Finite Group Databasebeta

← #11783808

Subgroups — #11783808

Order 1152.

594 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 94 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
2C2×#63780C212yesmaximal
3C4×#3792C212yesmaximal
4#10590208C212yesmaximal
5C22×#634C2211yescharacteristic
6C2×#3792C2214yes—
7C2×C32×C4⋊C4C411yescharacteristic
8C2×#3750C411yescharacteristic
9C2×#3750C2211yescharacteristic
10C2×C4×C3⋊Dic3C411yescharacteristic
11C2×C4×C3⋊Dic3C411yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64096—22no—
14#64096—22no—
15#63780C418yescomplemented
16#63777—22no—
17C4×#622—22no—
18C2×#887—62no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×#634—22no—
27C2×#634—22no—
28C2×#634C2×C414yes—
29#3792—24no—
30#3792C2×C418yes—
31C2×#622—24no—
32C32×C4⋊C4—22no—
33#3750—22no—
34#3750—22no—
35C4×C3⋊Dic3—21no—
36C4×C3⋊Dic3—21no—
37C4×C3⋊Dic3—21no—
38C4×C3⋊Dic3—21no—
39C4×C3⋊Dic3D412yes—
40C4×C3⋊Dic3D412yes—
41C4×#101—91nomaximal, Sylow
42C22×Dic6—62no—
43C2×C3×C4⋊C4—22no—
44C2×Dic3⋊C4—62no—
45C2×Dic3⋊C4—62no—
46C2×C4×Dic3—62no—
47C2×C4×Dic3—62no—
48C2×C4×Dic3—62no—
49#887—68no—
50#887—68no—
51C23×C32C22×C411yescharacteristic
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4C4212yes—
58C2×C32×C4C22⋊C412yes—
59C2×C3⋊Dic3—21no—
60C2×C3⋊Dic3—21no—
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3C4212yes—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22×C412yes—
68C2×C3⋊Dic3C2×D412yes—
69C2×C3⋊Dic3#4112yes—
70#634—28no—
71#622—28no—
72C2×C4×Q8—91no—
73C2×#101—92no—
74C4×M16—92no—
75#343—92no—
76C22×C3×C4—22no—
77C22×C3×C4—22no—
78C22×C3×C4—22no—
79C22×Dic3—62no—
80C22×Dic3—62no—
81C22×Dic3—62no—
82C22×Dic3—62no—
83C2×Dic6—68no—
84C2×Dic6—68no—
85C2×Dic6—68no—
86C3×C4⋊C4—28no—
87Dic3⋊C4—68no—
88Dic3⋊C4—68no—
89C4×Dic3—64no—
90C4×Dic3—64no—
91C4×Dic3—64no—
92C4×Dic3—64no—
93C4×Dic3—64no—
94C4×Dic3—64no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32C2×C4211yescharacteristic
98C22×C32C2×C22⋊C411yescharacteristic
99C22×C32#11711yescharacteristic
100C32×C4—22no—
101C32×C4—22no—
102C32×C4—41no—
103C3⋊Dic3—22no—
104C3⋊Dic3—21no—
105C3⋊Dic3—41no—
106C3⋊Dic3#10112yescomplemented
107C3⋊Dic3C4×D414yes—
108C22×Q8—91no—
109C2×M16—94no—
110C4×Q8—182no—
111C4×Q8—182no—
112C2×C4⋊C4—91no—
113C2×C4⋊C4—91no—
114C2×C4⋊C4#15711yescharacteristic
115C2×C42—91no—
116C2×C42—91no—
117C2×C42—91no—
118#101—98no—
119#97—182no—
120C4×C8—182no—
121C23×C3—22no—
122C2×C3×C4—24no—
123C2×C3×C4—24no—
124C2×C3×C4—24no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—44no—
128C2×C3×C4—44no—
129C2×Dic3—64no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132C2×Dic3—64no—
133C2×Dic3—64no—
134C2×Dic3—64no—
135C2×Dic3—64no—
136C2×Dic3—64no—
137C2×Dic3—68no—
138C2×Dic3—64no—
139C2×Dic3—124no—
140Dic6—632no—
141C2×C32—21no—
142C2×C32—21no—
143C2×C32C4×C22⋊C411yescharacteristic
144C2×C32C2×#10111yescharacteristic
145C2×C32#41311yescharacteristic
146C2×Q8—94no—
147C2×Q8—182no—
148C2×Q8—182no—
149C22×C4—91no—
150C22×C4—91no—
151C22×C4—91no—
152C22×C4—91no—
153C22×C4C2×#15711yescharacteristic
154C22×C4C2×#15711yescharacteristic
155C22×C4C2×#15711yescharacteristic
156M16—98no—
157M16—184no—
158C2×C8—184no—
159C4⋊C4—22no—
160C4⋊C4—182no—
161C4⋊C4—182no—
162C42—92no—
163C42—92no—
164C42—181no—
165C42—181no—
166C42—181no—
167C42—181no—
168C22×C3—24no—
169C22×C3—24no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—22no—
173C3×C4—28no—
174C3×C4—44no—
175C3×C4—44no—
176Dic3—68no—
177Dic3—64no—
178Dic3—68no—
179Dic3—64no—
180Dic3—124no—
181C32C4×#10111yescharacteristic, complemented, Sylow
182C23C22×#15711yescharacteristic
183Q8—188no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—92no—
190C2×C4—92no—
191C2×C4—91no—
192C2×C4—92no—
193C2×C4—92no—
194C2×C4—91no—
195C2×C4—182no—
196C2×C4—181no—
197C2×C4—181no—
198C2×C4—181no—
199C2×C4—361no—
200C2×C4C4×#15712yes—
201C2×C4C22⋊#15712yes—
202C8—188no—
203C2×C3—24no—
204C2×C3—24no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—22no—
208C22—21no—
209C22—21no—
210C22C2×C4×#15711yescharacteristic
211C22#6428611yescharacteristic
212C22C2×C22⋊#15711yescharacteristic
213C4—22no—
214C4—22no—
215C4—41no—
216C4—94no—
217C4—92no—
218C4—182no—
219C4—181no—
220C4—361no—
221C3—22no—
222C2—21no—
223C2—21no—
224C2C4×C22⋊#15711yescharacteristic
225C2#1059382411yescharacteristic
226C2#1059383611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32C4×#101
LCSG ▷ C22×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
15. #63780C4semidirect
106. C3⋊Dic3#101semidirect
181. C32C4×#101semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#637802
C4×#37922
#105902082
C4×#1019