Finite Group Databasebeta

← #11873593

Subgroups — #11873593

Order 1152.

850 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 111 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#10593948C211yesmaximal, characteristic, complemented
3#10593723C211yesmaximal, characteristic, complemented
4#10593365C214yesmaximal, complemented
5#10593356C218yesmaximal, complemented
6C2×#3802—22no—
7C2×#3802C2212yes—
8C2×#3787C2212yes—
9C42×C3⋊D3C2211yescharacteristic
10C3×#874—21no—
11C3×#870—21no—
12#63914—21no—
13#63914C2214yes—
14#63900C2212yes—
15#63883—22no—
16#63872—21no—
17#63870C2214yescomplemented
18#63777C2214yescomplemented
19#63739C22116yescomplemented
20D3×#127—61no—
21D3×#125—61no—
22C22×D32—22no—
23C2×C4×C3⋊D3D412yes—
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×C3×D12—24no—
26C2×C3×D12—22no—
27C2×#625—24no—
28C2×#625C2314yes—
29C2×#624—22no—
30#3802—28no—
31#3802—48no—
32C2×#622C2314yes—
33#3787—24no—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3C2312yes—
37C3×C4⋊Dic3—22no—
38C3×Dic3⋊C4—24no—
39#3724C2314yes—
40Dic3⋊Dic3—24no—
41C2×#490—91nomaximal, Sylow
42C2×D3×D4—62no—
43C2×D3×D4—64no—
44C3×#127—61no—
45C3×#125—61no—
46#940—64no—
47#940—62no—
48D3×C4⋊C4—62no—
49D3×C4⋊C4—64no—
50#890—62no—
51#889—64no—
52#874—21no—
53C42×D3—61no—
54C42×D3—61no—
55#870—21no—
56C22×C3⋊D3C2×D411yescharacteristic
57C22×C3×D3—24no—
58C2×D32—44no—
59C2×D32—48no—
60C2×C32×C4C2×D412yes—
61C2×C32×C4C2×D411yescharacteristic
62C2×C3⋊Dic3C2×D412yes—
63C2×C3⋊Dic3C2411yescharacteristic
64C4×C3⋊D3—24no—
65C4×C3⋊D3#4114yes—
66C2×C3×Dic3—24no—
67C3×D12—48no—
68C3×D12—44no—
69#625—28no—
70#625—48no—
71#624—44no—
72#622—24no—
73C2×#127—91no—
74C2×#125—91no—
75#490—98no—
76C2×#102—94no—
77C2×#97—91no—
78C23×D3—64no—
79C2×C3×D4—64no—
80C2×C3×D4—62no—
81C2×#67—64no—
82C2×#67—68no—
83D3×D4—128no—
84D3×D4—1216no—
85C2×D12—24no—
86C2×D12—22no—
87C2×C4×D3—61no—
88C2×C4×D3—62no—
89C2×C4×D3—61no—
90C2×C4×D3—62no—
91C2×C4×D3—64no—
92C3×C4⋊C4—64no—
93C3×C4⋊C4—62no—
94C3×C42—21no—
95C3×C42—21no—
96C4⋊Dic3—22no—
97C4⋊Dic3—64no—
98Dic3⋊C4—24no—
99Dic3⋊C4—64no—
100Dic3⋊C4—64no—
101C4×Dic3—62no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C4×Dic3—62no—
105C22×C32C22×D411yescharacteristic
106C2×C3⋊D3#12412yes—
107C2×C3⋊D3AGL(1,ℤ/8)14yes—
108C2×C3×D3—44no—
109C2×C3×D3—48no—
110D32—88no—
111C32×C4—22no—
112C32×C4#12412yes—
113C3⋊Dic3—22no—
114C3⋊Dic3C2×#4112yes—
115C3×Dic3—44no—
116C22×D4—92no—
117C22×D4—182no—
118C22×C8—92no—
119#127—61no—
120#127—94no—
121#127—181no—
122#125—61no—
123#125—94no—
124#125—181no—
125C2×C4⋊C4—92no—
126C2×C4⋊C4—182no—
127C2×C42—91no—
128#102—916no—
129#97—94no—
130C23×C3—64no—
131C22×D3—24no—
132C22×D3—61no—
133C22×D3—61no—
134C22×D3—128no—
135C22×D3—1216no—
136C3×D4—128no—
137C3×D4—124no—
138C2×C3×C4—21no—
139C2×C3×C4—22no—
140C2×C3×C4—21no—
141C2×C3×C4—22no—
142C2×C3×C4—64no—
143#67—128no—
144#67—1216no—
145C2×Dic3—24no—
146C2×Dic3—62no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—62no—
150D12—48no—
151D12—44no—
152C4×D3—64no—
153C4×D3—64no—
154C4×D3—68no—
155C4×D3—124no—
156C4×D3—128no—
157C2×C32C2×#12411yescharacteristic
158C2×C32C2×AGL(1,ℤ/8)12yes—
159C3⋊D3#49014yescomplemented
160C3×D3—84no—
161C24—182no—
162C2×D4—64no—
163C2×D4—62no—
164C2×D4—94no—
165C2×D4—188no—
166C2×D4—184no—
167C2×D4—368no—
168C22×C4—91no—
169C22×C4—92no—
170C22×C4—182no—
171C2×C8—94no—
172C2×C8—184no—
173C4⋊C4—62no—
174C4⋊C4—64no—
175C4⋊C4—94no—
176C4⋊C4—184no—
177C42—92no—
178C42—91no—
179C42GO+(4,𝔽2)11yescharacteristic
180C22×C3—21no—
181C22×C3—21no—
182C22×C3—124no—
183C22×C3—128no—
184C2×D3—44no—
185C2×D3—48no—
186C2×D3—62no—
187C2×D3—64no—
188C2×D3—62no—
189C2×D3—64no—
190C2×D3—2416no—
191C3×C4—24no—
192C3×C4—22no—
193C3×C4—22no—
194C3×C4—42no—
195C3×C4—124no—
196Dic3—44no—
197Dic3—62no—
198Dic3—62no—
199Dic3—64no—
200Dic3—122no—
201C32C2×#49011yescharacteristic, complemented, Sylow
202C23—64no—
203C23—91no—
204C23—364no—
205C23—368no—
206D4—128no—
207D4—124no—
208D4—188no—
209D4—368no—
210C2×C4—64no—
211C2×C4—91no—
212C2×C4—94no—
213C2×C4—92no—
214C2×C4—184no—
215C2×C4—364no—
216C2×C4C2×GO+(4,𝔽2)12yes—
217C2×C4C2×GO+(4,𝔽2)11yescharacteristic
218C8—184no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—22no—
222C2×C3—22no—
223C2×C3—244no—
224D3—64no—
225D3—64no—
226D3—84no—
227C22—92no—
228C22—94no—
229C22—124no—
230C22—128no—
231C22—728no—
232C22C22×GO+(4,𝔽2)11yescharacteristic
233C4—22no—
234C4—92no—
235C4—124no—
236C4—182no—
237C4#6422112yes—
238C3—21no—
239C3—21no—
240C2—94no—
241C2—244no—
242C2C2×#6422111yescharacteristic
243C2#1059650112yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radical#10594008C2
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#490
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. #10593948C2semidirect
3. #10593723C2semidirect
4. #10593365C2semidirect
5. #10593356C2semidirect
17. #63870C22semidirect
18. #63777C22semidirect
19. #63739C22semidirect
159. C3⋊D3#490semidirect
201. C32C2×#490semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105939482
#105937232
#105933652
#105933562
C2×#4909