Finite Group Databasebeta

← #11895235

Subgroups — #11895235

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#10593938C211yesmaximal, characteristic, complemented
2#10593932C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic, complemented
4C3×#4697C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590890C211yesmaximal, characteristic, complemented
7#10590863C211yesmaximal, characteristic, complemented
8#10590860C211yesmaximal, characteristic
9#10590815C211yesmaximal, characteristic, complemented
10#10590792C211yesmaximal, characteristic, complemented
11#10590760C211yesmaximal, characteristic, complemented
12#10590757C211yesmaximal, characteristic, complemented
13#10590745C211yesmaximal, characteristic
14#10590356C211yesmaximal, characteristic
15#10590292C211yesmaximal, characteristic, complemented
16#81632—31nomaximal
17#79926—31nomaximal
18C2×#3744C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C3×#875C2211yescharacteristic
22C3×#870C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63918C2211yescharacteristic
25#63895—21no—
26#63894C2211yescharacteristic
27#63894C2211yescharacteristic
28Dic3×D12C2211yescharacteristic
29#63888—21no—
30#63887—21no—
31#63883—21no—
32#63878—21no—
33#63869C2211yescharacteristic
34#63866C2211yescharacteristic
35#63865—21no—
36#63862—21no—
37#63860C2211yescharacteristic
38#63858—21no—
39Dic3×Dic6C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C32×C4×C8C2211yescharacteristic
43#63648C2211yescharacteristic
44#63644C2211yescharacteristic
45#63643C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×C4⋊(C3⋊C8)C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63563C2211yescharacteristic
61#5690—31no—
62#5671—31no—
63#5584—31no—
64#5579—31no—
65C3×#488—31no—
66C3×C8×Q8—31no—
67#5063—31no—
68#5057—31no—
69#4844—31no—
70#4844—31no—
71#4842—31no—
72#4841—31no—
73#4829—31no—
74#4829—31no—
75#4818—31no—
76#4799—31no—
77#4792—31no—
78#4788—31no—
79#4787—31no—
80#4768—31no—
81#4761—31no—
82#4756—31no—
83#4697—31no—
84#4697D311yescharacteristic, complemented
85C4×D24—31no—
86C4×#204—31no—
87C4×#204—31no—
88C4×#204—31no—
89C4×#204—61no—
90#4681—31no—
91C8×Dic6D311yescharacteristic, complemented
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×Dic6D411yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#624—21no—
100C2×#624—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105#3752—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3—21no—
110#3744—22no—
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3D411yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4D411yescharacteristic
119C3×Dic3⋊C4D411yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124#3724—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
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×#125—31no—
140C3×#124—31no—
141C3×C4×Q8—31no—
142#946—61no—
143#946—61no—
144Q8×Dic3—31no—
145#944—31no—
146C2×#215—31no—
147#936—31no—
148D4×Dic3—31no—
149C2×#213—31no—
150C2×D24—31no—
151C2×#204—31no—
152C2×#204—31no—
153C2×#204—31no—
154C2×#204—61no—
155#898—61no—
156#898—61no—
157#897—61no—
158#896—61no—
159#896—61no—
160#896—61no—
161#896—61no—
162#893—31no—
163#893—31no—
164#892—61no—
165D3×C4⋊C4—61no—
166D3×C4⋊C4—61no—
167#890—31no—
168#888—31no—
169#879—61no—
170#879—61no—
171#878—61no—
172#877—61no—
173#875—31no—
174#875C2×D311yescharacteristic
175C4×D12—31no—
176C4×D12—31no—
177C4×D12—31no—
178C4×D12—31no—
179C4×D12—31no—
180C4×D12—61no—
181#870—31no—
182#870C2×D311yescharacteristic
183#869—31no—
184#869—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C4×Dic6C2×D311yescharacteristic
