Finite Group Databasebeta

← #11895658

Subgroups — #11895658

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595422C211yesmaximal, characteristic, complemented
2#10594566C211yesmaximal, characteristic
3#10592487C211yesmaximal, characteristic, complemented
4C3×#4790C211yesmaximal, characteristic, complemented
5C3×#4788C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic
7#10591612C211yesmaximal, characteristic, complemented
8#10591607C211yesmaximal, characteristic, complemented
9#10590878C211yesmaximal, characteristic
10#10590872C211yesmaximal, characteristic, complemented
11#10590868C211yesmaximal, characteristic, complemented
12C8×#627C211yesmaximal, characteristic, complemented
13#10590556C211yesmaximal, characteristic, complemented
14#10590542C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#79701—31nomaximal
17#79624—31nomaximal
18Q8×C3⋊Dic3C2211yescharacteristic
19C2×#3755C2211yescharacteristic
20#64102C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#887C2211yescharacteristic
27#63918—21no—
28#63918C2211yescharacteristic
29C4×#627—21no—
30C4×#627C2211yescharacteristic
31#63911C2211yescharacteristic
32C4×#626—21no—
33#63872—21no—
34#63872C2211yescharacteristic
35#63869—21no—
36#63869C2211yescharacteristic
37#63864C2211yescharacteristic
38#63863C2211yescharacteristic
39#63853—21no—
40#63852—21no—
41#63850—21no—
42C32×#103C2211yescharacteristic
43#63648C2211yescharacteristic
44C8×C3⋊Dic3C2211yescharacteristic
45#63635C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×C8×Dic3C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52#63572C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5585—31no—
62#5570—31no—
63#5569—31no—
64#5559—31no—
65C3×C4×Q16—31no—
66C3×C4×SD16—31no—
67#5185—31no—
68#5185—31no—
69#5166—31no—
70#5163—31no—
71#5028—31no—
72#5027—31no—
73#5020—31no—
74#5009—31no—
75#4891—31no—
76#4891—31no—
77#4871—31no—
78#4854—31no—
79#4800—31no—
80#4800—31no—
81#4790D311yescharacteristic, complemented
82#4788—31no—
83#4788—31no—
84#4788—61no—
85#4788D311yescharacteristic, complemented
86#4768—31no—
87#4760—31no—
88#4697—31no—
89#4694—31no—
90C8×Dic6—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627D411yescharacteristic
100C2×#626—21no—
101C2×#626—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3755—22no—
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×#215—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126#3724—21no—
127#3724D411yescharacteristic
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138#3365—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×C4×Q8—31no—
142C3×C4×Q8—31no—
143C3×C4×Q8—31no—
144C3×C4×D4—31no—
145#947—31no—
146#947—31no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149Q8×Dic3—61no—
150Q8×Dic3C2×D311yescharacteristic
151Q8×Dic3C2×D311yescharacteristic
152C2×#216C2×D311yescharacteristic
153C2×#215—31no—
154C2×#215—31no—
155C2×#215—61no—
156C2×#215C2×D311yescharacteristic
157#940—31no—
158#936—31no—
159#929—61no—
160C4×#67—61no—
161#894—61no—
162#894—61no—
163#893—31no—
164#893—31no—
165#893—61no—
166#893C2×D311yescharacteristic
167#890—31no—
168#890—31no—
169#890—31no—
170#890—61no—
171#890—61no—
172#890—61no—
173#888—31no—
174#888—61no—
175#887C2×D311yescharacteristic
176#885—61no—
177#883—61no—
178#875—31no—
179#875—61no—
180#874—31no—
181C4×D12—61no—
182#870—31no—
183#870—61no—
184#869—31no—
185#869—61no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C4×Dic6—61no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#103—21no—
193C3×#103—31no—
194C3×#103C2×D311yescharacteristic
195C3×#103C2×D311yescharacteristic
196C3×#102—31no—
197C3×C4×C8—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#821—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—61no—
209#821C2×D311yescharacteristic
