Finite Group Databasebeta

← #11895269

Subgroups — #11895269

Order 1152.

762 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595273C211yesmaximal, characteristic, complemented
2#10594470C211yesmaximal, characteristic, complemented
3#10592486C211yesmaximal, characteristic
4C3×#4768C211yesmaximal, characteristic, complemented
5C3×#4761C211yesmaximal, characteristic, complemented
6#10591432C211yesmaximal, characteristic
7#10591403C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic
9#10590820C211yesmaximal, characteristic, complemented
10#10590760C211yesmaximal, characteristic, complemented
11#10590758C211yesmaximal, characteristic, complemented
12#10590644C211yesmaximal, characteristic, complemented
13#10590560C211yesmaximal, characteristic, complemented
14#10590490C211yesmaximal, characteristic, complemented
15#10590483C211yesmaximal, characteristic, complemented
16#81632—31nomaximal
17#81087—31nomaximal
18#64145C2211yescharacteristic
19C2×#3753C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21#64102C2211yescharacteristic
22C3×#936C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#888C2211yescharacteristic
26#63964—21no—
27#63956—21no—
28#63956—21no—
29#63955—21no—
30C4×#627C2211yescharacteristic
31#63895—21no—
32#63894C2211yescharacteristic
33#63894C2211yescharacteristic
34#63888—21no—
35#63883—21no—
36#63872C2211yescharacteristic
37#63871—21no—
38#63866C2211yescharacteristic
39#63844C2211yescharacteristic
40#63843C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C32×#102C2211yescharacteristic
43#63641C2211yescharacteristic
44#63637C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#817C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63576C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5730—31no—
62#5690—31no—
63#5671—31no—
64#5542—31no—
65C3×#488—31no—
66C3×#476—31no—
67#5093—31no—
68#5063—31no—
69#5057—31no—
70C4×#213—31no—
71#4857—31no—
72#4857—31no—
73#4852—31no—
74#4852—31no—
75#4841—31no—
76#4830—31no—
77#4818—31no—
78#4799—31no—
79#4792—31no—
80#4788—31no—
81#4787—31no—
82#4787—31no—
83#4787—31no—
84#4787—61no—
85#4768—31no—
86#4768—31no—
87#4768D311yescharacteristic, complemented
88#4761D311yescharacteristic, complemented
89#4756—31no—
90C4×#204—31no—
91C8×Dic6—31no—
92C2×C32×D4C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C22×C3×Dic3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627D411yescharacteristic
100C2×#624—21no—
101C2×#624—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3757—21no—
105#3757—21no—
106#3753—22no—
107#3752—21no—
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110#3744—22no—
111C3×#217—21no—
112C3×#217—21no—
113C3×#217—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124#3724—21no—
125#3724D411yescharacteristic
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3D411yescharacteristic
132Dic3⋊Dic3D411yescharacteristic
133#3722—21no—
134#3722—21no—
135Dic32—21no—
136Dic32—21no—
137#3717—22no—
138#3360—91noSylow
139C3×C4⋊Q8—31no—
140C3×#125—31no—
141C3×#124—31no—
142C3×C4×D4—31no—
143#946—61no—
144#946—61no—
145Q8×Dic3—31no—
146#944—31no—
147C2×#215—31no—
148#936—31no—
149#936—31no—
150#936—61no—
151#936C2×D311yescharacteristic
152D4×Dic3C2×D311yescharacteristic
153C2×#213—31no—
154C2×#213—31no—
155C2×#213—61no—
156#926—61no—
157#924—61no—
158C2×#204—31no—
159C2×#204—31no—
160C2×#204—31no—
161C2×#204—61no—
162#897—61no—
163#897—61no—
164#896—61no—
165#896—61no—
166#893—31no—
167#893—31no—
168#893—31no—
169#893—31no—
170#893—61no—
171D3×C4⋊C4—61no—
172D3×C4⋊C4—61no—
173#890—31no—
174#890—31no—
175#890C2×D311yescharacteristic
176#888C2×D311yescharacteristic
177#887—31no—
178#887—31no—
179#879—61no—
180#879—61no—
181#879—61no—
182#879—61no—
183#878—61no—
184#877—61no—
185C4×D12—31no—
186C4×D12—31no—
187#869—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C3×#106—31no—
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#102—21no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102C2×D311yescharacteristic
