Finite Group Databasebeta

← #11791440

Subgroups — #11791440

Order 1152.

566 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C2×#63919C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic
3C2×#63740C214yesmaximal
4#10591257C211yesmaximal, characteristic
5C22×#627C2212yes—
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C2×#3724—21no—
10C2×#3724C2212yes—
11C2×Dic32—21no—
12#63919—22no—
13#63919C414yescomplemented
14#63779—22no—
15#63740—28no—
16C3×C3⋊#95—21no—
17C2×#888—61no—
18#4649—61no—
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21C22×C3⋊Dic3C2311yescharacteristic
22C22×C3×Dic3—22no—
23C22×C3×Dic3—22no—
24C2×#627—24no—
25C2×#627—24no—
26C2×#627—22no—
27C2×#627C2×C414yes—
28C2×#622—22no—
29C2×#622—24no—
30C4×C3⋊Dic3C2×C412yes—
31C4×C3⋊Dic3D412yes—
32C3×C4⋊Dic3—24no—
33#3724—24no—
34#3724—22no—
35#3724D414yes—
36Dic32—42no—
37#1981—91nomaximal, Sylow
38C22×Dic6—62no—
39C2×C3×C4⋊C4—61no—
40C2×C4⋊Dic3—21no—
41C2×Dic3⋊C4—62no—
42C2×Dic3⋊C4—62no—
43C2×C4×Dic3—61no—
44C2×C4×Dic3—61no—
45C2×C4×Dic3—62no—
46#888—64no—
47#888—64no—
48C3×#95—61no—
49C3⋊#95—21no—
50C23×C32C2×D411yescharacteristic
51C2×C32×C4—22no—
52C2×C32×C4C22⋊C412yes—
53C2×C3⋊Dic3C22⋊C412yes—
54C2×C3⋊Dic3SD1612yes—
55C2×C3⋊Dic3Q1612yes—
56C2×C3⋊Dic3C22×C411yescharacteristic
57C2×C3⋊Dic3C2×D412yes—
58C2×C3⋊Dic3C2×D411yescharacteristic
59C2×C3⋊Dic3#4112yes—
60C2×C3×Dic3—24no—
61C2×C3×Dic3—24no—
62C2×C3×Dic3—44no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—42no—
65#627—28no—
66#627—42no—
67#627—42no—
68#622—42no—
69C2×C4⋊Q8—91no—
70C2×C4⋊C8—91no—
71C2×#103—94no—
72C4×C4⋊C4—91no—
73C22×C3×C4—21no—
74C22×C3×C4—21no—
75C22×C3×C4—62no—
76C22×C3×C4—62no—
77C22×Dic3—22no—
78C22×Dic3—22no—
79C22×Dic3—61no—
80C22×Dic3—61no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C2×Dic6—64no—
84C2×Dic6—64no—
85C2×Dic6—124no—
86C2×Dic6—124no—
87C3×C4⋊C4—64no—
88C4⋊Dic3—24no—
89Dic3⋊C4—64no—
90Dic3⋊C4—68no—
91Dic3⋊C4—64no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C4×Dic3—62no—
96C4×Dic3—124no—
97C22×C32C2×C22⋊C411yescharacteristic
98C22×C32#12112yes—
99C22×C32C2×SD1611yescharacteristic
100C22×C32C2×Q1611yescharacteristic
101C22×C32#13712yes—
102C32×C4—22no—
103C3⋊Dic3#10314yescomplemented
104C3⋊Dic3C4×D412yes—
105C3⋊Dic3#12411yescharacteristic
106C3⋊Dic3#12711yescharacteristic
107C3×Dic3—44no—
108C3×Dic3—44no—
109C22×Q8—92no—
110C22×C8—92no—
111C4⋊Q8—94no—
112C4⋊Q8—182no—
113C2×C4⋊C4—61no—
114C2×C4⋊C4—92no—
115C2×C4⋊C4—181no—
116C2×C42—91no—
117C2×C42—181no—
118C4⋊C8—182no—
119#103—188no—
120#95—61no—
121C23×C3—21no—
122C23×C3—21no—
123C2×C3×C4—24no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—42no—
127C2×C3×C4—64no—
128C2×C3×C4—64no—
129C2×C3×C4—122no—
130C2×C3×C4—124no—
131C2×C3×C4—122no—
132C2×Dic3—24no—
133C2×Dic3—24no—
134C2×Dic3—42no—
135C2×Dic3—44no—
136C2×Dic3—42no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—62no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—62no—
151Dic6—128no—
152Dic6—124no—
153Dic6—124no—
154C2×C32#39011yescharacteristic
155C2×C32C2×#10311yescharacteristic
156C2×C32#41911yescharacteristic
157C2×C32#46112yes—
158C2×C32#46212yes—
159C2×Q8—94no—
160C2×Q8—182no—
161C2×Q8—184no—
162C2×Q8—184no—
163C22×C4—62no—
164C22×C4—62no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4GO+(4,𝔽2)11yescharacteristic
168C2×C8—184no—
169C2×C8—182no—
170C4⋊C4—64no—
171C4⋊C4—94no—
172C4⋊C4—182no—
173C4⋊C4—184no—
174C42—92no—
175C42—92no—
176C42—362no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—21no—
180C22×C3—21no—
181C22×C3—22no—
182C22×C3—22no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—22no—
186C22×C3—22no—
187C3×C4—24no—
188C3×C4—42no—
189C3×C4—124no—
190C3×C4—124no—
191Dic3—44no—
192Dic3—44no—
193Dic3—62no—
194Dic3—61no—
195Dic3—61no—
196Dic3—64no—
197Dic3—64no—
198Dic3—62no—
199Dic3—61no—
200Dic3—61no—
201C32#198111yescharacteristic, complemented, Sylow
202C23C2×GO+(4,𝔽2)11yescharacteristic
203Q8—188no—
204Q8—362no—
205Q8—362no—
206C2×C4—22no—
207C2×C4—64no—
208C2×C4—64no—
209C2×C4—92no—
210C2×C4—92no—
211C2×C4—92no—
212C2×C4—92no—
213C2×C4—92no—
214C2×C4—91no—
215C2×C4—91no—
216C2×C4—122no—
217C2×C4—124no—
218C2×C4—122no—
219C2×C4D32⋊C412yes—
220C8—362no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—22no—
226C2×C3—22no—
227C2×C3—22no—
228C2×C3—22no—
229C2×C3—21no—
230C2×C3—21no—
231C22#6422711yescharacteristic
232C22#6422811yescharacteristic
233C22#6423012yes—
234C22C2×D32⋊C411yescharacteristic
235C22#6423912yes—
236C4—22no—
237C4—94no—
238C4—91no—
239C4—92no—
240C4—91no—
241C4—124no—
242C4—124no—
243C3—21no—
244C3—21no—
245C2#1059337511yescharacteristic
246C2#1059340511yescharacteristic
247C2#1059343812yes—
248C2#1059344812yes—
249C2#1059350311yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1981
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
13. #63919C4semidirect
103. C3⋊Dic3#103semidirect
201. C32#1981semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#637792
C2×#637402
#105912572
#19819