Finite Group Databasebeta

← #11773853

Subgroups — #11773853

Order 1152.

1114 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#3757C211yesmaximal, characteristic
2#10593845C212yesmaximal, complemented
3#10590222C214yesmaximal, complemented
4C25×C32C411yescharacteristic
5C23×C3⋊Dic3C411yescharacteristic
6C23×C3⋊Dic3C2211yescharacteristic
7C2×#3792—22no—
8C2×#3757—22no—
9C2×#3757—22no—
10C2×#3757C412yes—
11C2×#3757C2212yes—
12C22⋊#622—22no—
13C22⋊#622C2214yescomplemented
14C22×#217—62no—
15C24×C32—21no—
16C24×C32—21no—
17C24×C32—24no—
18C24×C32—42no—
19C24×C32—42no—
20C24×C32C2×C411yescharacteristic
21C24×C32C2×C412yes—
22C22×C3⋊Dic3—21no—
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3—42no—
25C22×C3⋊Dic3—42no—
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3D412yes—
29C22×C3⋊Dic3D412yes—
30C22×C3⋊Dic3C2311yescharacteristic
31#3792—44no—
32C2×#622—24no—
33#3757—24no—
34#3757—24no—
35#1462—91nomaximal, Sylow
36C25×C3—22no—
37C23×Dic3—62no—
38C23×Dic3—62no—
39C2×#217—64no—
40C2×#217—64no—
41C2×#217—68no—
42C2×#217—68no—
43C23×C32—22no—
44C23×C32—22no—
45C23×C32—22no—
46C23×C32—24no—
47C23×C32—24no—
48C23×C32—22no—
49C23×C32—22no—
50C23×C32—42no—
51C23×C32—42no—
52C23×C32—416no—
53C23×C32—42no—
54C23×C32—42no—
55C23×C32—42no—
56C23×C32—42no—
57C23×C32C22⋊C411yescharacteristic
58C23×C32C22⋊C411yescharacteristic
59C23×C32M1614yescomplemented
60C23×C32C22×C411yescharacteristic
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3—24no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3—42no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3—42no—
67C2×C3⋊Dic3—42no—
68C2×C3⋊Dic3—42no—
69C2×C3⋊Dic3C22⋊C412yes—
70C2×C3⋊Dic3C2×D412yes—
71#622—44no—
72C22×C22⋊C4—91no—
73#407—92no—
74#323—94no—
75C24×C3—216no—
76C24×C3—24no—
77C24×C3—24no—
78C24×C3—24no—
79C24×C3—22no—
80C24×C3—48no—
81C24×C3—48no—
82C22×Dic3—62no—
83C22×Dic3—64no—
84C22×Dic3—64no—
85C22×Dic3—64no—
86C22×Dic3—62no—
87C22×Dic3—64no—
88C22×Dic3—64no—
89C22×Dic3—128no—
90C22×Dic3—128no—
91#217—616no—
92#217—616no—
93C22×C32—28no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32—21no—
98C22×C32—21no—
99C22×C32—21no—
100C22×C32—24no—
101C22×C32—44no—
102C22×C32—48no—
103C22×C32—48no—
104C22×C32—44no—
105C22×C32—42no—
106C22×C32—42no—
107C22×C32#9912yes—
108C22×C32#10012yes—
109C22×C32C2×C22⋊C411yescharacteristic
110C22×C32C2×M1612yes—
111C3⋊Dic3—22no—
112C3⋊Dic3—22no—
113C3⋊Dic3—42no—
114C25#15711yescharacteristic
115C23×C4—91no—
116C23×C4—91no—
117C2×M16—182no—
118C2×C22⋊C4—92no—
119C2×C22⋊C4—92no—
120C2×C22⋊C4—182no—
121C2×C22⋊C4—182no—
122C22⋊C8—94no—
123C22⋊C8—182no—
124C23×C3—28no—
125C23×C3—28no—
126C23×C3—28no—
127C23×C3—28no—
128C23×C3—216no—
129C23×C3—216no—
130C23×C3—28no—
131C23×C3—22no—
132C23×C3—28no—
133C23×C3—22no—
