Finite Group Databasebeta

← #11771964

Subgroups — #11771964

Order 1152.

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

normal subgroups only

This group has 222 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#10591217C211yesmaximal, characteristic
2#10590208C211yesmaximal, characteristic
3#10589148C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×#3750C2211yescharacteristic
6C2×#3724C411yescharacteristic
7C3×C3⋊#95—21no—
8C3×#830—21no—
9#63579—21no—
10#63579C411yescharacteristic
11#4658—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—
24#1353—91nomaximal, Sylow
25C2×Dic3⋊C4—61no—
26C2×Dic3⋊C4—61no—
27C2×Dic3⋊C4—61no—
28C3×C22⋊C8—61no—
29C3×#95—61no—
30C3⋊#95—21no—
31C3⋊#95—61no—
32C3⋊#95—61no—
33C3⋊#95—61no—
34#830—21no—
35C23×C32C22⋊C411yescharacteristic
36C2×C32×C4—21no—
37C2×C32×C4—41no—
38C2×C3⋊Dic3—21no—
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—41no—
42C2×C3⋊Dic3SD1611yescharacteristic
43C2×C3⋊Dic3Q1611yescharacteristic
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—42no—
51C3×C3⋊C8—81no—
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—
65C2×C3×C8—121no—
66Dic3⋊C4—122no—
67Dic3⋊C4—122no—
68Dic3⋊C4—121no—
69Dic3⋊C4—121no—
70C2×C3⋊C8—41no—
71C22×C32—21no—
72C22×C32—21no—
73C22×C32#9911yescharacteristic
74C22×C32#10311yescharacteristic
75C22×C32#10411yescharacteristic
76C32×C4—41no—
77C3⋊Dic3—21no—
78C3⋊Dic3—21no—
79C3⋊Dic3—41no—
80C3×Dic3—81no—
81C3×Dic3—81no—
82C2×M16—181no—
83C2×C4⋊C4—91no—
84C2×C4⋊C4—91no—
85C22⋊C8—61no—
86#95—61no—
87#95—91no—
88#95—181no—
89C23×C3—21no—
90C23×C3—21no—
91C2×C3×C4—21no—
92C2×C3×C4—21no—
93C2×C3×C4—41no—
94C2×C3×C4—41no—
95C2×C3×C4—41no—
96C2×C3×C4—81no—
97C2×C3×C4—121no—
98C2×C3×C4—121no—
99C2×C3×C4—121no—
100C2×C3×C4—121no—
101C2×C3×C4—121no—
102C2×C3×C4—121no—
103C2×Dic3—41no—
104C2×Dic3—41no—
105C2×Dic3—41no—
106C2×Dic3—41no—
107C2×Dic3—41no—
108C2×Dic3—41no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—62no—
114C2×Dic3—121no—
115C2×Dic3—121no—
116C2×Dic3—121no—
117C2×Dic3—121no—
118C2×Dic3—121no—
119C2×Dic3—121no—
120C2×Dic3—121no—
121C2×Dic3—241no—
122C3×C8—241no—
123C3⋊C8—81no—
124C2×C32—21no—
125C2×C32—21no—
126C2×C32#32811yescharacteristic
127C2×C32#35211yescharacteristic
128C2×C32#35511yescharacteristic
129C22×C4—61no—
130C22×C4—61no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4GO+(4,𝔽2)11yescharacteristic
134M16—182no—
135M16—361no—
136C2×C8—121no—
137C2×C8—361no—
138C4⋊C4—361no—
139C4⋊C4—361no—
140C22×C3—21no—
141C22×C3—21no—
142C22×C3—21no—
143C22×C3—21no—
144C22×C3—21no—
145C22×C3—21no—
146C22×C3—21no—
147C22×C3—21no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—41no—
151C22×C3—41no—
152C3×C4—41no—
153C3×C4—41no—
154C3×C4—81no—
155C3×C4—241no—
156C3×C4—241no—
157Dic3—81no—
158Dic3—81no—
159Dic3—121no—
160Dic3—121no—
161Dic3—121no—
162Dic3—121no—
163Dic3—122no—
164Dic3—241no—
165C32#135311yescharacteristic, complemented, Sylow
166C23D32⋊C411yescharacteristic
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—121no—
172C2×C4—121no—
173C2×C4—121no—
174C2×C4—121no—
175C2×C4—121no—
176C2×C4—121no—
177C2×C4—181no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—361no—
181C8—241no—
182C8—362no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—41no—
194C2×C3—41no—
195C22—21no—
196C22—21no—
197C22#6373011yescharacteristic
198C22#6373111yescharacteristic
199C22#6373811yescharacteristic
200C4—41no—
201C4—181no—
202C4—181no—
203C4—241no—
204C4—241no—
205C4—361no—
206C3—21no—
207C3—21no—
208C2—21no—
209C2—21no—
210C2#1059003411yescharacteristic
211C2#1059005911yescharacteristic
212C2#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#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
165. C32#1353semidirect

Maximal subgroups

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

subgroupindex
#105912172
#105902082
#105891482
#13539