Finite Group Databasebeta

← #11796348

Subgroups — #11796348

Order 1152.

733 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 733 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#124C211yesmaximal, characteristic
2#10591527C212yesmaximal
3C3×#4541C212yesmaximal, complemented
4#10589181C212yesmaximal, complemented
5D3×#354—32nomaximal
6C2×Q8×C3⋊D3C411yescharacteristic, complemented
7C2×D4×C3⋊D3C2211yescharacteristic
8C32×#124C2211yescharacteristic
9#64156C411yescharacteristic, complemented
10#64145C2211yescharacteristic
11#64094—22no—
12C22⋊C4×C3⋊D3—22no—
13#64084C411yescharacteristic, complemented
14C42×C3⋊D3C411yescharacteristic, complemented
15#63974—22no—
16C3×#834C2214yes—
17#63581—22no—
18D3×#124—32no—
19D3×#124—61no—
20D3×#99—34no—
21C3×#354—32no—
22#4541D312yescomplemented
23#4473—34no—
24C23×C3⋊D3D412yes—
25C2×C32×Q8C2×C411yescharacteristic, complemented
26C2×C32×D4C2311yescharacteristic
27C2×#638D412yes—
28Q8×C3⋊D3—41no—
29Q8×C3⋊D3—41no—
30D4×C3⋊D3—41no—
31D4×C3⋊D3—41no—
32C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×#634—21no—
37C2×#634C2×C411yescharacteristic, complemented
38C2×#624—42no—
39C32×C22⋊C4—22no—
40C32×C42C2×C411yescharacteristic, complemented
41#3757—22no—
42#3752—22no—
43#3752—22no—
44C4×C3⋊Dic3—21no—
45C4×C3⋊Dic3C2×C411yescharacteristic, complemented
46C3×#217—24no—
47#3722—42no—
48C2×#354—91noSylow
49C2×D3×Q8—32no—
50C2×D3×Q8—61no—
51C2×D3×D4—32no—
52C2×D3×D4—61no—
53C3×#124—21no—
54C3×#124C2×D312yes—
55#947—32no—
56#947—61no—
57#936—32no—
58#936—61no—
59#885—64no—
60#885—64no—
61D3×C22⋊C4—64no—
62D3×C22⋊C4—64no—
63D3×C22⋊C4—64no—
64#875—32no—
65#875—61no—
66C42×D3—32no—
67C42×D3—61no—
68C3×#99—34no—
69#834C2×D314yes—
70#806—64no—
71C23×C32C2×D412yes—
72C22×C3⋊D3—22no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3—44no—
75C22×C3⋊D3C22⋊C411yescharacteristic
76C22×C3⋊D3C22⋊C412yes—
77C32×Q8—41no—
78C32×D4—41no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4C22×C411yescharacteristic
82#638—42no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C4⋊(C3⋊D3)—41no—
87C4×C3⋊D3—21no—
88C4×C3⋊D3—21no—
89C4×C3⋊D3—42no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3—41no—
92#634—42no—
93#634—41no—
94C2×C3×Dic3—44no—
95#624—84no—
96C2×#124—91no—
97C2×#99—92no—
98#354—32no—
99#354—92no—
100C23×D3—34no—
101C23×D3—62no—
102C2×C3×Q8—21no—
103C2×C3×Q8C4×D312yescomplemented
104C2×C3×D4—21no—
105C2×C3×D4C22×D312yes—
106C2×#67—34no—
107C2×#67—62no—
108D3×Q8—122no—
109D3×Q8—122no—
110D3×Q8—122no—
111D3×Q8—122no—
112D3×D4—122no—
113D3×D4—122no—
114D3×D4—122no—
115D3×D4—122no—
116C2×D12—32no—
117C2×D12—61no—
118C2×C4×D3—32no—
119C2×C4×D3—61no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—124no—
125C2×Dic6—32no—
126C2×Dic6—61no—
127C2×Dic6—62no—
128C2×Dic6—62no—
129C3×C22⋊C4—24no—
130C3×C22⋊C4—24no—
131C3×C22⋊C4—64no—
132C3×C42—21no—
133C3×C42C4×D312yescomplemented
134#217—24no—
135#217—64no—
136#217—64no—
137(C2×D3)⋊C4—64no—
138(C2×D3)⋊C4—64no—
139(C2×D3)⋊C4—64no—
140(C2×D3)⋊C4—64no—
141(C2×D3)⋊C4—124no—
142C4×Dic3—32no—
143C4×Dic3—61no—
144C4×Dic3—62no—
145C4×Dic3—62no—
146C22×C32—22no—
147C22×C32—42no—
148C22×C32C2×C22⋊C411yescharacteristic
149C2×C3⋊D3—22no—
150C2×C3⋊D3—22no—
151C2×C3⋊D3—42no—
152C2×C3⋊D3—44no—
153C2×C3⋊D3—82no—
154C2×C3⋊D3#9911yescharacteristic
155C2×C3⋊D3#9911yescharacteristic
156C32×C4—21no—
157C32×C4—41no—
158C32×C4—41no—
159C3⋊Dic3—21no—
160C3⋊Dic3—41no—
161C3⋊Dic3—41no—
162C3×Dic3—84no—
163C22×Q8—91no—
164C22×D4—91no—
165#124—91no—
166#124—91no—
167#124—91no—
168#124—182no—
169#124D3211yescharacteristic
170C2×C22⋊C4—182no—
171C2×C22⋊C4—182no—
172C2×C42—91no—
173#99—34no—
174#99—182no—
175C23×C3—22no—
176C23×C3D3×D414yes—
