Finite Group Databasebeta

← #11800073

Subgroups — #11800073

Order 1152.

341 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 341 conjugacy classes of subgroups — too many to draw. Only its 78 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#10592882C211yesmaximal, characteristic
2#10590902C211yesmaximal, characteristic
3C3×#4564C212yesmaximal
4#10589119C212yesmaximal
5#10589102C211yesmaximal, characteristic
6#69215—32nomaximal
7C2×C32×Q16C2211yescharacteristic
8#64153—21no—
9C2×#3756—21no—
10C2×#3746C2211yescharacteristic
11#63919—21no—
12C8×C3⋊Dic3C2211yescharacteristic
13C3×#818C2212yes—
14C2×C3×C3⋊C16C2212yes—
15#63576—21no—
16#5183—32no—
17#5183—61no—
18#4874—32no—
19C3×#358—32no—
20#4564D312yes—
21#4503—32no—
22Dic3×C16—32no—
23#4492—32no—
24C2×C32×Q8—21no—
25C2×#634—21no—
26C2×#627—41no—
27C32×Q16—22no—
28C2×C32×C8C2311yescharacteristic
29#3756—42no—
30#3750—41no—
31#3750—41no—
32C4×C3⋊Dic3D411yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34#3746—22no—
35C3×C4⋊Dic3—22no—
36#3724—41no—
37C3×C3⋊C16—22no—
38#2241—91noSylow
39C2×C3×Q16—21no—
40C2×C3×Q16C2×D312yes—
41#944—62no—
42#944—62no—
43C2×#216—62no—
44C2×#216—62no—
45C2×Dic12—32no—
46C2×Dic12—61no—
47#888—62no—
48C2×C3×C16—32no—
49C3×#107—32no—
50#818C2×D312yes—
51C8×Dic3—32no—
52C8×Dic3—61no—
53C2×C3⋊C16C2×D312yes—
54#807—62no—
55C32×Q8—41no—
56C32×Q8—41no—
57C2×C32×C4—41no—
58C2×C32×C4C2×D411yescharacteristic
59C2×C3⋊Dic3—41no—
60C2×C3⋊Dic3D811yescharacteristic
61C2×C3⋊Dic3D811yescharacteristic
62#634—41no—
63#634—41no—
64C2×C3×Dic3—42no—
65#627—82no—
66C32×C8#4112yes—
67C3⋊(C3⋊C8)SD1612yes—
68#500—91no—
69#494—91no—
70#358—32no—
71#358—92no—
72C4×C16—91no—
73C2×C3×Q8—22no—
74C2×C3×Q8—22no—
75C2×Dic6—62no—
76C2×Dic6—62no—
77C2×Dic6—122no—
78C3×Q16—22no—
79C3×Q16—22no—
80C3×Q16—42no—
81C2×C3×C8—21no—
82C2×C3×C8C22×D312yes—
83C3×C4⋊C4—62no—
84#216—124no—
85#216—124no—
86C4⋊Dic3—22no—
87Dic3⋊C4—122no—
88Dic3⋊C4—122no—
89Dic3⋊C4—122no—
90Dic3⋊C4—122no—
91Dic3⋊C4—122no—
92C4×Dic3—32no—
93C4×Dic3—61no—
94C2×C3⋊C8—32no—
95C2×C3⋊C8—61no—
96Dic12—62no—
97Dic12—62no—
98Dic12—122no—
99C3×C16—62no—
100C3⋊C16—22no—
101C22×C32C2×D811yescharacteristic
102C32×C4—81no—
103C32×C4#12411yescharacteristic
104C32×C4C2×SD1611yescharacteristic
105C3⋊Dic3—81no—
106C3⋊Dic3SD3212yes—
107C3⋊Dic3Q3212yes—
108C3×Dic3—82no—
109C2×Q16—91no—
110C2×Q16—181no—
111C2×Q16D3211yescharacteristic
112C4⋊Q8—181no—
113C4⋊Q8—181no—
114C2×C16—32no—
115#107—32no—
116#107—181no—
117C4×C8—91no—
118C3×Q8—42no—
119C3×Q8—42no—
120C3×Q8—42no—
121C3×Q8—42no—
122C2×C3×C4—21no—
123C2×C3×C4—42no—
124C2×C3×C4—42no—
125C2×C3×C4—122no—
126C2×C3×C4D3×D412yes—
127C2×Dic3—32no—
128C2×Dic3—32no—
129C2×Dic3—42no—
130C2×Dic3—61no—
131C2×Dic3—61no—
132C2×Dic3—122no—
133C2×Dic3—122no—
134Dic6—122no—
135Dic6—122no—
136Dic6—122no—
137Dic6—122no—
138Dic6—244no—
139C3×C8—22no—
140C3×C8#23512yes—
141C3×C8#23712yes—
142C3⋊C8—34no—
143C3⋊C8—62no—
144C2×C32#48611yescharacteristic
145C2×C32C2×SD3211yescharacteristic
146C2×C32C2×Q3211yescharacteristic
147C2×Q8—21no—
148C2×Q8—181no—
149C2×Q8—361no—
150Q16—22no—
151Q16—182no—
152Q16—362no—
153C2×C8—91no—
154C2×C8C2×D3211yescharacteristic
155C4⋊C4—62no—
156C4⋊C4—361no—
157C4⋊C4—361no—
158C4⋊C4—361no—
159C42—91no—
160C16—62no—
161C22×C3—21no—
162C22×C3D3×D812yes—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—82no—
166C3×C4—82no—
167C3×C4—242no—
168C3×C4#88512yes—
169C3×C4D3×SD1612yes—
170Dic3—34no—
171Dic3—34no—
172Dic3—62no—
173Dic3—62no—
174Dic3—82no—
175Dic3—242no—
176Dic3—242no—
177C32#224111yescharacteristic, complemented, Sylow
178Q8—41no—
179Q8—41no—
180Q8—361no—
181Q8—361no—
182Q8—722no—
183C2×C4—41no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—122no—
187C2×C4—361no—
188C2×C4#381111yescharacteristic
189C8—92no—
190C8#380412yes—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—21no—
194C2×C3#476012yes—
195C2×C3D3×SD3212yes—
196C2×C3D3×Q3212yes—
197C22#6392611yescharacteristic
198C4—81no—
199C4—92no—
200C4—92no—
201C4—242no—
202C4—721no—
203C4#6393011yescharacteristic
204C4#6395311yescharacteristic
205C3—21no—
206C3#6921512yescomplemented
207C2#1059103911yescharacteristic
208C2#1059104311yescharacteristic
209C2#1059140211yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socle, prime radicalC22×C32C2×D8
hypercenterC2×Q16D32
hypocenterC32#2241
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
177. C32#2241semidirect
206. C3#69215semidirect

Maximal subgroups

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

subgroupindex
#105928822
#105909022
C3×#45642
#105891192
#105891022
#692153