Finite Group Databasebeta

← #11895437

Subgroups — #11895437

Order 1152.

838 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic
3#10592783C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5#10590549C212yesmaximal, complemented
6#10590548C212yesmaximal, complemented
7#10590465C212yesmaximal, complemented
8#10590453C212yesmaximal, complemented
9#10590364C211yesmaximal, characteristic, complemented
10C4×#3717C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83703—31nomaximal
13#81588—31nomaximal
14C2×#3796—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#944—22no—
18C3×#888—21no—
19C3×#888C2212yes—
20C3×#887—21no—
21C3×#887C2212yes—
22C3×#874C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63916—21no—
26#63911C2212yes—
27Dic3×D12C2212yes—
28#63886—22no—
29C2×#3717C2211yescharacteristic
30C2×#3715C2212yes—
31#63636C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#809C2212yes—
35C3×#809C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2211yescharacteristic
40#63564C2211yescharacteristic
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×Q82—31no—
44#5722D311yescharacteristic, complemented
45#5718—31no—
46#5577—31no—
47C3×#486—31no—
48#5088—32no—
49#5088D311yescharacteristic, complemented
50#5084—31no—
51#5084—31no—
52#5084—32no—
53#5084—61no—
54#5075—31no—
55#5027—31no—
56#5027—32no—
57C4×#215—32no—
58C4×#215—31no—
59Q8×C3⋊C8—31no—
60#4762—32no—
61#4761—32no—
62#4760—32no—
63#4758—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C2×#626—22no—
76C2×#626—22no—
77C2×D3×Dic3—22no—
78#3796—44no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81C32×C42C2311yescharacteristic
82#3752—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96(C2×D3)⋊Dic3—22no—
97#3717—22no—
98#3715—24no—
99#3362—91noSylow
100C2×#239—61no—
101C2×#237—61no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—61no—
105C3×C4⋊Q8—62no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C2×D311yescharacteristic
108C3×#127—31no—
109C3×C4×Q8—31no—
110C3×C4×Q8—32no—
111C3×C4×Q8—31no—
112C3×C4×Q8—61no—
113#944—22no—
114C2×#215—32no—
115C2×#215—31no—
116#940—32no—
117#939—62no—
118#938—61no—
119D4×Dic3—32no—
120C2×#214—32no—
121C2×#204—31no—
122#895—62no—
123#895—61no—
124#888—21no—
125#888C2×D312yes—
126#887—21no—
127#887C2×D312yes—
128#874—32no—
129#874C2×D311yescharacteristic
130C4×D12—32no—
131C4×D12—31no—
132C4×D12—31no—
133C4×D12—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#102—32no—
137C3×#102—32no—
138C3×C4×C8—31no—
139#835—31no—
140#832—32no—
141#821—31no—
142#817—31no—
143#816—31no—
144Dic3⋊C8—32no—
145C8×Dic3—32no—
146#809—32no—
147#809—32no—
148#809—32no—
149#809—31no—
150#809—62no—
151#809C2×D312yes—
152#809C2×D312yes—
153#808—32no—
154#808—32no—
155#808—31no—
156#808—62no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3×D3—22no—
165C32×Q8—81no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—21no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—21no—
173C4×C3⋊D3—42no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—22no—
179C3×D12—22no—
180C3×D12—42no—
181C3×D12—81no—
182C3×Dic6—21no—
183C3×Dic6—82no—
184C3×Dic6SD1614yescomplemented
185C3×Dic6#4112yescomplemented
186#626—44no—
187#626—82no—
188D3×Dic3—44no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192Q82—31no—
193#550—91no—
194#486—31no—
195#486—92no—
196#476—92no—
197#476—91no—
198#460—92no—
199#460—91no—
200C8×Q8—91no—
201C4×SD16—91no—
202C4×SD16—92no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—31no—
206C2×C3×Q8—31no—
207C2×C3×Q8—41no—
208C2×C3×Q8—62no—
209C2×C3×D4—32no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C2×#67—62no—
213C2×#67—62no—
214C22×Dic3—62no—
215#239—124no—
216#237—124no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—31no—
220C2×D12—31no—
221C2×D12—61no—
222C2×D12—62no—
223C2×D12—62no—
224C2×D12C22×D312yes—
225C2×C4×D3—62no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—121no—
229C2×Dic6—22no—
230C2×Dic6#6711yescharacteristic
231C2×Dic6C22×D311yescharacteristic
232C2×C3×C8—31no—
233C2×C3×C8—31no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4C22×D312yes—
245C3×C4⋊C4C22×D312yes—
246C3×C42—21no—
247C3×C42—32no—
248C3×C42—62no—
249C3×C42—61no—
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252#217—62no—
253#215—62no—
254#215—64no—
255#214—64no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—121no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—61no—
263C4⋊Dic3#6711yescharacteristic
264C4⋊Dic3C22×D311yescharacteristic
265Dic3⋊C4—21no—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268Dic3⋊C4#6712yes—
269C4×Dic3—21no—
270C4×Dic3—22no—
271C4×Dic3C22×D312yes—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8C22×D311yescharacteristic
276C2×C3⋊C8C22×D311yescharacteristic
277#204—62no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—21no—
286C32×C4—42no—
