Finite Group Databasebeta

← #11895368

Subgroups — #11895368

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593963C211yesmaximal, characteristic, complemented
2#10593958C211yesmaximal, characteristic, complemented
3#10592542C211yesmaximal, characteristic
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590872C212yesmaximal, complemented
7#10590774C212yesmaximal, complemented
8#10590770C212yesmaximal, complemented
9#10590763C212yesmaximal, complemented
10C4×#3717C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#81134—31nomaximal
13#79927—31nomaximal
14C2×#3745C2212yes—
15#64083C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63900—21no—
21#63897—22no—
22#63894—21no—
23#63894C2212yes—
24#63894C2212yes—
25#63888—22no—
26#63871—21no—
27#63869C2212yes—
28#63864—21no—
29#63864C2212yes—
30C2×#3717C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63648C2212yes—
33C3×#818C2212yes—
34C3×#816C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63566C2211yescharacteristic
40#63564C2211yescharacteristic
41#63564C2212yes—
42#63564C2212yes—
43#5730—31no—
44#5585—31no—
45#5585—31no—
46#5579—31no—
47C3×#477—31no—
48C3×C8×Q8—31no—
49#5088—31no—
50C4×#215—31no—
51#4891—32no—
52#4872—32no—
53#4850D311yescharacteristic, complemented
54#4847—32no—
55#4844—32no—
56#4843—31no—
57#4843—31no—
58#4843—61no—
59#4830D311yescharacteristic, complemented
60#4819—32no—
61#4800—32no—
62#4697—32no—
63#4694—31no—
64C4×D24—32no—
65C4×#204—31no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#624—22no—
75C2×#624—22no—
76C2×C32×C8C2312yes—
77C32×C42C2311yescharacteristic
78#3752—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3745—24no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3D411yescharacteristic
83C3×C4⋊Dic3C2312yes—
84C3×C4⋊Dic3C2311yescharacteristic
85C3×Dic3⋊C4—21no—
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3—21no—
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91#3724—22no—
92Dic3⋊Dic3—22no—
93#3722—22no—
94#3722—22no—
95#3722—22no—
96#3722—22no—
97#3717—22no—
98#3361—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4×Q8—31no—
101C3×C4×Q8—31no—
102#947—32no—
103#947—61no—
104#946—61no—
105#946—62no—
106C2×#215—31no—
107C2×D24—32no—
108C2×D24—32no—
109C2×D24—62no—
110C2×#204—31no—
111#897—61no—
112#896—62no—
113#894—62no—
114#894—62no—
115#893—32no—
116#893—32no—
117#893—61no—
118D3×C4⋊C4—61no—
119D3×C4⋊C4—61no—
120#890—32no—
121#875—32no—
122#875—61no—
123#874—31no—
124#874—31no—
125#874—61no—
126C4×D12—31no—
127C4×D12—31no—
128C4×D12—32no—
129C4×D12—32no—
130C4×D12—61no—
131C4×D12—61no—
132#870—32no—
133#869C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#107—32no—
137C3×C4⋊C8—21no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8C2×D311yescharacteristic
140C3×C4⋊C8C2×D311yescharacteristic
141C3×#103—32no—
142C3×C4×C8—32no—
143C3×C4×C8—31no—
144#835—31no—
145#821—32no—
146#821—32no—
147#821—31no—
148#821—32no—
149#821—32no—
150#821—62no—
151#818C2×D312yes—
152#817—31no—
153#816—31no—
154#816C2×D312yes—
155Dic3⋊C8C2×D312yes—
156C8×Dic3C2×D312yes—
157#809—31no—
158#809—32no—
159#809—32no—
160#808—31no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3⋊D3—21no—
163C22×C3⋊D3—22no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—21no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)—21no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—42no—
