Finite Group Databasebeta

← #11790626

Subgroups — #11790626

Order 1152.

558 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 95 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#10593909C211yesmaximal, characteristic
2#10593735C211yesmaximal, characteristic
3C2×#63730C214yesmaximal
4C4×#3710C211yesmaximal, characteristic
5C2×#3797C2212yes—
6C2×C4⋊#157—22no—
7C2×C4⋊#157C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×#869—21no—
10#63919C414yescomplemented
11#63900—22no—
12#63873—21no—
13C2×#3710C2212yes—
14#63730—28no—
15C3×C4×C3⋊C8—21no—
16#63553—21no—
17D3×C4⋊Q8—61no—
18C4×D3×C8—61no—
19C22×#157—22no—
20C2×C4×C3⋊D3D412yes—
21C2×C4×C3⋊D3C2311yescharacteristic
22C2×C3×Dic6—22no—
23C2×#627C2×C414yes—
24C2×#624—22no—
25#3797—24no—
26#3797—24no—
27C4⋊#157—24no—
28C4⋊#157—44no—
29C32×C42D411yescharacteristic
30C4×C3⋊Dic3C2×C412yes—
31C4×C3⋊Dic3D411yescharacteristic
32C3×C4⋊Dic3—24no—
33C2×C3×C3⋊C8—22no—
34#3724—24no—
35#3710—22no—
36#3710D414yes—
37#1956—91nomaximal, Sylow
38C2×D3×Q8—62no—
39C3×C4⋊Q8—61no—
40#944—62no—
41C2×D3×C8—62no—
42D3×C4⋊C4—64no—
43#888—64no—
44C42×D3—61no—
45C42×D3—61no—
46#869—21no—
47C3×C4×C8—61no—
48C8×Dic3—62no—
49C4×C3⋊C8—21no—
50C22×C3⋊D3C2×D411yescharacteristic
51C2×#157—42no—
52C2×#157—44no—
53C2×C32×C4C22⋊C412yes—
54C2×C32×C4C2×D411yescharacteristic
55C2×C3⋊Dic3C22⋊C412yes—
56C2×C3⋊Dic3C22×C411yescharacteristic
57C4×C3⋊D3SD1614yes—
58C4×C3⋊D3Q1614yes—
59C4×C3⋊D3C2×D412yes—
60C4×C3⋊D3#4112yes—
61C2×C3×Dic3—24no—
62C3×Dic6—44no—
63#627—28no—
64#624—42no—
65#624—42no—
66C3×C3⋊C8—24no—
67C2×C4⋊Q8—91no—
68C2×#103—94no—
69C2×C4×C8—91no—
70#384—91no—
71C2×C3×Q8—62no—
72D3×Q8—124no—
73D3×Q8—124no—
74C2×C4×D3—62no—
75C2×C4×D3—61no—
76C2×C4×D3—61no—
77C2×C4×D3—62no—
78C2×C4×D3—64no—
79C2×Dic6—22no—
80C2×Dic6—64no—
81C2×C3×C8—62no—
82C3×C4⋊C4—64no—
83C3×C42—21no—
84C3×C42—21no—
85C4⋊Dic3—24no—
86Dic3⋊C4—68no—
87C4×Dic3—61no—
88C4×Dic3—62no—
89C4×Dic3—62no—
90C4×Dic3—61no—
91C2×C3⋊C8—22no—
92D3×C8—64no—
93D3×C8—64no—
94C22×C32C2×C22⋊C411yescharacteristic
95C2×C3⋊D3#12411yescharacteristic
96C2×C3⋊D3#12711yescharacteristic
97C2×C3⋊D3C2×SD1612yes—
98C2×C3⋊D3C2×Q1612yes—
99#157—82no—
100C32×C4#10314yescomplemented
101C32×C4#12112yes—
102C3⋊Dic3#10314yescomplemented
103C3⋊Dic3C4×D412yes—
104C3×Dic3—44no—
105C22×Q8—92no—
106C22×C8—92no—
107C4⋊Q8—61no—
108C4⋊Q8—94no—
109C4⋊Q8—181no—
110C2×C4⋊C4—92no—
111C2×C4⋊C4—182no—
112C2×C4⋊C4—182no—
113C2×C42—91no—
114#103—188no—
115C4×C8—61no—
116C4×C8—181no—
117C22×D3—61no—
118C22×D3—61no—
119C3×Q8—124no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×C3×C4—64no—
125C2×Dic3—24no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130C4×D3—64no—
131C4×D3—64no—
132C4×D3—64no—
133C4×D3—64no—
134C4×D3—62no—
135C4×D3—62no—
136C4×D3—62no—
137C4×D3—62no—
138C4×D3—124no—
139C4×D3—124no—
140Dic6—44no—
141Dic6—128no—
142C3×C8—64no—
143C3⋊C8—24no—
144C2×C32#39011yescharacteristic
145C2×C32C2×#10312yes—
146C3⋊D3#48712yes—
147C3⋊D3#49211yescharacteristic
148C3⋊D3#49411yescharacteristic
149C2×Q8—62no—
150C2×Q8—94no—
151C2×Q8—184no—
152C2×Q8—184no—
153C22×C4—91no—
154C22×C4—92no—
155C22×C4—182no—
156C22×C4—182no—
157C2×C8—62no—
158C2×C8—94no—
159C2×C8—182no—
160C4⋊C4—64no—
161C4⋊C4—184no—
162C4⋊C4—184no—
163C4⋊C4—364no—
164C42—91no—
165C42—92no—
166C42GO+(4,𝔽2)11yescharacteristic
167C22×C3—21no—
168C22×C3—21no—
169C2×D3—61no—
170C2×D3—61no—
171C2×D3—61no—
172C2×D3—61no—
173C2×D3—62no—
174C2×D3—62no—
175C2×D3—62no—
176C2×D3—62no—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—24no—
180C3×C4—24no—
181C3×C4—124no—
182Dic3—44no—
183Dic3—62no—
184Dic3—64no—
185Dic3—64no—
186Dic3—62no—
187C32#195611yescharacteristic, complemented, Sylow
188C23—91no—
189Q8—124no—
190Q8—188no—
191C2×C4—64no—
192C2×C4—92no—
193C2×C4—91no—
194C2×C4—92no—
195C2×C4—92no—
196C2×C4—94no—
197C2×C4—94no—
198C2×C4—362no—
199C2×C4—362no—
200C2×C4—362no—
201C2×C4—364no—
202C2×C4D32⋊C412yes—
203C2×C4C2×GO+(4,𝔽2)11yescharacteristic
204C8—64no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—21no—
208C2×C3—21no—
209D3—62no—
210D3—62no—
211D3—61no—
212D3—61no—
213D3—61no—
214D3—61no—
215C22—92no—
216C22—92no—
217C22—91no—
218C22—91no—
219C22C2×D32⋊C411yescharacteristic
220C4—94no—
221C4—92no—
222C4—124no—
223C4—722no—
224C4#6373014yescomplemented
225C4#6423012yes—
226C3—21no—
227C3—21no—
228C2—91no—
229C2—92no—
230C2—91no—
231C2C2×#6373012yes—
232C2#1059340511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1956
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
10. #63919C4semidirect
100. C32×C4#103semidirect
102. C3⋊Dic3#103semidirect
187. C32#1956semidirect
224. C4#63730semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105937352
C2×#637302
C4×#37102
#19569