Finite Group Databasebeta

← #11790767

Subgroups — #11790767

Order 1152.

734 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 75 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#10594008C211yesmaximal, characteristic
2#10593736C211yesmaximal, characteristic, complemented
3C2×#63729C214yesmaximal, complemented
4#10590322C211yesmaximal, characteristic, complemented
5C2×#3802—22no—
6C2×#3802C2212yes—
7C2×C4⋊#157C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×#874—21no—
10#63914—21no—
11#63914C414yescomplemented
12C2×#3710C2212yes—
13#63781—22no—
14#63729—28no—
15C3×#803—21no—
16#63555—21no—
17D3×#127—61no—
18D3×#97—61no—
19C22×D32—22no—
20C22×#157—22no—
21C2×C4×C3⋊D3D412yes—
22C2×C4×C3⋊D3C2311yescharacteristic
23C2×C3×D12—24no—
24C2×C3×D12—22no—
25C2×#625—24no—
26C2×#625C2×C414yes—
27#3802—24no—
28#3802—24no—
29#3802—48no—
30C4⋊#157—24no—
31C32×C42D411yescharacteristic
32C4×C3⋊Dic3C2×C412yes—
33C4×C3⋊Dic3D411yescharacteristic
34C2×C3×C3⋊C8—22no—
35#3710—22no—
36#3710D414yescomplemented
37#1961—91nomaximal, Sylow
38C2×D3×D4—62no—
39C2×D3×D4—64no—
40C3×#127—61no—
41#940—64no—
42#940—62no—
43C2×D3×C8—62no—
44#874—21no—
45C42×D3—61no—
46C42×D3—61no—
47C3×#97—61no—
48#815—62no—
49#803—21no—
50C22×C3⋊D3C2×D411yescharacteristic
51C22×C3×D3—24no—
52C2×D32—42no—
53C2×D32—42no—
54C2×D32—48no—
55C2×#157—42no—
56C2×#157—44no—
57C2×C32×C4C22⋊C412yes—
58C2×C32×C4C2×D411yescharacteristic
59C2×C3⋊Dic3C22⋊C412yes—
60C2×C3⋊Dic3C22×C411yescharacteristic
61C4×C3⋊D3—24no—
62C4×C3⋊D3C2×D412yes—
63C4×C3⋊D3#4112yes—
64C3×D12—48no—
65C3×D12—44no—
66#625—28no—
67#625—48no—
68C3×C3⋊C8—24no—
69C2×#127—91no—
70C2×#102—94no—
71C2×#97—91no—
72#382—91no—
73C23×D3—64no—
74C2×C3×D4—62no—
75C2×C3×D4—64no—
76C2×#67—64no—
77C2×#67—68no—
78D3×D4—124no—
79D3×D4—124no—
80D3×D4—1216no—
81C2×D12—22no—
82C2×D12—24no—
83C2×C4×D3—61no—
84C2×C4×D3—62no—
85C2×C4×D3—61no—
86C2×C4×D3—62no—
87C2×C3×C8—62no—
88C3×C42—21no—
89C3×C42—21no—
90C4×Dic3—61no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93C4×Dic3—61no—
94C2×C3⋊C8—22no—
95D3×C8—64no—
96D3×C8—64no—
97C22×C32C2×C22⋊C411yescharacteristic
98C2×C3⋊D3#12411yescharacteristic
99C2×C3⋊D3#12711yescharacteristic
100C2×C3⋊D3AGL(1,ℤ/8)14yes—
101C2×C3×D3—44no—
102C2×C3×D3—48no—
103D32—84no—
104D32—84no—
105#157—82no—
106C32×C4—22no—
107C32×C4#12112yes—
108C3⋊Dic3—22no—
109C3⋊Dic3C4×D412yes—
110C22×D4—92no—
111C22×D4—182no—
112C22×C8—92no—
113#127—61no—
114#127—94no—
115#127—181no—
116C2×C4⋊C4—92no—
117C2×C42—91no—
118#102—188no—
119#97—61no—
120#97—181no—
121#95—182no—
122C23×C3—64no—
123C22×D3—24no—
124C22×D3—61no—
125C22×D3—61no—
126C22×D3—124no—
127C22×D3—124no—
128C22×D3—1216no—
129C3×D4—128no—
130C3×D4—124no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—22no—
134C2×C3×C4—22no—
135#67—128no—
136#67—1216no—
137C2×Dic3—62no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140C2×Dic3—62no—
141D12—48no—
142D12—44no—
143C4×D3—62no—
144C4×D3—62no—
145C4×D3—62no—
146C4×D3—62no—
147C4×D3—68no—
148C4×D3—124no—
149C3×C8—64no—
150C3⋊C8—24no—
151C2×C32#39011yescharacteristic
152C2×C32#41812yes—
153C3⋊D3#49012yes—
154C3⋊D3#49612yes—
155C3×D3—84no—
156C24—182no—
157C2×D4—62no—
158C2×D4—64no—
159C2×D4—94no—
160C2×D4—184no—
161C2×D4—184no—
162C2×D4—184no—
163C2×D4—368no—
164C22×C4—91no—
165C22×C4—92no—
166C22×C4—182no—
167C2×C8—62no—
168C2×C8—94no—
169C2×C8—182no—
170C4⋊C4—184no—
171C42—91no—
172C42—92no—
173C42GO+(4,𝔽2)11yescharacteristic
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—128no—
177C22×C3—124no—
178C2×D3—48no—
179C2×D3—44no—
180C2×D3—61no—
181C2×D3—61no—
182C2×D3—64no—
183C2×D3—61no—
184C2×D3—61no—
185C2×D3—64no—
186C2×D3—248no—
187C2×D3—248no—
188C3×C4—24no—
189C3×C4—22no—
190C3×C4—22no—
191C3×C4—42no—
192Dic3—62no—
193Dic3—62no—
194Dic3—64no—
195Dic3—122no—
196C32#196111yescharacteristic, complemented, Sylow
197C23—64no—
198C23—91no—
199C23—362no—
200C23—362no—
201C23—368no—
202D4—128no—
203D4—124no—
204D4—188no—
205D4—368no—
206C2×C4—91no—
207C2×C4—92no—
208C2×C4—92no—
209C2×C4—92no—
210C2×C4—184no—
211C2×C4—362no—
212C2×C4—364no—
213C2×C4D32⋊C412yes—
214C2×C4C2×GO+(4,𝔽2)11yescharacteristic
215C8—64no—
216C2×C3—22no—
217C2×C3—22no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—244no—
221D3—62no—
222D3—62no—
223D3—62no—
224D3—62no—
225D3—84no—
226C22—94no—
227C22—91no—
228C22—91no—
229C22—128no—
230C22—124no—
231C22—724no—
232C22—724no—
233C22C2×D32⋊C411yescharacteristic
234C4—22no—
235C4—92no—
236C4—182no—
237C4—722no—
238C4#6423012yes—
239C3—21no—
240C3—21no—
241C2—92no—
242C2—92no—
243C2—244no—
244C2#1059331812yes—
245C2#1059340511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10594008C2
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1961
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593736C2semidirect
3. C2×#63729C2semidirect
4. #10590322C2semidirect
11. #63914C4semidirect
36. #3710D4semidirect
196. C32#1961semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105937362
C2×#637292
#105903222
#19619