Finite Group Databasebeta

← #11895278

Subgroups — #11895278

Order 1152.

761 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#10595384C211yesmaximal, characteristic, complemented
2#10594470C211yesmaximal, characteristic, complemented
3#10592487C211yesmaximal, characteristic, complemented
4C3×#4800C211yesmaximal, characteristic, complemented
5C3×#4792C211yesmaximal, characteristic, complemented
6#10591615C211yesmaximal, characteristic, complemented
7#10591568C211yesmaximal, characteristic
8#10591565C211yesmaximal, characteristic, complemented
9#10590868C211yesmaximal, characteristic, complemented
10#10590792C211yesmaximal, characteristic, complemented
11C8×#627C211yesmaximal, characteristic, complemented
12#10590745C211yesmaximal, characteristic
13#10590540C211yesmaximal, characteristic
14#10590491C211yesmaximal, characteristic, complemented
15#10590465C211yesmaximal, characteristic, complemented
16#81632—31nomaximal
17#81621—31nomaximal
18Q8×C3⋊Dic3C2211yescharacteristic
19C2×#3755C2211yescharacteristic
20#64102C2211yescharacteristic
21C3×#947C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C3×#890C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C4×#627C2211yescharacteristic
26#63895—21no—
27#63894C2211yescharacteristic
28#63894C2211yescharacteristic
29#63893—21no—
30Dic3×D12C2211yescharacteristic
31#63888—21no—
32#63883—21no—
33#63878—21no—
34#63872C2211yescharacteristic
35#63871—21no—
36#63863C2211yescharacteristic
37#63862—21no—
38#63861—21no—
39Dic3×Dic6C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63648C2211yescharacteristic
44C8×C3⋊Dic3C2211yescharacteristic
45#63635C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#809C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63565C2211yescharacteristic
60#63562C2211yescharacteristic
61#5732—31no—
62#5730—31no—
63#5690—31no—
64#5671—31no—
65C3×#488—31no—
66C3×#487—31no—
67#5084—31no—
68#5083—31no—
69#5063—31no—
70#5057—31no—
71#4819—31no—
72#4819—31no—
73#4818—31no—
74#4800—31no—
75#4800D311yescharacteristic, complemented
76#4799—31no—
77#4796—31no—
78#4796—31no—
79#4792D311yescharacteristic, complemented
80#4788—31no—
81#4788—31no—
82#4788—31no—
83#4788—61no—
84#4787—31no—
85#4768—31no—
86#4761—31no—
87#4756—31no—
88C4×D24—31no—
89C4×#204—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×Dic6—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×#627D411yescharacteristic
99C2×#624—21no—
100C2×#624—21no—
101C2×D3×Dic3—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×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
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—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136#3717—22no—
137#3714—22no—
138#3360—91noSylow
139C3×C4⋊Q8—31no—
140C3×C4⋊Q8—31no—
141C3×#125—31no—
142C3×#124—31no—
143#947—31no—
144#947C2×D311yescharacteristic
145#946—61no—
146#946—61no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150Q8×Dic3—61no—
151#944C2×D311yescharacteristic
152C2×#215—31no—
153C2×#215—31no—
154C2×#215—31no—
155C2×#215—61no—
156#936—31no—
157D4×Dic3—31no—
158C2×#213—31no—
159C2×D24—31no—
160C2×#204—31no—
161#898—61no—
162#898—61no—
163#897—61no—
164#897—61no—
165#897—61no—
166#896—61no—
167#896—61no—
168#893—31no—
169#893—31no—
170#893—31no—
171#893—31no—
172#893—61no—
173#892—61no—
174D3×C4⋊C4—61no—
175D3×C4⋊C4—61no—
176#890—31no—
177#890—31no—
178#890C2×D311yescharacteristic
179#888C2×D311yescharacteristic
180#879—61no—
181#879—61no—
182#878—61no—
183#877—61no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C3×#103—21no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103C2×D311yescharacteristic
196C3×#103C2×D311yescharacteristic
197C3×#102—31no—
198C3×#102—31no—
199C3×C4×C8—31no—
200C3×C4×C8—31no—
201#835—31no—
202#835C2×D311yescharacteristic
203#835C2×D311yescharacteristic
204#832—31no—
205#821—31no—
206#821—31no—
207#821—61no—
208#821C2×D311yescharacteristic
209#818—31no—
210#817—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#810C2×D311yescharacteristic
223#809—31no—
224#809C2×D311yescharacteristic
225#808—31no—
226#808—31no—
227#808—31no—
228#808—61no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
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)#4112yes—
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×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—81no—
257#627—22no—
258#624—42no—
259#624—81no—
260D3×Dic3—42no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#556—91no—
266#554—91no—
267#488—31no—
268#488—91no—
269#487—31no—
270#479—91no—
271#479—91no—
272#476—91no—
273#463—91no—
274#463—91no—
275#461—91no—
276C8×Q8—91no—
277C4×SD16—91no—
278C4×SD16—91no—
279C4×D8—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×D4—31no—
286C22×Dic3—61no—
287C2×D12—31no—
288C2×D12—31no—
289C2×D12—61no—
290C2×D12C22×D311yescharacteristic
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—121no—
299C2×Dic6—21no—
300C2×Dic6—31no—
301C2×Dic6—31no—
302C2×Dic6C22×D311yescharacteristic
