Finite Group Databasebeta

← #11776188

Subgroups — #11776188

Order 1152.

434 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 68 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#10596093C211yesmaximal, characteristic
2#10593801C211yesmaximal, characteristic
3C2×#63779C211yesmaximal, characteristic
4#10590220C212yesmaximal, complemented
5#10590162C212yesmaximal, complemented
6C22×#622—21no—
7C32×C22⋊Q8C411yescharacteristic
8Q8×C3⋊Dic3C411yescharacteristic
9#64153C2211yescharacteristic
10#64133C411yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64098—21no—
13#64097C2211yescharacteristic
14#64096—21no—
15#64096C411yescharacteristic
16#64087—21no—
17#64086—21no—
18C22⋊#622—21no—
19#63779—21no—
20#63779C2212yes—
21#63779C2212yes—
22C4×#622—21no—
23#5622—62no—
24C2×C32×Q8C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×#634—21no—
29C2×#634C2×C411yescharacteristic
30C2×#622—22no—
31C2×#622—22no—
32C2×#622—42no—
33C32×C4⋊C4—21no—
34C32×C4⋊C4C2×C411yescharacteristic
35C32×C22⋊C4—21no—
36#3757—21no—
37C4⋊(C3⋊Dic3)—21no—
38C4⋊(C3⋊Dic3)C2×C411yescharacteristic
39#3750—21no—
40#3750—21no—
41#3750—21no—
42#3750—21no—
43#3750—21no—
44C4×C3⋊Dic3—21no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3C2311yescharacteristic
50#1542—91nomaximal, Sylow
51C3×C22⋊Q8—22no—
52Q8×Dic3—62no—
53#944—62no—
54#924—62no—
55C2×C4×Dic3—62no—
56#889—64no—
57#888—62no—
58#887—62no—
59#887—64no—
60#878—64no—
61#877—64no—
62C23×C32C22⋊C411yescharacteristic
63C32×Q8—41no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4—41no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22×C411yescharacteristic
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3SD1612yes—
75C2×C3⋊Dic3Q1612yes—
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78#634—42no—
79#634—41no—
80#622—42no—
81#622—42no—
82#533—91no—
83#431—91no—
84C2×C4⋊C8—91no—
85#333—92no—
86#332—92no—
87C2×C3×Q8—22no—
88C22×C3×C4—22no—
89C22×Dic3—62no—
90C22×Dic3—62no—
91C2×Dic6—62no—
92C2×Dic6—64no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—22no—
95C3×C22⋊C4—24no—
96#217—64no—
97C4⋊Dic3—62no—
98C4⋊Dic3—64no—
99Dic3⋊C4—64no—
100Dic3⋊C4—64no—
101Dic3⋊C4—64no—
102Dic3⋊C4—64no—
103Dic3⋊C4—64no—
104C4×Dic3—62no—
105C4×Dic3—62no—
106C4×Dic3—62no—
107C4×Dic3—62no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32#10312yes—
113C22×C32C2×C22⋊C411yescharacteristic
114C32×C4—21no—
115C32×C4—21no—
116C32×C4—41no—
117C32×C4—41no—
118C3⋊Dic3—21no—
119C3⋊Dic3—41no—
120C3⋊Dic3—41no—
121C3⋊Dic3#10312yes—
122C3⋊Dic3C2×SD1611yescharacteristic
123C3⋊Dic3C2×Q1611yescharacteristic
124C3⋊Dic3#13512yes—
125C22×C8—181no—
126C4⋊Q8—91no—
127C4⋊Q8—91no—
128#125—181no—
129C22⋊Q8—91no—
130C22⋊Q8—181no—
131C22⋊Q8#15711yescharacteristic
132C4×Q8—91no—
133C4×Q8—91no—
134C4×Q8—181no—
135#117—181no—
136C2×C42—91no—
137C4⋊C8—92no—
138C4⋊C8—92no—
139C4⋊C8—181no—
140C22⋊C8—181no—
141C4×C8—181no—
142C23×C3—22no—
143C3×Q8—44no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—44no—
149C2×Dic3—62no—
150C2×Dic3—64no—
151C2×Dic3—64no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—124no—
158Dic6—128no—
159Dic6—124no—
160C2×C32—22no—
161C2×C32#41311yescharacteristic
162C2×C32C2×#10311yescharacteristic
163C2×C32#41611yescharacteristic
164C2×Q8—91no—
165C2×Q8—181no—
166C2×Q8C2×#15711yescharacteristic
167C22×C4—91no—
168C22×C4—91no—
169C22×C4C2×#15711yescharacteristic
170C2×C8—182no—
171C2×C8—182no—
172C2×C8—362no—
173C4⋊C4—21no—
174C4⋊C4—91no—
175C4⋊C4—181no—
176C4⋊C4—181no—
177C4⋊C4—181no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C4⋊C4—181no—
181C4⋊C4C2×#15711yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—181no—
184C42—91no—
185C42—91no—
186C42—91no—
187C42—91no—
188C42—181no—
189C42—181no—
190C22×C3—22no—
191C22×C3—24no—
192C22×C3—42no—
193C22×C3—42no—
194C3×C4—24no—
195C3×C4—42no—
196C3×C4—44no—
197C3×C4—44no—
198Dic3—64no—
199Dic3—64no—
200Dic3—62no—
201Dic3—62no—
202Dic3—122no—
203Dic3—124no—
204Dic3—124no—
205C32#154211yescharacteristic, complemented, Sylow
206C23C22⋊#15711yescharacteristic
207Q8—41no—
208Q8—361no—
209Q8—362no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—91no—
216C2×C4—92no—
217C2×C4—92no—
218C2×C4—91no—
219C2×C4—182no—
220C2×C4—181no—
221C2×C4—181no—
222C2×C4C22⋊#15711yescharacteristic
223C2×C4C22×#15711yescharacteristic
224C8—362no—
225C8—362no—
226C2×C3—22no—
227C2×C3—22no—
228C2×C3—22no—
229C2×C3—44no—
230C22—21no—
231C22—21no—
232C22#6378412yes—
233C22C2×C22⋊#15711yescharacteristic
234C4—21no—
235C4—21no—
236C4—41no—
237C4—41no—
238C4—91no—
239C4—92no—
240C4—91no—
241C4—92no—
242C4—181no—
243C4—361no—
244C4—361no—
245C3—22no—
246C2—22no—
247C2#1059382411yescharacteristic
248C2C2×#6378411yescharacteristic
249C2#1059384111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22⋊Q8#157
hypocenterC32#1542
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10590220C2semidirect
5. #10590162C2semidirect
205. C32#1542semidirect

Maximal subgroups

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

subgroupindex
#105960932
#105938012
C2×#637792
#105902202
#105901622
#15429