Finite Group Databasebeta

← #11771845

Subgroups — #11771845

Order 1152.

238 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 29 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#10591356C211yesmaximal, characteristic
2#10590208C211yesmaximal, characteristic
3#10589148C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×#3750C2211yescharacteristic
6C2×#3724C411yescharacteristic
7C2×Dic3⋊Dic3—21no—
8C3×C3⋊#95—21no—
9C3×#830—21no—
10#63579C411yescharacteristic
11#4657—61no—
12#4469—61no—
13C22×C32×C4D411yescharacteristic
14C22×C3⋊Dic3C2×C411yescharacteristic
15C22×C3⋊Dic3D411yescharacteristic
16C22×C3×Dic3—21no—
17C22×C3×Dic3—21no—
18#3792—22no—
19#3792—41no—
20C2×#622—41no—
21#3750—41no—
22C2×C3×C3⋊C8—41no—
23#3724—41no—
24Dic3⋊Dic3—41no—
25Dic3⋊Dic3—41no—
26#1346—91nomaximal, Sylow
27C2×C4⋊Dic3—61no—
28C2×Dic3⋊C4—61no—
29C2×Dic3⋊C4—61no—
30C2×Dic3⋊C4—61no—
31C2×Dic3⋊C4—61no—
32C3×C22⋊C8—61no—
33C3×#95—61no—
34C3⋊#95—21no—
35C3⋊#95—61no—
36#830—21no—
37C23×C32C22⋊C411yescharacteristic
38C2×C32×C4—21no—
39C2×C32×C4—41no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3—41no—
44C2×C3⋊Dic3D811yescharacteristic
45C2×C3⋊Dic3SD1611yescharacteristic
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—42no—
53C3×C3⋊C8—81no—
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—
67C2×C3×C8—121no—
68C4⋊Dic3—121no—
69C4⋊Dic3—121no—
70Dic3⋊C4—121no—
71Dic3⋊C4—121no—
72Dic3⋊C4—122no—
73Dic3⋊C4—122no—
74Dic3⋊C4—121no—
75Dic3⋊C4—121no—
76C2×C3⋊C8—41no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32#9911yescharacteristic
80C22×C32#10211yescharacteristic
81C22×C32#10411yescharacteristic
82C32×C4—41no—
83C3⋊Dic3—21no—
84C3⋊Dic3—21no—
85C3⋊Dic3—41no—
86C3×Dic3—42no—
87C3×Dic3—81no—
88C2×M16—181no—
89C2×C4⋊C4—91no—
90C2×C4⋊C4—91no—
91C2×C4⋊C4—181no—
92C22⋊C8—61no—
93#95—61no—
94#95—91no—
95C23×C3—21no—
96C23×C3—21no—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×C3×C4—41no—
100C2×C3×C4—41no—
101C2×C3×C4—41no—
102C2×C3×C4—62no—
103C2×C3×C4—81no—
104C2×C3×C4—121no—
105C2×C3×C4—121no—
106C2×C3×C4—121no—
107C2×C3×C4—121no—
108C2×C3×C4—121no—
109C2×Dic3—22no—
110C2×Dic3—41no—
111C2×Dic3—41no—
112C2×Dic3—41no—
113C2×Dic3—41no—
114C2×Dic3—41no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—62no—
120C2×Dic3—121no—
121C2×Dic3—121no—
122C2×Dic3—121no—
123C2×Dic3—121no—
124C2×Dic3—121no—
125C2×Dic3—121no—
126C2×Dic3—121no—
127C2×Dic3—241no—
128C3×C8—241no—
129C3⋊C8—81no—
130C2×C32—21no—
131C2×C32—21no—
132C2×C32#32711yescharacteristic
133C2×C32#35211yescharacteristic
134C2×C32#35611yescharacteristic
135C22×C4—61no—
136C22×C4—61no—
137C22×C4—91no—
138C22×C4—91no—
139C22×C4GO+(4,𝔽2)11yescharacteristic
140M16—182no—
141M16—361no—
142C2×C8—121no—
143C2×C8—361no—
144C4⋊C4—361no—
145C4⋊C4—361no—
146C4⋊C4—361no—
147C4⋊C4—361no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—21no—
151C22×C3—21no—
152C22×C3—21no—
153C22×C3—21no—
154C22×C3—21no—
155C22×C3—21no—
156C22×C3—21no—
157C22×C3—21no—
158C22×C3—41no—
159C22×C3—41no—
160C3×C4—41no—
161C3×C4—41no—
162C3×C4—81no—
163C3×C4—122no—
164C3×C4—241no—
165Dic3—42no—
166Dic3—81no—
167Dic3—121no—
168Dic3—121no—
169Dic3—121no—
170Dic3—121no—
171Dic3—122no—
172Dic3—241no—
173C32#134611yescharacteristic, complemented, Sylow
174C23D32⋊C411yescharacteristic
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—62no—
178C2×C4—91no—
179C2×C4—91no—
180C2×C4—121no—
181C2×C4—121no—
182C2×C4—121no—
183C2×C4—121no—
184C2×C4—121no—
185C2×C4—181no—
186C2×C4—181no—
187C2×C4—181no—
188C2×C4—361no—
189C8—241no—
190C8—362no—
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—21no—
200C2×C3—21no—
201C2×C3—41no—
202C2×C3—41no—
203C22—21no—
204C22—21no—
205C22#6372911yescharacteristic
206C22#6373111yescharacteristic
207C22#6373811yescharacteristic
208C4—41no—
209C4—122no—
210C4—181no—
211C4—181no—
212C4—241no—
213C4—361no—
214C3—21no—
215C3—21no—
216C2—21no—
217C2—21no—
218C2#1059003311yescharacteristic
219C2#1059006011yescharacteristic
220C2#1059007911yescharacteristic
subgroupG/H
centerC22#63738
commutatorC22×C3⋊Dic3C2×C4
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×#3750C22
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
173. C32#1346semidirect

Maximal subgroups

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

subgroupindex
#105913562
#105902082
#105891482
#13469