Finite Group Databasebeta

← #11777229

Subgroups — #11777229

Order 1152.

274 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 66 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
1Q8×#622C211yesmaximal, characteristic
2#10593750C211yesmaximal, characteristic
3#10592489C211yesmaximal, characteristic
4Q8⋊#622C211yesmaximal, characteristic
5#10590173C211yesmaximal, characteristic
6C8×#622C211yesmaximal, characteristic
7#10590161C211yesmaximal, characteristic
8Q8×C3⋊Dic3C2211yescharacteristic
9C2×#3756C411yescharacteristic
10#64096C2211yescharacteristic
11#63779—21no—
12C4⋊#622—21no—
13C4⋊#622C2211yescharacteristic
14C4⋊#622C2211yescharacteristic
15C4×#622—21no—
16C4×#622—21no—
17C4×#622C2211yescharacteristic
18C4×#622C2211yescharacteristic
19C32×#103C411yescharacteristic
20#63643C411yescharacteristic
21C8×C3⋊Dic3C2211yescharacteristic
22#63634C411yescharacteristic
23#4790—62no—
24C2×C32×Q8C2×C411yescharacteristic
25C2×#634C2×C411yescharacteristic
26C2×#622—21no—
27C2×#622—21no—
28C2×#622—21no—
29C2×#622D411yescharacteristic
30C2×#622D411yescharacteristic
31C2×C32×C8C2×C411yescharacteristic
32C32×C4⋊C4C2×C411yescharacteristic
33#3756C814yescomplemented
34C4⋊(C3⋊Dic3)—21no—
35C4⋊(C3⋊Dic3)C2×C411yescharacteristic
36#3750—21no—
37C4×C3⋊Dic3—21no—
38C4×C3⋊Dic3—21no—
39C4×C3⋊Dic3C2311yescharacteristic
40C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
41C8×Q16—91nomaximal, Sylow
42Q8×Dic3—62no—
43C2×#216—62no—
44#887—62no—
45C3×#103—22no—
46#816—62no—
47C8×Dic3—62no—
48#807—62no—
49C32×Q8—21no—
50C32×Q8C2×C812yes—
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4C22×C411yescharacteristic
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3C2×D411yescharacteristic
57C2×C3⋊Dic3#4111yescharacteristic
58#634—21no—
59#634C2×C812yes—
60#622—22no—
61#622—21no—
62#622—41no—
63#622—41no—
64#622Q1612yescomplemented
65C32×C8—21no—
66C3⋊(C3⋊C8)C2×C812yes—
67C8×Q8—91no—
68C8×Q8—91no—
69C4×Q16—91no—
70#335—91no—
71Q8⋊C8—91no—
72Q8⋊C8—91no—
73C82—91no—
74C2×C3×Q8—22no—
75C2×Dic6—62no—
76C2×C3×C8—22no—
77C3×C4⋊C4—22no—
78#216—68no—
79C4⋊Dic3—62no—
80C4⋊Dic3—122no—
81Dic3⋊C4—122no—
82C4×Dic3—62no—
83C4×Dic3—122no—
84C4×Dic3—122no—
85C2×C3⋊C8—62no—
86C22×C32C4×D411yescharacteristic
87C32×C4—22no—
88C32×C4—41no—
89C32×C4C22×C811yescharacteristic
90C32×C4#13111yescharacteristic
91C3⋊Dic3—22no—
92C3⋊Dic3—21no—
93C3⋊Dic3—41no—
94C3⋊Dic3C2×Q1611yescharacteristic
95C3⋊Dic3#13511yescharacteristic
96C2×Q16—91no—
97C4×Q8—91no—
98C4×Q8—91no—
99#107—91no—
100C4⋊C8—91no—
101C4⋊C8—91no—
102C4⋊C8—181no—
103C4⋊C8—181no—
104#103—91no—
105#103#15711yescharacteristic
106C4×C8—91no—
107C4×C8—91no—
108C4×C8—91no—
109C4×C8—181no—
110C4×C8—181no—
111C3×Q8—24no—
112C3×Q8—42no—
113C2×C3×C4—22no—
114C2×C3×C4—42no—
115C2×C3×C4—42no—
116C2×Dic3—62no—
117C2×Dic3—62no—
118C2×Dic3—122no—
119C2×Dic3—122no—
120Dic6—64no—
121Dic6—122no—
122C3×C8—42no—
123C3⋊C8—64no—
124C2×C32C8×D411yescharacteristic
125C2×C32C4×Q1611yescharacteristic
126C2×C32#44311yescharacteristic
127C2×Q8—91no—
128C2×Q8C2×#15711yescharacteristic
129Q16—94no—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—91no—
133C2×C8—181no—
134C2×C8—181no—
135C2×C8—181no—
136C2×C8C2×#15711yescharacteristic
137C4⋊C4—91no—
138C4⋊C4—181no—
139C4⋊C4—181no—
140C4⋊C4C2×#15711yescharacteristic
141C42—91no—
142C42—181no—
143C42—181no—
144C22×C3—22no—
145C3×C4—22no—
146C3×C4—22no—
147C3×C4—44no—
148C3×C4—82no—
149Dic3—62no—
150Dic3—62no—
151Dic3—124no—
152Dic3—122no—
153Dic3—242no—
154C32C8×Q1611yescharacteristic, complemented, Sylow
155Q8—21no—
156Q8—92no—
157Q8—181no—
158Q8#378712yes—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—181no—
164C2×C4—181no—
165C2×C4C22×#15711yescharacteristic
166C8—21no—
167C8—92no—
168C8—92no—
169C8—181no—
170C8—182no—
171C8—361no—
172C8—361no—
173C2×C3—22no—
174C2×C3—22no—
175C2×C3—22no—
176C22D4×#15711yescharacteristic
177C4—22no—
178C4—41no—
179C4—91no—
180C4—91no—
181C4—182no—
182C4—181no—
183C4—361no—
184C4C2×#378711yescharacteristic
185C4#6428711yescharacteristic
186C3—22no—
187C2#1059373911yescharacteristic
188C2#1059378311yescharacteristic
189C2Q16×#15711yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×#103C4
socle, prime radicalC22×C32C4×D4
cosocleC4×C3⋊Dic3C23
hypercenter#103#157
hypocenterC32C8×Q16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
33. #3756C8semidirect
64. #622Q16semidirect
154. C32C8×Q16semidirect

Maximal subgroups

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

subgroupindex
Q8×#6222
#105937502
#105924892
Q8⋊#6222
#105901732
C8×#6222
#105901612
C8×Q169