Finite Group Databasebeta

← #11783755

Subgroups — #11783755

Order 1152.

838 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 838 conjugacy classes of subgroups — too many to draw. Only its 94 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×#64102C211yesmaximal, characteristic
2C4×C22⋊#157C212yesmaximal, complemented
3C2×#63774C212yesmaximal
4#10590206C212yesmaximal, complemented
5C22×C4⋊(C3⋊D3)C2211yescharacteristic
6C22×C4×C3⋊D3C411yescharacteristic, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157C2214yes—
9C2×C4×#157—22no—
10C2×C32×C4⋊C4C411yescharacteristic, complemented
11C2×#3752C411yescharacteristic, complemented
12C2×#3752C2211yescharacteristic
13C2×C4×C3⋊Dic3C411yescharacteristic, complemented
14#64102—22no—
15#64102—22no—
16#63781—22no—
17#63774C418yescomplemented
18C2×#893—62no—
19C23×C3⋊D3C2×C411yescharacteristic
20C23×C3⋊D3C2311yescharacteristic
21C22×#157—24no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C2×C4⋊(C3⋊D3)—22no—
28C2×C4⋊(C3⋊D3)—22no—
29C2×C4⋊(C3⋊D3)C2×C414yes—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—42no—
33C2×C4×C3⋊D3—42no—
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3D412yes—
36C22⋊#157—24no—
37C22⋊#157C2×C418yescomplemented
38C4×#157—44no—
39C32×C4⋊C4—22no—
40#3752—22no—
41#3752—22no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3—21no—
44C4×#99—91nomaximal, Sylow
45C22×D12—62no—
46C22×C4×D3—62no—
47C22×C4×D3—62no—
48C2×C3×C4⋊C4—22no—
49C2×(C2×D3)⋊C4—62no—
50C2×(C2×D3)⋊C4—62no—
51C2×C4×Dic3—62no—
52#893—68no—
53#893—68no—
54C23×C32C22×C411yescharacteristic
55C22×C3⋊D3—21no—
56C22×C3⋊D3—21no—
57C22×C3⋊D3—41no—
58C22×C3⋊D3—41no—
59C22×C3⋊D3—41no—
60C22×C3⋊D3—41no—
61C22×C3⋊D3C4212yescomplemented
62C22×C3⋊D3C22×C412yes—
63C22×C3⋊D3C2×D412yes—
64C22×C3⋊D3#4112yes—
65C2×#157—28no—
66C2×#157—44no—
67C2×#157—44no—
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4C4212yescomplemented
74C2×C32×C4C22⋊C412yes—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C4⋊(C3⋊D3)—28no—
81C4×C3⋊D3—24no—
82C4×C3⋊D3—42no—
83C4×C3⋊D3—42no—
84C4×C3⋊D3—42no—
85C2×C4×D4—91no—
86C2×#99—92no—
87C4×C22⋊C4—92no—
88#342—92no—
89C23×D3—62no—
90C23×D3—62no—
91C22×C3×C4—22no—
92C22×C3×C4—22no—
93C22×C3×C4—22no—
94C22×Dic3—62no—
95C22×Dic3—62no—
96C2×D12—68no—
97C2×D12—68no—
98C2×D12—68no—
99C2×C4×D3—64no—
100C2×C4×D3—64no—
101C2×C4×D3—64no—
102C2×C4×D3—64no—
103C2×C4×D3—128no—
104C2×C4×D3—128no—
105C3×C4⋊C4—28no—
106(C2×D3)⋊C4—68no—
107(C2×D3)⋊C4—68no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32C2×C4211yescharacteristic
113C22×C32C2×C22⋊C411yescharacteristic
114C22×C32#11711yescharacteristic
115C2×C3⋊D3—22no—
116C2×C3⋊D3—22no—
117C2×C3⋊D3—22no—
118C2×C3⋊D3—42no—
119C2×C3⋊D3—42no—
120C2×C3⋊D3—42no—
121C2×C3⋊D3—41no—
122C2×C3⋊D3—41no—
123C2×C3⋊D3—42no—
124C2×C3⋊D3C4×D414yes—
125#157—48no—
126C32×C4—22no—
127C32×C4—22no—
128C32×C4—41no—
129C3⋊Dic3—21no—
130C3⋊Dic3—41no—
131C3⋊Dic3#9912yescomplemented
132C22×D4—91no—
133C23×C4—91no—
134C23×C4—91no—
135C4×D4—182no—
136C4×D4—182no—
137C2×C4⋊C4#15711yescharacteristic, complemented
138C2×C22⋊C4—94no—
139C2×C22⋊C4—91no—
140C2×C22⋊C4—91no—
141C2×C42—91no—
142C2×C42—182no—
