Finite Group Databasebeta

← #11785722

Subgroups — #11785722

Order 1152.

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

normal subgroups only

This group has 734 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×#3750C211yesmaximal, characteristic
2#10593845C212yesmaximal
3#10590208C214yesmaximal, complemented
4C23×C32×C4C411yescharacteristic
5C23×C3⋊Dic3C411yescharacteristic
6C23×C3⋊Dic3C2211yescharacteristic
7C2×#3792C2214yes—
8C2×#3750—22no—
9C2×#3750—22no—
10C2×#3750C412yes—
11C2×#3750C2212yes—
12C22⋊#622—22no—
13C22⋊#622—22no—
14C22×Dic3⋊C4—62no—
15C24×C32C2×C411yescharacteristic
16C22×C32×C4—21no—
17C22×C32×C4—21no—
18C22×C32×C4—42no—
19C22×C32×C4C2×C412yes—
20C22×C3⋊Dic3—24no—
21C22×C3⋊Dic3—21no—
22C22×C3⋊Dic3—21no—
23C22×C3⋊Dic3—42no—
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C412yes—
26C22×C3⋊Dic3D412yes—
27C22×C3⋊Dic3D412yes—
28C22×C3⋊Dic3C2311yescharacteristic
29#3792—28no—
30C2×#622—24no—
31#3750—24no—
32#3750—24no—
33#1821—91nomaximal, Sylow
34C23×C3×C4—22no—
35C23×Dic3—62no—
36C23×Dic3—62no—
37C2×Dic3⋊C4—64no—
38C2×Dic3⋊C4—64no—
39C2×Dic3⋊C4—68no—
40C2×Dic3⋊C4—68no—
41C23×C32—22no—
42C23×C32—22no—
43C23×C32—22no—
44C23×C32C22⋊C411yescharacteristic
45C23×C32C22⋊C411yescharacteristic
46C23×C32C22×C411yescharacteristic
47C2×C32×C4—22no—
48C2×C32×C4—42no—
49C2×C32×C4—42no—
50C2×C32×C4—42no—
51C2×C3⋊Dic3—22no—
52C2×C3⋊Dic3—24no—
53C2×C3⋊Dic3—24no—
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3—42no—
56C2×C3⋊Dic3—42no—
57C2×C3⋊Dic3—42no—
58C2×C3⋊Dic3C22⋊C412yes—
59C2×C3⋊Dic3C2×D412yes—
60C2×C3⋊Dic3#4114yes—
61#622—44no—
62C22×C4⋊C4—91no—
63#407—92no—
64#343—94no—
65C24×C3—22no—
66C22×C3×C4—24no—
67C22×C3×C4—24no—
68C22×C3×C4—24no—
69C22×C3×C4—48no—
70C22×Dic3—62no—
71C22×Dic3—64no—
72C22×Dic3—64no—
73C22×Dic3—62no—
74C22×Dic3—64no—
75C22×Dic3—616no—
76C22×Dic3—64no—
77C22×Dic3—64no—
78C22×Dic3—128no—
79Dic3⋊C4—616no—
80Dic3⋊C4—616no—
81C22×C32—28no—
82C22×C32—21no—
83C22×C32—21no—
84C22×C32—21no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32#10012yes—
89C22×C32#10112yes—
90C22×C32C2×C22⋊C411yescharacteristic
91C22×C32#11712yes—
92C32×C4—42no—
93C3⋊Dic3—22no—
94C3⋊Dic3—42no—
95C3⋊Dic3#12314yes—
96C23×C4—91no—
97C23×C4—91no—
98C23×C4#15711yescharacteristic
99C2×M16—94no—
100C2×C4⋊C4—92no—
101C2×C4⋊C4—92no—
102C2×C4⋊C4—182no—
103C2×C4⋊C4—182no—
104C22⋊C8—182no—
105C22⋊C8—182no—
106C23×C3—28no—
107C23×C3—28no—
108C23×C3—28no—
109C23×C3—22no—
110C23×C3—22no—
111C23×C3—22no—
112C2×C3×C4—28no—
113C2×C3×C4—48no—
114C2×C3×C4—48no—
115C2×C3×C4—48no—
116C2×Dic3—64no—
117C2×Dic3—64no—
118C2×Dic3—68no—
119C2×Dic3—616no—
120C2×Dic3—616no—
121C2×Dic3—68no—
122C2×Dic3—68no—
123C2×Dic3—128no—
124C2×Dic3—128no—
125C2×Dic3—128no—
126C2×C32—22no—
127C2×C32—22no—
128C2×C32—22no—
129C2×C32#38111yescharacteristic
130C2×C32C2×#10011yescharacteristic
131C2×C32C2×#10111yescharacteristic
132C24C2×#15711yescharacteristic
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—42no—
136C22×C4—91no—
137C22×C4—91no—
138C22×C4—92no—
139C22×C4—92no—
140C22×C4—92no—
141C22×C4—184no—
142C22×C4—181no—
143C22×C4—181no—
144C22×C4—362no—
145C22×C4C2×#15712yes—
146M16—188no—
147C2×C8—184no—
148C4⋊C4—184no—
149C4⋊C4—184no—
150C22×C3—24no—
151C22×C3—24no—
152C22×C3—24no—
153C22×C3—24no—
154C22×C3—232no—
155C22×C3—24no—
156C22×C3—24no—
157C22×C3—24no—
158C22×C3—24no—
159C22×C3—22no—
160C22×C3—24no—
161C3×C4—48no—
162Dic3—68no—
163Dic3—68no—
164Dic3—128no—
165C32#182111yescharacteristic, complemented, Sylow
166C23—22no—
167C23—22no—
168C23—22no—
169C23C22⋊#15711yescharacteristic
170C23C22⋊#15711yescharacteristic
171C23C22×#15711yescharacteristic
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—94no—
177C2×C4—92no—
178C2×C4—92no—
179C2×C4—184no—
180C2×C4—184no—
181C2×C4—182no—
182C2×C4—182no—
183C2×C4—362no—
184C2×C4—362no—
185C2×C4—362no—
186C8—364no—
187C2×C3—28no—
188C2×C3—28no—
189C2×C3—28no—
190C2×C3—22no—
191C2×C3—22no—
192C2×C3—22no—
193C22—28no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22#6378012yes—
201C22#6378812yes—
202C22#6428612yes—
203C22C2×C22⋊#15711yescharacteristic
204C4—42no—
205C4—94no—
206C4—182no—
207C4—362no—
208C3—22no—
209C2—22no—
210C2—22no—
211C2—22no—
212C2C2×#6378011yescharacteristic
213C2#1059381111yescharacteristic
214C2C2×#6378811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC23×C32×C4C4
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC23×C4#157
hypocenterC32#1821
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10590208C2semidirect
165. C32#1821semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
#105938452
#105902082
#18219