Finite Group Databasebeta

← #11774711

Subgroups — #11774711

Order 1152.

550 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 68 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×#64096C211yesmaximal, characteristic
2#10593806C211yesmaximal, characteristic
3C4×#3792C211yesmaximal, characteristic
4#10590161C214yesmaximal, complemented
5C22×#634C411yescharacteristic
6C2×#3792—21no—
7C2×C32×C4⋊C4C411yescharacteristic
8C2×#3750—21no—
9C2×C4×C3⋊Dic3—21no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11#64096—21no—
12#64096—21no—
13#64096C412yes—
14#64096C2212yes—
15C22⋊#622—21no—
16#63777—21no—
17#63777—21no—
18C4⋊#622C2212yes—
19C4×#622C2212yes—
20C2×#887—62no—
21C22×C32×C4—21no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×#634—21no—
27C2×#634—24no—
28C2×#634C2×C412yes—
29#3792—24no—
30C2×#622—22no—
31C2×#622—22no—
32C32×C4⋊C4—21no—
33C32×C4⋊C4C2×C412yes—
34#3750—22no—
35#3750—22no—
36C4×C3⋊Dic3—22no—
37C4×C3⋊Dic3—22no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42#1491—91nomaximal, Sylow
43C22×Dic6—62no—
44C2×C3×C4⋊C4—22no—
45C2×Dic3⋊C4—64no—
46C2×C4×Dic3—62no—
47C2×C4×Dic3—64no—
48#887—64no—
49#887—64no—
50#887—64no—
51#887—64no—
52C23×C32C22⋊C411yescharacteristic
53C2×C32×C4—22no—
54C2×C32×C4—22no—
55C2×C32×C4—42no—
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4C22×C411yescharacteristic
58C2×C3⋊Dic3—24no—
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66#634—24no—
67#634—22no—
68#634M1614yescomplemented
69#622—24no—
70#622—42no—
71C2×C4×Q8—91no—
72#432—91no—
73C4×M16—91no—
74Q8⋊C8—94no—
75C22×C3×C4—24no—
76C22×C3×C4—22no—
77C22×Dic3—62no—
78C22×Dic3—62no—
79C22×Dic3—64no—
80C2×Dic6—64no—
81C2×Dic6—64no—
82C2×Dic6—616no—
83C3×C4⋊C4—24no—
84C3×C4⋊C4—24no—
85Dic3⋊C4—68no—
86Dic3⋊C4—68no—
87C4×Dic3—62no—
88C4×Dic3—62no—
89C4×Dic3—62no—
90C4×Dic3—62no—
91C4×Dic3—68no—
92C4×Dic3—68no—
93C22×C32—21no—
94C22×C32—21no—
95C22×C32#10412yes—
96C22×C32C2×C22⋊C411yescharacteristic
97C32×C4—21no—
98C32×C4—42no—
99C32×C4C2×M1612yes—
100C3⋊Dic3—24no—
101C3⋊Dic3—21no—
102C3⋊Dic3—21no—
103C3⋊Dic3—21no—
104C3⋊Dic3#13712yes—
105C22×Q8—91no—
106C2×M16—181no—
107C4×Q8—92no—
108C4×Q8—92no—
109C4×Q8—181no—
110C4×Q8—181no—
111C2×C4⋊C4—181no—
112C2×C4⋊C4#15711yescharacteristic
113C2×C42—91no—
114C2×C42—181no—
115C4⋊C8—92no—
116C22⋊C8—181no—
117#97—181no—
118#97—181no—
119C4×C8—92no—
120C23×C3—22no—
121C2×C3×C4—28no—
122C2×C3×C4—28no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—48no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128C2×Dic3—62no—
129C2×Dic3—62no—
130C2×Dic3—68no—
131C2×Dic3—616no—
132C2×Dic3—68no—
133C2×Dic3—124no—
134Dic6—68no—
135Dic6—616no—
136Dic6—68no—
137C2×C32—22no—
138C2×C32#40711yescharacteristic
139C2×C32#41911yescharacteristic
140C2×C32C2×#10411yescharacteristic
141C2×Q8—92no—
142C2×Q8—184no—
143C2×Q8—181no—
144C22×C4—21no—
145C22×C4—91no—
146C22×C4—91no—
147C22×C4—181no—
148C22×C4C2×#15711yescharacteristic
149M16—184no—
150C2×C8—182no—
151C2×C8—182no—
152C4⋊C4—21no—
153C4⋊C4—182no—
154C4⋊C4—182no—
155C4⋊C4C2×#15712yes—
156C42—91no—
157C42—91no—
158C42—91no—
159C42—91no—
160C42—182no—
161C42—182no—
162C22×C3—24no—
163C22×C3—24no—
164C22×C3—22no—
165C22×C3—24no—
166C3×C4—24no—
167C3×C4—24no—
168C3×C4—48no—
169Dic3—64no—
170Dic3—616no—
171Dic3—64no—
172Dic3—122no—
173Dic3—122no—
174C32#149111yescharacteristic, complemented, Sylow
175C23C22⋊#15711yescharacteristic
176Q8—94no—
177Q8—184no—
178Q8—182no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—182no—
187C2×C4—184no—
188C2×C4—182no—
189C2×C4—182no—
190C2×C4C22⋊#15711yescharacteristic
191C2×C4C22×#15711yescharacteristic
192C8—184no—
193C8—362no—
194C2×C3—28no—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—22no—
198C22—21no—
199C22—21no—
200C22#6378312yes—
201C22C2×C22⋊#15711yescharacteristic
202C4—21no—
203C4—42no—
204C4—92no—
205C4—184no—
206C4—181no—
207C4—181no—
208C4—181no—
209C4#6428312yes—
210C3—22no—
211C2—22no—
212C2#1059380211yescharacteristic
213C2C2×#6378311yescharacteristic
214C2#1059382911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590161C2semidirect
68. #634M16semidirect
174. C32#1491semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105938062
C4×#37922
#105901612
#14919