Finite Group Databasebeta

← #11796404

Subgroups — #11796404

Order 1152.

739 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 739 conjugacy classes of subgroups — too many to draw. Only its 78 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
1#10596145C211yesmaximal, characteristic
2#10591527C212yesmaximal, complemented
3C3×#4541C212yesmaximal, complemented
4#10589179C212yesmaximal, complemented
5#69157—32nomaximal
6C2×#3832C411yescharacteristic, complemented
7C2×D4×C3⋊D3C2211yescharacteristic
8C32×#124C2211yescharacteristic
9#64156C411yescharacteristic, complemented
10#64149C2211yescharacteristic
11#64093—22no—
12#64091—22no—
13#64083C411yescharacteristic, complemented
14#64081C411yescharacteristic, complemented
15#63974—22no—
16C3×#834C2214yes—
17#63581—22no—
18#5674—32no—
19#5674—61no—
20D3×#99—34no—
21C3×#354—32no—
22#4541D312yescomplemented
23#4474—34no—
24C23×C3⋊D3D412yes—
25C2×C32×Q8C2×C411yescharacteristic, complemented
26C2×C32×D4C2311yescharacteristic
27C2×#638—22no—
28C2×#638D412yes—
29#3832—42no—
30D4×C3⋊D3—42no—
31C2×C4⋊(C3⋊D3)—21no—
32C2×C4⋊(C3⋊D3)—22no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×#624—42no—
38C32×C22⋊C4—22no—
39C32×C42C2×C411yescharacteristic, complemented
40#3752—21no—
41#3752—22no—
42#3750—21no—
43C4×C3⋊Dic3C2×C411yescharacteristic, complemented
44C3×#217—24no—
45#3722—42no—
46#2127—91noSylow
47C2×#239—32no—
48C2×#239—61no—
49C2×D3×D4—32no—
50C2×D3×D4—61no—
51C3×#124—21no—
52C3×#124C2×D312yes—
53#947—32no—
54#947—61no—
55#940—32no—
56#940—61no—
57#884—64no—
58#884—64no—
59#882—64no—
60#882—64no—
61D3×C22⋊C4—64no—
62#874—32no—
63#874—61no—
64#872—32no—
65#872—61no—
66C3×#99—34no—
67#834C2×D314yes—
68#806—64no—
69C23×C32C2×D412yes—
70C22×C3⋊D3—21no—
71C22×C3⋊D3—22no—
72C22×C3⋊D3—22no—
73C22×C3⋊D3—82no—
74C22×C3⋊D3C22⋊C412yes—
75C22×C3⋊D3C22⋊C411yescharacteristic
76C32×Q8—41no—
77C32×D4—41no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4C22×C411yescharacteristic
81#638—42no—
82#638—82no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C4⋊(C3⋊D3)—41no—
86C4⋊(C3⋊D3)—41no—
87C4⋊(C3⋊D3)—42no—
88C4⋊(C3⋊D3)—82no—
89C4×C3⋊D3—22no—
90C4×C3⋊D3—42no—
91C2×C3×Dic3—44no—
92#624—84no—
93#535—91no—
94C2×#99—92no—
95#354—32no—
96#353—92no—
97C23×D3—34no—
98C23×D3—62no—
99C2×C3×Q8—21no—
100C2×C3×Q8C4×D312yescomplemented
101C2×C3×D4—21no—
102C2×C3×D4C22×D312yes—
103C2×#67—34no—
104C2×#67—62no—
105C2×#67—64no—
106C2×#67—64no—
107#239—124no—
108#239—124no—
109D3×D4—124no—
110D3×D4—124no—
111C2×D12—32no—
112C2×D12—32no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—62no—
116C2×D12—62no—
117C2×D12—64no—
118C2×D12—64no—
119C2×C4×D3—32no—
120C2×C4×D3—61no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—124no—
124C3×C22⋊C4—24no—
125C3×C22⋊C4—24no—
126C3×C22⋊C4—64no—
127C3×C42—21no—
128C3×C42C4×D312yescomplemented
129#217—24no—
130(C2×D3)⋊C4—62no—
131(C2×D3)⋊C4—64no—
132(C2×D3)⋊C4—62no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—124no—
135Dic3⋊C4—62no—
136Dic3⋊C4—62no—
137C4×Dic3—32no—
138C4×Dic3—61no—
139C22×C32—22no—
140C22×C32—42no—
141C22×C32C2×C22⋊C411yescharacteristic
142C2×C3⋊D3—22no—
143C2×C3⋊D3—41no—
144C2×C3⋊D3—42no—
145C2×C3⋊D3—42no—
146C2×C3⋊D3—41no—
147C2×C3⋊D3—44no—
148C2×C3⋊D3—82no—
149C2×C3⋊D3#9912yes—
150C32×C4—21no—
151C32×C4—41no—
152C32×C4—41no—
153C3⋊Dic3—21no—
154C3⋊Dic3—41no—
155C3×Dic3—84no—
156C2×#41—91no—
157C22×D4—91no—
158#127—91no—
159#127—91no—
160#124—91no—
161#124D3211yescharacteristic
162#121—182no—
163#120—182no—
164#117—91no—
165C2×C22⋊C4—182no—
166#99—34no—
167#99—182no—
168C23×C3—22no—
169C23×C3D3×D414yes—
170C22×D3—32no—
171C22×D3—34no—
