Finite Group Databasebeta

← #11774056

Subgroups — #11774056

Order 1152.

430 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 62 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×#64099C211yesmaximal, characteristic
2#10593806C211yesmaximal, characteristic
3#10593801C211yesmaximal, characteristic
4#10590203C214yesmaximal
5C2×C32×C4⋊C4C411yescharacteristic
6C2×C4⋊(C3⋊Dic3)C411yescharacteristic
7C2×C4⋊(C3⋊Dic3)C412yes—
8C2×#3750C2212yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10#64099—21no—
11#64099—21no—
12#64099—21no—
13#64099—21no—
14C22⋊#622C2212yes—
15C22⋊#622C2212yes—
16#63779—21no—
17#63777—21no—
18C4⋊#622—21no—
19C4×#622—21no—
20C2×#890—62no—
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2×C412yes—
23C22×C3⋊Dic3C2×C412yes—
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×#622—22no—
27C2×#622—22no—
28C32×C4⋊C4—21no—
29C32×C4⋊C4—21no—
30C4⋊(C3⋊Dic3)—21no—
31C4⋊(C3⋊Dic3)—21no—
32C4⋊(C3⋊Dic3)—22no—
33C4⋊(C3⋊Dic3)—22no—
34#3750—22no—
35#3750—22no—
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40#1470—91nomaximal, Sylow
41C2×C3×C4⋊C4—22no—
42C2×C4⋊Dic3—64no—
43C2×C4⋊Dic3—62no—
44C2×Dic3⋊C4—64no—
45C2×C4×Dic3—62no—
46#890—64no—
47#890—64no—
48#890—64no—
49#890—64no—
50C23×C32C22×C411yescharacteristic
51C2×C32×C4—22no—
52C2×C32×C4—22no—
53C2×C32×C4—42no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—24no—
59C2×C3⋊Dic3—41no—
60C2×C3⋊Dic3C22⋊C411yescharacteristic
61C2×C3⋊Dic3C22⋊C411yescharacteristic
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3⋊Dic3C2×D411yescharacteristic
64#622—42no—
65#622—42no—
66C2×#125—91no—
67#432—91no—
68#431—91no—
69#324—94no—
70C22×C3×C4—24no—
71C22×C3×C4—22no—
72C22×Dic3—62no—
73C22×Dic3—62no—
74C22×Dic3—64no—
75C3×C4⋊C4—24no—
76C3×C4⋊C4—24no—
77C4⋊Dic3—68no—
78C4⋊Dic3—68no—
79C4⋊Dic3—64no—
80C4⋊Dic3—64no—
81Dic3⋊C4—68no—
82Dic3⋊C4—68no—
83C4×Dic3—62no—
84C4×Dic3—62no—
85C4×Dic3—62no—
86C4×Dic3—62no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32C2×C22⋊C411yescharacteristic
90C22×C32#13112yes—
91C32×C4—21no—
92C32×C4—42no—
93C32×C4#10112yes—
94C3⋊Dic3—21no—
95C3⋊Dic3—21no—
96C3⋊Dic3—21no—
97C3⋊Dic3—21no—
98C3⋊Dic3—42no—
99#125—181no—
100#125—181no—
101#125—181no—
102#125—181no—
103C2×C4⋊C4—92no—
104C2×C4⋊C4—92no—
105C2×C4⋊C4—91no—
106C2×C4⋊C4#15711yescharacteristic
107C2×C42—91no—
108C4⋊C8—181no—
109C4⋊C8—181no—
110C22⋊C8—92no—
111C22⋊C8—92no—
112#97—181no—
113C4×C8—181no—
114C23×C3—22no—
115C2×C3×C4—28no—
116C2×C3×C4—28no—
117C2×C3×C4—22no—
118C2×C3×C4—22no—
119C2×C3×C4—48no—
120C2×Dic3—62no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—68no—
125C2×Dic3—124no—
126C2×Dic3—128no—
127C2×Dic3—124no—
128C2×C32—22no—
129C2×C32#40811yescharacteristic
130C2×C32#41011yescharacteristic
131C2×C32C2×#10111yescharacteristic
132C22×C4—91no—
133C22×C4—91no—
134C22×C4—92no—
135C22×C4C2×#15712yes—
136C22×C4C2×#15711yescharacteristic
137C2×C8—182no—
138C2×C8—182no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—182no—
142C4⋊C4—182no—
143C4⋊C4—182no—
144C4⋊C4—182no—
145C4⋊C4—181no—
146C4⋊C4—181no—
147C42—91no—
148C42—91no—
149C42—91no—
150C42—91no—
151C22×C3—24no—
152C22×C3—24no—
153C22×C3—24no—
154C22×C3—22no—
155C3×C4—24no—
156C3×C4—24no—
157C3×C4—48no—
158Dic3—122no—
159Dic3—122no—
160Dic3—122no—
161Dic3—122no—
162Dic3—128no—
163C32#147011yescharacteristic, complemented, Sylow
164C23C22×#15711yescharacteristic
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—91no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—182no—
173C2×C4—184no—
174C2×C4—182no—
175C2×C4—361no—
176C2×C4C22⋊#15711yescharacteristic
177C2×C4C22⋊#15711yescharacteristic
178C8—362no—
179C8—362no—
180C2×C3—28no—
181C2×C3—22no—
182C2×C3—22no—
183C2×C3—22no—
184C22—21no—
185C22—21no—
186C22#6428912yes—
187C22C2×C22⋊#15711yescharacteristic
188C4—21no—
189C4—42no—
190C4—181no—
191C4—181no—
192C4—181no—
193C4—181no—
194C4—362no—
195C4#6378012yes—
196C3—22no—
197C2—22no—
198C2C2×#6378011yescharacteristic
199C2#1059381811yescharacteristic
200C2#1059383411yescharacteristic
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#1470
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
163. C32#1470semidirect

Maximal subgroups

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

subgroupindex
C2×#640992
#105938062
#105938012
#105902032
#14709