Finite Group Databasebeta

← #11771844

Subgroups — #11771844

Order 1152.

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

normal subgroups only

This group has 248 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#10591215C211yesmaximal, characteristic
2#10590202C211yesmaximal, characteristic
3#10589168C211yesmaximal, characteristic
4C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
5C2×C3×Dic3⋊C4—21no—
6C2×C3×#208—21no—
7C2×#3724C411yescharacteristic
8C22⋊#622—21no—
9#63579—21no—
10#63579C411yescharacteristic
11#4982—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×Dic3⋊C4—41no—
21C3×Dic3⋊C4—41no—
22C3×#208—22no—
23C3×#208—41no—
24C2×C3×C3⋊C8—41no—
25#3724—41no—
26#1346—91nomaximal, Sylow
27C2×C3×M16—61no—
28C2×C3×C4⋊C4—61no—
29C2×C4⋊Dic3—61no—
30C2×C4⋊Dic3—61no—
31C2×Dic3⋊C4—21no—
32C2×Dic3⋊C4—61no—
33C2×#208—21no—
34C3⋊#95—61no—
35C3⋊#95—61no—
36C3⋊#95—61no—
37C23×C32C22⋊C411yescharacteristic
38C2×C32×C4—21no—
39C2×C32×C4—21no—
40C2×C32×C4D811yescharacteristic
41C2×C32×C4SD1611yescharacteristic
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3—21no—
44C2×C3⋊Dic3—41no—
45C2×C3⋊Dic3—41no—
46C2×C3×Dic3—22no—
47C2×C3×Dic3—41no—
48C2×C3×Dic3—41no—
49C2×C3×Dic3—41no—
50C2×C3×Dic3—41no—
51C2×C3×Dic3—41no—
52#622—81no—
53C3×C3⋊C8—42no—
54#398—91no—
55#343—91no—
56#324—91no—
57C22×C3×C4—21no—
58C22×C3×C4—21no—
59C22×C3×C4—61no—
60C22×C3×C4—61no—
61C22×Dic3—21no—
62C22×Dic3—21no—
63C22×Dic3—61no—
64C22×Dic3—61no—
65C22×Dic3—61no—
66C22×Dic3—61no—
67C3×M16—62no—
68C3×M16—121no—
69C2×C3×C8—121no—
70C3×C4⋊C4—121no—
71C3×C4⋊C4—121no—
72C4⋊Dic3—122no—
73C4⋊Dic3—121no—
74C4⋊Dic3—121no—
75Dic3⋊C4—41no—
76Dic3⋊C4—41no—
77Dic3⋊C4—122no—
78#208—22no—
79#208—41no—
80C2×C3⋊C8—41no—
81C22×C32—21no—
82C22×C32—21no—
83C22×C32#9911yescharacteristic
84C22×C32#10211yescharacteristic
85C22×C32#10411yescharacteristic
86C32×C4—21no—
87C32×C4—21no—
88C3⋊Dic3—41no—
89C3⋊Dic3—41no—
90C3×Dic3—42no—
91C3×Dic3—81no—
92C2×M16—61no—
93C2×C4⋊C4—61no—
94C2×C4⋊C4—91no—
95C2×C4⋊C4—91no—
96C22⋊C8—181no—
97#95—91no—
98#95—181no—
99C23×C3—21no—
100C23×C3—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—41no—
110C2×C3×C4—41no—
111C2×C3×C4—62no—
112C2×C3×C4—121no—
113C2×C3×C4—121no—
114C2×C3×C4—121no—
115C2×C3×C4—121no—
116C2×C3×C4—121no—
117C2×Dic3—22no—
118C2×Dic3—41no—
119C2×Dic3—41no—
120C2×Dic3—41no—
121C2×Dic3—41no—
122C2×Dic3—41no—
123C2×Dic3—62no—
124C2×Dic3—121no—
125C2×Dic3—121no—
126C2×Dic3—121no—
127C2×Dic3—121no—
128C2×Dic3—121no—
129C2×Dic3—121no—
130C2×Dic3—121no—
131C2×Dic3—241no—
132C2×Dic3—241no—
133C3×C8—122no—
134C3⋊C8—42no—
135C2×C32—21no—
136C2×C32—21no—
137C2×C32#32711yescharacteristic
138C2×C32#35211yescharacteristic
139C2×C32#35611yescharacteristic
140C22×C4—61no—
141C22×C4—61no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4GO+(4,𝔽2)11yescharacteristic
145M16—62no—
146M16—121no—
147C2×C8—121no—
148C2×C8—361no—
149C4⋊C4—121no—
150C4⋊C4—121no—
151C4⋊C4—361no—
152C4⋊C4—361no—
153C22×C3—21no—
154C22×C3—21no—
155C22×C3—21no—
156C22×C3—21no—
157C22×C3—21no—
158C22×C3—21no—
159C22×C3—21no—
160C22×C3—21no—
161C22×C3—21no—
162C22×C3—21no—
163C22×C3—41no—
164C22×C3—41no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—41no—
170C3×C4—41no—
171C3×C4—122no—
172C3×C4—241no—
173Dic3—42no—
174Dic3—81no—
175Dic3—122no—
176Dic3—241no—
177Dic3—241no—
178Dic3—241no—
179C32#134611yescharacteristic, complemented, Sylow
180C23D32⋊C411yescharacteristic
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—62no—
184C2×C4—121no—
185C2×C4—121no—
186C2×C4—121no—
187C2×C4—121no—
188C2×C4—121no—
189C2×C4—181no—
190C2×C4—181no—
191C2×C4—361no—
192C2×C4—361no—
193C2×C4#377411yescharacteristic
194C2×C4#377511yescharacteristic
195C8—122no—
196C8—721no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—21no—
205C2×C3—21no—
206C2×C3—21no—
207C2×C3—41no—
208C2×C3—41no—
209C22—21no—
210C22—21no—
211C22#6373811yescharacteristic
212C22#6373911yescharacteristic
213C22#6374111yescharacteristic
214C4—21no—
215C4—21no—
216C4—122no—
217C4—241no—
218C4—361no—
219C4—361no—
220C3—21no—
221C3—21no—
222C2—21no—
223C2—21no—
224C2#1059005811yescharacteristic
225C2#1059006011yescharacteristic
226C2#1059007111yescharacteristic
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#1346
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
179. C32#1346semidirect

Maximal subgroups

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

subgroupindex
#105912152
#105902022
#105891682
#13469