×D3—241no—
506C4×D3—241no—
507C4×D3—242no—
508Dic6—21no—
509Dic6—22no—
510Dic6—21no—
511Dic6—21no—
512Dic6—122no—
513Dic6—122no—
514Dic6#23712yes—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—41no—
520C3×C8—41no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C2×C32#54811yescharacteristic
526C2×C32C2×#13511yescharacteristic
527C2×C32#57711yescharacteristic
528C3⋊D3—81no—
529C3×D3—81no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—181no—
534C2×D4—31no—
535C2×D4—91no—
536C2×D4—181no—
537C2×D4—181no—
538C22×C4—181no—
539C22×C4—181no—
540Q16—62no—
541SD16—62no—
542SD16—182no—
543C2×C8—31no—
544C2×C8—31no—
545C2×C8C2×D3211yescharacteristic
546C2×C8C2×D3211yescharacteristic
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—61no—
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⋊C4—181no—
562C4⋊C4—181no—
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—181no—
573C42—181no—
574C42—181no—
575C42C2×D3211yescharacteristic
576C22×C3—21no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3C22×D1211yescharacteristic
581C22×C3C2×D3×D411yescharacteristic
582C2×D3—41no—
583C2×D3—41no—
584C2×D3—41no—
585C2×D3—122no—
586C2×D3—121no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—241no—
593C2×D3—241no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—32no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—62no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4C2×#23711yescharacteristic
610C3×C4#100711yescharacteristic
611C3×C4D3×#4111yescharacteristic
612C3×C4#101011yescharacteristic
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3—22no—
617Dic3—41no—
618Dic3—41no—
619Dic3—121no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—241no—
626Dic3—241no—
627Dic3—241no—
628Dic3#90412yes—
629C32#336511yescharacteristic, complemented, Sylow
630C23—61no—
631C23—181no—
632Q8—32no—
633Q8—62no—
634Q8—61no—
635Q8—61no—
636Q8—61no—
637Q8—362no—
638D4—61no—
639D4—61no—
640D4—181no—
641D4—181no—
642D4—362no—
643D4—721no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—721no—
655C2×C4—721no—
656C2×C4D3×D1211yescharacteristic
657C2×C4D3×D1211yescharacteristic
658C2×C4C22×D3211yescharacteristic
659C8—21no—
660C8—21no—
661C8—61no—
662C8—61no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—241no—
667C2×C3#557611yescharacteristic
668C2×C3#559811yescharacteristic
669C2×C3C2×#90411yescharacteristic
670C2×C3#575111yescharacteristic
671C2×C3D3×#13511yescharacteristic
672C2×C3#577811yescharacteristic
673D3—81no—
674D3—242no—
675D3—241no—
676D3—241no—
677C22—121no—
678C22—121no—
679C22—121no—
680C22—361no—
681C22—361no—
682C22—361no—
683C22C2×D3×D1211yescharacteristic
684C4—21no—
685C4—21no—
686C4—32no—
687C4—62no—
688C4—61no—
689C4—61no—
690C4—61no—
691C4—121no—
692C4—121no—
693C4—361no—
694C4—361no—
695C4—361no—
696C4D3×#23711yescharacteristic
697C4#6431511yescharacteristic
698C3—21no—
699C3#7993511yescharacteristic, complemented
700C3#8058111yescharacteristic, complemented
701C2—241no—
702C2—721no—
703C2#1059438211yescharacteristic
704C2D3×#90411yescharacteristic
705C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#63911C22
hypercenterC4⋊C8D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593851C2semidirect
3. #10592546C2semidirect
4. C3×#4845C2semidirect
5. C3×#4830C2semidirect
7. #10590872C2semidirect
8. Dic3×Dic12C2semidirect
9. #10590803C2semidirect
10. #10590801C2semidirect
12. #10590767C2semidirect
13. Dic3×#204C2semidirect
14. C4×#3717C2semidirect
15. #10590274C2semidirect
80. #4845D3semidirect
81. #4830D3semidirect
629. C32#3365semidirect
699. C3#79935semidirect
700. C3#80581semidirect

Maximal subgroups

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

subgroupindex
#105939392
#105938512
#105925462
C3×#48452
C3×#48302
#105908782
#105908722
Dic3×Dic122
#105908032
#105908012
#105907992
#105907672
Dic3×#2042
C4×#37172
#105902742
#805813
#799353