210#816—31no—
211#816C2×D311yescharacteristic
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3—61no—
219C8×Dic3C2×D311yescharacteristic
220C8×Dic3C2×D311yescharacteristic
221#810—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#808—31no—
226#808—31no—
227#808—61no—
228#808C2×D311yescharacteristic
229#807C2×D311yescharacteristic
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8#4112yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)—21no—
244C4×C3⋊D3—81no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—21no—
253C3×D12—21no—
254C3×C4×D3—81no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257#627—22no—
258#627—42no—
259#626—42no—
260#626—81no—
261C32×C8—21no—
262C3⋊(C3⋊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—91no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—31no—
278C4×SD16—31no—
279C4×SD16—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×D4—31no—
285C22×C3×C4—61no—
286C2×#67—61no—
287C2×#67—61no—
288C2×D12—31no—
289C2×D12—31no—
290C2×D12—61no—
291C2×D12—61no—
292C2×D12—61no—
293C2×D12C22×D311yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—121no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6C22×D311yescharacteristic
303C3×Q16—62no—
304C3×SD16—62no—
305C2×C3×C8—21no—
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C3×C4⋊C4—21no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C22⋊C4—61no—
319C3×C42—31no—
320C3×C42—31no—
321C3×C42—61no—
322C3×C42—61no—
323C3×C42—61no—
324#217—61no—
325#217—61no—
326#216—22no—
327#215—22no—
328#215—64no—
329#215—62no—
330#215—62no—
331(C2×D3)⋊C4—21no—
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—121no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—121no—
355C4⋊Dic3C22×D311yescharacteristic
356C4⋊Dic3C22×D311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368C4×Dic3—21no—
369C4×Dic3—21no—
370C4×Dic3—21no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—121no—
377C4×Dic3C22×D311yescharacteristic
378C4×Dic3C22×D311yescharacteristic
379C2×C3⋊C8—31no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—61no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384C22×C32C22×D411yescharacteristic
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C32×C4—22no—
392C32×C4—41no—
393C32×C4C2×#4111yescharacteristic
394C32×C42−1+411yescharacteristic
395C3⋊Dic3—21no—
396C3⋊Dic3—21no—
397C3⋊Dic3—41no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3#13512yes—
405C2×Q16—31no—
406C2×SD16—31no—
407C2×SD16—91no—
408C4⋊Q8—91no—
409C4⋊Q8—181no—
410#127—91no—
411#125—91no—
412#125—91no—
413#125—181no—
414#125—181no—
415#124—91no—
416#124—91no—
417#124—181no—
418#123—181no—
419#123—181no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—181no—
426C4×D4—31no—
427C4×D4—91no—
428C4×D4—181no—
429#107—31no—
430#106—31no—
431#106—91no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434C4⋊C8—91no—
435#103—31no—
436#103—91no—
437#103—91no—
438#103D3211yescharacteristic
439#102—31no—
440#102—91no—
441#102—91no—
442#102—91no—
443#102—91no—
444#102—91no—
445C4×C8—31no—
446C4×C8—31no—
447C4×C8—91no—
448C23×C3—61no—
449C22×D3—21no—
450C22×D3—61no—
451C22×D3—61no—
452C22×D3—121no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8#23512yes—
460C3×Q8#23512yes—
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—61no—
477C2×C3×C4—241no—
478C2×C3×C4C23×D311yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480#67—122no—
481#67—241no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—121no—
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497C2×Dic3D3×D411yescharacteristic
498D12—21no—
499D12—21no—
500D12—62no—
501D12—61no—
502D12—61no—
503D12—61no—
504D12—61no—
505D12—121no—
506D12—122no—
507D12—241no—
508C4×D3—81no—
509C4×D3—241no—
510C4×D3—241no—
511C4×D3—242no—