134C23×C3—22no—
135C23×C3—48no—
136C23×C3—48no—
137C23×C3—48no—
138C23×C3—48no—
139C23×C3—464no—
140C23×C3—48no—
141C23×C3—48no—
142C2×Dic3—64no—
143C2×Dic3—64no—
144C2×Dic3—68no—
145C2×Dic3—128no—
146C2×Dic3—124no—
147C2×Dic3—128no—
148C2×Dic3—124no—
149C2×Dic3—128no—
150C2×Dic3—128no—
151C2×Dic3—128no—
152C2×C32—22no—
153C2×C32—22no—
154C2×C32—22no—
155C2×C32—44no—
156C2×C32#40711yescharacteristic
157C2×C32C2×#9911yescharacteristic
158C2×C32C2×#10011yescharacteristic
159C24—24no—
160C24—21no—
161C24—21no—
162C24—42no—
163C24—42no—
164C24C2×#15712yes—
165C24C2×#15711yescharacteristic
166C22×C4—92no—
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—92no—
170C22×C4—92no—
171C22×C4—181no—
172C22×C4—181no—
173C22×C4—362no—
174C22×C4—362no—
175M16—364no—
176C2×C8—184no—
177C22⋊C4—184no—
178C22⋊C4—184no—
179C22×C3—24no—
180C22×C3—24no—
181C22×C3—24no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—24no—
185C22×C3—232no—
186C22×C3—216no—
187C22×C3—24no—
188C22×C3—22no—
189C22×C3—24no—
190C22×C3—24no—
191C22×C3—416no—
192C22×C3—416no—
193C22×C3—432no—
194C22×C3—432no—
195C22×C3—48no—
196C22×C3—48no—
197Dic3—124no—
198Dic3—124no—
199Dic3—128no—
200C32#146211yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23—22no—
204C23—24no—
205C23—24no—
206C23—22no—
207C23—22no—
208C23—42no—
209C23—42no—
210C23—416no—
211C23—42no—
212C23—42no—
213C23—42no—
214C23—42no—
215C23#379214yescomplemented
216C23C22⋊#15711yescharacteristic
217C23C22⋊#15711yescharacteristic
218C23C22×#15711yescharacteristic
219C2×C4—92no—
220C2×C4—92no—
221C2×C4—184no—
222C2×C4—182no—
223C2×C4—361no—
224C2×C4—362no—
225C2×C4—361no—
226C2×C4—362no—
227C2×C4—362no—
228C2×C4—362no—
229C8—364no—
230C2×C3—28no—
231C2×C3—28no—
232C2×C3—28no—
233C2×C3—22no—
234C2×C3—22no—
235C2×C3—22no—
236C2×C3—416no—
237C22—28no—
238C22—21no—
239C22—21no—
240C22—21no—
241C22—21no—
242C22—21no—
243C22—21no—
244C22—24no—
245C22—44no—
246C22—44no—
247C22—48no—
248C22—48no—
249C22—42no—
250C22—42no—
251C22#6378612yes—
252C22#6378812yes—
253C22C2×#379212yes—
254C22C2×C22⋊#15711yescharacteristic
255C4—182no—
256C4—182no—
257C4—362no—
258C3—22no—
259C2—22no—
260C2—22no—
261C2—22no—
262C2—44no—
263C2C2×#6378611yescharacteristic
264C2#1059384511yescharacteristic
265C2C2×#6378811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
Fitting, prime radicalC25×C32C4
socleC22×C32C2×C22⋊C4
cosocleC22×C3⋊Dic3C23
hypercenterC25#157
hypocenterC32#1462
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
2. #10593845C2semidirect
3. #10590222C2semidirect
13. C22⋊#622C22semidirect
59. C23×C32M16semidirect
200. C32#1462semidirect
215. C23#3792semidirect

Maximal subgroups

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

subgroupindex
C22×#37572
#105938452
#105902222
#14629