Finite Group Databasebeta

← #11896093

Subgroups — #11896093

Order 1152.

724 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594335C211yesmaximal, characteristic
2#10594312C211yesmaximal, characteristic, complemented
3#10592553C211yesmaximal, characteristic, complemented
4C3×#4870C211yesmaximal, characteristic
5C3×#4853C211yesmaximal, characteristic, complemented
6#10590895C211yesmaximal, characteristic
7#10590800C211yesmaximal, characteristic, complemented
8#10590797C211yesmaximal, characteristic
9#10590786C211yesmaximal, characteristic, complemented
10#10590560C211yesmaximal, characteristic, complemented
11#10590556C211yesmaximal, characteristic, complemented
12#10590541C211yesmaximal, characteristic
13#10590532C211yesmaximal, characteristic
14#10590485C211yesmaximal, characteristic, complemented
15#10590475C211yesmaximal, characteristic
16#81091—31nomaximal
17#79815—31nomaximal
18#64097C2211yescharacteristic
19#64096C2211yescharacteristic
20C2×C3×Dic12C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#888C2211yescharacteristic
23C3×#887C2211yescharacteristic
24C3×#887C2211yescharacteristic
25#63918C2211yescharacteristic
26C4×#627C2211yescharacteristic
27#63866—21no—
28#63866C2211yescharacteristic
29#63863C2211yescharacteristic
30#63862—21no—
31#63860C2211yescharacteristic
32#63859—21no—
33#63855—21no—
34#63851—21no—
35#63843C2211yescharacteristic
36Dic3×Dic6C2211yescharacteristic
37#63840—21no—
38#63839—21no—
39#63837—21no—
40C2×#3719C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C32×#106C2211yescharacteristic
43#63643C2211yescharacteristic
44#63641C2211yescharacteristic
45#63637C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#815C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5722—31no—
62#5568—31no—
63Q8×Dic6—31no—
64#5542—31no—
65C3×#476—31no—
66C3×#441—31no—
67#5185—31no—
68#5182—31no—
69#5093—31no—
70#5028—31no—
71#5020—31no—
72C4×#214—31no—
73#4870D311yescharacteristic
74#4854—31no—
75#4854—31no—
76#4854—31no—
77#4854—61no—
78#4853—31no—
79#4853D311yescharacteristic, complemented
80#4849—31no—
81#4831—31no—
82#4794—31no—
83#4792—31no—
84#4789—31no—
85#4788—31no—
86#4767—31no—
87#4767—31no—
88#4765—31no—
89#4765—31no—
90#4714—31no—
91#4701—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105#3750—21no—
106#3750—21no—
107C4×C3⋊Dic3—21no—
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×(C2×D3)⋊C4—21no—
111C3×C4⋊Dic3C2311yescharacteristic
112C3×Dic3⋊C4—21no—
113C3×Dic3⋊C4—21no—
114C3×Dic3⋊C4—21no—
115C3×C4×Dic3—21no—
116C3×C4×Dic3—21no—
117C3×C4×Dic3C2311yescharacteristic
118C3×C4×Dic3C2311yescharacteristic
119C2×C3×C3⋊C8C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C3×Dic12—22no—
122#3724D411yescharacteristic
123Dic3⋊Dic3—21no—
124Dic3⋊Dic3—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3719—22no—
137#3715—22no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C3×C4⋊Q8—31no—
141C3×C4×Q8—31no—
142C3×C4×Q8—31no—
143C3×C4×D4—31no—
144#947—31no—
145Q8×Dic3—31no—
146Q8×Dic3—31no—
147#944—31no—
148#944—61no—
149#944—61no—
150C2×#216—31no—
151C2×#215—31no—
152#936—31no—
153#936—31no—
154C2×#214—31no—
155#926—61no—
156#924—61no—
157C2×Dic12—31no—
158C2×Dic12C2×D311yescharacteristic
159#898—61no—
160#896—61no—
161#893C2×D311yescharacteristic
162#888—31no—
163#888—31no—
164#888—31no—
165#888—61no—
166#888—61no—
167#888—61no—
168#888—61no—
169#888C2×D311yescharacteristic
170#887—31no—
171#887—31no—
172#887—31no—
173#887—61no—
174#887—61no—
175#887C2×D311yescharacteristic
176#887C2×D311yescharacteristic
177#879—61no—
178#879—61no—
179#876—61no—
180#875—31no—
181#872—61no—
182#869—31no—
183#869—31no—
184#869—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#106—21no—
190C3×#106—31no—
191C3×#106C2×D311yescharacteristic
192C3×#106C2×D311yescharacteristic
193C3×C4⋊C8—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#97—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#821—31no—