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—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
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×C22⋊C4—61no—
320C3×C42—31no—
321C3×C42—31no—
322#217—61no—
323#217—61no—
324#217—61no—
325#215—62no—
326#215—62no—
327#215—62no—
328#215—64no—
329#213—62no—
330(C2×D3)⋊C4—21no—
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—61no—
341(C2×D3)⋊C4—121no—
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—121no—
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—121no—
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382D24—62no—
383#204—62no—
384C22×C32C22×D411yescharacteristic
385C2×C3⋊D3—22no—
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C32×C4—41no—
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×SD16—91no—
406C2×SD16—91no—
407C2×D8—91no—
408C4⋊Q8—31no—
409C4⋊Q8—31no—
410#126—181no—
411#126—181no—
412#125—31no—
413#125—91no—
414#124—31no—
415#124—91no—
416C22⋊Q8—181no—
417C22⋊Q8—181no—
418C22⋊Q8—181no—
419C22⋊Q8—181no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×D4—91no—
424C4×D4—91no—
425C4×D4—91no—
426C4×D4—91no—
427#117—181no—
428C2×C4⋊C4—181no—
429#107—91no—
430#106—91no—
431#106—91no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434C4⋊C8—91no—
435#103—31no—
436#103—31no—
437#103—31no—
438#103—31no—
439#103—91no—
440#103D3211yescharacteristic
441#102—31no—
442#102—31no—
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—22no—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—41no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×Q8—241no—
462C3×D4—61no—
463C3×D4—61no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4C23×D311yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—121no—
492C2×Dic3—122no—
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497D12—21no—
498D12—21no—
499D12—32no—
500D12—32no—
501D12—62no—
502D12—61no—
503D12—61no—
504D12—121no—
505C4×D3—122no—
506C4×D3—122no—
507C4×D3—122no—
508C4×D3—241no—
509C4×D3—241no—
510C4×D3—241no—
511C4×D3—241no—
512C4×D3—242no—
513Dic6—21no—
514Dic6—21no—
515Dic6—62no—
516Dic6—62no—
517Dic6—81no—
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—42no—
532C3×D3—81no—
533C2×Q8—31no—
534C2×Q8—61no—
535C2×Q8—91no—
536C2×Q8C2×D3211yescharacteristic
537C2×D4—31no—
538C2×D4—91no—
539C22×C4—181no—
540C22×C4—181no—
541C22×C4—181no—
542C22×C4—181no—
543SD16—182no—
544SD16—182no—
545D8—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—61no—
556C4⋊C4—61no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C42—31no—
575C42—31no—
576C42—91no—
577C42—181no—
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—62no—
589C2×D3—62no—
590C2×D3—122no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—241no—
596C2×D3—241no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—32no—
600C3×C4—42no—
601C3×C4—41no—
602C3×C4—41no—
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×C4D3×#4111yescharacteristic
613C3×C4D3×#4111yescharacteristic
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#336011yescharacteristic, complemented, Sylow
633C23—61no—
634C23—181no—
635Q8—21no—
636Q8—21no—
637Q8—61no—
638Q8—61no—
639Q8—182no—
640Q8—241no—
641D4—61no—
642D4—61no—
643D4—92no—
644D4—181no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—181no—
657C2×C4—362no—
658C2×C4—362no—
659C2×C4—721no—
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#567711yescharacteristic
671C2×C3#567711yescharacteristic
672C2×C3#576211yescharacteristic
673C2×C3C2×#91911yescharacteristic
674C2×C3D3×#13511yescharacteristic
675C2×C3#577011yescharacteristic
676D3—81no—
677D3—122no—
678D3—122no—
679D3—242no—
680C22—121no—
681C22—121no—
682C22—121no—
683C22—182no—
684C22—361no—
685C22—361no—
686C22D32×D411yescharacteristic
687C4—32no—
688C4—41no—
689C4—41no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—121no—
694C4—121no—
695C4—121no—
696C4—181no—
697C4—181no—
698C4—361no—
699C4#6430611yescharacteristic
700C4#6430911yescharacteristic
701C3—21no—
702C3#8162111yescharacteristic, complemented
703C3#8163211yescharacteristic, complemented
704C2—241no—
705C2—362no—
706C2#1059419111yescharacteristic
707C2#1059475311yescharacteristic
708C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenter#103D32
hypocenterC32#3360
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. #10595384C2semidirect
2. #10594470C2semidirect
3. #10592487C2semidirect
4. C3×#4800C2semidirect
5. C3×#4792C2semidirect
6. #10591615C2semidirect
8. #10591565C2semidirect
9. #10590868C2semidirect
10. #10590792C2semidirect
11. C8×#627C2semidirect
14. #10590491C2semidirect
15. #10590465C2semidirect
75. #4800D3semidirect
79. #4792D3semidirect
632. C32#3360semidirect
702. C3#81621semidirect
703. C3#81632semidirect

Maximal subgroups

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

subgroupindex
#105953842
#105944702
#105924872
C3×#48002
C3×#47922
#105916152
#105915682
#105915652
#105908682
#105907922
C8×#6272
#105907452
#105905402
#105904912
#105904652
#816323
#816213