Finite Group Databasebeta

← #11775324

Subgroups — #11775324

Order 1152.

596 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 60 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×#64106C211yesmaximal, characteristic
2#10593811C211yesmaximal, characteristic
3#10593802C211yesmaximal, characteristic
4#10590158C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#634C411yescharacteristic, complemented
7C2×C22⋊#157—21no—
8C2×#3792—21no—
9C2×C32×C4⋊C4C411yescharacteristic, complemented
10C2×#3752—21no—
11C2×C4⋊(C3⋊Dic3)—21no—
12#64106—21no—
13#64106—21no—
14#64106C412yescomplemented
15#64106C2212yes—
16#63781—21no—
17#63781C2212yes—
18#63778—21no—
19#63778C2212yes—
20C2×#897—62no—
21C23×C3⋊D3D411yescharacteristic
22C22×#157—22no—
23C22×C32×C4—21no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3—21no—
26C22×C3⋊Dic3D411yescharacteristic
27C2×C4×C3⋊D3—42no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×#634—21no—
33C2×#634—42no—
34C2×#634C2×C412yes—
35C22⋊#157—42no—
36#3792—42no—
37C2×#622—22no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4C2×C412yes—
40#3752—22no—
41#3752—22no—
42C4⋊(C3⋊Dic3)—22no—
43C4⋊(C3⋊Dic3)—22no—
44#1511—91nomaximal, Sylow
45C22×C4×D3—62no—
46C22×Dic6—62no—
47C2×C3×C4⋊C4—22no—
48C2×(C2×D3)⋊C4—64no—
49C2×C4⋊Dic3—64no—
50#897—64no—
51#897—64no—
52#897—64no—
53#897—64no—
54C23×C32C22⋊C411yescharacteristic
55C22×C3⋊D3—22no—
56C22×C3⋊D3—22no—
57C22×C3⋊D3—41no—
58C22×C3⋊D3C22⋊C411yescharacteristic
59C22×C3⋊D3C2×D411yescharacteristic
60C2×#157—42no—
61C2×#157—42no—
62C2×#157—42no—
63C2×C32×C4—22no—
64C2×C32×C4—22no—
65C2×C32×C4—42no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C22×C411yescharacteristic
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—42no—
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C2×D411yescharacteristic
73C4×C3⋊D3—41no—
74C4×C3⋊D3—41no—
75C4×C3⋊D3—41no—
76C4×C3⋊D3—41no—
77#634—42no—
78#634—42no—
79#622—42no—
80C2×C22⋊Q8—91no—
81#407—91no—
82#381—91no—
83#328—94no—
84C23×D3—62no—
85C22×C3×C4—24no—
86C22×C3×C4—22no—
87C22×Dic3—62no—
88C22×Dic3—64no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—62no—
92C2×C4×D3—62no—
93C2×C4×D3—128no—
94C2×Dic6—64no—
95C2×Dic6—64no—
96C2×Dic6—128no—
97C3×C4⋊C4—24no—
98C3×C4⋊C4—24no—
99(C2×D3)⋊C4—68no—
100(C2×D3)⋊C4—68no—
101C4⋊Dic3—68no—
102C4⋊Dic3—68no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32#9912yes—
106C22×C32C2×C22⋊C411yescharacteristic
107C2×C3⋊D3—21no—
108C2×C3⋊D3—21no—
109C2×C3⋊D3—21no—
110C2×C3⋊D3—21no—
111C2×C3⋊D3—21no—
112C2×C3⋊D3—44no—
113C2×C3⋊D3#13712yes—
114#157—82no—
115C32×C4—21no—
116C32×C4—21no—
117C32×C4—42no—
118C3⋊Dic3—21no—
119C3⋊Dic3—21no—
120C3⋊Dic3—42no—
121C22×Q8—91no—
122C23×C4—91no—
123C2×M16—181no—
124C22⋊Q8—92no—
