Finite Group Databasebeta

← #11775605

Subgroups — #11775605

Order 1152.

610 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 70 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×#64155C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3#10593800C211yesmaximal, characteristic
4#10590215C214yesmaximal, complemented
5C22×C32×Q8C411yescharacteristic, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×C4⋊#157—21no—
9C2×#3787—21no—
10#64155—21no—
11#64155—21no—
12#64155C412yescomplemented
13#64155C2212yes—
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
16C2×#3750—21no—
17C22⋊#622—21no—
18#63781C2212yes—
19#63778C2212yes—
20C2×#946—62no—
21C23×C3⋊D3D411yescharacteristic
22C22×#157—22no—
23C2×C32×Q8—21no—
24C2×C32×Q8—42no—
25C2×C32×Q8C2×C412yes—
26C22×C32×C4—21no—
27C22×C32×C4C2×C411yescharacteristic
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3D411yescharacteristic
30C2×C4×C3⋊D3—42no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3C2311yescharacteristic
35C22⋊#157—42no—
36C2×#622—22no—
37C4⋊#157—42no—
38#3787—42no—
39#3752—22no—
40#3752—22no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)C2×C412yes—
43#3750—22no—
44#3750—22no—
45#1520—91nomaximal, Sylow
46C22×C3×Q8—22no—
47C22×C4×D3—62no—
48#946—64no—
49#946—64no—
50#946—64no—
51#946—64no—
52C2×(C2×D3)⋊C4—64no—
53C2×C4⋊Dic3—62no—
54C2×Dic3⋊C4—64no—
55C23×C32C22⋊C411yescharacteristic
56C22×C3⋊D3—41no—
57C22×C3⋊D3—41no—
58C22×C3⋊D3C22⋊C411yescharacteristic
59C22×C3⋊D3SD1612yes—
60C22×C3⋊D3Q1612yes—
61C22×C3⋊D3C2×D411yescharacteristic
62C2×#157—42no—
63C2×#157—42no—
64C2×#157—42no—
65C32×Q8—42no—
66C32×Q8—42no—
67C2×C32×C4—22no—
68C2×C32×C4—22no—
69C2×C32×C4—42no—
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22×C411yescharacteristic
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3—42no—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C4×C3⋊D3—22no—
78C4×C3⋊D3—22no—
79C4×C3⋊D3—41no—
80C4×C3⋊D3—41no—
81#622—42no—
82C2×C22⋊Q8—91no—
83C2×C22⋊C8—91no—
84#380—91no—
85#328—94no—
86C23×D3—62no—
87C2×C3×Q8—24no—
88C2×C3×Q8—24no—
89C2×C3×Q8—48no—
90C22×C3×C4—24no—
91C22×C3×C4—22no—
92C22×Dic3—62no—
93C22×Dic3—64no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C4×D3—62no—
98C2×C4×D3—128no—
99(C2×D3)⋊C4—68no—
100(C2×D3)⋊C4—68no—
101C4⋊Dic3—64no—
102C4⋊Dic3—64no—
103Dic3⋊C4—68no—
104Dic3⋊C4—68no—
105C22×C32—21no—
106C22×C32—21no—
107C22×C32#10312yes—
108C22×C32C2×C22⋊C411yescharacteristic
109C2×C3⋊D3—21no—
110C2×C3⋊D3—21no—
111C2×C3⋊D3—21no—
112C2×C3⋊D3—21no—
113C2×C3⋊D3—42no—
114C2×C3⋊D3—42no—
115C2×C3⋊D3#10312yes—
116C2×C3⋊D3C2×SD1611yescharacteristic
117C2×C3⋊D3C2×Q1611yescharacteristic
118#157—82no—
119C32×C4—21no—
120C32×C4—42no—
121C32×C4#9912yes—
122C3⋊Dic3—21no—
123C3⋊Dic3—21no—
124C3⋊Dic3—42no—
125C22×Q8#15711yescharacteristic, complemented
126C23×C4—91no—
127C22×C8—181no—
128C22⋊Q8—92no—
129C22⋊Q8—92no—
130C22⋊Q8—181no—
