Finite Group Databasebeta

← #11776366

Subgroups — #11776366

Order 1152.

444 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 69 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
2#10593805C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4#10590040C214yesmaximal, complemented
5C22×#627C412yes—
6C2×#3792—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C2×#3724—21no—
10#63919—21no—
11#63919—21no—
12#63919C412yes—
13#63919C2212yes—
14#63779—21no—
15C4⋊#622C2212yes—
16C3×#830—21no—
17#63572C2212yes—
18#63553—21no—
19C2×#888—61no—
20#4718—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3×Dic3—22no—
25C2×#627—22no—
26C2×#627—44no—
27C2×#627C2×C414yes—
28#3792—42no—
29C2×#622—22no—
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C4×C3⋊Dic3C2311yescharacteristic
34C3×C4⋊Dic3—22no—
35C3×C4⋊Dic3—22no—
36C2×C3×C3⋊C8—22no—
37#3724—22no—
38#3724—22no—
39#1548—91nomaximal, Sylow
40C22×Dic6—62no—
41C2×C3×C4⋊C4—61no—
42C2×C4⋊Dic3—21no—
43C2×Dic3⋊C4—62no—
44C2×C4×Dic3—61no—
45C2×C4×Dic3—61no—
46#888—62no—
47#888—62no—
48#888—62no—
49#888—62no—
50C3×C22⋊C8—61no—
51#830—21no—
52Dic3⋊C8—62no—
53C8×Dic3—62no—
54C23×C32C22⋊C411yescharacteristic
55C2×C32×C4—22no—
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3C22⋊C411yescharacteristic
60C2×C3⋊Dic3C22⋊C411yescharacteristic
61C2×C3⋊Dic3SD1612yes—
62C2×C3⋊Dic3Q1612yes—
63C2×C3⋊Dic3C22×C411yescharacteristic
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3×Dic3—24no—
66C2×C3×Dic3—44no—
67#627—44no—
68#627—44no—
69#622—42no—
70C3×C3⋊C8—42no—
71C2×C4⋊Q8—91no—
72#431—91no—
73#423—91no—
74#333—94no—
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4—62no—
78C22×Dic3—22no—
79C22×Dic3—61no—
80C22×Dic3—61no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C2×Dic6—64no—
84C2×Dic6—64no—
85C2×Dic6—128no—
86C2×C3×C8—62no—
87C3×C4⋊C4—62no—
88C3×C4⋊C4—62no—
89C4⋊Dic3—22no—
90C4⋊Dic3—22no—
91Dic3⋊C4—64no—
92Dic3⋊C4—64no—
93C4×Dic3—61no—
94C4×Dic3—61no—
95C4×Dic3—61no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C2×C3⋊C8—22no—
102C22×C32—21no—
103C22×C32—21no—
104C22×C32#10312yes—
105C22×C32C2×C22⋊C411yescharacteristic
106C32×C4—21no—
107C32×C4#13712yes—
108C3⋊Dic3—21no—
109C3⋊Dic3#10012yes—
110C3⋊Dic3#10312yes—
111C3⋊Dic3C2×SD1611yescharacteristic
112C3⋊Dic3C2×Q1611yescharacteristic
113C3×Dic3—44no—
114C22×Q8—92no—
115C2×M16—181no—
116C4⋊Q8—92no—
117C4⋊Q8—92no—
118C4⋊Q8—181no—
119C4⋊Q8—181no—
120C2×C4⋊C4—61no—
121C2×C4⋊C4—181no—
122C2×C42—91no—
123C4⋊C8—92no—
124C4⋊C8—92no—
125C4⋊C8—181no—
126C22⋊C8—61no—
127C4×C8—181no—
128C23×C3—21no—
129C23×C3—21no—
130C2×C3×C4—24no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—42no—
136C2×C3×C4—64no—
137C2×C3×C4—124no—
138C2×Dic3—24no—
139C2×Dic3—44no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—64no—
153C2×Dic3—122no—
154Dic6—128no—
155Dic6—128no—
156C3×C8—122no—
157C3⋊C8—42no—
158C2×C32—22no—
159C2×C32C2×#10011yescharacteristic
160C2×C32C2×#10311yescharacteristic
161C2×C32#41911yescharacteristic
162C2×Q8—94no—
163C2×Q8—182no—
164C2×Q8—364no—
165C22×C4—62no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4GO+(4,𝔽2)11yescharacteristic
169M16—362no—
170C2×C8—62no—
171C2×C8—182no—
172C4⋊C4—62no—
173C4⋊C4—62no—
174C4⋊C4—182no—
175C4⋊C4—182no—
176C42—91no—
177C42—91no—
178C42—91no—
179C42—91no—
180C22×C3—22no—
181C22×C3—22no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—22no—
185C22×C3—22no—
186C22×C3—41no—
187C22×C3—41no—
188C3×C4—22no—
189C3×C4—22no—
190C3×C4—22no—
191C3×C4—41no—
192C3×C4—124no—
193Dic3—44no—
194Dic3—62no—
195Dic3—62no—
196Dic3—62no—
197Dic3—61no—
198Dic3—61no—
199Dic3—61no—
200Dic3—61no—
201Dic3—62no—
202Dic3—62no—
203Dic3—121no—
204C32#154811yescharacteristic, complemented, Sylow
205C23D32⋊C411yescharacteristic
206Q8—364no—
207Q8—364no—
208C2×C4—22no—
209C2×C4—64no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—92no—
214C2×C4—92no—
215C2×C4—91no—
216C2×C4—124no—
217C2×C4—182no—
218C2×C4D32⋊C411yescharacteristic
219C2×C4C2×GO+(4,𝔽2)11yescharacteristic
220C8—122no—
221C8—362no—
222C2×C3—24no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—42no—
230C22—21no—
231C22—21no—
232C22#6373012yes—
233C22C2×D32⋊C411yescharacteristic
234C4—21no—
235C4—92no—
236C4—91no—
237C4—91no—
238C4—92no—
239C4—124no—
240C4—181no—
241C4#6423912yes—
242C3—21no—
243C3—21no—
244C2—22no—
245C2#1059331211yescharacteristic
246C2C2×#6373011yescharacteristic
247C2#1059350311yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1548
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590040C2semidirect
204. C32#1548semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
#105938052
#105910612
#105900402
#15489