203#821C2×D311yescharacteristic
204#816—31no—
205#816—31no—
206#816—31no—
207#816—31no—
208#816—61no—
209#815—31no—
210#815—31no—
211#815C2×D311yescharacteristic
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—61no—
216Dic3⋊C8C2×D311yescharacteristic
217C8×Dic3—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—61no—
223#810C2×D311yescharacteristic
224#810C2×D311yescharacteristic
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—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240#634—21no—
241#634—21no—
242#634—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—42no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—81no—
257C3×Dic6#4112yes—
258#627—22no—
259#627—81no—
260C32×C8—21no—
261C3⋊(C3⋊C8)—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264Q82—91no—
265#556—91no—
266#489—91no—
267#489—91no—
268#487—91no—
269#476—31no—
270#475—91no—
271#475—91no—
272#464—91no—
273#464—91no—
274#462—91no—
275#446—91no—
276#441—31no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—31no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×D4—31no—
283C22×C3×C4—61no—
284C2×D12C22×D311yescharacteristic
285C2×C4×D3—21no—
286C2×Dic6—21no—
287C2×Dic6—31no—
288C2×Dic6—31no—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—121no—
297C2×Dic6C22×D311yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C3×Q16—62no—
300C2×C3×C8—21no—
301C2×C3×C8—31no—
302C2×C3×C8—31no—
303C2×C3×C8C22×D311yescharacteristic
304C2×C3×C8C22×D311yescharacteristic
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—61no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4C22×D311yescharacteristic
312C3×C4⋊C4C22×D311yescharacteristic
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C22⋊C4—61no—
316C3×C42—31no—
317C3×C42—31no—
318C3×C42—61no—
319C3×C42—61no—
320#217—61no—
321#217—61no—
322#217—61no—
323#217—61no—
324#216—62no—
325#215—62no—
326#214—62no—
327(C2×D3)⋊C4—21no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3C22×D311yescharacteristic
343Dic3⋊C4—21no—
344Dic3⋊C4—21no—
345Dic3⋊C4—21no—
346Dic3⋊C4—31no—
347Dic3⋊C4—31no—
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—121no—
360Dic3⋊C4—121no—
361C4×Dic3—21no—
362C4×Dic3—21no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—121no—
373C4×Dic3C22×D311yescharacteristic
374C4×Dic3C22×D311yescharacteristic
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—61no—
378C2×C3⋊C8C22×D311yescharacteristic
379C2×C3⋊C8C22×D311yescharacteristic
380Dic12—22no—
381Dic12—62no—
382C22×C32C22×D411yescharacteristic
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C32×C4—41no—
387C32×C4—41no—
388C32×C4C2×#4111yescharacteristic
389C32×C42−1+411yescharacteristic
390C3⋊Dic3—21no—
391C3⋊Dic3—21no—
392C3⋊Dic3—41no—
393C3⋊Dic3—41no—
394C3×Dic3—22no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3#13712yes—
401C2×Q16—31no—
402C2×Q16—91no—
403C2×SD16—91no—
404C4⋊Q8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409C4⋊Q8—181no—
410C4⋊Q8—181no—
411#126—181no—
412#126—181no—
413#124—91no—
414#124—91no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—181no—
423C4×D4—31no—
424#117—181no—
425#106—31no—
426#106—91no—
427#106D3211yescharacteristic
428C4⋊C8—31no—
429C4⋊C8—91no—
430C4⋊C8—91no—
431#103—31no—
432#103—31no—
433#103—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—31no—
440#102—91no—
441#97—31no—
442#97—91no—
443C4×C8—91no—
444C23×C3—61no—
445C22×D3—21no—
446C3×Q8—32no—
447C3×Q8—61no—
448C3×Q8—61no—
449C3×Q8—61no—
450C3×Q8—241no—
451C3×D4—61no—
452C3×D4—61no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—122no—
468C2×C3×C4C23×D311yescharacteristic
469C2×C3×C4C23×D311yescharacteristic
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—31no—
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×Dic3D3×D411yescharacteristic
486C2×Dic3D3×D411yescharacteristic
487C2×Dic3D3×D411yescharacteristic
488C2×Dic3D3×D411yescharacteristic
489D12—21no—
490D12—21no—
491C4×D3—42no—
