Finite Group Databasebeta

← #11895439

Subgroups — #11895439

Order 1152.

843 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#10593902C211yesmaximal, characteristic
3#10592787C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590549C212yesmaximal, complemented
6#10590548C212yesmaximal, complemented
7#10590466C212yesmaximal, complemented
8#10590458C212yesmaximal, complemented
9#10590367C211yesmaximal, characteristic, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83703—31nomaximal
13#81090—31nomaximal
14C2×#3799—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64083C2211yescharacteristic
17C3×#944—22no—
18C3×#888—21no—
19C3×#888C2212yes—
20C3×#887—21no—
21C3×#887C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63911C2212yes—
26#63910—22no—
27#63909—21no—
28#63894C2212yes—
29C2×#3717C2212yes—
30C2×#3715C2211yescharacteristic
31#63636C2212yes—
32#63636C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#809C2212yes—
35C3×#808C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63574C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2211yescharacteristic
40#63564C2212yes—
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×Q82—31no—
44#5722D311yescharacteristic, complemented
45#5577—31no—
46#5553—31no—
47C3×#476—31no—
48#5088—31no—
49#5088—31no—
50#5088—32no—
51#5088—61no—
52#5084—32no—
53#5084D311yescharacteristic, complemented
54#5027—32no—
55#5027—31no—
56C4×#215—31no—
57C4×#215—32no—
58Q8×C3⋊C8—31no—
59C4×#214—31no—
60#4870—32no—
61#4852—32no—
62#4848—31no—
63#4830—31no—
64#4762—32no—
65#4760—32no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C2×#626—22no—
76C2×#626—22no—
77C2×#624—22no—
78#3799—44no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81C32×C42C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×(C2×D3)⋊C4—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—21no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96#3722—22no—
97#3717—24no—
98#3715—22no—
99#3362—91noSylow
100C2×#239—61no—
101C2×#235—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×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×Q8—31no—
111C3×C4×Q8—61no—
112C3×C4×D4—31no—
113#944—22no—
114C2×#215—31no—
115C2×#215—32no—
116#940—32no—
117C2×#214—31no—
118#930—61no—
119C2×#204—32no—
120#895—62no—
121#895—61no—
122#893—32no—
123#888—21no—
124#888C2×D312yes—
125#887—21no—
126#887C2×D312yes—
127#884—62no—
128#874—32no—
129#874—31no—
130#874—31no—
131#874—61no—
132C4×D12—32no—
133C4×D12C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#106—32no—
137C3×C4⋊C8—31no—
138C3×#102—32no—
139#835—31no—
140#832—31no—
141#821—32no—
142Dic3⋊C8—32no—
143C8×Dic3—32no—
144#810—31no—
145#809—31no—
146#809—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—62no—
152#809—62no—
153#809C2×D312yes—
154#808—31no—
155#808—31no—
156#808C2×D312yes—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8—61no—
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C32×Q8—81no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—42no—
173C4⋊(C3⋊D3)—81no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—21no—
180C3×D12—21no—
181C3×C4×D3—42no—
182C3×Dic6—21no—
183C3×Dic6—82no—
184C3×Dic6SD1614yescomplemented
185C3×Dic6#4112yescomplemented
186#626—44no—
187#626—82no—
188#624—44no—
189C3⋊(C3⋊C8)—21no—
190C3⋊(C3⋊C8)—21no—
191C3×C3⋊C8—22no—
192Q82—31no—
193#550—91no—
194#486—92no—
195#486—91no—
196#476—31no—
197#476—92no—
198#460—92no—
199#460—91no—
200C8×Q8—91no—
201C4×SD16—92no—
202C4×SD16—91no—
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—31no—
210C22×C3×C4—61no—
211C2×#67—62no—
212C2×#67—62no—
213#239—124no—
214#235—124no—
215C2×D12—32no—
216C2×D12—32no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—62no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—121no—
225C2×D12—121no—
226C2×D12C22×D311yescharacteristic
227C2×C4×D3—21no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×Dic6—22no—
231C2×Dic6#6711yescharacteristic
232C2×Dic6C22×D311yescharacteristic
233C2×C3×C8—32no—
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—31no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4C22×D312yes—
246C3×C4⋊C4C22×D312yes—
247C3×C22⋊C4—61no—
248C3×C42—21no—
249C3×C42—32no—
250C3×C42—62no—
251C3×C42—61no—
252C3×C42C22×D311yescharacteristic
253C3×C42C22×D311yescharacteristic
254#215—64no—
255#215—62no—
256#214—62no—
257(C2×D3)⋊C4—21no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260C4⋊Dic3#6711yescharacteristic
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—21no—
264Dic3⋊C4—22no—
265Dic3⋊C4—22no—
266Dic3⋊C4#6712yes—
267C4×Dic3—21no—
268C4×Dic3—22no—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8C22×D312yes—
277#204—64no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C32×C4—21no—
286C32×C4—42no—
