Finite Group Databasebeta

← #11895701

Subgroups — #11895701

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#10594566C211yesmaximal, characteristic
2#10594321C211yesmaximal, characteristic, complemented
3#10592590C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4873C211yesmaximal, characteristic, complemented
6#10590878C211yesmaximal, characteristic
7#10590801C211yesmaximal, characteristic, complemented
8#10590797C211yesmaximal, characteristic, complemented
9#10590644C211yesmaximal, characteristic, complemented
10#10590556C211yesmaximal, characteristic, complemented
11#10590549C211yesmaximal, characteristic
12#10590539C211yesmaximal, characteristic, complemented
13#10590537C211yesmaximal, characteristic, complemented
14#10590483C211yesmaximal, characteristic, complemented
15#10590475C211yesmaximal, characteristic, complemented
16#81151—31nomaximal
17#79701—31nomaximal
18#64102C2211yescharacteristic
19#64099C2211yescharacteristic
20C2×C3×Dic12C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#890C2211yescharacteristic
23C3×#887C2211yescharacteristic
24C3×#887C2211yescharacteristic
25#63918—21no—
26#63918C2211yescharacteristic
27C4×#627C2211yescharacteristic
28#63911C2211yescharacteristic
29C4×#626—21no—
30#63864C2211yescharacteristic
31#63863C2211yescharacteristic
32#63853—21no—
33#63852—21no—
34#63850—21no—
35#63846—21no—
36#63845—21no—
37#63843C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63837—21no—
40C2×#3717C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C32×#107C2211yescharacteristic
43#63648C2211yescharacteristic
44#63641C2211yescharacteristic
45#63636C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5685—31no—
62#5585—31no—
63#5570—31no—
64#5559—31no—
65C3×#478—31no—
66C3×C4×Q16—31no—
67#5185—31no—
68#5185—31no—
69#5068—31no—
70#5027—31no—
71#5020—31no—
72C4×#214—31no—
73#4891—31no—
74#4891—31no—
75#4891—61no—
76#4891D311yescharacteristic, complemented
77#4873D311yescharacteristic, complemented
78#4854—31no—
79#4852—31no—
80#4845—31no—
81#4830—31no—
82#4800—31no—
83#4800—31no—
84#4788—31no—
85#4788—31no—
86#4768—31no—
87#4767—31no—
88#4762—31no—
89#4760—31no—
90#4694—31no—
91C8×Dic6—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627D411yescharacteristic
100C2×#626—21no—
101C2×#626—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×(C2×D3)⋊C4—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×Dic12—22no—
124#3724D411yescharacteristic
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130#3722—21no—
131#3722—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3717—22no—
137#3715—22no—
138#3365—91noSylow
139C2×C3×Q16—31no—
140C3×#125—31no—
141C3×C4×Q8—31no—
142C3×C4×Q8—31no—
143C3×C4×D4—31no—
144#947—31no—
145#947—31no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148C2×#215—31no—
149C2×#215—31no—
150#940—31no—
151#936—31no—
152C2×#214—31no—
153#929—61no—
154C4×#67—61no—
155C2×Dic12C2×D311yescharacteristic
156C2×#204—31no—
157#894—61no—
158#894—61no—
159#893—31no—
160#893—31no—
161#893—61no—
162#893C2×D311yescharacteristic
163#890—31no—
164#890—31no—
165#890—61no—
166#890—61no—
167#890—61no—
168#890C2×D311yescharacteristic
169#889—61no—
170#889—61no—
171#888—31no—
172#888—61no—
173#887—31no—
174#887—61no—
175#887C2×D311yescharacteristic
176#887C2×D311yescharacteristic
177#885—61no—
178#883—61no—
179#875—31no—
180#875—61no—
181#874—31no—
182C4×D12—61no—
183#869—31no—
184#869—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#107—21no—
190C3×#107C2×D311yescharacteristic
191C3×#107C2×D311yescharacteristic
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#821—31no—
203#821—31no—
204#821—31no—
205#821—31no—
206#821—61no—
207#821C2×D311yescharacteristic
208#816—31no—
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—61no—
213Dic3⋊C8C2×D311yescharacteristic
214C8×Dic3—31no—
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3C2×D311yescharacteristic
218#810—31no—
219#810C2×D311yescharacteristic
220#810C2×D311yescharacteristic
221#809—31no—
222#809—31no—
223#809—31no—
224#809—61no—
225#809C2×D311yescharacteristic
226#808—31no—
227#808—31no—
228#808—61no—
229#808C2×D311yescharacteristic
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
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×C4×D3—81no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6#4112yes—
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—31no—
271#478—91no—
272#475—91no—
273#464—91no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—31no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×D4—31no—
283C22×C3×C4—61no—
284C2×#67—61no—
285C2×#67—61no—
286C2×D12—31no—
287C2×D12—31no—
288C2×D12—61no—
289C2×D12—61no—
290C2×D12—61no—
291C2×D12C22×D311yescharacteristic
292C2×C4×D3—21no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—121no—
296C2×Dic6—31no—
297C2×Dic6—31no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6C22×D311yescharacteristic
301C2×Dic6C22×D311yescharacteristic
302C3×Q16—62no—
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C4⋊C4C22×D311yescharacteristic
319C3×C22⋊C4—61no—
320C3×C42—31no—
321C3×C42—31no—
322C3×C42—61no—
323C3×C42—61no—
324#217—61no—
325#217—61no—
326#215—62no—
327#215—62no—
328#214—62no—
329(C2×D3)⋊C4—21no—
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—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—121no—
339C4⋊Dic3—21no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—121no—
