Finite Group Databasebeta

← #11895663

Subgroups — #11895663

Order 1152.

814 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596056C211yesmaximal, characteristic
2C3×#5567C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4C4×#3719C211yesmaximal, characteristic, complemented
5#10590368C212yesmaximal, complemented
6#10590367C211yesmaximal, characteristic
7C4×#3717C212yesmaximal, complemented
8#10590308C212yesmaximal, complemented
9#10590307C211yesmaximal, characteristic, complemented
10#10590293C212yesmaximal, complemented
11#10590281C211yesmaximal, characteristic
12#83697—31nomaximal
13#79935—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64156—21no—
16#64103—22no—
17#64102—21no—
18#64084C2212yes—
19#64083C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2212yes—
21C4×#634C2211yescharacteristic
22C3×#944—21no—
23C3×#889—22no—
24C3×#887—21no—
25C3×#870C2212yes—
26C3×#869C2211yescharacteristic
27C3×C4×Dic6C2212yes—
28C3×C4×Dic6C2211yescharacteristic
29C2×#3719C2211yescharacteristic
30C2×#3717C2212yes—
31C3×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×C4⋊(C3⋊C8)C2212yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34C3×C4×C3⋊C8C2212yes—
35#63575C2211yescharacteristic
36#63573C2212yes—
37#63567C2211yescharacteristic
38#63567C2212yes—
39#63566C2211yescharacteristic
40#63564C2212yes—
41#63564C2212yes—
42#63564C2212yes—
43C3×#557—31no—
44#5585—31no—
45#5585—31no—
46#5585—61no—
47#5567D311yescharacteristic, complemented
48C3×C8×Q8—31no—
49#5094—31no—
50#5088—31no—
51#5068—32no—
52#5066—32no—
53C4×#216—31no—
54#5028—32no—
55#5027—31no—
56C4×#215—32no—
57Q8×C3⋊C8D311yescharacteristic, complemented
58#4851—31no—
59#4848—31no—
60#4847—32no—
61#4845—32no—
62C4×Dic12—31no—
63#4697—32no—
64#4694—31no—
65C4×#204—32no—
66C2×C32×Q8D411yescharacteristic
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4×C3⋊D3—22no—
71C2×#634C2311yescharacteristic
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2311yescharacteristic
74C32×C4⋊C4D411yescharacteristic
75C32×C4⋊C4D412yes—
76C32×C42C2311yescharacteristic
77C32×C42C2312yes—
78#3752—22no—
79#3752—22no—
80#3752—22no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83C4×C3⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3C2312yes—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3—21no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96#3719—22no—
97#3717—24no—
98#3365—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8—61no—
101C3×#125—32no—
102C3×#125—62no—
103C3×C4×Q8—21no—
104C3×C4×Q8—32no—
105C3×C4×Q8—31no—
106C3×C4×Q8—61no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109#947—62no—
110#947—61no—
111#947—61no—
112#944—21no—
113C2×#216—31no—
114C2×#215—32no—
115C2×Dic12—31no—
116C2×#204—32no—
117#894—64no—
118#894—62no—
119#894—62no—
120#893—62no—
121#893—61no—
122#893—61no—
123#889—22no—
124#887—21no—
125#875—32no—
126#875—32no—
127#875—62no—
128#874—31no—
129#874—31no—
130#874—61no—
131C4×D12—32no—
132C4×D12—32no—
133C4×D12—62no—
134#870C2×D312yes—
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6C2×D312yes—
140C4×Dic6C2×D311yescharacteristic
141C3×C4⋊C8—32no—
142C3×C4⋊C8—31no—
143C3×C4×C8—32no—
144C3×C4×C8—31no—
145#835—31no—
146#821—32no—
147#821—32no—
148#821—32no—
149#818—31no—
150#817—32no—
151#816—31no—
152#816—31no—
153#816—32no—
154#810—32no—
155#810—31no—
156#809—32no—
157#809—32no—
158#809—32no—
159#808—32no—
160#807—31no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C4⋊(C3⋊C8)C2×D312yes—
163C4×C3⋊C8C2×D312yes—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—22no—
166C32×Q8—22no—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—22no—
176C4⋊(C3⋊D3)—42no—
177C4⋊(C3⋊D3)—81no—
178C4×C3⋊D3—82no—
179#634—21no—
180#634—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C3×Dic6—21no—
185C3×Dic6—42no—
186C3×Dic6#4112yes—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—21no—
190#559—91no—
191#557—31no—
192#488—92no—
193#486—91no—
194#478—92no—
195#475—91no—
196#464—92no—
197#460—91no—
198C8×Q8—31no—
199C4×Q16—91no—
200C4×SD16—92no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—61no—
204C2×C3×Q8D1211yescharacteristic
205C2×C3×Q8#6711yescharacteristic
206C2×D12—32no—
207C2×D12—32no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—62no—
213C2×D12—61no—
214C2×D12—61no—
215C2×C4×D3—64no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×Dic6—21no—
219C2×Dic6—31no—
220C2×Dic6—31no—
221C2×Dic6—61no—
222C2×Dic6C22×D311yescharacteristic
223C2×C3×C8—31no—
224C2×C3×C8—32no—
225C2×C3×C8—31no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4D1211yescharacteristic
236C3×C4⋊C4D1212yes—
237C3×C4⋊C4#6711yescharacteristic
238C3×C4⋊C4#6712yes—
239C3×C42—21no—
240C3×C42—22no—
241C3×C42—62no—
242C3×C42—61no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D312yes—
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D312yes—
247#216—62no—
248#215—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—21no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—61no—
262C4⋊Dic3C22×D312yes—
