Finite Group Databasebeta

← #11783905

Subgroups — #11783905

Order 1152.

630 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C4×#3830C211yesmaximal, characteristic
2C2×#63783C212yesmaximal
3#10593733C211yesmaximal, characteristic, complemented
4C4×#3788C211yesmaximal, characteristic, complemented
5#10590164C212yesmaximal, complemented
6C2×#3830C2211yescharacteristic
7C2×C4×#157C2212yes—
8C2×#3788C2212yes—
9C32×C4×D4C411yescharacteristic, complemented
10D4×C3⋊Dic3C411yescharacteristic, complemented
11C4×#638—21no—
12C2×C4×C3⋊Dic3—21no—
13#64101C2211yescharacteristic
14#64096C411yescharacteristic, complemented
15#64090—21no—
16#64086—21no—
17C42×C3⋊D3C2211yescharacteristic
18C4×#634C411yescharacteristic, complemented
19#63783C418yescomplemented
20#63781—21no—
21#63781—21no—
22#63777—21no—
23C4×#622—21no—
24C4×#237—62no—
25C22×#157—22no—
26C2×C32×D4C2×C411yescharacteristic
27C22×C32×C4—21no—
28C2×#638—21no—
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—21no—
31#3830—22no—
32#3830C2×C414yes—
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×#634C2×C411yescharacteristic
37C2×#622—22no—
38C4×#157—22no—
39C4×#157C2×C414yescomplemented
40#3788—22no—
41#3788C2×C414yescomplemented
42C32×C4⋊C4C2×C411yescharacteristic
43C32×C22⋊C4—21no—
44C32×C42C2×C411yescharacteristic
45#3757—21no—
46#3752—21no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49#3750—21no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56#1759—91nomaximal, Sylow
57C2×#237—62no—
58C3×C4×D4—22no—
59D4×Dic3—62no—
60C4×#67—64no—
61C2×C4×Dic3—64no—
62#892—62no—
63#887—62no—
64#67⋊C4—64no—
65#877—64no—
66C42×D3—62no—
67C4×Dic6—62no—
68C23×C32—21no—
69C22×C3⋊D3C2×D411yescharacteristic
70C2×#157—24no—
71C2×#157—42no—
72C2×#157—42no—
73C32×D4—21no—
74C32×D4C4212yes—
75C2×C32×C4—21no—
76C2×C32×C4—42no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22×C411yescharacteristic
80#638—24no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—24no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C2×D411yescharacteristic
88C4×C3⋊D3—41no—
89C4×C3⋊D3—41no—
90C4×C3⋊D3C22×C412yes—
91C4×C3⋊D3#4112yes—
92#634—21no—
93#634C4212yes—
94#622—24no—
95C4×#41—91no—
96C2×#104—92no—
97C4×M16—91no—
98#376—91no—
99#339—92no—
100C2×C3×D4—22no—
101C22×C3×C4—24no—
102C2×#67—64no—
103C22×Dic3—64no—
104C22×Dic3—64no—
105#237—68no—
106#237—68no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×Dic6—62no—
111C3×C4⋊C4—22no—
112C3×C22⋊C4—24no—
113C3×C42—22no—
114#217—64no—
115(C2×D3)⋊C4—64no—
116C4⋊Dic3—62no—
117Dic3⋊C4—64no—
118Dic3⋊C4—64no—
119C4×Dic3—62no—
120C4×Dic3—62no—
121C4×Dic3—62no—
122C4×Dic3—64no—
123C4×Dic3—64no—
124C4×Dic3—64no—
125C22×C32—22no—
126C22×C32—41no—
127C22×C32—41no—
128C22×C32C2×C22⋊C411yescharacteristic
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3C4×D412yes—
132#157—44no—
133C32×C4—21no—
134C32×C4—21no—
135C32×C4—41no—
136C32×C4C2×C4211yescharacteristic
137C32×C4#11711yescharacteristic
138C3⋊Dic3—22no—
139C3⋊Dic3—21no—
140C3⋊Dic3—21no—
141C3⋊Dic3—41no—
142C3⋊Dic3C4×D412yes—
143C2×#41—91no—
144C2×M16—92no—
145C4×Q8—91no—