512Dic6—21no—
513Dic6—21no—
514Dic6—62no—
515Dic6—62no—
516Dic6—122no—
517Dic6—122no—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—41no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—62no—
526C3⋊C8—61no—
527C3⋊C8—61no—
528C2×C32#54811yescharacteristic
529C2×C32C2×#13511yescharacteristic
530C2×C32#57711yescharacteristic
531C3⋊D3—81no—
532C3×D3—81no—
533C2×Q8—31no—
534C2×Q8—91no—
535C2×Q8—181no—
536C2×Q8C2×D3211yescharacteristic
537C2×D4—31no—
538C2×D4—91no—
539C2×D4—181no—
540C2×D4—181no—
541C22×C4—61no—
542C22×C4—181no—
543Q16—62no—
544SD16—62no—
545SD16—182no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—91no—
549C2×C8C2×D3211yescharacteristic
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—61no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—31no—
574C42—61no—
575C42—61no—
576C42—61no—
577C42—91no—
578C42—181no—
579C22×C3—21no—
580C22×C3—121no—
581C22×C3—121no—
582C22×C3—121no—
583C22×C3C2×D3×D411yescharacteristic
584C22×C3C2×D3×D411yescharacteristic
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—122no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—241no—
596C2×D3—241no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—32no—
602C3×C4—42no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—81no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4C2×#23511yescharacteristic
613C3×C4C2×#23511yescharacteristic
614C3×C4#101011yescharacteristic
615C3×C4#101011yescharacteristic
616Dic3—21no—
617Dic3—21no—
618Dic3—21no—
619Dic3—41no—
620Dic3—41no—
621Dic3—41no—
622Dic3—62no—
623Dic3—61no—
624Dic3—61no—
625Dic3—61no—
626Dic3—61no—
627Dic3—121no—
628Dic3—121no—
629Dic3—121no—
630Dic3—241no—
631Dic3#91912yes—
632C32#336511yescharacteristic, complemented, Sylow
633C23—61no—
634C23—181no—
635Q8—21no—
636Q8—61no—
637Q8—61no—
638Q8—182no—
639Q8—362no—
640Q8#379812yes—
641D4—61no—
642D4—61no—
643D4—181no—
644D4—181no—
645D4—362no—
646D4—721no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—181no—
659C2×C4—241no—
660C2×C4—721no—
661C2×C4C22×D3211yescharacteristic
662C8—21no—
663C8—61no—
664C8—61no—
665C8—181no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—241no—
670C2×C3#555211yescharacteristic
671C2×C3#555211yescharacteristic
672C2×C3#576211yescharacteristic
673C2×C3C2×#91911yescharacteristic
674C2×C3D3×#13511yescharacteristic
675C2×C3#577011yescharacteristic
676D3—81no—
677D3—242no—
678D3—241no—
679D3—241no—
680C22—121no—
681C22—121no—
682C22—121no—
683C22—361no—
684C22—361no—
685C22—361no—
686C22D32×D411yescharacteristic
687C4—22no—
688C4—32no—
689C4—41no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—121no—
694C4—121no—
695C4—121no—
696C4—181no—
697C4—181no—
698C4—361no—
699C4C2×#379811yescharacteristic
700C4#6430911yescharacteristic
701C3—21no—
702C3#7962411yescharacteristic, complemented
703C3#7970111yescharacteristic, complemented
704C2—241no—
705C2—721no—
706C2#1059418911yescharacteristic
707C2#1059475311yescharacteristic
708C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#63911C22
hypercenter#103D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595422C2semidirect
3. #10592487C2semidirect
4. C3×#4790C2semidirect
5. C3×#4788C2semidirect
7. #10591612C2semidirect
8. #10591607C2semidirect
10. #10590872C2semidirect
11. #10590868C2semidirect
12. C8×#627C2semidirect
13. #10590556C2semidirect
14. #10590542C2semidirect
15. #10590435C2semidirect
81. #4790D3semidirect
85. #4788D3semidirect
632. C32#3365semidirect
702. C3#79624semidirect
703. C3#79701semidirect

Maximal subgroups

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

subgroupindex
#105954222
#105945662
#105924872
C3×#47902
C3×#47882
#105916172
#105916122
#105916072
#105908782
#105908722
#105908682
C8×#6272
#105905562
#105905422
#105904352
#797013
#796243