Finite Group Databasebeta

← #11774552

Subgroups — #11774552

Order 1152.

738 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 78 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#10593805C211yesmaximal, characteristic, complemented
3#10593801C211yesmaximal, 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#63779—21no—
17#63779—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—42no—
30C22×C3⋊Dic3—42no—
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33#3792—42no—
34C2×#622—22no—
35C2×#622—22no—
36#3757—22no—
37#3757—22no—
38C4⋊(C3⋊Dic3)—21no—
39C4⋊(C3⋊Dic3)C2×C412yes—
40C4×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3C2311yescharacteristic
44#1486—91nomaximal, Sylow
45C22×C3×D4—22no—
46C23×Dic3—64no—
47C2×#217—64no—
48D4×Dic3—64no—
49D4×Dic3—64no—
50D4×Dic3—64no—
51D4×Dic3—64no—
52C2×C4⋊Dic3—62no—
53C2×C4×Dic3—62no—
54C23×C32—24no—
55C23×C32—22no—
56C23×C32—42no—
57C23×C32—42no—
58C23×C32C22⋊C411yescharacteristic
59C32×D4—24no—
60C32×D4—22no—
61C32×D4M1614yescomplemented
62C2×C32×C4—22no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C22×C411yescharacteristic
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3—42no—
68C2×C3⋊Dic3—44no—
69C2×C3⋊Dic3—42no—
70C2×C3⋊Dic3—42no—
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3D812yes—
74C2×C3⋊Dic3SD1612yes—
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77#622—42no—
78#622—42no—
79C2×C4×D4—91no—
80#431—91no—
81#423—91no—
82D4⋊C8—94no—
83C24×C3—24no—
84C2×C3×D4—24no—
85C2×C3×D4—216no—
86C2×C3×D4—24no—
87C22×C3×C4—22no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C22×Dic3—64no—
91C22×Dic3—68no—
92C22×Dic3—68no—
93C22×Dic3—128no—
94C22×Dic3—128no—
95#217—68no—
96#217—68no—
97C4⋊Dic3—64no—
98C4⋊Dic3—64no—
99C4×Dic3—62no—
100C4×Dic3—62no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32—24no—
106C22×C32—48no—
107C22×C32—42no—
108C22×C32—42no—
109C22×C32#10212yes—
110C22×C32C2×C22⋊C411yescharacteristic
111C32×C4—21no—
112C32×C4C2×M1612yes—
113C3⋊Dic3—21no—
114C3⋊Dic3—21no—
115C3⋊Dic3—42no—
116C3⋊Dic3#10212yes—
117C3⋊Dic3C2×D811yescharacteristic
118C3⋊Dic3C2×SD1611yescharacteristic
119C22×D4#15711yescharacteristic
120C23×C4—181no—
121C2×M16—181no—
122C4×D4—92no—
123C4×D4—92no—
124C4×D4—181no—
125C4×D4—181no—
126C2×C4⋊C4—91no—
127C2×C22⋊C4—181no—
128C2×C42—91no—
129C4⋊C8—92no—
130C4⋊C8—181no—
131C4⋊C8—181no—
132C22⋊C8—181no—
133C4×C8—92no—
134C23×C3—28no—
135C23×C3—216no—
136C23×C3—22no—
137C23×C3—48no—
138C23×C3—48no—
139C3×D4—216no—
140C3×D4—28no—
141C3×D4—28no—
142C2×C3×C4—28no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×Dic3—62no—
146C2×Dic3—64no—
147C2×Dic3—64no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—62no—
151C2×Dic3—68no—
152C2×Dic3—1216no—
153C2×Dic3—128no—
154C2×Dic3—128no—
155C2×Dic3—124no—
156C2×Dic3—128no—
157C2×C32—22no—
158C2×C32—44no—
159C2×C32#40711yescharacteristic
160C2×C32C2×#10211yescharacteristic
161C2×C32#42111yescharacteristic
162C24—21no—
163C2×D4—24no—
164C2×D4—21no—
165C2×D4C2×#15712yes—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—182no—
169C22×C4—182no—
170C22×C4—181no—
171C22×C4—362no—
172C22×C4—362no—
173C22×C4C2×#15711yescharacteristic
174M16—362no—
175C2×C8—182no—
176C2×C8—182no—
177C4⋊C4—92no—
178C4⋊C4—181no—
179C22⋊C4—182no—
180C22⋊C4—182no—
181C42—91no—
182C42—91no—
183C42—91no—
184C42—91no—
185C22×C3—24no—
186C22×C3—24no—
187C22×C3—216no—
188C22×C3—22no—
189C22×C3—24no—
190C22×C3—48no—
191C22×C3—432no—
192C22×C3—48no—
193C3×C4—24no—
194C3×C4—24no—
195Dic3—64no—
196Dic3—62no—
197Dic3—62no—
198Dic3—122no—
199Dic3—122no—
200Dic3—128no—
201C32#148611yescharacteristic, complemented, Sylow
202C23—24no—
203C23—22no—
204C23—42no—
205C23—42no—
206C23C22⋊#15711yescharacteristic
207D4—24no—
208D4—22no—
209D4#379214yescomplemented
210C2×C4—22no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—92no—
214C2×C4—92no—
215C2×C4—91no—
216C2×C4—91no—
217C2×C4—182no—
218C2×C4—362no—
219C2×C4—362no—
220C2×C4—364no—
221C2×C4—361no—
222C2×C4—362no—
223C2×C4C22⋊#15711yescharacteristic
224C2×C4C22×#15711yescharacteristic
225C8—362no—
226C8—362no—
227C2×C3—28no—
228C2×C3—22no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—416no—
232C22—21no—
233C22—21no—
234C22—24no—
235C22—48no—
236C22—42no—
237C22—42no—
238C22#6378212yes—
239C22C2×C22⋊#15711yescharacteristic
240C4—21no—
241C4—91no—
242C4—91no—
243C4—92no—
244C4—181no—
245C4—181no—
246C4—362no—
247C4C2×#379212yes—
248C3—22no—
249C2—22no—
250C2—44no—
251C2C2×#6378211yescharacteristic
252C2#1059381611yescharacteristic
253C2#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#1486
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. #10593805C2semidirect
3. #10593801C2semidirect
4. D4⋊#622C2semidirect
18. C4⋊#622C22semidirect
19. C4×#622C22semidirect
61. C32×D4M16semidirect
201. C32#1486semidirect
209. 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
#105938052
#105938012
D4⋊#6222
#14869