Finite Group Databasebeta

← #11791873

Subgroups — #11791873

Order 1152.

550 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 76 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×#64097C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic
3C4×#3792C211yesmaximal, characteristic
4#10590208C214yesmaximal
5C22×#634C412yes—
6C2×#3792C2212yes—
7C2×#3792C2212yes—
8C2×C32×C4⋊C4C411yescharacteristic
9C2×C4⋊(C3⋊Dic3)C411yescharacteristic
10C2×#3750C2212yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64097—21no—
13#64097—21no—
14#64097—21no—
15#64097—21no—
16#63779—21no—
17#63777—21no—
18C4⋊#622—21no—
19C4×#622—21no—
20C2×#888—62no—
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2×C412yes—
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C412yes—
25C22×C3⋊Dic3C2311yescharacteristic
26C2×#634—22no—
27C2×#634—22no—
28C2×#634—44no—
29#3792—22no—
30#3792—24no—
31#3792Q814yescomplemented
32C2×#622—22no—
33C2×#622—22no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4—21no—
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)—21no—
38#3750—22no—
39#3750—22no—
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44#1997—91nomaximal, Sylow
45C22×Dic6—64no—
46C2×C3×C4⋊C4—22no—
47C2×C4⋊Dic3—62no—
48C2×Dic3⋊C4—64no—
49C2×C4×Dic3—62no—
50#888—64no—
51#888—64no—
52#888—64no—
53#888—64no—
54C23×C32C22×C411yescharacteristic
55C2×C32×C4—22no—
56C2×C32×C4—22no—
57C2×C32×C4—42no—
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3—42no—
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3C2×Q812yes—
68C2×C3⋊Dic3#4112yes—
69#634—44no—
70#634—44no—
71#622—24no—
72#622—42no—
73C2×C4⋊Q8—91no—
74#423—91no—
75C4×M16—91no—
76#343—94no—
77C22×C3×C4—24no—
78C22×C3×C4—22no—
79C22×Dic3—62no—
80C22×Dic3—62no—
81C22×Dic3—64no—
82C2×Dic6—68no—
83C2×Dic6—68no—
84C2×Dic6—1216no—
85C3×C4⋊C4—24no—
86C3×C4⋊C4—24no—
87C4⋊Dic3—64no—
88C4⋊Dic3—64no—
89Dic3⋊C4—68no—
90Dic3⋊C4—68no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32C2×C22⋊C411yescharacteristic
98C22×C32C4×Q812yes—
99C32×C4—21no—
100C32×C4—42no—
101C32×C4#10112yes—
102C3⋊Dic3—21no—
103C3⋊Dic3—42no—
104C3⋊Dic3#10012yes—
105C3⋊Dic3C22⋊Q812yes—
106C3⋊Dic3#12411yescharacteristic
107C3⋊Dic3C4⋊Q811yescharacteristic
108C22×Q8—92no—
109C2×M16—92no—
110C2×M16—92no—
111C4⋊Q8—181no—
112C4⋊Q8—181no—
113C4⋊Q8—181no—
114C4⋊Q8—181no—
115C2×C4⋊C4—92no—
116C2×C4⋊C4—91no—
117C2×C4⋊C4#15711yescharacteristic
118C2×C42—91no—
119C4⋊C8—181no—
120C4⋊C8—181no—
121#97—181no—
122C4×C8—181no—
123C23×C3—22no—
124C2×C3×C4—28no—
125C2×C3×C4—28no—
126C2×C3×C4—22no—
127C2×C3×C4—22no—
128C2×C3×C4—48no—
129C2×Dic3—62no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133C2×Dic3—64no—
134C2×Dic3—64no—
135C2×Dic3—68no—
136C2×Dic3—68no—
137C2×Dic3—128no—
138Dic6—1216no—
139Dic6—1216no—
140C2×C32—22no—
141C2×C32#39111yescharacteristic
142C2×C32C2×#10011yescharacteristic
143C2×C32C2×#10111yescharacteristic
144C2×Q8—182no—
145C2×Q8—182no—
146C2×Q8—364no—
147C22×C4—91no—
148C22×C4—91no—
149C22×C4—92no—
150C22×C4C2×#15712yes—
151C22×C4C2×#15711yescharacteristic
152M16—94no—
153M16—182no—
154M16—184no—
155C2×C8—182no—
156C2×C8—182no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—182no—
160C4⋊C4—182no—
161C4⋊C4—181no—
162C4⋊C4—181no—
163C42—91no—
164C42—91no—
165C42—91no—
166C42—91no—
167C22×C3—24no—
168C22×C3—24no—
169C22×C3—24no—
170C22×C3—22no—
171C3×C4—24no—
172C3×C4—24no—
173C3×C4—48no—
174Dic3—64no—
175Dic3—64no—
176Dic3—62no—
177Dic3—62no—
178Dic3—64no—
179Dic3—128no—
180C32#199711yescharacteristic, complemented, Sylow
181C23C22×#15711yescharacteristic
182Q8—364no—
183Q8—364no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—92no—
188C2×C4—92no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—182no—
194C2×C4—182no—
195C2×C4—362no—
196C2×C4C22⋊#15711yescharacteristic
197C2×C4C22⋊#15711yescharacteristic
198C8—184no—
199C8—362no—
200C2×C3—28no—
201C2×C3—22no—
202C2×C3—22no—
203C2×C3—22no—
204C22—21no—
205C22—21no—
206C22Q8×#15712yes—
207C22C2×C22⋊#15711yescharacteristic
208C4—21no—
209C4—42no—
210C4—92no—
211C4—92no—
212C4—91no—
213C4—91no—
214C4—181no—
215C4—362no—
216C4#6378012yes—
217C3—22no—
218C2—22no—
219C2C2×#6378011yescharacteristic
220C2#1059382511yescharacteristic
221C2#1059383711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutator, prime radicalC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1997
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
31. #3792Q8semidirect
180. C32#1997semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
#105938052
C4×#37922
#105902082
#19979