Finite Group Databasebeta

← #11771209

Subgroups — #11771209

Order 1152.

336 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 61 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#10593795C211yesmaximal, characteristic
2C4×#3724C211yesmaximal, characteristic
3#10591120C211yesmaximal, characteristic
4C2×C4×C3⋊Dic3C2211yescharacteristic
5C2×C3×C4×Dic3—21no—
6C2×C3×#208—21no—
7C2×#3724—21no—
8C22⋊#622—21no—
9C4⋊#622C412yescomplemented
10C4×#622—21no—
11#63579C412yes—
12#63572—21no—
13#63572C412yescomplemented
14#5118—61no—
15C4×Dic3⋊C4—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×C4×Dic3—41no—
26C3×C4×Dic3—41no—
27C3×#208—41no—
28C3×#208—41no—
29C2×C3×C3⋊C8—22no—
30#3724—24no—
31#1303—91nomaximal, Sylow
32C2×C3×M16—61no—
33C2×C3×C42—61no—
34C2×Dic3⋊C4—62no—
35C2×C4×Dic3—21no—
36C2×C4×Dic3—61no—
37C2×C4×Dic3—61no—
38C2×#208—21no—
39C3⋊#95—62no—
40Dic3⋊C8—62no—
41Dic3⋊C8—62no—
42C23×C32C22⋊C411yescharacteristic
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C32×C4D811yescharacteristic
46C2×C32×C4SD1611yescharacteristic
47C2×C32×C4SD1611yescharacteristic
48C2×C32×C4Q1611yescharacteristic
49C2×C3⋊Dic3—22no—
50C2×C3⋊Dic3—41no—
51C2×C3⋊Dic3C4211yescharacteristic
52C2×C3⋊Dic3C22⋊C411yescharacteristic
53C2×C3⋊Dic3C4⋊C411yescharacteristic
54C2×C3⋊Dic3C4⋊C411yescharacteristic
55C2×C3×Dic3—24no—
56C2×C3×Dic3—42no—
57C2×C3×Dic3—42no—
58#622—42no—
59C3×C3⋊C8—42no—
60#431—91no—
61#423—91no—
62C4×C4⋊C4—91no—
63C22×C3×C4—21no—
64C22×C3×C4—21no—
65C22×C3×C4—62no—
66C22×Dic3—22no—
67C22×Dic3—61no—
68C22×Dic3—61no—
69C22×Dic3—61no—
70C22×Dic3—61no—
71C3×M16—121no—
72C3×M16—121no—
73C2×C3×C8—62no—
74C3×C42—121no—
75C3×C42—121no—
76Dic3⋊C4—68no—
77C4×Dic3—41no—
78C4×Dic3—41no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C4×Dic3—61no—
82C4×Dic3—61no—
83C4×Dic3—61no—
84C4×Dic3—61no—
85C4×Dic3—61no—
86C4×Dic3—61no—
87#208—41no—
88#208—41no—
89C2×C3⋊C8—22no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32#9511yescharacteristic
93C22×C32#10211yescharacteristic
94C22×C32#10311yescharacteristic
95C32×C4#10211yescharacteristic
96C32×C4#10311yescharacteristic
97C32×C4#10611yescharacteristic
98C32×C4#10711yescharacteristic
99C3⋊Dic3—21no—
100C3⋊Dic3—21no—
101C3⋊Dic3—21no—
102C3⋊Dic3#10412yes—
103C3×Dic3—44no—
104C2×M16—61no—
105C2×C4⋊C4—181no—
106C2×C42—61no—
107C2×C42—91no—
108C4⋊C8—92no—
109C4⋊C8—92no—
110C4⋊C8—181no—
111C22⋊C8—181no—
112C4×C8—181no—
113#95—92no—
114C23×C3—21no—
115C23×C3—21no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—64no—
129C2×C3×C4—122no—
130C2×C3×C4—122no—
131C2×Dic3—24no—
132C2×Dic3—42no—
133C2×Dic3—42no—
134C2×Dic3—61no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—64no—
143C2×Dic3—122no—
144C2×Dic3—122no—
145C2×Dic3—122no—
146C3×C8—122no—
147C3⋊C8—42no—
148C2×C32—21no—
149C2×C32—21no—
150C2×C32#33911yescharacteristic
151C2×C32#34011yescharacteristic
152C2×C32#34411yescharacteristic
153C22×C4—62no—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4GO+(4,𝔽2)11yescharacteristic
157M16—121no—
158M16—121no—
159C2×C8—62no—
160C2×C8—182no—
161C4⋊C4—184no—
162C42—91no—
163C42—91no—
164C42—91no—
165C42—91no—
166C42—121no—
167C42—121no—
168C22×C3—22no—
169C22×C3—22no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—41no—
177C22×C3—41no—
178C3×C4—21no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—124no—
187Dic3—44no—
188Dic3—62no—
189Dic3—62no—
190Dic3—62no—
191Dic3—62no—
192Dic3—121no—
193Dic3—121no—
194Dic3—121no—
195Dic3—121no—
196C32#130311yescharacteristic, complemented, Sylow
197C23D32⋊C411yescharacteristic
198C2×C4—64no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—122no—
204C2×C4—122no—
205C2×C4—182no—
206C2×C4—361no—
207C2×C4D32⋊C411yescharacteristic
208C2×C4#377311yescharacteristic
209C2×C4#377411yescharacteristic
210C2×C4#377511yescharacteristic
211C2×C4#377511yescharacteristic
212C2×C4#377611yescharacteristic
213C8—122no—
214C8—362no—
215C2×C3—22no—
216C2×C3—22no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—41no—
224C2×C3—41no—
225C22—21no—
226C22—21no—
227C22#6373711yescharacteristic
228C22#6373911yescharacteristic
229C22#6374011yescharacteristic
230C4—92no—
231C4—124no—
232C4—181no—
233C4—181no—
234C4—181no—
235C4#6373911yescharacteristic
236C4#6374011yescharacteristic
237C4#6374211yescharacteristic
238C4#6374311yescharacteristic
239C3—21no—
240C3—21no—
241C2—21no—
242C2—21no—
243C2#1059004811yescharacteristic
244C2#1059005411yescharacteristic
245C2#1059007511yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C32C22⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypocenterC32#1303
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
9. C4⋊#622C4semidirect
13. #63572C4semidirect
196. C32#1303semidirect

Maximal subgroups

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

subgroupindex
#105937952
C4×#37242
#105911202
#13039