Finite Group Databasebeta

← #11885782

Subgroups — #11885782

Order 1152.

1048 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#64225C212yesmaximal, complemented
2#10594618C212yesmaximal, complemented
3#10593749C211yesmaximal, characteristic, complemented
4#10593425C214yesmaximal, complemented
5#10593423C212yesmaximal, complemented
6#10593418C211yesmaximal, characteristic, complemented
7#10593417C212yesmaximal, complemented
8C4×#3774C211yesmaximal, characteristic, complemented
9C2×#3802C2214yescomplemented
10C2×D3×D12—22no—
11C2×#3787C2212yescomplemented
12C2×#3774C2211yescharacteristic
13C2×#3774C2214yescomplemented
14C2×#3774C2212yescomplemented
15C2×#3774C2212yescomplemented
16#64225—28no—
17#64102C2211yescharacteristic
18C3×#895—22no—
19#63922—24no—
20#63914C2212yescomplemented
21#63912C2214yescomplemented
22C4×#625C2212yescomplemented
23#63778C2212yescomplemented
24C4⋊#622C2211yescharacteristic, complemented
25C4×#622C2211yescharacteristic, complemented
26#63743C2211yescharacteristic, complemented
27#63739C2212yescomplemented
28#63739C2214yescomplemented
29#5609—62no—
30C22×D32—24no—
31C2×C4⋊(C3⋊D3)D411yescharacteristic
32C2×C4×C3⋊D3C2312yes—
33C2×C3×D12—22no—
34C2×C3×D12—24no—
35C2×C3×C4×D3—22no—
36C2×#626—24no—
37C2×#625—22no—
38C2×#625C2314yes—
39C2×#625C2312yes—
40#3802—28no—
41#3802—44no—
42D3×D12—48no—
43C2×#622C2312yes—
44C2×#622C2311yescharacteristic
45C2×#622C2311yescharacteristic
46#3787—24no—
47#3774—28no—
48#3774—24no—
49#3774—42no—
50#3774D414yescomplemented
51C32×C4⋊C4D411yescharacteristic
52#3752D412yes—
53C4×C3⋊Dic3C2311yescharacteristic
54C3×(C2×D3)⋊C4—24no—
55#3724C2312yes—
56(C2×D3)⋊Dic3—22no—
57D4×D8—91nomaximal, Sylow
58C2×D3×D4—64no—
59C2×D3×D4—62no—
60C22×D12—62no—
61C3×#121—62no—
62#940—62no—
63#937—64no—
64C4×#67—62no—
65#895—22no—
66#893—62no—
67#884—64no—
68#882—64no—
69C22×C3⋊D3C2×D412yes—
70C22×C3×D3—22no—
71C22×C3×D3—24no—
72C2×D32—48no—
73C2×D32—48no—
74C2×D32—84no—
75C2×C32×C4C2×D412yes—
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C2×C3⋊Dic3C2411yescharacteristic
79C4⋊(C3⋊D3)D814yescomplemented
80C4×C3⋊D3—22no—
81C4×C3⋊D3—22no—
82C2×C3×Dic3—22no—
83C3×D12—48no—
84C3×D12—44no—
85C3×C4×D3—44no—
86#626—48no—
87#625—22no—
88#625—24no—
89#625—24no—
90#625—82no—
91#625C2×D414yescomplemented
92#622—22no—
93#622—21no—
94#622C2×D412yescomplemented
95C22×D8—92no—
96D42—92no—
97#493—91no—
98#466—92no—
99#459—92no—
100#447—94no—
101C4×D8—91no—
102C8×D4—91no—
103C23×D3—64no—
104C23×D3—64no—
105C2×C3×D4—64no—
106C2×C3×D4—62no—
107C22×C3×C4—62no—
108C2×#67—62no—
109C2×#67—64no—
110C2×#67—64no—
111C2×#67—64no—
112D3×D4—128no—
113D3×D4—128no—
114D3×D4—128no—
115C2×D12—24no—
116C2×D12—22no—
117C2×D12—62no—
118C2×D12—64no—
119C2×D12—128no—
120C2×C4×D3—22no—
121C2×C4×D3—64no—
122C3×C4⋊C4—22no—
123C3×C22⋊C4—64no—
124#217—62no—
125(C2×D3)⋊C4—24no—
126(C2×D3)⋊C4—64no—
127(C2×D3)⋊C4—62no—
128Dic3⋊C4—62no—
129C4×Dic3—62no—
130C22×C32C22×D411yescharacteristic
131C2×C3⋊D3—22no—
132C2×C3⋊D3—22no—
133C2×C3⋊D3C2×D814yescomplemented
134C2×C3×D3—24no—
135C2×C3×D3—42no—
136C2×C3×D3—42no—
137C2×C3×D3—44no—
138C2×C3×D3—44no—
139C2×C3×D3—44no—
140D32—816no—
141C32×C4—22no—
142C32×C4C2×D812yescomplemented
143C3⋊Dic3—21no—
144C3⋊Dic3C22×D411yescharacteristic
145C3⋊Dic3H(5,𝔽2)11yescharacteristic
146C3×Dic3—42no—
147C22×D4—94no—
148C22×D4—182no—
149C2×D8—91no—
150C2×D8—94no—
151C2×D8—92no—
152C2×D8—92no—
153C2×D8—188no—
154C22×C8—92no—
155#127—92no—
156#121—62no—
157#121—94no—
158#120—184no—
159C4×D4—91no—
160C4×D4—92no—
161#107—91no—
162C4⋊C8—91no—
163#102—92no—