200C3×#102C2×D311yescharacteristic
201C3×C4×C8—31no—
202#835—31no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
205#821—31no—
206#817C2×D311yescharacteristic
207#816—31no—
208#816—31no—
209#816C2×D311yescharacteristic
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—61no—
214Dic3⋊C8C2×D311yescharacteristic
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3C2×D311yescharacteristic
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#810C2×D311yescharacteristic
226#809—31no—
227#808C2×D311yescharacteristic
228#807—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C23×C32—21no—
233C22×C3⋊D3—21no—
234C32×D4—21no—
235C32×D4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)#4112yes—
243C4×C3⋊D3—81no—
244#634—21no—
245#634—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—42no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—81no—
258#627—22no—
259#624—42no—
260#624—81no—
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—91no—
270#479—91no—
271#479—91no—
272#476—31no—
273#463—91no—
274#463—91no—
275#461—91no—
276C8×Q8—91no—
277C4×SD16—91no—
278C4×SD16—91no—
279C4×D8—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×D4—21no—
283C2×C3×D4C22×D311yescharacteristic
284C2×C3×D4C22×D311yescharacteristic
285C22×C3×C4—61no—
286C22×Dic3—21no—
287C2×D12—31no—
288C2×D12—31no—
289C2×D12—61no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—121no—
297C2×Dic6—21no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—31no—
302C2×Dic6—61no—
303C2×Dic6C22×D311yescharacteristic
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C3×C4⋊C4—21no—
310C3×C4⋊C4—31no—
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×C22⋊C4—61no—
320C3×C22⋊C4—61no—
321C3×C42—31no—
322C3×C42—31no—
323#217—21no—
324#217—21no—
325#217—21no—
326#217—61no—
327#217—61no—
328#217—61no—
329#217—61no—
330#217—121no—
331#217—121no—
332#215—62no—
333#213—62no—
334#213—62no—
335#213—122no—
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—61no—
342(C2×D3)⋊C4—121no—
343C4⋊Dic3—21no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3C22×D311yescharacteristic
352C4⋊Dic3C22×D311yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
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×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
381#204—62no—
382#204—62no—
383#204—62no—
384#204—122no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32C22×D411yescharacteristic
389C2×C3⋊D3—22no—
390C2×C3⋊D3—41no—
391C2×C3⋊D3—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—41no—
405C3×Dic3#13512yes—
406C2×SD16—91no—
407C2×SD16—91no—
408C2×D8—91no—
409C4⋊Q8—31no—
410C4⋊Q8—91no—
411#126—181no—
412#126—181no—
413#125—31no—
414#125—91no—
415#124—31no—
416#124—91no—
417C22⋊Q8—181no—
418C22⋊Q8—181no—
419C22⋊Q8—181no—
420C22⋊Q8—181no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×D4—31no—
425C4×D4—91no—
426C4×D4—91no—
427C4×D4—91no—
428#117—181no—
429C2×C4⋊C4—181no—
430#107—91no—
431#106—31no—
432#106—31no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#103—31no—
437#103—31no—
438#103—91no—
439#103—91no—
440#103—91no—
441#103—91no—
442#102—31no—
443#102—31no—
444#102—91no—
445#102D3211yescharacteristic
446C4×C8—31no—
447C4×C8—91no—
448C4×C8—91no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—41no—
452C22×D3—61no—
453C22×D3—61no—
454C22×D3—121no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—241no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—41no—
463C3×D4—41no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—41no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—122no—
477C2×C3×C4C23×D311yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—42no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—121no—
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497D12—32no—
498D12—32no—
499D12—62no—
500D12—61no—
501D12—61no—
502D12—121no—
503C4×D3—122no—
504C4×D3—122no—
505C4×D3—241no—
506C4×D3—241no—
507C4×D3—241no—