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—121no—
365C4×Dic3—21no—
366C4×Dic3—21no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381Dic12—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—41no—
391C32×C4—41no—
392C32×C4C2×#4111yescharacteristic
393C32×C42−1+411yescharacteristic
394C3⋊Dic3—21no—
395C3⋊Dic3—21no—
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—91no—
406C2×SD16—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409#127—91no—
410#125—31no—
411#125—91no—
412#125—181no—
413#125—181no—
414#124—91no—
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—31no—
426C4×D4—91no—
427C4×D4—181no—
428#107D3211yescharacteristic
429#106—31no—
430#106—91no—
431C4⋊C8—31no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#103—31no—
435#103—31no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—31no—
440#102—91no—
441#102—91no—
442#102—91no—
443#102—91no—
444C4×C8—31no—
445C4×C8—91no—
446C4×C8—91no—
447C23×C3—61no—
448C22×D3—21no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—121no—
452C3×Q8—32no—
453C3×Q8—61no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×D4—61no—
457C3×D4—61no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—241no—
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—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—121no—
489C2×Dic3D3×D411yescharacteristic
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493D12—21no—
494D12—21no—
495D12—62no—
496D12—61no—
497D12—61no—
498D12—61no—
499D12—61no—
500D12—121no—
501D12—122no—
502D12—241no—
503C4×D3—81no—
504C4×D3—241no—
505C4×D3—241no—
506C4×D3—242no—
507Dic6—21no—
508Dic6—21no—
509Dic6—21no—
510Dic6—62no—
511Dic6—62no—
512Dic6—122no—
513Dic6—122no—
514Dic6#23512yes—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—41no—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C2×C32#54811yescharacteristic
526C2×C32C2×#13511yescharacteristic
527C2×C32#57711yescharacteristic
528C3⋊D3—81no—
529C3×D3—81no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—91no—
533C2×Q8—181no—
534C2×D4—31no—
535C2×D4—91no—
536C2×D4—181no—
537C2×D4—181no—
538C22×C4—61no—
539C22×C4—181no—
540Q16—62no—
541SD16—182no—
542SD16—182no—
543C2×C8—31no—
544C2×C8—31no—
545C2×C8—91no—
546C2×C8C2×D3211yescharacteristic
547C4⋊C4—31no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4C2×D3211yescharacteristic
562C4⋊C4C2×D3211yescharacteristic
563C22⋊C4—61no—
564C22⋊C4—181no—
565C22⋊C4—181no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C42—31no—
570C42—31no—
571C42—61no—
572C42—61no—
573C42—91no—
574C42—181no—
575C42—181no—
576C22×C3—21no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3C2×D3×D411yescharacteristic
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—32no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—62no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—81no—
606C3×C4—81no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4C2×#23511yescharacteristic
610C3×C4#100711yescharacteristic
611C3×C4D3×#4111yescharacteristic
612C3×C4#101011yescharacteristic
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3—22no—
617Dic3—41no—
618Dic3—41no—
619Dic3—61no—
620Dic3—61no—
621Dic3—61no—
622Dic3—61no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628Dic3#91912yes—
629C32#336511yescharacteristic, complemented, Sylow
630C23—61no—
631C23—181no—
632Q8—32no—
633Q8—61no—
634Q8—61no—
635Q8—61no—
636Q8—182no—
637Q8—362no—
638D4—61no—
639D4—61no—
640D4—181no—
641D4—181no—
642D4—362no—
643D4—721no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—91no—
654C2×C4—91no—
655C2×C4—181no—
656C2×C4—241no—
657C2×C4—721no—
658C2×C4C22×D3211yescharacteristic
659C8—21no—
660C8—61no—
661C8—61no—
662C8—181no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—241no—
667C2×C3#555211yescharacteristic
668C2×C3#563311yescharacteristic
669C2×C3C2×#91911yescharacteristic
670C2×C3D3×#13511yescharacteristic
671C2×C3#577011yescharacteristic
672C2×C3#577511yescharacteristic
673D3—81no—
674D3—242no—
675D3—241no—
676D3—241no—
677C22—121no—
678C22—121no—
679C22—121no—
680C22—361no—
681C22—361no—
682C22—361no—
683C22D32×D411yescharacteristic
684C4—32no—
685C4—41no—
686C4—41no—
687C4—62no—
688C4—61no—
689C4—61no—
690C4—61no—
691C4—121no—
692C4—121no—
693C4—181no—
694C4—181no—
695C4—361no—
696C4D3×#23511yescharacteristic
697C4#6431511yescharacteristic
698C3—21no—
699C3#7970111yescharacteristic, complemented
700C3#8115111yescharacteristic, complemented
701C2—241no—
702C2—721no—
703C2#1059437511yescharacteristic
704C2#1059473611yescharacteristic
705C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#63911C22
hypercenter#107D32
hypocenterC32#3365
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
2. #10594321C2semidirect
3. #10592590C2semidirect
4. C3×#4891C2semidirect
5. C3×#4873C2semidirect
7. #10590801C2semidirect
8. #10590797C2semidirect
9. #10590644C2semidirect
10. #10590556C2semidirect
12. #10590539C2semidirect
13. #10590537C2semidirect
14. #10590483C2semidirect
15. #10590475C2semidirect
76. #4891D3semidirect
77. #4873D3semidirect
629. C32#3365semidirect
699. C3#79701semidirect
700. C3#81151semidirect

Maximal subgroups

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

subgroupindex
#105945662
#105943212
#105925902
C3×#48912
C3×#48732
#105908782
#105908012
#105907972
#105906442
#105905562
#105905492
#105905392
#105905372
#105904832
#105904752
#811513
#797013