177C22×D3—32no—
178C22×D3—34no—
179C22×D3—61no—
180C22×D3—62no—
181C22×D3—64no—
182C22×D3—64no—
183C22×D3—122no—
184C22×D3—122no—
185C22×D3—128no—
186C22×D3—128no—
187C3×Q8—42no—
188C3×Q8—42no—
189C3×D4—42no—
190C3×D4—42no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—124no—
197C2×C3×C4C2×C4×D312yes—
198#67—124no—
199#67—124no—
200C2×Dic3—32no—
201C2×Dic3—44no—
202C2×Dic3—61no—
203C2×Dic3—62no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—62no—
207D12—122no—
208D12—122no—
209C4×D3—62no—
210C4×D3—62no—
211C4×D3—62no—
212C4×D3—62no—
213C4×D3—122no—
214C4×D3—122no—
215C4×D3—124no—
216C4×D3—124no—
217C4×D3—122no—
218C4×D3—122no—
219C4×D3—248no—
220Dic6—124no—
221Dic6—124no—
222Dic6—122no—
223Dic6—122no—
224C2×C32—21no—
225C2×C32—42no—
226C2×C32C2×#9911yescharacteristic
227C3⋊D3—21no—
228C3⋊D3—42no—
229C3⋊D3#35412yescomplemented
230C24—92no—
231C2×Q8—91no—
232C2×Q8—181no—
233C2×Q8—361no—
234C2×Q8—361no—
235C2×Q8#62411yescharacteristic, complemented
236C2×D4—92no—
237C2×D4—91no—
238C2×D4—361no—
239C2×D4—361no—
240C2×D4C2×D3211yescharacteristic
241C22×C4—91no—
242C22×C4—181no—
243C22×C4—181no—
244C22×C4—362no—
245C22⋊C4—22no—
246C22⋊C4—64no—
247C22⋊C4—182no—
248C22⋊C4—182no—
249C22⋊C4—182no—
250C22⋊C4—362no—
251C42—91no—
252C42—181no—
253C42#62411yescharacteristic, complemented
254C22×C3—24no—
255C22×C3—21no—
256C22×C3—42no—
257C22×C3—44no—
258C22×C3—44no—
259C22×C3D3×C22⋊C412yes—
260C2×D3—32no—
261C2×D3—32no—
262C2×D3—61no—
263C2×D3—61no—
264C2×D3—64no—
265C2×D3—64no—
266C2×D3—64no—
267C2×D3—122no—
268C2×D3—128no—
269C2×D3—124no—
270C2×D3—124no—
271C2×D3—244no—
272C2×D3—244no—
273C2×D3—244no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—42no—
277C3×C4—42no—
278C3×C4—42no—
279C3×C4—42no—
280C3×C4—244no—
281Dic3—62no—
282Dic3—62no—
283Dic3—84no—
284Dic3—122no—
285Dic3—122no—
286Dic3—122no—
287Dic3—122no—
288C32C2×#35411yescharacteristic, complemented, Sylow
289C23—91no—
290C23—92no—
291C23—182no—
292C23—182no—
293C23—364no—
294C23#381112yes—
295Q8—41no—
296Q8—361no—
297Q8—362no—
298D4—41no—
299D4—361no—
300D4—362no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—91no—
304C2×C4—124no—
305C2×C4—181no—
306C2×C4—181no—
307C2×C4—181no—
308C2×C4—181no—
309C2×C4—361no—
310C2×C4—361no—
311C2×C4—362no—
312C2×C4—724no—
313C2×C4C2×#62411yescharacteristic
314C2×C3—22no—
315C2×C3—22no—
316C2×C3—21no—
317C2×C3—44no—
318C2×C3—82no—
319C2×C3D3×#9912yes—
320D3—34no—
321D3—62no—
322D3—62no—
323D3—62no—
324D3—124no—
325D3—242no—
326C22—22no—
327C22—42no—
328C22—91no—
329C22—91no—
330C22—182no—
331C22—182no—
332C22—362no—
333C22—364no—
334C22—722no—
335C22#6397411yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—181no—
340C4—244no—
341C4—361no—
342C4—361no—
343C3—21no—
344C3D3×#35412yescomplemented
345C2—21no—
346C2—42no—
347C2—92no—
348C2—181no—
349C2—362no—
350C2#1059152711yescharacteristic
subgroupG/H
centerC2#10591527
commutatorC2×C32×C4C22×C4
FrattiniC2×D4C2×D32
FittingC32×#124C22
socleC2×C32C2×#99
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C32×D4C23
hypercenter#124D32
hypocenterC32C2×#354
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
3. C3×#4541C2semidirect
4. #10589181C2semidirect
6. C2×Q8×C3⋊D3C4semidirect
9. #64156C4semidirect
13. #64084C4semidirect
14. C42×C3⋊D3C4semidirect
22. #4541D3semidirect
25. C2×C32×Q8C2×C4semidirect
37. C2×#634C2×C4semidirect
40. C32×C42C2×C4semidirect
45. C4×C3⋊Dic3C2×C4semidirect
103. C2×C3×Q8C4×D3semidirect
133. C3×C42C4×D3semidirect
229. C3⋊D3#354semidirect
235. C2×Q8#624semidirect
253. C42#624semidirect
288. C32C2×#354semidirect
344. C3D3×#354semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1242
#105915272
C3×#45412
#105891812
D3×#3543