508C4×D3—241no—
509C4×D3—242no—
510Dic6—21no—
511Dic6—21no—
512Dic6—62no—
513Dic6—62no—
514Dic6—61no—
515Dic6—61no—
516Dic6—61no—
517Dic6—61no—
518Dic6—81no—
519Dic6—121no—
520Dic6—121no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C3⋊C8—61no—
529C3⋊C8—61no—
530C3⋊C8—121no—
531C2×C32—81no—
532C2×C32#54811yescharacteristic
533C2×C32C2×#13511yescharacteristic
534C2×C32#57711yescharacteristic
535C3⋊D3—42no—
536C2×Q8—31no—
537C2×Q8—61no—
538C2×Q8—91no—
539C2×Q8—91no—
540C2×D4—91no—
541C2×D4C2×D3211yescharacteristic
542C22×C4—61no—
543C22×C4—181no—
544C22×C4—181no—
545C22×C4—181no—
546SD16—182no—
547SD16—182no—
548D8—182no—
549C2×C8—31no—
550C2×C8—31no—
551C2×C8—91no—
552C2×C8C2×D3211yescharacteristic
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4C2×D3211yescharacteristic
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C22⋊C4—181no—
575C22⋊C4—181no—
576C22⋊C4—181no—
577C42—31no—
578C42—31no—
579C42—91no—
580C42—181no—
581C42—181no—
582C22×C3—21no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—81no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3C2×D3×D411yescharacteristic
593C22×C3C2×D3×D411yescharacteristic
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—122no—
597C2×D3—121no—
598C2×D3—121no—
599C2×D3—121no—
600C2×D3—121no—
601C2×D3—241no—
602C2×D3—241no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—32no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—81no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4#100711yescharacteristic
617C3×C4D3×#4111yescharacteristic
618C3×C4D3×#4111yescharacteristic
619C3×C4#101011yescharacteristic
620Dic3—21no—
621Dic3—21no—
622Dic3—21no—
623Dic3—41no—
624Dic3—41no—
625Dic3—41no—
626Dic3—41no—
627Dic3—61no—
628Dic3—61no—
629Dic3—61no—
630Dic3—61no—
631Dic3—121no—
632Dic3—121no—
633Dic3—121no—
634Dic3—121no—
635Dic3—241no—
636Dic3#91612yes—
637C32#336011yescharacteristic, complemented, Sylow
638C23—21no—
639C23—181no—
640Q8—61no—
641Q8—61no—
642Q8—182no—
643Q8—181no—
644Q8—181no—
645Q8—241no—
646D4—21no—
647D4—21no—
648D4—92no—
649D4—181no—
650C2×C4—21no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—122no—
662C2×C4—181no—
663C2×C4—362no—
664C2×C4—721no—
665C2×C4—721no—
666C2×C4C22×D3211yescharacteristic
667C8—21no—
668C8—61no—
669C8—61no—
670C8—181no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—81no—
675C2×C3—81no—
676C2×C3—161no—
677C2×C3#563311yescharacteristic
678C2×C3#567711yescharacteristic
679C2×C3C2×#91611yescharacteristic
680C2×C3D3×#13511yescharacteristic
681C2×C3#577011yescharacteristic
682C2×C3#577511yescharacteristic
683D3—122no—
684D3—122no—
685D3—242no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—182no—
690C22—361no—
691C22—361no—
692C22D32×D411yescharacteristic
693C4—32no—
694C4—41no—
695C4—61no—
696C4—61no—
697C4—61no—
698C4—121no—
699C4—121no—
700C4—121no—
701C4—121no—
702C4—181no—
703C4—181no—
704C4—361no—
705C4#6429711yescharacteristic
706C4#6431211yescharacteristic
707C3—21no—
708C3#8108711yescharacteristic, complemented
709C3#8163211yescharacteristic, complemented
710C2—81no—
711C2—362no—
712C2#1059407511yescharacteristic
713C2#1059473611yescharacteristic
714C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenter#102D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595273C2semidirect
2. #10594470C2semidirect
4. C3×#4768C2semidirect
5. C3×#4761C2semidirect
7. #10591403C2semidirect
9. #10590820C2semidirect
10. #10590760C2semidirect
11. #10590758C2semidirect
12. #10590644C2semidirect
13. #10590560C2semidirect
14. #10590490C2semidirect
15. #10590483C2semidirect
87. #4768D3semidirect
88. #4761D3semidirect
637. C32#3360semidirect
708. C3#81087semidirect
709. C3#81632semidirect

Maximal subgroups

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

subgroupindex
#105952732
#105944702
#105924862
C3×#47682
C3×#47612
#105914322
#105914032
#105914002
#105908202
#105907602
#105907582
#105906442
#105905602
#105904902
#105904832
#816323
#810873