287C32×C4C2×SD1612yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3⋊Dic3—41no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3C2×SD1614yes—
295C2×#41—181no—
296C2×SD16—91no—
297C2×SD16—92no—
298C4⋊Q8—32no—
299C4⋊Q8—61no—
300C4⋊Q8—62no—
301C4⋊Q8D3211yescharacteristic
302#127—31no—
303#127—92no—
304#121—181no—
305#121—182no—
306C4×Q8—31no—
307C4×Q8—32no—
308C4×Q8—31no—
309C4×Q8—61no—
310C4×D4—92no—
311C4×D4—91no—
312#106—91no—
313#106—92no—
314C4⋊C8—92no—
315C4⋊C8—91no—
316#103—91no—
317#102—32no—
318#102—32no—
319#102—91no—
320#102—92no—
321#102—92no—
322C4×C8—31no—
323C4×C8—92no—
324C23×C3—62no—
325C22×D3—22no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—121no—
329C3×Q8—34no—
330C3×Q8—32no—
331C3×Q8—61no—
332C3×Q8—81no—
333C3×Q8—81no—
334C3×Q8—82no—
335C3×Q8—242no—
336C3×D4—62no—
337C3×D4—62no—
338C3×D4—122no—
339C3×D4—241no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—32no—
346C2×C3×C4—32no—
347C2×C3×C4—42no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356#67—124no—
357#67—242no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—121no—
363C2×Dic3—124no—
364C2×Dic3C2×#6712yes—
365C2×Dic3C2×#6712yes—
366D12—22no—
367D12—22no—
368D12—42no—
369D12—62no—
370D12—61no—
371D12—61no—
372D12—61no—
373D12—61no—
374D12—81no—
375D12—121no—
376D12—124no—
377D12—242no—
378C4×D3—124no—
379C4×D3—122no—
380C4×D3—122no—
381C4×D3—242no—
382Dic6—21no—
383Dic6—82no—
384Dic6#21514yescomplemented
385Dic6#23912yescomplemented
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—21no—
390C3⋊C8—62no—
391C3⋊C8—62no—
392C3⋊C8—122no—
393C2×C32#54811yescharacteristic
394C2×C32C22×SD1611yescharacteristic
395C2×C32#57611yescharacteristic
396C3⋊D3—81no—
397C3×D3—82no—
398#41—364no—
399C2×Q8—21no—
400C2×Q8—31no—
401C2×Q8—31no—
402C2×Q8—62no—
403C2×D4—32no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—91no—
407C2×D4—182no—
408C2×D4—182no—
409C22×C4—182no—
410C22×C4—181no—
411SD16—182no—
412SD16—184no—
413C2×C8—31no—
414C2×C8—31no—
415C2×C8—92no—
416C4⋊C4—21no—
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—31no—
420C4⋊C4—62no—
421C4⋊C4—62no—
422C4⋊C4—61no—
423C4⋊C4—91no—
424C4⋊C4C2×D3212yes—
425C22⋊C4—182no—
426C22⋊C4—181no—
427C42—32no—
428C42—62no—
429C42—61no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—42no—
440C2×D3—122no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—241no—
448C2×D3—241no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—34no—
455C3×C4—41no—
456C3×C4—42no—
457C3×C4—42no—
458C3×C4—62no—
459C3×C4—62no—
460C3×C4—82no—
461C3×C4—121no—
462C3×C4D3×SD1612yes—
463C3×C4C2×#21512yes—
464C3×C4C2×#23911yescharacteristic
465C3×C4#100711yescharacteristic
466C3×C4D3×#4111yescharacteristic
467C3×C4#101011yescharacteristic
468Dic3—22no—
469Dic3—22no—
470Dic3—41no—
471Dic3—121no—
472Dic3—121no—
473Dic3—241no—
474Dic3C2×#21514yes—
475C32#336211yescharacteristic, complemented, Sylow
476C23—62no—
477C23—181no—
478Q8—34no—
479Q8—32no—
480Q8—61no—
481Q8—81no—
482Q8—242no—
483D4—62no—
484D4—62no—
485D4—122no—
486D4—181no—
487D4—181no—
488D4—241no—
489D4—364no—
490D4—722no—
491C2×C4—22no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—181no—
497C2×C4—364no—
498C2×C4—362no—
499C2×C4D3×#6711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—61no—
503C8—61no—
504C8—182no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—242no—
509C2×C3#567711yescharacteristic
510C2×C3#575711yescharacteristic
511C2×C3C2×D3×SD1611yescharacteristic
512C2×C3C22×#21511yescharacteristic
513C2×C3#581711yescharacteristic
514C2×C3#583511yescharacteristic
515D3—82no—
516D3—242no—
517D3—241no—
518D3—241no—
519C22—122no—
520C22—122no—
521C22—122no—
522C22—361no—
523C22—361no—
524C22—361no—
525C22C2×D3×#6711yescharacteristic
526C4—21no—
527C4—34no—
528C4—42no—
529C4—62no—
530C4—62no—
531C4—121no—
532C4—361no—
533C4D3×#21512yes—
534C4#6431511yescharacteristic
535C4D3×#23911yescharacteristic
536C3—21no—
537C3#8158811yescharacteristic, complemented
538C3#8370311yescharacteristic, complemented
539C2—242no—
540C2—721no—
541C2#1059509611yescharacteristic
542C2C2×D3×#21511yescharacteristic
543C2#1059540111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593900C2
hypercenterC4⋊Q8D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5722C2semidirect
3. #10592783C2semidirect
4. C3×#5088C2semidirect
5. #10590549C2semidirect
6. #10590548C2semidirect
7. #10590465C2semidirect
8. #10590453C2semidirect
9. #10590364C2semidirect
10. C4×#3717C2semidirect
11. C3⋊C8×Dic6C2semidirect
44. #5722D3semidirect
49. #5088D3semidirect
184. C3×Dic6SD16semidirect
185. C3×Dic6#41semidirect
384. Dic6#215semidirect
385. Dic6#239semidirect
475. C32#3362semidirect
537. C3#81588semidirect
538. C3#83703semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
#105939002
#105927832
C3×#50882
#105905492
#105905482
#105904652
#105904532
#105903642
C4×#37172
C3⋊C8×Dic62
#837033
#815883