Finite Group Databasebeta

← #11771152

Subgroups — #11771152

Order 1152.

332 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 45 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
1#10593804C211yesmaximal, characteristic
2#10591252C211yesmaximal, characteristic
3#10591060C211yesmaximal, characteristic
4C2×C4×C3⋊Dic3C2211yescharacteristic
5C2×C3×#208—21no—
6C2×Dic32—21no—
7C22⋊#622—21no—
8#63779C412yescomplemented
9#63777—21no—
10C3×C3⋊#95—21no—
11#63579C412yes—
12#63555C412yescomplemented
13#63553—21no—
14Dic3×M16—61no—
15#4648—61no—
16C22×C32×C4D411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C22×C3×Dic3—22no—
20C2×#622—22no—
21C4×C3⋊Dic3C2×C411yescharacteristic
22C4×C3⋊Dic3C2×C411yescharacteristic
23C4×C3⋊Dic3D411yescharacteristic
24C4×C3⋊Dic3Q811yescharacteristic
25C3×#208—24no—
26C2×C3×C3⋊C8—22no—
27Dic32—24no—
28#1300—91nomaximal, Sylow
29C2×C3×M16—61no—
30C2×C4×Dic3—61no—
31C2×C4×Dic3—61no—
32C2×C4×Dic3—62no—
33C2×#208—21no—
34C3×#95—61no—
35C3⋊#95—21no—
36C3⋊#95—62no—
37#815—62no—
38C8×Dic3—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—42no—
53C3×C3⋊C8—24no—
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—
65C3×M16—64no—
66C2×C3×C8—62no—
67C4×Dic3—61no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C4×Dic3—61no—
73C4×Dic3—61no—
74C4×Dic3—61no—
75C4×Dic3—68no—
76#208—24no—
77C2×C3⋊C8—22no—
78C22×C32—21no—
79C22×C32—21no—
80C22×C32#9511yescharacteristic
81C22×C32#10412yes—
82C32×C4—21no—
83C32×C4—21no—
84C3⋊Dic3—21no—
85C3⋊Dic3—21no—
86C3⋊Dic3—21no—
87C3⋊Dic3#10412yes—
88C3×Dic3—44no—
89C2×M16—61no—
90C2×C42—91no—
91C2×C42—181no—
92C4⋊C8—92no—
93C22⋊C8—181no—
94#97—92no—
95#97—181no—
96C4×C8—181no—
97#95—61no—
98#95—92no—
99C23×C3—21no—
100C23×C3—21no—
101C2×C3×C4—22no—
102C2×C3×C4—22no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—42no—
108C2×C3×C4—64no—
109C2×C3×C4—122no—
110C2×C3×C4—122no—
111C2×Dic3—24no—
112C2×Dic3—42no—
113C2×Dic3—42no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C2×Dic3—61no—
122C2×Dic3—64no—
123C2×Dic3—122no—
124C2×Dic3—122no—
125C2×Dic3—121no—
126C2×Dic3—121no—
127C3×C8—64no—
128C3⋊C8—24no—
129C2×C32—22no—
130C2×C32#33911yescharacteristic
131C2×C32#33911yescharacteristic
132C2×C32#34411yescharacteristic
133C22×C4—62no—
134C22×C4—91no—
135C22×C4—91no—
136C22×C4GO+(4,𝔽2)11yescharacteristic
137M16—64no—
138C2×C8—62no—
139C2×C8—182no—
140C42—91no—
141C42—91no—
142C42—91no—
143C42—91no—
144C42—184no—
145C22×C3—22no—
146C22×C3—21no—
147C22×C3—21no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—22no—
151C22×C3—22no—
152C22×C3—41no—
153C22×C3—41no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—22no—
157C3×C4—41no—
158C3×C4—41no—
159C3×C4—124no—
160Dic3—44no—
161Dic3—62no—
162Dic3—62no—
163Dic3—62no—
164Dic3—62no—
165Dic3—121no—
166Dic3—121no—
167Dic3—121no—
168Dic3—121no—
169C32#130011yescharacteristic, complemented, Sylow
170C23D32⋊C411yescharacteristic
171C2×C4—22no—
172C2×C4—64no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—122no—
178C2×C4—122no—
179C2×C4—182no—
180C2×C4—361no—
181C2×C4D32⋊C411yescharacteristic
182C2×C4#377311yescharacteristic
183C8—64no—
184C8—362no—
185C2×C3—22no—
186C2×C3—22no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—42no—
194C22—21no—
195C22—21no—
196C22#6373711yescharacteristic
197C22#6374112yes—
198C4—21no—
199C4—21no—
200C4—92no—
201C4—124no—
202C4—181no—
203C4—181no—
204C4—181no—
205C3—21no—
206C3—21no—
207C2—22no—
208C2#1059004811yescharacteristic
209C2#1059005611yescharacteristic
210C2#1059007411yescharacteristic
subgroupG/H
centerC22#63737
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 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #63779C4semidirect
12. #63555C4semidirect
169. C32#1300semidirect

Maximal subgroups

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

subgroupindex
#105938042
#105912522
#105910602
#13009