Finite Group Databasebeta

← #11860135

Subgroups — #11860135

Order 1152.

778 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 159 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×#64228C211yesmaximal, characteristic
2C4×#3797C212yesmaximal
3#10593723C211yesmaximal, characteristic
4#10593387C211yesmaximal, characteristic
5#10593375C212yesmaximal
6#10593369C218yesmaximal, complemented
7C2×#3797C2212yes—
8C2×#3787C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10C2×#3776C2214yes—
11#64228C418yescomplemented
12C42×C3⋊D3C2211yescharacteristic
13C3×C4×Dic6—22no—
14C4×#627C2214yes—
15#63900C2212yes—
16#63883—22no—
17C4×#624—22no—
18#63843—22no—
19#63838C2214yes—
20#63777C2214yes—
21#63742C2214yes—
22#63740C2218yes—
23C4×D3×Q8—62no—
24C2×C4×C3⋊D3D412yes—
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×Dic6—22no—
27C2×#627C2314yes—
28C2×#624—22no—
29C2×#624—22no—
30#3797—24no—
31#3797C2×C418yes—
32C2×#622C2312yes—
33C2×#622C2312yes—
34#3787—22no—
35#3787C2×C414yes—
36#3776C2×C4116yescomplemented
37C32×C42D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3C2312yes—
40C3×C4⋊Dic3—22no—
41C3×Dic3⋊C4—24no—
42C3×C4×Dic3—24no—
43#3724C2314yes—
44Dic3⋊Dic3—24no—
45Dic32—24no—
46C2×#441—91nomaximal, Sylow
47C2×D3×Q8—62no—
48C3×C4×Q8—62no—
49Q8×Dic3—62no—
50D3×C4⋊C4—62no—
51D3×C4⋊C4—64no—
52#887—64no—
53#887—62no—
54C42×D3—62no—
55C42×D3—64no—
56C4×Dic6—22no—
57C4×Dic6—64no—
58C22×C3⋊D3C2×D411yescharacteristic
59C2×C32×C4C2×D412yes—
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D412yes—
62C2×C3⋊Dic3C2411yescharacteristic
63C4×C3⋊D3—24no—
64C4×C3⋊D3C22×C412yes—
65C4×C3⋊D3#4112yes—
66C2×C3×Dic3—24no—
67C2×C3×Dic3—24no—
68C3×Dic6—28no—
69#627—24no—
70#627C22×C418yes—
71#624—28no—
72#624—44no—
73#622—22no—
74#622C22×C414yes—
75C22×Q16—91no—
76C2×C4×Q8—92no—
77#441—98no—
78C2×#106—91no—
79C2×#103—92no—
80C2×#97—91no—
81C2×C3×Q8—62no—
82D3×Q8—68no—
83D3×Q8—68no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—64no—
88C2×C4×D3—64no—
89C2×Dic6—22no—
90C2×Dic6—64no—
91C3×C4⋊C4—64no—
92C3×C4⋊C4—62no—
93C3×C42—22no—
94C3×C42—64no—
95C4⋊Dic3—22no—
96C4⋊Dic3—64no—
97Dic3⋊C4—24no—
98Dic3⋊C4—64no—
99Dic3⋊C4—64no—
100C4×Dic3—24no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C4×Dic3—62no—
104C4×Dic3—64no—
105C4×Dic3—64no—
106C22×C32C22×D411yescharacteristic
107C2×C3⋊D3C4×D412yes—
108C2×C3⋊D3#13714yes—
109C32×C4—22no—
110C32×C4C4×D412yes—
111C3⋊Dic3—22no—
112C3⋊Dic3C23×C411yescharacteristic
113C3⋊Dic3C2×#4111yescharacteristic
114C3×Dic3—28no—
115C3×Dic3—44no—
116C22×Q8—92no—
117C2×Q16—94no—
118C2×Q16—98no—
119C22×C8—91no—
120C22×C8—91no—
121C4×Q8—62no—
122C4×Q8—94no—
123C4×Q8—94no—
124C4×Q8—182no—
125C2×C4⋊C4—92no—
126C2×C4⋊C4—182no—
127C2×C42—91no—
128C2×C42—182no—
129#106—94no—
130#103—98no—
131#97—94no—
132C22×D3—62no—
133C3×Q8—68no—
134C2×C3×C4—22no—
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137C2×C3×C4—64no—
138C2×C3×C4—64no—
139C2×Dic3—24no—
140C2×Dic3—24no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144C4×D3—64no—
145C4×D3—64no—
146C4×D3—616no—
147C4×D3—68no—
148C4×D3—124no—
149C4×D3—128no—
150Dic6—28no—
151Dic6—68no—
152Dic6—68no—
153C2×C32C2×C4×D411yescharacteristic
154C2×C32C2×#13712yes—
155C3⋊D3#44114yescomplemented
156C2×Q8—62no—
157C2×Q8—94no—
158C2×Q8—98no—
159C2×Q8—184no—
160C22×C4—91no—
161C22×C4—92no—
162C22×C4—182no—
163C22×C4—182no—
164Q16—916no—
165C2×C8—92no—
166C2×C8—94no—
167C2×C8—92no—
168C2×C8—182no—
169C4⋊C4—62no—
170C4⋊C4—64no—
171C4⋊C4—94no—
172C4⋊C4—184no—
173C42—64no—
174C42—92no—
175C42—91no—
176C42—184no—
177C42GO+(4,𝔽2)11yescharacteristic
178C22×C3—22no—
179C2×D3—64no—
180C2×D3—64no—
181C2×D3—64no—
182C3×C4—24no—
183C3×C4—24no—
184C3×C4—42no—
185C3×C4—68no—
186C3×C4—124no—
187Dic3—28no—
188Dic3—44no—
189Dic3—62no—
190Dic3—62no—
191Dic3—64no—
192Dic3—122no—
193C32C2×#44111yescharacteristic, complemented, Sylow
194C23—91no—
195Q8—68no—
196Q8—98no—
197Q8—184no—
198C2×C4—64no—
199C2×C4—64no—
200C2×C4—91no—
201C2×C4—92no—
202C2×C4—92no—
203C2×C4—92no—
204C2×C4—184no—
205C2×C4—188no—
206C2×C4—364no—
207C2×C4C2×GO+(4,𝔽2)12yes—
208C2×C4C2×GO+(4,𝔽2)11yescharacteristic
209C8—94no—
210C8—182no—
211C2×C3—22no—
212C2×C3—22no—
213C2×C3—22no—
214D3—68no—
215C22—94no—
216C22—92no—
217C22C22×GO+(4,𝔽2)11yescharacteristic
218C4—22no—
219C4—68no—
220C4—91no—
221C4—91no—
222C4—124no—
223C4—182no—
224C4C4×GO+(4,𝔽2)12yes—
225C3—22no—
226C2—94no—
227C2#1059650512yes—
228C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C3⋊Dic3C24
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#441
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
6. #10593369C2semidirect
11. #64228C4semidirect
36. #3776C2×C4semidirect
155. C3⋊D3#441semidirect
193. C32C2×#441semidirect

Maximal subgroups

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

subgroupindex
C2×#642282
C4×#37972
#105937232
#105933872
#105933752
#105933692
C2×#4419