492Dic6—21no—
493Dic6—21no—
494Dic6—21no—
495Dic6—62no—
496Dic6—62no—
497Dic6—62no—
498Dic6—61no—
499Dic6—61no—
500Dic6—61no—
501Dic6—61no—
502Dic6—81no—
503Dic6—121no—
504Dic6—241no—
505Dic6—241no—
506Dic6—241no—
507Dic6—241no—
508Dic6—242no—
509Dic6#23512yes—
510C3×C8—21no—
511C3×C8—21no—
512C3×C8—41no—
513C3×C8—61no—
514C3×C8—61no—
515C3⋊C8—21no—
516C3⋊C8—21no—
517C3⋊C8—61no—
518C3⋊C8—61no—
519C3⋊C8—121no—
520C2×C32#54811yescharacteristic
521C2×C32C2×#13711yescharacteristic
522C2×C32#57711yescharacteristic
523C3×D3—81no—
524C2×Q8—31no—
525C2×Q8—31no—
526C2×Q8—61no—
527C2×Q8—91no—
528C2×Q8—91no—
529C2×Q8—181no—
530C2×Q8—181no—
531C2×D4—31no—
532C22×C4—61no—
533Q16—62no—
534Q16—182no—
535SD16—182no—
536C2×C8—31no—
537C2×C8—31no—
538C2×C8—91no—
539C2×C8C2×D3211yescharacteristic
540C4⋊C4—31no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—91no—
545C4⋊C4—91no—
546C4⋊C4—91no—
547C4⋊C4—91no—
548C4⋊C4—181no—
549C4⋊C4—181no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4C2×D3211yescharacteristic
556C4⋊C4C2×D3211yescharacteristic
557C22⋊C4—61no—
558C22⋊C4—181no—
559C22⋊C4—181no—
560C22⋊C4—181no—
561C22⋊C4—181no—
562C42—31no—
563C42—31no—
564C42—61no—
565C42—61no—
566C42—91no—
567C42—181no—
568C42—181no—
569C42—181no—
570C22×C3—21no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—121no—
574C22×C3C2×D3×D411yescharacteristic
575C22×C3C2×D3×D411yescharacteristic
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—32no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—41no—
586C3×C4—62no—
587C3×C4—61no—
588C3×C4—61no—
589C3×C4—61no—
590C3×C4—81no—
591C3×C4—81no—
592C3×C4—121no—
593C3×C4—121no—
594C3×C4C2×#23511yescharacteristic
595C3×C4#100711yescharacteristic
596C3×C4D3×#4111yescharacteristic
597C3×C4#101011yescharacteristic
598Dic3—21no—
599Dic3—21no—
600Dic3—21no—
601Dic3—22no—
602Dic3—41no—
603Dic3—41no—
604Dic3—62no—
605Dic3—61no—
606Dic3—61no—
607Dic3—61no—
608Dic3—61no—
609Dic3—121no—
610Dic3—122no—
611Dic3—121no—
612Dic3—121no—
613Dic3—121no—
614Dic3—121no—
615Dic3—241no—
616Dic3#91512yes—
617C32#336911yescharacteristic, complemented, Sylow
618C23—61no—
619Q8—32no—
620Q8—61no—
621Q8—61no—
622Q8—61no—
623Q8—182no—
624Q8—181no—
625Q8—181no—
626Q8—241no—
627Q8—721no—
628Q8—721no—
629D4—61no—
630D4—61no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—91no—
641C2×C4—91no—
642C2×C4—122no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4C22×D3211yescharacteristic
646C8—21no—
647C8—61no—
648C8—61no—
649C8—181no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—241no—
654C2×C3#555211yescharacteristic
655C2×C3#563311yescharacteristic
656C2×C3C2×#91511yescharacteristic
657C2×C3#577511yescharacteristic
658C2×C3D3×#13711yescharacteristic
659C2×C3#577811yescharacteristic
660D3—81no—
661C22—121no—
662C22—121no—
663C22—121no—
664C22D32×D411yescharacteristic
665C4—32no—
666C4—41no—
667C4—41no—
668C4—62no—
669C4—61no—
670C4—61no—
671C4—61no—
672C4—121no—
673C4—121no—
674C4—181no—
675C4—181no—
676C4—361no—
677C4—361no—
678C4D3×#23511yescharacteristic
679C4#6431511yescharacteristic
680C3—21no—
681C3#7981511yescharacteristic, complemented
682C3#8109111yescharacteristic, complemented
683C2—241no—
684C2#1059437511yescharacteristic
685C2D3×#91511yescharacteristic
686C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenter#106D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594312C2semidirect
3. #10592553C2semidirect
5. C3×#4853C2semidirect
7. #10590800C2semidirect
9. #10590786C2semidirect
10. #10590560C2semidirect
11. #10590556C2semidirect
14. #10590485C2semidirect
79. #4853D3semidirect
617. C32#3369semidirect
681. C3#79815semidirect
682. C3#81091semidirect

Maximal subgroups

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

subgroupindex
#105943352
#105943122
#105925532
C3×#48702
C3×#48532
#105908952
#105908002
#105907972
#105907862
#105905602
#105905562
#105905412
#105905322
#105904852
#105904752
#810913
#798153