Finite Group Databasebeta

← #11774682

Subgroups — #11774682

Order 1152.

742 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 72 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×D4×C3⋊Dic3C211yesmaximal, characteristic
2#10593806C211yesmaximal, characteristic, complemented
3C4×#3792C211yesmaximal, characteristic, complemented
4D4⋊#622C214yesmaximal, complemented
5C22×C32×D4C411yescharacteristic
6C23×C3⋊Dic3—21no—
7C2×#3792—21no—
8C2×#3757—21no—
9D4×C3⋊Dic3—21no—
10D4×C3⋊Dic3—21no—
11D4×C3⋊Dic3C412yes—
12D4×C3⋊Dic3C2212yes—
13C2×C4⋊(C3⋊Dic3)C411yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C22⋊#622—21no—
16#63777—21no—
17#63777—21no—
18C4⋊#622C2212yescomplemented
19C4×#622C2212yescomplemented
20C2×D4×Dic3—62no—
21C24×C32—21no—
22C2×C32×D4—24no—
23C2×C32×D4—21no—
24C2×C32×D4C2×C412yes—
25C22×C32×C4C2×C411yescharacteristic
26C22×C3⋊Dic3—21no—
27C22×C3⋊Dic3—22no—
28C22×C3⋊Dic3—22no—
29C22×C3⋊Dic3—44no—
30C22×C3⋊Dic3D411yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32#3792—24no—
33C2×#622—22no—
34C2×#622—22no—
35#3757—22no—
36#3757—22no—
37C4⋊(C3⋊Dic3)—21no—
38C4⋊(C3⋊Dic3)C2×C412yes—
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3C2311yescharacteristic
43#1490—91nomaximal, Sylow
44C22×C3×D4—22no—
45C23×Dic3—64no—
46C2×#217—64no—
47D4×Dic3—64no—
48D4×Dic3—64no—
49D4×Dic3—64no—
50D4×Dic3—64no—
51C2×C4⋊Dic3—62no—
52C2×C4×Dic3—62no—
53C23×C32—24no—
54C23×C32—22no—
55C23×C32—42no—
56C23×C32—42no—
57C23×C32C22⋊C411yescharacteristic
58C32×D4—24no—
59C32×D4—22no—
60C32×D4M1614yescomplemented
61C2×C32×C4—22no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22×C411yescharacteristic
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—44no—
68C2×C3⋊Dic3—42no—
69C2×C3⋊Dic3—44no—
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C2×D411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74#622—24no—
75#622—42no—
76C2×C4×D4—91no—
77#432—91no—
78C4×M16—91no—
79D4⋊C8—94no—
80C24×C3—24no—
81C2×C3×D4—24no—
82C2×C3×D4—216no—
83C2×C3×D4—24no—
84C22×C3×C4—22no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87C22×Dic3—64no—
88C22×Dic3—68no—
89C22×Dic3—68no—
90C22×Dic3—1216no—
91#217—68no—
92#217—68no—
93C4⋊Dic3—64no—
94C4⋊Dic3—64no—
95C4×Dic3—62no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C22×C32—21no—
100C22×C32—21no—
101C22×C32—24no—
102C22×C32—48no—
103C22×C32—42no—
104C22×C32—42no—
105C22×C32#10412yes—
106C22×C32C2×C22⋊C411yescharacteristic
107C32×C4—21no—
108C32×C4C2×M1612yes—
109C3⋊Dic3—21no—
110C3⋊Dic3—21no—
111C3⋊Dic3—21no—
112C3⋊Dic3—42no—
113C3⋊Dic3AGL(1,ℤ/8)12yes—
114C22×D4#15711yescharacteristic
115C23×C4—181no—
116C2×M16—181no—
117C4×D4—92no—
118C4×D4—92no—
119C4×D4—181no—
120C4×D4—181no—
121C2×C4⋊C4—91no—
122C2×C22⋊C4—181no—
123C2×C42—91no—
124C4⋊C8—92no—
125C22⋊C8—181no—
126#97—181no—
127#97—181no—
128C4×C8—92no—
129C23×C3—28no—
130C23×C3—216no—
131C23×C3—22no—
132C23×C3—48no—
133C23×C3—48no—
134C3×D4—216no—
135C3×D4—28no—
136C3×D4—28no—
137C2×C3×C4—28no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144C2×Dic3—68no—
145C2×Dic3—68no—
146C2×Dic3—124no—
147C2×Dic3—1216no—
148C2×Dic3—1216no—
149C2×Dic3—128no—
150C2×C32—22no—
151C2×C32—44no—
152C2×C32#40711yescharacteristic
153C2×C32#41811yescharacteristic
154C2×C32C2×#10411yescharacteristic
155C24—21no—
156C2×D4—24no—
157C2×D4—21no—
158C2×D4C2×#15712yes—
159C22×C4—91no—
160C22×C4—91no—
161C22×C4—182no—
162C22×C4—182no—
163C22×C4—181no—
164C22×C4—364no—
165C22×C4C2×#15711yescharacteristic
166M16—184no—
167C2×C8—182no—
168C2×C8—182no—
169C4⋊C4—92no—
170C4⋊C4—181no—
171C22⋊C4—182no—
172C22⋊C4—182no—
173C42—91no—
174C42—91no—
175C42—91no—
176C42—91no—
177C22×C3—24no—
178C22×C3—24no—
179C22×C3—216no—
180C22×C3—22no—
181C22×C3—24no—
182C22×C3—48no—
183C22×C3—432no—
184C22×C3—48no—
185C3×C4—24no—
186C3×C4—24no—
187Dic3—64no—
188Dic3—64no—
189Dic3—122no—
190Dic3—122no—
191Dic3—128no—
192C32#149011yescharacteristic, complemented, Sylow
193C23—24no—
194C23—22no—
195C23—42no—
196C23—42no—
197C23C22⋊#15711yescharacteristic
198D4—24no—
199D4—22no—
200D4#379214yescomplemented
201C2×C4—22no—
202C2×C4—91no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—182no—
207C2×C4—182no—
208C2×C4—182no—
209C2×C4—364no—
210C2×C4—364no—
211C2×C4—362no—
212C2×C4C22⋊#15711yescharacteristic
213C2×C4C22×#15711yescharacteristic
214C8—184no—
215C8—362no—
216C2×C3—28no—
217C2×C3—22no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—416no—
221C22—21no—
222C22—21no—
223C22—24no—
224C22—48no—
225C22—42no—
226C22—42no—
227C22#6378312yes—
228C22C2×C22⋊#15711yescharacteristic
229C4—21no—
230C4—92no—
231C4—181no—
232C4—181no—
233C4—181no—
234C4—362no—
235C4C2×#379212yes—
236C3—22no—
237C2—22no—
238C2—44no—
239C2#1059381411yescharacteristic
240C2C2×#6378311yescharacteristic
241C2#1059384511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
Fitting, prime radicalC22×C32×D4C4
socleC22×C32C2×C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×D4#157
hypocenterC32#1490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10593806C2semidirect
3. C4×#3792C2semidirect
4. D4⋊#622C2semidirect
18. C4⋊#622C22semidirect
19. C4×#622C22semidirect
60. C32×D4M16semidirect
192. C32#1490semidirect
200. D4#3792semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
#105938062
C4×#37922
D4⋊#6222
#14909