Finite Group Databasebeta

← #11771151

Subgroups — #11771151

Order 1152.

316 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C4×#3792C211yesmaximal, characteristic
2#10591222C211yesmaximal, characteristic
3#10591066C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C2×C3×C4×Dic3—21no—
7#63777C412yescomplemented
8C4×#622—21no—
9C3×#830—21no—
10#63579—21no—
11#63579C412yes—
12#63572C412yescomplemented
13#63555—21no—
14#4932—61no—
15#4719—61no—
16C22×C32×C4D411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C22×C3×Dic3—22no—
20#3792—24no—
21C2×#622—22no—
22C4×C3⋊Dic3C2×C411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3Q811yescharacteristic
26C3×C4×Dic3—24no—
27C2×C3×C3⋊C8—22no—
28#1300—91nomaximal, Sylow
29C2×C3×C42—61no—
30C2×C4×Dic3—21no—
31C2×C4×Dic3—61no—
32C2×C4×Dic3—61no—
33C3×C22⋊C8—61no—
34C3⋊#95—62no—
35C3⋊#95—62no—
36#830—21no—
37#815—62no—
38Dic3⋊C8—62no—
39C23×C32C22⋊C411yescharacteristic
40C2×C32×C4—22no—
41C2×C32×C4C22⋊C411yescharacteristic
42C2×C32×C4C4⋊C411yescharacteristic
43C2×C3⋊Dic3—22no—
44C2×C3⋊Dic3—41no—
45C2×C3⋊Dic3C4211yescharacteristic
46C2×C3⋊Dic3C22⋊C411yescharacteristic
47C2×C3⋊Dic3C4⋊C411yescharacteristic
48C2×C3⋊Dic3C4⋊C411yescharacteristic
49C2×C3×Dic3—24no—
50C2×C3×Dic3—42no—
51C2×C3×Dic3—42no—
52#622—24no—
53C3×C3⋊C8—42no—
54#432—91no—
55C4×M16—91no—
56#376—91no—
57C22×C3×C4—21no—
58C22×C3×C4—21no—
59C22×C3×C4—62no—
60C22×Dic3—22no—
61C22×Dic3—61no—
62C22×Dic3—61no—
63C22×Dic3—61no—
64C22×Dic3—61no—
65C2×C3×C8—62no—
66C3×C42—64no—
67C4×Dic3—24no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C4×Dic3—61no—
73C4×Dic3—61no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76C2×C3⋊C8—22no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32#9511yescharacteristic
80C22×C32#10412yes—
81C32×C4—21no—
82C32×C4#10412yes—
83C3⋊Dic3—21no—
84C3⋊Dic3—21no—
85C3⋊Dic3—21no—
86C3⋊Dic3—21no—
87C3×Dic3—44no—
88C2×M16—181no—
89C2×C42—61no—
90C2×C42—91no—
91C4⋊C8—92no—
92C22⋊C8—61no—
93#97—92no—
94#97—181no—
95C4×C8—181no—
96#95—92no—
97#95—181no—
98C23×C3—21no—
99C23×C3—21no—
100C2×C3×C4—22no—
101C2×C3×C4—22no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—42no—
107C2×C3×C4—64no—
108C2×C3×C4—122no—
109C2×C3×C4—122no—
110C2×Dic3—24no—
111C2×Dic3—42no—
112C2×Dic3—42no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C2×Dic3—122no—
122C2×Dic3—122no—
123C2×Dic3—122no—
124C2×Dic3—122no—
125C3×C8—122no—
126C3⋊C8—42no—
127C2×C32—22no—
128C2×C32#33911yescharacteristic
129C2×C32#33911yescharacteristic
130C2×C32#34411yescharacteristic
131C22×C4—62no—
132C22×C4—91no—
133C22×C4—91no—
134C22×C4GO+(4,𝔽2)11yescharacteristic
135M16—184no—
136C2×C8—62no—
137C2×C8—182no—
138C42—64no—
139C42—91no—
140C42—91no—
141C42—91no—
142C42—91no—
143C22×C3—21no—
144C22×C3—22no—
145C22×C3—21no—
146C22×C3—22no—
147C22×C3—22no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—41no—
151C22×C3—41no—
152C3×C4—22no—
153C3×C4—22no—
154C3×C4—22no—
155C3×C4—41no—
156C3×C4—124no—
157Dic3—44no—
158Dic3—62no—
159Dic3—121no—
160Dic3—121no—
161Dic3—121no—
162Dic3—121no—
163Dic3—121no—
164Dic3—121no—
165Dic3—121no—
166C32#130011yescharacteristic, complemented, Sylow
167C23D32⋊C411yescharacteristic
168C2×C4—22no—
169C2×C4—64no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—122no—
175C2×C4—122no—
176C2×C4—182no—
177C2×C4—361no—
178C2×C4D32⋊C411yescharacteristic
179C2×C4#377311yescharacteristic
180C8—122no—
181C8—184no—
182C2×C3—22no—
183C2×C3—22no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—42no—
191C22—21no—
192C22—21no—
193C22#6373112yes—
194C22#6373711yescharacteristic
195C4—21no—
196C4—124no—
197C4—181no—
198C4—181no—
199C4—181no—
200C4—181no—
201C4#6374112yes—
202C3—21no—
203C3—21no—
204C2—22no—
205C2#1059004711yescharacteristic
206C2#1059005411yescharacteristic
207C2#1059007411yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C32C22⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypocenterC32#1300
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
7. #63777C4semidirect
12. #63572C4semidirect
166. C32#1300semidirect

Maximal subgroups

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

subgroupindex
C4×#37922
#105912222
#105910662
#13009