Finite Group Databasebeta

← #11771963

Subgroups — #11771963

Order 1152.

232 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 31 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#10591218C211yesmaximal, characteristic
2#10590202C211yesmaximal, characteristic
3#10589168C211yesmaximal, characteristic
4C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
5C2×C3×#208—21no—
6C2×#3724C411yescharacteristic
7C22⋊#622—21no—
8C3×C3⋊#95—21no—
9#63579—21no—
10#63579C411yescharacteristic
11#4660—61no—
12#4554—61no—
13C22×C32×C4D411yescharacteristic
14C22×C3⋊Dic3C2×C411yescharacteristic
15C22×C3⋊Dic3D411yescharacteristic
16C22×C3×Dic3—21no—
17C22×C3×Dic3—21no—
18C2×#622—41no—
19C4⋊(C3⋊Dic3)—41no—
20C3×#208—22no—
21C3×#208—41no—
22C2×C3×C3⋊C8—41no—
23#3724—41no—
24#1353—91nomaximal, Sylow
25C2×C3×M16—61no—
26C2×C4⋊Dic3—61no—
27C2×C4⋊Dic3—61no—
28C2×Dic3⋊C4—61no—
29C2×#208—21no—
30C3×#95—61no—
31C3⋊#95—21no—
32C3⋊#95—61no—
33C3⋊#95—61no—
34C3⋊#95—61no—
35C23×C32C22⋊C411yescharacteristic
36C2×C32×C4—21no—
37C2×C32×C4—21no—
38C2×C32×C4SD1611yescharacteristic
39C2×C32×C4Q1611yescharacteristic
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—41no—
43C2×C3⋊Dic3—41no—
44C2×C3×Dic3—41no—
45C2×C3×Dic3—41no—
46C2×C3×Dic3—41no—
47C2×C3×Dic3—41no—
48C2×C3×Dic3—41no—
49C2×C3×Dic3—41no—
50#622—81no—
51C3×C3⋊C8—42no—
52#400—91no—
53#343—91no—
54#324—91no—
55C22×C3×C4—21no—
56C22×C3×C4—21no—
57C22×C3×C4—61no—
58C22×C3×C4—61no—
59C22×Dic3—21no—
60C22×Dic3—21no—
61C22×Dic3—61no—
62C22×Dic3—61no—
63C22×Dic3—61no—
64C22×Dic3—61no—
65C3×M16—62no—
66C3×M16—121no—
67C2×C3×C8—121no—
68C4⋊Dic3—122no—
69C4⋊Dic3—121no—
70C4⋊Dic3—121no—
71Dic3⋊C4—122no—
72#208—22no—
73#208—41no—
74C2×C3⋊C8—41no—
75C22×C32—21no—
76C22×C32—21no—
77C22×C32#9911yescharacteristic
78C22×C32#10311yescharacteristic
79C22×C32#10411yescharacteristic
80C32×C4—21no—
81C32×C4—21no—
82C3⋊Dic3—41no—
83C3⋊Dic3—41no—
84C3×Dic3—81no—
85C3×Dic3—81no—
86C2×M16—61no—
87C2×C4⋊C4—91no—
88C2×C4⋊C4—91no—
89C22⋊C8—181no—
90#95—61no—
91#95—91no—
92#95—181no—
93C23×C3—21no—
94C23×C3—21no—
95C2×C3×C4—21no—
96C2×C3×C4—21no—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—41no—
104C2×C3×C4—41no—
105C2×C3×C4—121no—
106C2×C3×C4—121no—
107C2×C3×C4—121no—
108C2×C3×C4—121no—
109C2×C3×C4—121no—
110C2×C3×C4—121no—
111C2×Dic3—41no—
112C2×Dic3—41no—
113C2×Dic3—41no—
114C2×Dic3—41no—
115C2×Dic3—41no—
116C2×Dic3—41no—
117C2×Dic3—62no—
118C2×Dic3—121no—
119C2×Dic3—121no—
120C2×Dic3—121no—
121C2×Dic3—121no—
122C2×Dic3—121no—
123C2×Dic3—121no—
124C2×Dic3—121no—
125C2×Dic3—241no—
126C2×Dic3—241no—
127C3×C8—122no—
128C3⋊C8—42no—
129C2×C32—21no—
130C2×C32—21no—
131C2×C32#32811yescharacteristic
132C2×C32#35211yescharacteristic
133C2×C32#35511yescharacteristic
134C22×C4—61no—
135C22×C4—61no—
136C22×C4—91no—
137C22×C4—91no—
138C22×C4GO+(4,𝔽2)11yescharacteristic
139M16—62no—
140M16—121no—
141C2×C8—121no—
142C2×C8—361no—
143C4⋊C4—361no—
144C4⋊C4—361no—
145C22×C3—21no—
146C22×C3—21no—
147C22×C3—21no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—21no—
151C22×C3—21no—
152C22×C3—21no—
153C22×C3—21no—
154C22×C3—21no—
155C22×C3—41no—
156C22×C3—41no—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—41no—
162C3×C4—41no—
163C3×C4—241no—
164C3×C4—241no—
165Dic3—81no—
166Dic3—81no—
167Dic3—122no—
168Dic3—241no—
169Dic3—241no—
170Dic3—241no—
171C32#135311yescharacteristic, complemented, Sylow
172C23D32⋊C411yescharacteristic
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—121no—
176C2×C4—121no—
177C2×C4—121no—
178C2×C4—121no—
179C2×C4—121no—
180C2×C4—121no—
181C2×C4—181no—
182C2×C4—181no—
183C2×C4—361no—
184C2×C4—361no—
185C2×C4#377511yescharacteristic
186C2×C4#377611yescharacteristic
187C8—122no—
188C8—721no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—41no—
200C2×C3—41no—
201C22—21no—
202C22—21no—
203C22#6373811yescharacteristic
204C22#6374011yescharacteristic
205C22#6374111yescharacteristic
206C4—21no—
207C4—21no—
208C4—241no—
209C4—241no—
210C4—361no—
211C4—361no—
212C3—21no—
213C3—21no—
214C2—21no—
215C2—21no—
216C2#1059005811yescharacteristic
217C2#1059005911yescharacteristic
218C2#1059007211yescharacteristic
subgroupG/H
centerC22#63738
commutatorC22×C3⋊Dic3C2×C4
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C4⋊(C3⋊Dic3)C22
hypocenterC32#1353
LCSG ▷ C22×C3⋊Dic3 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
171. C32#1353semidirect

Maximal subgroups

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

subgroupindex
#105912182
#105902022
#105891682
#13539