287C32×C4C2×SD1612yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C3×Dic3C2×SD1614yes—
295C2×#41—181no—
296C2×SD16—92no—
297C2×SD16—91no—
298C4⋊Q8—32no—
299C4⋊Q8—61no—
300C4⋊Q8—62no—
301C4⋊Q8D3211yescharacteristic
302#127—92no—
303#127—91no—
304#121—182no—
305#121—181no—
306C4×Q8—31no—
307C4×Q8—32no—
308C4×Q8—31no—
309C4×Q8—61no—
310C4×D4—31no—
311C4×D4—92no—
312#106—32no—
313#106—91no—
314C4⋊C8—31no—
315C4⋊C8—92no—
316#103—91no—
317#102—32no—
318#102—92no—
319#102—91no—
320#102—92no—
321#102—92no—
322C4×C8—92no—
323C4×C8—91no—
324C23×C3—61no—
325C22×D3—21no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—122no—
329C3×Q8—34no—
330C3×Q8—32no—
331C3×Q8—61no—
332C3×Q8—81no—
333C3×Q8—81no—
334C3×Q8—82no—
335C3×Q8—242no—
336C3×D4—61no—
337C3×D4—61no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—42no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—122no—
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—21no—
361C2×Dic3C2×#6712yes—
362C2×Dic3C2×#6712yes—
363D12—21no—
364D12—21no—
365D12—62no—
366D12—62no—
367D12—62no—
368D12—62no—
369D12—122no—
370D12—122no—
371D12—124no—
372D12—122no—
373D12—122no—
374D12—242no—
375D12—241no—
376D12—241no—
377D12—242no—
378D12—242no—
379C4×D3—42no—
380C4×D3—124no—
381C4×D3—124no—
382Dic6—21no—
383Dic6—82no—
384Dic6#21514yescomplemented
385Dic6#23912yescomplemented
386C3×C8—62no—
387C3⋊C8—22no—
388C3⋊C8—61no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—61no—
392C3⋊C8—121no—
393C3⋊C8—121no—
394C2×C32#54811yescharacteristic
395C2×C32C22×SD1611yescharacteristic
396C2×C32#57611yescharacteristic
397C3⋊D3—82no—
398C3×D3—81no—
399#41—364no—
400C2×Q8—21no—
401C2×Q8—31no—
402C2×Q8—31no—
403C2×Q8—62no—
404C2×D4—31no—
405C2×D4—92no—
406C2×D4—182no—
407C2×D4—182no—
408C2×D4—181no—
409C2×D4—181no—
410C22×C4—61no—
411C22×C4—182no—
412SD16—184no—
413SD16—182no—
414C2×C8—32no—
415C2×C8—91no—
416C2×C8—91no—
417C4⋊C4—21no—
418C4⋊C4—32no—
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—31no—
422C4⋊C4—62no—
423C4⋊C4—62no—
424C4⋊C4—61no—
425C4⋊C4C2×D3212yes—
426C22⋊C4—61no—
427C22⋊C4—182no—
428C42—32no—
429C42—62no—
430C42—61no—
431C42C2×D3211yescharacteristic
432C22×C3—21no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3C2×D3×D411yescharacteristic
437C22×C3C22×#6711yescharacteristic
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—41no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—242no—
448C2×D3—242no—
449C2×D3—242no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—34no—
457C3×C4—42no—
458C3×C4—42no—
459C3×C4—62no—
460C3×C4—62no—
461C3×C4—82no—
462C3×C4—121no—
463C3×C4—121no—
464C3×C4D3×SD1612yes—
465C3×C4C2×#21512yes—
466C3×C4C2×#23911yescharacteristic
467C3×C4#100711yescharacteristic
468C3×C4#100711yescharacteristic
469C3×C4D3×#4111yescharacteristic
470Dic3—22no—
471Dic3—22no—
472Dic3—41no—
473Dic3—41no—
474Dic3C2×#21514yes—
475C32#336211yescharacteristic, complemented, Sylow
476C23—61no—
477C23—182no—
478Q8—34no—
479Q8—32no—
480Q8—61no—
481Q8—81no—
482Q8—242no—
483D4—61no—
484D4—61no—
485D4—182no—
486D4—182no—
487D4—364no—
488D4—362no—
489D4—721no—
490D4—722no—
491C2×C4—22no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—122no—
498C2×C4—364no—
499C2×C4D3×#6711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—62no—
503C8—181no—
504C8—181no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—241no—
509C2×C3#563311yescharacteristic
510C2×C3C2×D3×SD1611yescharacteristic
511C2×C3#577411yescharacteristic
512C2×C3C22×#21511yescharacteristic
513C2×C3#581711yescharacteristic
514C2×C3#583511yescharacteristic
515D3—81no—
516D3—242no—
517D3—242no—
518D3—482no—
519C22—121no—
520C22—121no—
521C22—121no—
522C22—362no—
523C22—362no—
524C22—362no—
525C22C2×D3×#6711yescharacteristic
526C4—21no—
527C4—34no—
528C4—42no—
529C4—62no—
530C4—62no—
531C4—121no—
532C4—121no—
533C4D3×#21512yes—
534C4#6431611yescharacteristic
535C4D3×#23911yescharacteristic
536C3—21no—
537C3#8109011yescharacteristic, complemented
538C3#8370311yescharacteristic, complemented
539C2—241no—
540C2—722no—
541C2#1059509711yescharacteristic
542C2C2×D3×#21511yescharacteristic
543C2#1059540211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593902C2
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. #10592787C2semidirect
4. C3×#5084C2semidirect
5. #10590549C2semidirect
6. #10590548C2semidirect
7. #10590466C2semidirect
8. #10590458C2semidirect
9. #10590367C2semidirect
10. C4×#3715C2semidirect
11. #10590250C2semidirect
44. #5722D3semidirect
53. #5084D3semidirect
184. C3×Dic6SD16semidirect
185. C3×Dic6#41semidirect
384. Dic6#215semidirect
385. Dic6#239semidirect
475. C32#3362semidirect
537. C3#81090semidirect
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
#105939022
#105927872
C3×#50842
#105905492
#105905482
#105904662
#105904582
#105903672
C4×#37152
#105902502
#837033
#810903