172C22×D3—61no—
173C22×D3—62no—
174C22×D3—64no—
175C22×D3—64no—
176C22×D3—62no—
177C22×D3—62no—
178C22×D3—122no—
179C22×D3—122no—
180C22×D3—244no—
181C22×D3—244no—
182C3×Q8—42no—
183C3×Q8—42no—
184C3×D4—42no—
185C3×D4—42no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—21no—
191C2×C3×C4—124no—
192C2×C3×C4C2×C4×D312yes—
193#67—124no—
194#67—124no—
195#67—244no—
196#67—244no—
197C2×Dic3—32no—
198C2×Dic3—44no—
199C2×Dic3—61no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202D12—122no—
203D12—122no—
204D12—122no—
205D12—122no—
206D12—124no—
207D12—124no—
208D12—244no—
209D12—244no—
210C4×D3—64no—
211C4×D3—64no—
212C4×D3—124no—
213C4×D3—124no—
214C4×D3—248no—
215C2×C32—21no—
216C2×C32—42no—
217C2×C32C2×#9911yescharacteristic
218C3⋊D3—22no—
219C3⋊D3—42no—
220C3⋊D3—81no—
221C24—92no—
222#41—362no—
223C2×Q8#62411yescharacteristic, complemented
224C2×D4—92no—
225C2×D4—91no—
226C2×D4—91no—
227C2×D4—181no—
228C2×D4—182no—
229C2×D4—182no—
230C2×D4—362no—
231C2×D4C2×D3211yescharacteristic
232C22×C4—91no—
233C22×C4—181no—
234C22×C4—362no—
235C4⋊C4—181no—
236C22⋊C4—22no—
237C22⋊C4—64no—
238C22⋊C4—181no—
239C22⋊C4—182no—
240C22⋊C4—362no—
241C42—91no—
242C42#62411yescharacteristic, complemented
243C22×C3—24no—
244C22×C3—21no—
245C22×C3—42no—
246C22×C3—44no—
247C22×C3—44no—
248C22×C3D3×C22⋊C412yes—
249C2×D3—34no—
250C2×D3—62no—
251C2×D3—64no—
252C2×D3—122no—
253C2×D3—122no—
254C2×D3—128no—
255C2×D3—122no—
256C2×D3—124no—
257C2×D3—122no—
258C2×D3—124no—
259C2×D3—124no—
260C2×D3—124no—
261C2×D3—122no—
262C2×D3—244no—
263C2×D3—244no—
264C2×D3—244no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—42no—
268C3×C4—42no—
269C3×C4—42no—
270C3×C4—42no—
271C3×C4—244no—
272Dic3—62no—
273Dic3—62no—
274Dic3—84no—
275Dic3—122no—
276Dic3—122no—
277C32#212711yescharacteristic, complemented, Sylow
278C23—91no—
279C23—92no—
280C23—182no—
281C23—182no—
282C23—181no—
283C23—722no—
284C23#381112yes—
285Q8—41no—
286D4—41no—
287D4—361no—
288D4—361no—
289D4—362no—
290D4—362no—
291D4—722no—
292D4—722no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—91no—
296C2×C4—124no—
297C2×C4—182no—
298C2×C4—181no—
299C2×C4—362no—
300C2×C4—724no—
301C2×C4C2×#62411yescharacteristic
302C2×C3—22no—
303C2×C3—22no—
304C2×C3—21no—
305C2×C3—44no—
306C2×C3—82no—
307C2×C3D3×#9912yes—
308D3—64no—
309D3—122no—
310D3—124no—
311D3—242no—
312D3—242no—
313D3—242no—
314C22—22no—
315C22—42no—
316C22—92no—
317C22—182no—
318C22—361no—
319C22—362no—
320C22—362no—
321C22—364no—
322C22—361no—
323C22—722no—
324C22#6397411yescharacteristic
325C4—21no—
326C4—41no—
327C4—41no—
328C4—181no—
329C4—244no—
330C4—361no—
331C3—21no—
332C3#6915712yescomplemented
333C2—21no—
334C2—42no—
335C2—182no—
336C2—362no—
337C2—721no—
338C2#1059152711yescharacteristic
subgroupG/H
centerC2#10591527
commutatorC2×C32×C4C22×C4
FrattiniC2×D4C2×D32
FittingC32×#124C22
socleC2×C32C2×#99
prime radical#10596145C2
cosocleC2×C32×D4C23
hypercenter#124D32
hypocenterC32#2127
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
2. #10591527C2semidirect
3. C3×#4541C2semidirect
4. #10589179C2semidirect
6. C2×#3832C4semidirect
9. #64156C4semidirect
13. #64083C4semidirect
14. #64081C4semidirect
22. #4541D3semidirect
25. C2×C32×Q8C2×C4semidirect
34. C2×C4⋊(C3⋊D3)C2×C4semidirect
39. C32×C42C2×C4semidirect
43. C4×C3⋊Dic3C2×C4semidirect
100. C2×C3×Q8C4×D3semidirect
128. C3×C42C4×D3semidirect
223. C2×Q8#624semidirect
242. C42#624semidirect
277. C32#2127semidirect
332. C3#69157semidirect

Maximal subgroups

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

subgroupindex
#105961452
#105915272
C3×#45412
#105891792
#691573