172C4⋊(C3⋊D3)—81no—
173C4⋊(C3⋊D3)#4112yes—
174C4×C3⋊D3—42no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×Dic6—22no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6—81no—
184#624—82no—
185#624—82no—
186C32×C8—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#559—91no—
190#554—91no—
191#488—92no—
192#486—91no—
193#478—92no—
194#477—31no—
195#463—92no—
196#459—91no—
197C8×Q8—31no—
198C4×SD16—91no—
199C4×D8—92no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×D12—31no—
204C2×D12—31no—
205C2×D12—32no—
206C2×D12—32no—
207C2×D12—61no—
208C2×D12—62no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—121no—
214C2×D12—121no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—121no—
222C2×Dic6—21no—
223C2×Dic6D1211yescharacteristic
224C2×Dic6C22×D311yescharacteristic
225C2×C3×C8—22no—
226C2×C3×C8—31no—
227C2×C3×C8—31no—
228C2×C3×C8C22×D312yes—
229C2×C3×C8C22×D312yes—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—61no—
236C3×C42—21no—
237C3×C42—32no—
238C3×C42—61no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#215—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—61no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—121no—
253C4⋊Dic3—21no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—61no—
257C4⋊Dic3—62no—
258C4⋊Dic3D1211yescharacteristic
259C4⋊Dic3C22×D312yes—
260C4⋊Dic3C22×D311yescharacteristic
261Dic3⋊C4—21no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4D1212yes—
266C4×Dic3—21no—
267C4×Dic3C22×D312yes—
268C2×C3⋊C8C22×D311yescharacteristic
269C2×C3⋊C8C22×D311yescharacteristic
270D24—64no—
271D24—64no—
272D24—124no—
273#204—62no—
274C22×C32C22×D411yescharacteristic
275C2×C3⋊D3—22no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C32×C4—21no—
282C32×C4#13512yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3⋊Dic3—41no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3—42no—
291C2×SD16—91no—
292C2×D8—92no—
293C4⋊Q8—31no—
294#127—91no—
295#125—92no—
296#124—92no—
297#124—181no—
298#123—182no—
299C22⋊Q8—182no—
300C22⋊Q8—181no—
301C4×Q8—31no—
302C4×Q8—31no—
303C4×D4—92no—
304C4×D4—92no—
305C4×D4—91no—
306C4×D4—181no—
307C2×C4⋊C4—181no—
308#107—32no—
309#106—91no—
310C4⋊C8—32no—
311C4⋊C8D3211yescharacteristic
312#103—32no—
313#103—91no—
314#102—91no—
315#102—92no—
316#102—92no—
317#102—92no—
318C4×C8—32no—
319C4×C8—31no—
320C22×D3—61no—
321C22×D3—61no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—121no—
325C22×D3—122no—
326C3×Q8—62no—
327C3×Q8—61no—
328C3×Q8—61no—
329C3×Q8—241no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—62no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—22no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—121no—
350C2×Dic3C2×D1212yes—
351C2×Dic3C2×D1212yes—
352D12—32no—
353D12—32no—
354D12—62no—
355D12—61no—
356D12—61no—
357D12—62no—
358D12—62no—
359D12—62no—
360D12—62no—
361D12—121no—
362D12—122no—
363D12—122no—
364D12—122no—
365D12—122no—
366D12—242no—
367D12—241no—
368D12—241no—
369D12—242no—
370C4×D3—122no—
371C4×D3—122no—
372C4×D3—242no—
373C4×D3—242no—
374C4×D3—242no—
375C4×D3—242no—
376C4×D3—242no—
377Dic6—22no—
378Dic6—21no—
379Dic6—21no—
380Dic6—81no—
381C3×C8—22no—
382C3×C8—22no—
383C3×C8—42no—
384C3×C8—61no—
385C3×C8—61no—
386C3⋊C8—21no—
387C3⋊C8—21no—
388C2×C32#54811yescharacteristic
