Finite Group Databasebeta

← #11873627

Subgroups — #11873627

Order 1152.

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

normal subgroups only

This group has 642 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#10593948C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic
3#10593723C211yesmaximal, characteristic
4#10593378C218yesmaximal, complemented
5#10593375C214yesmaximal
6C2×#3797C2212yes—
7C2×#3787C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×#870—21no—
10C3×#869—21no—
11#63919C2214yes—
12#63900—22no—
13#63900C2212yes—
14#63883—22no—
15#63873—21no—
16#63872—21no—
17#63870C2214yes—
18#63777C2214yes—
19#63740C22116yes—
20D3×C4⋊Q8—61no—
21D3×#125—61no—
22C2×C4×C3⋊D3D412yes—
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×C3×Dic6—22no—
25C2×#627C2314yes—
26C2×#624—22no—
27C2×#624—22no—
28#3797—28no—
29C2×#622C2314yes—
30#3787—24no—
31C32×C42D411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C4×C3⋊Dic3C2312yes—
34C3×C4⋊Dic3—22no—
35C3×C4⋊Dic3—24no—
36C3×Dic3⋊C4—24no—
37#3724—24no—
38#3724C2314yes—
39Dic3⋊Dic3—24no—
40C2×#491—91nomaximal, Sylow
41C2×D3×Q8—62no—
42C3×C4⋊Q8—61no—
43C3×#125—61no—
44#944—62no—
45D3×C4⋊C4—62no—
46D3×C4⋊C4—64no—
47D3×C4⋊C4—64no—
48#890—62no—
49#889—64no—
50#888—64no—
51C42×D3—61no—
52C42×D3—61no—
53#870—21no—
54#869—21no—
55C22×C3⋊D3C2×D411yescharacteristic
56C2×C32×C4C2×D412yes—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3C2×D412yes—
59C2×C3⋊Dic3C2411yescharacteristic
60C4×C3⋊D3—24no—
61C4×C3⋊D3#4114yes—
62C2×C3×Dic3—24no—
63C2×C3×Dic3—24no—
64C3×Dic6—44no—
65#627—28no—
66#624—44no—
67#624—44no—
68#622—24no—
69C2×C4⋊Q8—91no—
70C2×#125—91no—
71#491—98no—
72C2×#103—94no—
73C2×#97—91no—
74C2×C3×Q8—62no—
75D3×Q8—128no—
76C2×C4×D3—62no—
77C2×C4×D3—61no—
78C2×C4×D3—61no—
79C2×C4×D3—62no—
80C2×C4×D3—64no—
81C2×C4×D3—64no—
82C2×Dic6—22no—
83C2×Dic6—64no—
84C3×C4⋊C4—64no—
85C3×C4⋊C4—64no—
86C3×C4⋊C4—62no—
87C3×C42—21no—
88C3×C42—21no—
89C4⋊Dic3—24no—
90C4⋊Dic3—22no—
91C4⋊Dic3—64no—
92Dic3⋊C4—24no—
93Dic3⋊C4—64no—
94Dic3⋊C4—68no—
95Dic3⋊C4—64no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C22×C32C22×D411yescharacteristic
101C2×C3⋊D3#12412yes—
102C2×C3⋊D3#13714yes—
103C32×C4—22no—
104C32×C4#12412yes—
105C3⋊Dic3—22no—
106C3⋊Dic3C2×#4112yes—
107C3×Dic3—44no—
108C3×Dic3—44no—
109C22×Q8—92no—
110C22×C8—92no—
111C4⋊Q8—61no—
112C4⋊Q8—94no—
113C4⋊Q8—181no—
114#125—61no—
115#125—94no—
116#125—181no—
117C2×C4⋊C4—92no—
118C2×C4⋊C4—182no—
119C2×C4⋊C4—182no—
120C2×C42—91no—
121#103—916no—
122#97—94no—
123C22×D3—61no—
124C22×D3—61no—
125C3×Q8—124no—
126C2×C3×C4—22no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—22no—
130C2×C3×C4—64no—
131C2×C3×C4—64no—
132C2×Dic3—24no—
133C2×Dic3—24no—
134C2×Dic3—62no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—62no—
138C4×D3—64no—
139C4×D3—64no—
140C4×D3—68no—
141C4×D3—124no—
142C4×D3—128no—
143C4×D3—128no—
144Dic6—44no—
145Dic6—128no—
146C2×C32C2×#12411yescharacteristic
147C2×C32C2×#13712yes—
148C3⋊D3#49114yescomplemented
149C2×Q8—62no—
150C2×Q8—94no—
151C2×Q8—188no—
152C22×C4—91no—
153C22×C4—92no—
154C22×C4—182no—
155C22×C4—182no—
156C2×C8—94no—
157C2×C8—184no—
158C4⋊C4—62no—
159C4⋊C4—64no—
160C4⋊C4—64no—
161C4⋊C4—94no—
162C4⋊C4—184no—
163C4⋊C4—184no—
164C42—92no—
165C42—91no—
166C42GO+(4,𝔽2)11yescharacteristic
167C22×C3—21no—
168C22×C3—21no—
169C2×D3—62no—
170C2×D3—62no—
171C2×D3—64no—
172C2×D3—64no—
173C3×C4—24no—
174C3×C4—22no—
175C3×C4—22no—
176C3×C4—42no—
177C3×C4—124no—
178C3×C4—124no—
179Dic3—44no—
180Dic3—44no—
181Dic3—62no—
182Dic3—62no—
183Dic3—64no—
184Dic3—122no—
185C32C2×#49111yescharacteristic, complemented, Sylow
186C23—91no—
187Q8—124no—
188Q8—188no—
189C2×C4—64no—
190C2×C4—64no—
191C2×C4—91no—
192C2×C4—94no—
193C2×C4—92no—
194C2×C4—184no—
195C2×C4—364no—
196C2×C4—364no—
197C2×C4C2×GO+(4,𝔽2)12yes—
198C2×C4C2×GO+(4,𝔽2)11yescharacteristic
199C8—184no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—22no—
203C2×C3—22no—
204D3—64no—
205D3—64no—
206C22—92no—
207C22—94no—
208C22C22×GO+(4,𝔽2)11yescharacteristic
209C4—22no—
210C4—92no—
211C4—124no—
212C4—124no—
213C4—182no—
214C4#6422112yes—
215C3—21no—
216C3—21no—
217C2—94no—
218C2C2×#6422111yescharacteristic
219C2#1059650512yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#491
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10593378C2semidirect
148. C3⋊D3#491semidirect
185. C32C2×#491semidirect

Maximal subgroups

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

subgroupindex
#105939482
#105939092
#105937232
#105933782
#105933752
C2×#4919