146C4×Q8—91no—
147C4×D4—91no—
148C4×D4—181no—
149C4×D4—181no—
150C4×D4#15711yescharacteristic, complemented
151#117—91no—
152#117—181no—
153C2×C42—91no—
154C2×C42—92no—
155C2×C42—181no—
156#104—98no—
157#97—181no—
158C4×C8—181no—
159#95—181no—
160#95—181no—
161C23×C3—24no—
162C22×D3—62no—
163C3×D4—24no—
164C3×D4—24no—
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—48no—
170#67—616no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—64no—
175C2×Dic3—616no—
176C2×Dic3—64no—
177C2×Dic3—128no—
178C4×D3—64no—
179C4×D3—64no—
180C4×D3—124no—
181C4×D3—124no—
182Dic6—64no—
183Dic6—64no—
184C2×C32—42no—
185C2×C32C4×C22⋊C411yescharacteristic
186C2×C32#42111yescharacteristic
187C2×C32#42111yescharacteristic
188C3⋊D3—22no—
189#41—94no—
190#41—182no—
191C2×Q8—91no—
192C2×D4—181no—
193C2×D4C2×#15711yescharacteristic
194C22×C4—21no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—181no—
199C22×C4—181no—
200C22×C4—182no—
201M16—94no—
202M16—182no—
203C2×C8—182no—
204C4⋊C4—91no—
205C4⋊C4—181no—
206C4⋊C4—181no—
207C4⋊C4C2×#15711yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—181no—
210C22⋊C4—181no—
211C42—91no—
212C42—91no—
213C42—91no—
214C42—94no—
215C42—181no—
216C42—181no—
217C42—182no—
218C42—181no—
219C42C2×#15711yescharacteristic
220C22×C3—28no—
221C22×C3—22no—
222C22×C3—44no—
223C22×C3—44no—
224C2×D3—64no—
225C2×D3—122no—
226C2×D3—122no—
227C3×C4—24no—
228C3×C4—22no—
229C3×C4—22no—
230C3×C4—42no—
231C3×C4—44no—
232Dic3—64no—
233Dic3—68no—
234Dic3—64no—
235Dic3—122no—
236Dic3—124no—
237C32#175911yescharacteristic, complemented, Sylow
238C23—21no—
239C23—91no—
240Q8—92no—
241Q8—181no—
242D4—21no—
243D4—184no—
244D4C4×#15712yes—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—91no—
248C2×C4—92no—
249C2×C4—92no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—184no—
253C2×C4—181no—
254C2×C4—184no—
255C2×C4—181no—
256C2×C4—361no—
257C2×C4—361no—
258C2×C4—362no—
259C2×C4—362no—
260C2×C4—362no—
261C2×C4C22⋊#15711yescharacteristic
262C2×C4C22⋊#15711yescharacteristic
263C2×C4C22×#15711yescharacteristic
264C8—184no—
265C2×C3—22no—
266C2×C3—22no—
267C2×C3—22no—
268C2×C3—48no—
269D3—124no—
270C22—22no—
271C22—41no—
272C22—41no—
273C22—92no—
274C22—181no—
275C22—181no—
276C22C2×C22⋊#15711yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—92no—
281C4—182no—
282C4—181no—
283C4—181no—
284C4—364no—
285C4—361no—
286C4C2×C4×#15711yescharacteristic
287C4#6428611yescharacteristic
288C3—22no—
289C2—42no—
290C2—182no—
291C2C4×C22⋊#15711yescharacteristic
292C2#1059381611yescharacteristic
293C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3830C22
cosocleC2×C4×C3⋊D3C23
hypercenterC4×D4#157
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593733C2semidirect
4. C4×#3788C2semidirect
5. #10590164C2semidirect
9. C32×C4×D4C4semidirect
10. D4×C3⋊Dic3C4semidirect
14. #64096C4semidirect
18. C4×#634C4semidirect
19. #63783C4semidirect
39. C4×#157C2×C4semidirect
41. #3788C2×C4semidirect
150. C4×D4#157semidirect
237. C32#1759semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
C2×#637832
#105937332
C4×#37882
#105901642
#17599