389C2×C32C2×#13511yescharacteristic
390C2×C32#57611yescharacteristic
391C3⋊D3—42no—
392C3⋊D3—82no—
393C2×Q8—31no—
394C2×Q8—31no—
395C2×Q8—61no—
396C2×D4—91no—
397C2×D4—92no—
398C2×D4—181no—
399C2×D4—181no—
400C22×C4—182no—
401C22×C4—182no—
402C22×C4—181no—
403SD16—182no—
404D8—184no—
405C2×C8—31no—
406C2×C8—31no—
407C2×C8C2×D3212yes—
408C4⋊C4—31no—
409C4⋊C4—32no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C4⋊C4—91no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C22⋊C4—182no—
418C22⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22⋊C4—181no—
422C42—32no—
423C42—61no—
424C42C2×D3211yescharacteristic
425C22×C3—21no—
426C22×C3C22×D1211yescharacteristic
427C22×C3C2×D3×D411yescharacteristic
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—122no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—241no—
442C2×D3—241no—
443C2×D3—242no—
444C2×D3—242no—
445C2×D3—242no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—62no—
453C3×C4—62no—
454C3×C4—121no—
455C3×C4—122no—
456C3×C4—121no—
457C3×C4#90412yes—
458C3×C4#91912yes—
459C3×C4#100711yescharacteristic
460C3×C4#100711yescharacteristic
461C3×C4D3×#4111yescharacteristic
462C3×C4D3×#4111yescharacteristic
463Dic3—22no—
464Dic3—22no—
465Dic3—41no—
466Dic3—42no—
467Dic3—41no—
468Dic3—121no—
469Dic3—121no—
470Dic3—241no—
471C32#336111yescharacteristic, complemented, Sylow
472C23—181no—
473C23—182no—
474Q8—62no—
475Q8—61no—
476Q8—61no—
477Q8—241no—
478D4—92no—
479D4—182no—
480D4—181no—
481D4—182no—
482D4—362no—
483D4—721no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—181no—
490C2×C4—362no—
491C2×C4—722no—
492C2×C4—722no—
493C2×C4D3×D1211yescharacteristic
494C2×C4D3×D1211yescharacteristic
495C2×C4C22×D3211yescharacteristic
496C8—22no—
497C8—61no—
498C8—61no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3#557611yescharacteristic
503C2×C3#563311yescharacteristic
504C2×C3C2×#90411yescharacteristic
505C2×C3#575211yescharacteristic
506C2×C3C2×#91911yescharacteristic
507C2×C3#577411yescharacteristic
508D3—122no—
509D3—122no—
510D3—242no—
511D3—242no—
512D3—242no—
513D3—482no—
514C22—182no—
515C22—361no—
516C22—361no—
517C22—362no—
518C22—362no—
519C22—362no—
520C22C2×D3×D1211yescharacteristic
521C4—21no—
522C4—62no—
523C4—62no—
524C4—121no—
525C4—121no—
526C4—122no—
527C4—361no—
528C4#6380812yes—
529C4#6431211yescharacteristic
530C4#6431611yescharacteristic
531C3—21no—
532C3#7992711yescharacteristic, complemented
533C3#8113411yescharacteristic, complemented
534C2—362no—
535C2—722no—
536C2#1059432911yescharacteristic
537C2C2×#6380811yescharacteristic
538C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10592542C2
hypercenterC4⋊C8D32
hypocenterC32#3361
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. #10593963C2semidirect
2. #10593958C2semidirect
4. C3×#4850C2semidirect
5. C3×#4830C2semidirect
6. #10590872C2semidirect
7. #10590774C2semidirect
8. #10590770C2semidirect
9. #10590763C2semidirect
10. C4×#3717C2semidirect
11. #10590281C2semidirect
53. #4850D3semidirect
59. #4830D3semidirect
471. C32#3361semidirect
532. C3#79927semidirect
533. C3#81134semidirect

Maximal subgroups

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

subgroupindex
#105939632
#105939582
#105925422
C3×#48502
C3×#48302
#105908722
#105907742
#105907702
#105907632
C4×#37172
#105902812
#811343
#799273