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—22no—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268Dic3⋊C4—62no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271C4×Dic3—22no—
272C4×Dic3—21no—
273C4×Dic3—62no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D312yes—
279Dic12—62no—
280#204—64no—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—42no—
285C32×C4—22no—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4#13512yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C3×Dic3—41no—
296C2×Q16—91no—
297C2×SD16—92no—
298C4⋊Q8—31no—
299C4⋊Q8—61no—
300#127—91no—
301#125—32no—
302#125—62no—
303#124—92no—
304#124—181no—
305#123—182no—
306C4×Q8—32no—
307C4×Q8—31no—
308C4×Q8—61no—
309C4×Q8—91no—
310C4×Q8D3211yescharacteristic
311C4×D4—92no—
312C4×D4—181no—
313#107—91no—
314#106—92no—
315C4⋊C8—31no—
316C4⋊C8—32no—
317#103—91no—
318#103—92no—
319#103—91no—
320#102—92no—
321#102—92no—
322#102—92no—
323C4×C8—32no—
324C4×C8—31no—
325C22×D3—64no—
326C22×D3—62no—
327C22×D3—62no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—32no—
331C3×Q8—42no—
332C3×Q8—61no—
333C3×Q8—122no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—62no—
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4C2×D1212yes—
344C2×C3×C4C2×D1212yes—
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×#6712yes—
347C2×C3×C4C2×#6712yes—
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3—22no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361D12—62no—
362D12—62no—
363D12—62no—
364D12—62no—
365D12—122no—
366D12—122no—
367D12—124no—
368D12—122no—
369D12—122no—
370D12—241no—
371D12—241no—
372D12—242no—
373C4×D3—242no—
374C4×D3—242no—
375C4×D3—244no—
376Dic6—21no—
377Dic6—42no—
378Dic6—61no—
379Dic6—61no—
380Dic6—61no—
381Dic6—61no—
382Dic6—121no—
383Dic6—121no—
384Dic6#23912yes—
385C3×C8—62no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—22no—
390C3⋊C8—21no—
391C2×C32#54811yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—82no—
395C2×Q8—31no—
396C2×Q8—61no—
397C2×Q8—91no—
398C2×Q8#62611yescharacteristic
399C2×D4—92no—
400C2×D4—181no—
401C2×D4—181no—
402C22×C4—182no—
403Q16—182no—
404SD16—184no—
405C2×C8—31no—
406C2×C8—31no—
407C2×C8—32no—
408C4⋊C4—32no—
409C4⋊C4—31no—
410C4⋊C4—61no—
411C4⋊C4—62no—
412C4⋊C4—62no—
413C4⋊C4—62no—
414C4⋊C4—61no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4#62611yescharacteristic
418C4⋊C4#62612yes—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22⋊C4—182no—
422C42—62no—
423C42—61no—
424C42—181no—
425C42C2×D3212yes—
426C42C2×D3211yescharacteristic
427C22×C3—21no—
428C22×C3C22×D1211yescharacteristic
429C22×C3C22×#6711yescharacteristic
430C2×D3—124no—
431C2×D3—124no—
432C2×D3—124no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C3×C4—22no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—42no—
449C3×C4—41no—
450C3×C4—42no—
451C3×C4—62no—
452C3×C4—122no—
453C3×C4—121no—
454C3×C4#90412yes—
455C3×C4#95012yes—
456C3×C4C2×#23911yescharacteristic
457C3×C4#100711yescharacteristic
458C3×C4#100711yescharacteristic
459C3×C4D3×#4111yescharacteristic
460Dic3—22no—
461Dic3—42no—
462Dic3—41no—
463Dic3—122no—
464Dic3—122no—
465Dic3—121no—
466Dic3—121no—
467Dic3—121no—
468Dic3—121no—
469C32#336511yescharacteristic, complemented, Sylow
470C23—182no—
471Q8—22no—
472Q8—32no—
473Q8—61no—
474Q8—122no—
475Q8—181no—
476Q8—181no—
477D4—182no—
478D4—182no—
479D4—362no—
480D4—721no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—722no—
487C2×C4C2×#62612yes—
488C2×C4C2×#62612yes—
489C2×C4C2×#62611yescharacteristic
490C2×C4C2×#62611yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—61no—
493C8—62no—
494C8—61no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3#557611yescharacteristic
499C2×C3C2×#90411yescharacteristic
500C2×C3#575111yescharacteristic
501C2×C3#581711yescharacteristic
502C2×C3C2×#95011yescharacteristic
503C2×C3#583711yescharacteristic
504D3—244no—
505D3—242no—
506D3—242no—
507C22—362no—
508C22—362no—
509C22—362no—
510C22C22×#62611yescharacteristic
511C4—22no—
512C4—21no—
513C4—22no—
514C4—62no—
515C4—121no—
516C4—122no—
517C4—361no—
518C4—361no—
519C4#6382912yes—
520C4#6431611yescharacteristic
521C4D3×#23911yescharacteristic
522C3—21no—
523C3#7993511yescharacteristic, complemented
524C3#8369711yescharacteristic, complemented
525C2—722no—
526C2C2×#6382911yescharacteristic
527C2#1059534211yescharacteristic
528C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#64083C22
hypercenterC4×Q8D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5567C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
4. C4×#3719C2semidirect
5. #10590368C2semidirect
7. C4×#3717C2semidirect
8. #10590308C2semidirect
9. #10590307C2semidirect
10. #10590293C2semidirect
47. #5567D3semidirect
57. Q8×C3⋊C8D3semidirect
469. C32#3365semidirect
523. C3#79935semidirect
524. C3#83697semidirect

Maximal subgroups

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

subgroupindex
#105960562
C3×#55672
C3×Q8×C3⋊C82
C4×#37192
#105903682
#105903672
C4×#37172
#105903082
#105903072
#105902932
#105902812
#836973
#799353