164#102—94no—
165C22⋊C8—92no—
166C4×C8—91no—
167C23×C3—62no—
168C23×C3—64no—
169C22×D3—22no—
170C22×D3—24no—
171C22×D3—64no—
172C22×D3—128no—
173C22×D3—128no—
174C22×D3—128no—
175C22×D3—128no—
176C22×D3—244no—
177C22×D3—244no—
178C3×D4—124no—
179C3×D4—128no—
180C2×C3×C4—22no—
181C2×C3×C4—24no—
182C2×C3×C4—62no—
183C2×C3×C4—124no—
184#67—64no—
185#67—64no—
186#67—124no—
187#67—124no—
188#67—128no—
189#67—244no—
190C2×Dic3—22no—
191C2×Dic3—62no—
192C2×Dic3—62no—
193D12—44no—
194D12—48no—
195D12—68no—
196D12—128no—
197C4×D3—44no—
198C4×D3—124no—
199C4×D3—124no—
200C2×C32D4211yescharacteristic
201C2×C32C22×D811yescharacteristic
202C2×C32#57611yescharacteristic
203C3⋊D3—24no—
204C3×D3—44no—
205C3×D3—84no—
206C24—184no—
207C2×D4—64no—
208C2×D4—62no—
209C2×D4—92no—
210C2×D4—94no—
211C2×D4—91no—
212C2×D4—184no—
213C2×D4—182no—
214C2×D4—188no—
215C2×D4—368no—
216C2×D4—364no—
217C22×C4—62no—
218C22×C4—92no—
219D8—94no—
220D8—184no—
221D8—188no—
222D8—362no—
223C2×C8—91no—
224C2×C8—91no—
225C2×C8—92no—
226C2×C8—184no—
227C4⋊C4—92no—
228C4⋊C4GO+(4,𝔽2)11yescharacteristic
229C22⋊C4—64no—
230C22⋊C4—92no—
231C22⋊C4—182no—
232C42—91no—
233C22×C3—22no—
234C22×C3—64no—
235C22×C3—122no—
236C22×C3—122no—
237C22×C3—124no—
238C22×C3—124no—
239C22×C3—124no—
240C2×D3—24no—
241C2×D3—42no—
242C2×D3—42no—
243C2×D3—44no—
244C2×D3—44no—
245C2×D3—44no—
246C2×D3—68no—
247C2×D3—124no—
248C2×D3—124no—
249C2×D3—2416no—
250C2×D3—2416no—
251C3×C4—24no—
252C3×C4—44no—
253C3×C4—122no—
254Dic3—42no—
255Dic3—62no—
256Dic3—62no—
257Dic3—122no—
258C32D4×D811yescharacteristic, complemented, Sylow
259C23—62no—
260C23—64no—
261C23—92no—
262C23—368no—
263C23—368no—
264C23—724no—
265D4—94no—
266D4—94no—
267D4—128no—
268D4—124no—
269D4—182no—
270D4—184no—
271D4—184no—
272D4—368no—
273D4—722no—
274C2×C4—62no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—124no—
278C2×C4—182no—
279C2×C4—182no—
280C2×C4C2×GO+(4,𝔽2)12yes—
281C2×C4C2×GO+(4,𝔽2)11yescharacteristic
282C8—92no—
283C8—182no—
284C8—181no—
285C2×C3—22no—
286C2×C3—22no—
287C2×C3—22no—
288C2×C3—124no—
289C2×C3—244no—
290D3—44no—
291D3—84no—
292D3—128no—
293C22—64no—
294C22—94no—
295C22—122no—
296C22—122no—
297C22—124no—
298C22—124no—
299C22—124no—
300C22—182no—
301C22—182no—
302C22—7216no—
303C22C22×GO+(4,𝔽2)11yescharacteristic
304C4—22no—
305C4—91no—
306C4—91no—
307C4—122no—
308C4—181no—
309C4#6422512yescomplemented
310C3—22no—
311C2—124no—
312C2—184no—
313C2—244no—
314C2C2×#6422511yescharacteristic
315C2D4×GO+(4,𝔽2)11yescharacteristic
316C2#1059652211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32D4×D8
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64225C2semidirect
2. #10594618C2semidirect
3. #10593749C2semidirect
4. #10593425C2semidirect
5. #10593423C2semidirect
6. #10593418C2semidirect
7. #10593417C2semidirect
8. C4×#3774C2semidirect
9. C2×#3802C22semidirect
11. C2×#3787C22semidirect
13. C2×#3774C22semidirect
14. C2×#3774C22semidirect
15. C2×#3774C22semidirect
20. #63914C22semidirect
21. #63912C22semidirect
22. C4×#625C22semidirect
23. #63778C22semidirect
24. C4⋊#622C22semidirect
25. C4×#622C22semidirect
26. #63743C22semidirect
27. #63739C22semidirect
28. #63739C22semidirect
50. #3774D4semidirect
79. C4⋊(C3⋊D3)D8semidirect
91. #625C2×D4semidirect
94. #622C2×D4semidirect
133. C2×C3⋊D3C2×D8semidirect
142. C32×C4C2×D8semidirect
258. C32D4×D8semidirect
309. C4#64225semidirect

Maximal subgroups

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

subgroupindex
C2×#642252
#105946182
#105937492
#105934252
#105934232
#105934182
#105934172
C4×#37742
D4×D89