190C3×C4⋊C8—31no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×C4×C8—21no—
198C3×C4×C8—31no—
199C3×C4×C8—31no—
200C3×C4×C8C2×D311yescharacteristic
201C3×C4×C8C2×D311yescharacteristic
202#835—31no—
203#832—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—61no—
208#821C2×D311yescharacteristic
209#821C2×D311yescharacteristic
210#818—31no—
211#817—31no—
212#817—31no—
213#817—31no—
214#817—61no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—61no—
221#816C2×D311yescharacteristic
222#816C2×D311yescharacteristic
223Dic3⋊C8C2×D311yescharacteristic
224Dic3⋊C8C2×D311yescharacteristic
225C8×Dic3C2×D311yescharacteristic
226C8×Dic3C2×D311yescharacteristic
227#810—31no—
228#810—31no—
229#808—31no—
230#807—31no—
231C4⋊(C3⋊C8)C2×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)#4112yes—
242C4×C3⋊D3—81no—
243#634—21no—
244#634—21no—
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—22no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257#627—81no—
258#624—42no—
259#624—81no—
260D3×Dic3—42no—
261C32×C8—21no—
262C32×C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#556—91no—
266#554—91no—
267#488—31no—
268#488—91no—
269#487—91no—
270#479—91no—
271#479—91no—
272#476—91no—
273#463—91no—
274#463—91no—
275#461—91no—
276C8×Q8—31no—
277C4×SD16—91no—
278C4×SD16—91no—
279C4×D8—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×D4—31no—
283C22×Dic3—61no—
284C2×D12—31no—
285C2×D12—31no—
286C2×D12—61no—
287C2×D12C22×D311yescharacteristic
288C2×C4×D3—61no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
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×Dic6—61no—
301C2×Dic6D1211yescharacteristic
302C2×Dic6C22×D311yescharacteristic
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C42—21no—
321C3×C42—31no—
322C3×C42—31no—
323C3×C42C22×D311yescharacteristic
324C3×C42C22×D311yescharacteristic
325#217—61no—
326#217—61no—
327#217—61no—
328#215—62no—
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—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3D1211yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—121no—
368Dic3⋊C4D1211yescharacteristic
369Dic3⋊C4D1211yescharacteristic
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—121no—
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377C2×C3⋊C8C22×D311yescharacteristic
378C2×C3⋊C8C22×D311yescharacteristic
379D24—62no—
380#204—62no—
381#204—62no—
382#204—64no—
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—21no—
392C32×C4—21no—
393C32×C4C2×#4111yescharacteristic
394C32×C42−1+411yescharacteristic
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
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—91no—
409C4⋊Q8—91no—
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—31no—
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—31no—
433C4⋊C8—31no—
434C4⋊C8—31no—
435#103—31no—
436#103—31no—
437#103—91no—
438#103—91no—
439#103—91no—
440#103—91no—
441#102—31no—
442#102—31no—
443#102—91no—
444#102—91no—
445C4×C8—31no—
446C4×C8—31no—
447C4×C8D3211yescharacteristic
448C23×C3—61no—
449C22×D3—21no—
450C22×D3—61no—
451C22×D3—61no—
452C22×D3—121no—
453C3×Q8—62no—
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—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4C2×D1211yescharacteristic
469C2×C3×C4C2×D1211yescharacteristic
470C2×C3×C4D3×D411yescharacteristic
471C2×C3×C4D3×D411yescharacteristic
472C2×C3×C4C23×D311yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—121no—
484C2×Dic3—121no—
485C2×Dic3—121no—
486C2×Dic3—122no—
487C2×Dic3C2×D1211yescharacteristic
488C2×Dic3C2×D1211yescharacteristic
489C2×Dic3C2×D1211yescharacteristic
490C2×Dic3C2×D1211yescharacteristic
491D12—21no—