125C22⋊Q8—92no—
126C22⋊Q8—181no—
127C22⋊Q8—181no—
128C2×C4⋊C4—181no—
129C2×C4⋊C4#15711yescharacteristic, complemented
130C2×C22⋊C4—181no—
131C2×C22⋊C4—181no—
132C22⋊C8—92no—
133C22⋊C8—181no—
134#95—92no—
135#95—181no—
136C23×C3—22no—
137C22×D3—62no—
138C22×D3—62no—
139C22×D3—68no—
140C22×D3—124no—
141C22×D3—124no—
142C2×C3×C4—28no—
143C2×C3×C4—28no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—48no—
147C2×Dic3—62no—
148C2×Dic3—62no—
149C2×Dic3—68no—
150C2×Dic3—124no—
151C2×Dic3—128no—
152C4×D3—124no—
153C4×D3—124no—
154C4×D3—124no—
155C4×D3—124no—
156Dic6—128no—
157Dic6—128no—
158C2×C32—22no—
159C2×C32C2×#9911yescharacteristic
160C2×C32#41911yescharacteristic
161C2×C32#42111yescharacteristic
162C3⋊D3—22no—
163C3⋊D3—41no—
164C24—91no—
165C2×Q8—92no—
166C2×Q8—181no—
167C2×Q8—362no—
168C22×C4—21no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—181no—
175C22×C4—182no—
176C22×C4—362no—
177C22×C4C2×#15711yescharacteristic
178M16—362no—
179C2×C8—182no—
180C4⋊C4—21no—
181C4⋊C4—182no—
182C4⋊C4—182no—
183C4⋊C4C2×#15712yes—
184C22⋊C4—182no—
185C22⋊C4—182no—
186C22⋊C4—362no—
187C22×C3—24no—
188C22×C3—24no—
189C22×C3—24no—
190C22×C3—22no—
191C2×D3—64no—
192C2×D3—64no—
193C2×D3—122no—
194C2×D3—122no—
195C2×D3—122no—
196C2×D3—122no—
197C2×D3—1216no—
198C3×C4—24no—
199C3×C4—24no—
200C3×C4—48no—
201Dic3—122no—
202Dic3—122no—
203Dic3—128no—
204C32#151111yescharacteristic, complemented, Sylow
205C23—91no—
206C23—91no—
207C23—182no—
208C23—182no—
209C23—361no—
210C23C22⋊#15711yescharacteristic
211Q8—362no—
212Q8—362no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—91no—
217C2×C4—91no—
218C2×C4—182no—
219C2×C4—182no—
220C2×C4—361no—
221C2×C4—361no—
222C2×C4—361no—
223C2×C4—361no—
224C2×C4—362no—
225C2×C4—362no—
226C2×C4—362no—
227C2×C4—362no—
228C2×C4C22⋊#15711yescharacteristic
229C2×C4C22×#15711yescharacteristic
230C8—362no—
231C2×C3—28no—
232C2×C3—22no—
233C2×C3—22no—
234C2×C3—22no—
235D3—124no—
236D3—124no—
237C22—21no—
238C22—21no—
239C22—92no—
240C22—181no—
241C22—181no—
242C22—181no—
243C22—181no—
244C22—181no—
245C22—364no—
246C22#6377412yes—
247C22C2×C22⋊#15711yescharacteristic
248C4—21no—
249C4—21no—
250C4—42no—
251C4—181no—
252C4—181no—
253C4—362no—
254C4—722no—
255C3—22no—
256C2—22no—
257C2—182no—
258C2—361no—
259C2C2×#6377411yescharacteristic
260C2#1059381611yescharacteristic
261C2#1059382911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1511
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590158C2semidirect
6. C22×#634C4semidirect
9. C2×C32×C4⋊C4C4semidirect
14. #64106C4semidirect
129. C2×C4⋊C4#157semidirect
204. C32#1511semidirect

Maximal subgroups

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

subgroupindex
C2×#641062
#105938112
#105938022
#105901582
#15119