Finite Group Databasebeta

← #11771909

Subgroups — #11771909

Order 1152.

253 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 253 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C3×#5116C211yesmaximal, characteristic
2#10589418C211yesmaximal, characteristic
3C3×#4549C211yesmaximal, characteristic
4#67777—31nomaximal
5#67529—31nomaximal
6C22×C32×C8C2211yescharacteristic
7C2×#3748—21no—
8C3×#924—21no—
9C2×C3×Dic12C411yescharacteristic
10C3×#818C411yescharacteristic
11C3×#816—21no—
12C2×C3×C3⋊C16—21no—
13C3×#467—31no—
14#5116D311yescharacteristic
15C3×C22⋊C16—31no—
16#4552—31no—
17#4552—31no—
18#4552—61no—
19#4549D311yescharacteristic
20C22×C32×C4D411yescharacteristic
21C2×C3×Dic6—21no—
22C2×C32×C8—41no—
23C2×C32×C8C2×C411yescharacteristic
24C2×C32×C8D411yescharacteristic
25#3748—22no—
26#3748—41no—
27C2×C3⋊(C3⋊C8)—41no—
28C3×#217—41no—
29C3×C4⋊Dic3—21no—
30C3×Dic3⋊C4—41no—
31C3×Dic12—41no—
32C3×C3⋊C16—41no—
33#1350—91noSylow
34C2×C3×Q16—31no—
35C22×C3×C8—21no—
36C22×C3×C8C2×D311yescharacteristic
37C22×C3×C8C2×D311yescharacteristic
38C3×C22⋊Q8—61no—
39#924—21no—
40C2×#208—62no—
41C2×#208—61no—
42C2×#208—61no—
43C2×Dic12Dic311yescharacteristic
44C2×C3×C16—61no—
45C3×#107—31no—
46C3×#103—61no—
47#818Dic311yescharacteristic
48#816—21no—
49C2×C3⋊C16—21no—
50C23×C32SD1611yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4C22⋊C411yescharacteristic
54C2×C32×C4D811yescharacteristic
55C2×C3×Dic3—41no—
56C2×C3×Dic3—41no—
57C3×Dic6—41no—
58C3×Dic6—41no—
59C32×C8—21no—
60C32×C8—21no—
61C3⋊(C3⋊C8)—42no—
62#467—31no—
63C22⋊C16—31no—
64#341—91no—
65C2×C3×Q8—61no—
66C22×C3×C4—21no—
67C22×C3×C4D1211yescharacteristic
68C22×C3×C4#6711yescharacteristic
69C2×Dic6—21no—
70C3×Q16—121no—
71C2×C3×C8—21no—
72C2×C3×C8—21no—
73C2×C3×C8—41no—
74C2×C3×C8—41no—
75C2×C3×C8—42no—
76C2×C3×C8C4×D311yescharacteristic
77C2×C3×C8C2×Dic311yescharacteristic
78C2×C3×C8#6711yescharacteristic
79C2×C3×C8#6711yescharacteristic
80C3×C4⋊C4—61no—
81C3×C4⋊C4—121no—
82C3×C22⋊C4—121no—
83#217—41no—
84C4⋊Dic3—21no—
85Dic3⋊C4—41no—
86#208—64no—
87#208—62no—
88#208—62no—
89#208—122no—
90#208—121no—
91#208—121no—
92C2×C3⋊C8—122no—
93C2×C3⋊C8—121no—
94C2×C3⋊C8—121no—
95Dic12—41no—
96C3×C16—121no—
97C3⋊C16—41no—
98C22×C32—21no—
99C22×C32—21no—
100C22×C32—21no—
101C22×C32#10211yescharacteristic
102C32×C4—21no—
103C32×C4#9911yescharacteristic
104C32×C4#10411yescharacteristic
105C3×Dic3—81no—
106C3×Dic3—81no—
107C2×Q16—31no—
108C2×M16—181no—
109C22×C8D3211yescharacteristic
110C22⋊Q8—61no—
111C2×C16—61no—
112#107—31no—
113#103—61no—
114C23×C3—21no—
115C23×C3#20411yescharacteristic
116C23×C3#21411yescharacteristic
117C3×Q8—121no—
118C3×Q8—121no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
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—121no—
128C2×C3×C4—121no—
129C2×C3×C4D2411yescharacteristic
130C2×C3×C4(C2×D3)⋊C411yescharacteristic
131C2×C3×C4#21311yescharacteristic
132C2×C3×C4#21711yescharacteristic
133C2×Dic3—41no—
134C2×Dic3—41no—
135Dic6—41no—
136Dic6—41no—
137C3×C8—21no—
138C3×C8—21no—
139C3×C8—21no—
140C3×C8—21no—
141C3×C8—41no—
142C3×C8—41no—
143C3⋊C8—124no—
144C3⋊C8—122no—
145C3⋊C8—122no—
146C2×C32—41no—
147C2×C32#32711yescharacteristic
148C2×C32#35911yescharacteristic
149C2×C32#36211yescharacteristic
150C2×Q8—61no—
151C22×C4#62611yescharacteristic
152Q16—121no—
153M16—182no—
154M16—361no—
155C2×C8—41no—
156C2×C8—361no—
157C2×C8D3×Dic311yescharacteristic
158C2×C8#62511yescharacteristic
159C4⋊C4—61no—
160C4⋊C4—121no—
161C22⋊C4—121no—
162C16—121no—
163C22×C3—22no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—21no—
168C22×C3—21no—
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—41no—
172C22×C3—41no—
173C22×C3#82111yescharacteristic
174C22×C3#83211yescharacteristic
175C3×C4—22no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4—21no—
179C3×C4—21no—
180C3×C4—241no—
181C3×C4—241no—
182C3×C4#80611yescharacteristic
183C3×C4#82511yescharacteristic
184C3×C4#83411yescharacteristic
185C3×C4#83711yescharacteristic
186Dic3—81no—
187Dic3—81no—
188C32#135011yescharacteristic, complemented, Sylow
189C23#371611yescharacteristic
190Q8—121no—
191Q8—121no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—121no—
195C2×C4—121no—
196C2×C4#371411yescharacteristic
197C2×C4(C2×D3)⋊Dic311yescharacteristic
198C8—21no—
199C8—21no—
200C8—362no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—42no—
205C2×C3—41no—
206C2×C3—41no—
207C2×C3#447011yescharacteristic
208C2×C3#451011yescharacteristic
209C2×C3#451711yescharacteristic
210C2×C3#453711yescharacteristic
211C2×C3#456511yescharacteristic
212C2×C3#456711yescharacteristic
213C22—21no—
214C22—21no—
215C22—21no—
216C22#6356311yescharacteristic
217C4—21no—
218C4—241no—
219C4—241no—
220C4#6356811yescharacteristic
221C4#6358011yescharacteristic
222C3—21no—
223C3#6752911yescharacteristic, complemented
224C3#6777711yescharacteristic, complemented
225C2—41no—
226C2#1058912111yescharacteristic
227C2#1058913011yescharacteristic
228C2#1058915011yescharacteristic
subgroupG/H
centerC22#63563
commutatorC2×C32×C8C2×C4
Frattini, hypercenterC22×C8D32
Fitting, cosocleC22×C32×C8C22
socleC22×C32#102
prime radicalC23×C32SD16
hypocenterC32#1350
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
188. C32#1350semidirect
223. C3#67529semidirect
224. C3#67777semidirect

Maximal subgroups

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

subgroupindex
C3×#51162
#105894182
C3×#45492
#677773
#675293