492D12—21no—
493D12—32no—
494D12—32no—
495D12—62no—
496D12—61no—
497D12—61no—
498D12—121no—
499C4×D3—122no—
500C4×D3—122no—
501C4×D3—122no—
502C4×D3—241no—
503C4×D3—241no—
504C4×D3—241no—
505C4×D3—241no—
506C4×D3—242no—
507Dic6—22no—
508Dic6—21no—
509Dic6—21no—
510Dic6—62no—
511Dic6—61no—
512Dic6—61no—
513Dic6—61no—
514Dic6—61no—
515Dic6—121no—
516Dic6—241no—
517Dic6—241no—
518C3×C8—22no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C2×C32#54811yescharacteristic
529C2×C32C2×#13511yescharacteristic
530C2×C32#57711yescharacteristic
531C3⋊D3—42no—
532C3×D3—81no—
533C2×Q8—31no—
534C2×Q8—31no—
535C2×Q8—91no—
536C2×Q8—181no—
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×C8C2×D3211yescharacteristic
549C2×C8C2×D3211yescharacteristic
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
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⋊C4—181no—
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—181no—
577C42—181no—
578C42C2×D3211yescharacteristic
579C22×C3—21no—
580C22×C3—121no—
581C22×C3—121no—
582C22×C3—121no—
583C22×C3C22×D1211yescharacteristic
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—22no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—32no—
605C3×C4—41no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4#100711yescharacteristic
613C3×C4D3×#4111yescharacteristic
614C3×C4D3×#4111yescharacteristic
615C3×C4#101011yescharacteristic
616Dic3—21no—
617Dic3—21no—
618Dic3—21no—
619Dic3—41no—
620Dic3—41no—
621Dic3—41no—
622Dic3—122no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—121no—
628Dic3—121no—
629Dic3—241no—
630Dic3—241no—
631Dic3#90412yes—
632C32#336011yescharacteristic, complemented, Sylow
633C23—61no—
634C23—181no—
635Q8—62no—
636Q8—61no—
637Q8—61no—
638Q8—181no—
639Q8—181no—
640Q8—721no—
641D4—61no—
642D4—61no—
643D4—92no—
644D4—181no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—362no—
656C2×C4—362no—
657C2×C4—721no—
658C2×C4—721no—
659C2×C4D3×D1211yescharacteristic
660C2×C4D3×D1211yescharacteristic
661C2×C4C22×D3211yescharacteristic
662C8—21no—
663C8—21no—
664C8—61no—
665C8—61no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—241no—
670C2×C3#557611yescharacteristic
671C2×C3#567711yescharacteristic
672C2×C3C2×#90411yescharacteristic
673C2×C3#575111yescharacteristic
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—
686C22C2×D3×D1211yescharacteristic
687C4—21no—
688C4—21no—
689C4—32no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—121no—
694C4—121no—
695C4—121no—
696C4—361no—
697C4—361no—
698C4—361no—
699C4#6429711yescharacteristic
700C4#6430611yescharacteristic
701C3—21no—
702C3#7992611yescharacteristic, complemented
703C3#8163211yescharacteristic, complemented
704C2—241no—
705C2—362no—
706C2#1059390111yescharacteristic
707C2D3×#90411yescharacteristic
708C2#1059467911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4×C8D32
hypocenterC32#3360
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
1. #10593938C2semidirect
2. #10593932C2semidirect
3. C4×#3744C2semidirect
4. C3×#4697C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590890C2semidirect
7. #10590863C2semidirect
9. #10590815C2semidirect
10. #10590792C2semidirect
11. #10590760C2semidirect
12. #10590757C2semidirect
15. #10590292C2semidirect
84. #4697D3semidirect
91. C8×Dic6D3semidirect
632. C32#3360semidirect
702. C3#79926semidirect
703. C3#81632semidirect

Maximal subgroups

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

subgroupindex
#105939382
#105939322
C4×#37442
C3×#46972
C3×C8×Dic62
#105908902
#105908632
#105908602
#105908152
#105907922
#105907602
#105907572
#105907452
#105903562
#105902922
#816323
#799263