131C22⋊Q8—181no—
132C2×C4⋊C4—91no—
133C2×C4⋊C4—181no—
134C2×C4⋊C4—181no—
135C2×C22⋊C4—181no—
136C2×C22⋊C4—181no—
137C22⋊C8—92no—
138C22⋊C8—181no—
139#95—92no—
140C23×C3—22no—
141C22×D3—62no—
142C22×D3—64no—
143C22×D3—64no—
144C22×D3—62no—
145C22×D3—124no—
146C22×D3—124no—
147C3×Q8—48no—
148C3×Q8—48no—
149C2×C3×C4—28no—
150C2×C3×C4—28no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—48no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—68no—
157C2×Dic3—124no—
158C2×Dic3—128no—
159C4×D3—124no—
160C4×D3—124no—
161C4×D3—124no—
162C4×D3—124no—
163C2×C32—22no—
164C2×C32C2×#9911yescharacteristic
165C2×C32C2×#10311yescharacteristic
166C2×C32#42111yescharacteristic
167C3⋊D3—21no—
168C3⋊D3—22no—
169C3⋊D3—21no—
170C24—91no—
171C2×Q8—21no—
172C2×Q8—42no—
173C2×Q8C2×#15712yes—
174C22×C4—21no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—91no—
179C22×C4—91no—
180C22×C4—181no—
181C22×C4—182no—
182C22×C4—362no—
183C22×C4C2×#15711yescharacteristic
184C2×C8—182no—
185C2×C8—362no—
186C4⋊C4—92no—
187C4⋊C4—182no—
188C4⋊C4—182no—
189C4⋊C4—181no—
190C4⋊C4—362no—
191C22⋊C4—182no—
192C22⋊C4—182no—
193C22⋊C4—362no—
194C22×C3—24no—
195C22×C3—24no—
196C22×C3—22no—
197C22×C3—24no—
198C2×D3—64no—
199C2×D3—62no—
200C2×D3—62no—
201C2×D3—122no—
202C2×D3—122no—
203C2×D3—122no—
204C2×D3—122no—
205C2×D3—128no—
206C2×D3—128no—
207C3×C4—24no—
208C3×C4—24no—
209C3×C4—48no—
210Dic3—122no—
211Dic3—122no—
212Dic3—128no—
213C32#152011yescharacteristic, complemented, Sylow
214C23—91no—
215C23—91no—
216C23—92no—
217C23—92no—
218C23—361no—
219C23—361no—
220C23C22⋊#15711yescharacteristic
221Q8—42no—
222Q8—42no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—182no—
229C2×C4—182no—
230C2×C4—182no—
231C2×C4—361no—
232C2×C4—361no—
233C2×C4—361no—
234C2×C4—362no—
235C2×C4—362no—
236C2×C4—362no—
237C2×C4—362no—
238C2×C4C22⋊#15711yescharacteristic
239C2×C4C22×#15711yescharacteristic
240C8—362no—
241C2×C3—28no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—22no—
245D3—122no—
246D3—124no—
247D3—122no—
248C22—21no—
249C22—21no—
250C22—91no—
251C22—91no—
252C22—92no—
253C22—181no—
254C22—181no—
255C22—181no—
256C22—181no—
257C22—362no—
258C22—362no—
259C22#6378412yes—
260C22C2×C22⋊#15711yescharacteristic
261C4—21no—
262C4—42no—
263C4—181no—
264C4—181no—
265C4—362no—
266C4—722no—
267C4#6378612yes—
268C3—22no—
269C2—22no—
270C2—181no—
271C2—181no—
272C2—182no—
273C2C2×#6378411yescharacteristic
274C2#1059383111yescharacteristic
275C2C2×#6378611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×Q8#157
hypocenterC32#1520
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10590215C2semidirect
5. C22×C32×Q8C4semidirect
12. #64155C4semidirect
15. C2×C4⋊(C3⋊Dic3)C4semidirect
125. C22×Q8#157semidirect
213. C32#1520semidirect

Maximal subgroups

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

subgroupindex
C2×#641552
#105938122
#105938002
#105902152
#15209