143#99—98no—
144#95—182no—
145C23×C3—22no—
146C22×D3—64no—
147C22×D3—64no—
148C22×D3—64no—
149C22×D3—64no—
150C22×D3—64no—
151C22×D3—64no—
152C22×D3—124no—
153C22×D3—124no—
154C22×D3—124no—
155C22×D3—124no—
156C2×C3×C4—24no—
157C2×C3×C4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—24no—
160C2×C3×C4—24no—
161C2×C3×C4—44no—
162C2×C3×C4—44no—
163C2×Dic3—62no—
164C2×Dic3—62no—
165C2×Dic3—68no—
166C2×Dic3—64no—
167C2×Dic3—124no—
168D12—632no—
169C4×D3—128no—
170C4×D3—128no—
171C4×D3—128no—
172C4×D3—128no—
173C2×C32—21no—
174C2×C32—21no—
175C2×C32C4×C22⋊C411yescharacteristic
176C2×C32C2×#9911yescharacteristic
177C2×C32#41011yescharacteristic
178C3⋊D3—24no—
179C3⋊D3—42no—
180C24—91no—
181C24—91no—
182C2×D4—94no—
183C2×D4—182no—
184C2×D4—182no—
185C22×C4—91no—
186C22×C4—92no—
187C22×C4—92no—
188C22×C4—91no—
189C22×C4—181no—
190C22×C4—181no—
191C22×C4—184no—
192C22×C4—362no—
193C22×C4—362no—
194C22×C4C2×#15711yescharacteristic
195C22×C4C2×#15711yescharacteristic
196C22×C4C2×#15711yescharacteristic
197C4⋊C4—22no—
198C22⋊C4—98no—
199C22⋊C4—182no—
200C22⋊C4—184no—
201C22⋊C4—182no—
202C42—181no—
203C42—181no—
204C42—364no—
205C22×C3—24no—
206C22×C3—24no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—22no—
210C2×D3—68no—
211C2×D3—68no—
212C2×D3—124no—
213C2×D3—124no—
214C2×D3—124no—
215C2×D3—128no—
216C2×D3—128no—
217C2×D3—128no—
218C2×D3—128no—
219C2×D3—124no—
220C3×C4—28no—
221C3×C4—44no—
222C3×C4—44no—
223Dic3—64no—
224Dic3—64no—
225Dic3—124no—
226C32C4×#9911yescharacteristic, complemented, Sylow
227C23—92no—
228C23—92no—
229C23—92no—
230C23—92no—
231C23—181no—
232C23—181no—
233C23—361no—
234C23—361no—
235C23—361no—
236C23—361no—
237C23C22×#15711yescharacteristic
238D4—188no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—184no—
247C2×C4—182no—
248C2×C4—188no—
249C2×C4—181no—
250C2×C4—362no—
251C2×C4—362no—
252C2×C4—362no—
253C2×C4—364no—
254C2×C4—364no—
255C2×C4—361no—
256C2×C4C4×#15712yescomplemented
257C2×C4C22⋊#15712yes—
258C2×C3—24no—
259C2×C3—24no—
260C2×C3—22no—
261C2×C3—22no—
262C2×C3—22no—
263D3—128no—
264D3—128no—
265C22—21no—
266C22—21no—
267C22—94no—
268C22—182no—
269C22—182no—
270C22—182no—
271C22—362no—
272C22—362no—
273C22—362no—
274C22—362no—
275C22—361no—
276C22—361no—
277C22C2×C4×#15711yescharacteristic
278C22#6428611yescharacteristic
279C22C2×C22⋊#15711yescharacteristic
280C4—22no—
281C4—22no—
282C4—41no—
283C4—92no—
284C4—181no—
285C4—368no—
286C4—361no—
287C3—22no—
288C2—21no—
289C2—21no—
290C2—184no—
291C2—362no—
292C2C4×C22⋊#15711yescharacteristic
293C2#1059381711yescharacteristic
294C2#1059383211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC23×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#157C2semidirect
4. #10590206C2semidirect
6. C22×C4×C3⋊D3C4semidirect
10. C2×C32×C4⋊C4C4semidirect
11. C2×#3752C4semidirect
13. C2×C4×C3⋊Dic3C4semidirect
17. #63774C4semidirect
37. C22⋊#157C2×C4semidirect
61. C22×C3⋊D3C42semidirect
73. C2×C32×C4C42semidirect
131. C3⋊Dic3#99semidirect
137. C2×C4⋊C4#157semidirect
226. C32C4×#99semidirect
256. C2×C4C4×#157semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C4×C22⋊#1572
C2×#637742
#105902062
C4×#999