Finite Group Databasebeta

← #11861341

Subgroups — #11861341

Order 1152.

586 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 166 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#10596159C211yesmaximal, characteristic
2#10593755C212yesmaximal
3#10593754C214yesmaximal, complemented
4#10593750C214yesmaximal, complemented
5#10593748C212yesmaximal
6#10593729C211yesmaximal, characteristic
7C4×#3787C211yesmaximal, characteristic
8C2×#3788C2212yes—
9C2×#3787C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C32×#125C411yescharacteristic
12#64105C414yes—
13#64101C2212yes—
14#64097C412yes—
15#64096C2214yes—
16C42×C3⋊D3C2211yescharacteristic
17#64079C411yescharacteristic
18#63779C2214yes—
19#63779C2214yes—
20#63777C2214yes—
21C4⋊#622C2214yes—
22C4×#622C2212yes—
23C4×#622C2212yes—
24C4×#622C2214yes—
25#5688—62no—
26C2×C4×C3⋊D3C2×C412yes—
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×#634C2×C414yes—
29C2×#622C2312yes—
30C2×#622C2314yes—
31C2×#622C2311yescharacteristic
32C2×#622C2311yescharacteristic
33#3788—24no—
34#3787—22no—
35#3787Q814yescomplemented
36C32×C4⋊C4C2×C414yes—
37C32×C4⋊C4C2×C412yes—
38C32×C42C2×C411yescharacteristic
39#3752C2×C414yes—
40C4⋊(C3⋊Dic3)C2×C412yes—
41#3750C2×C414yes—
42#3750C2×C414yes—
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3C2312yes—
45C4×C3⋊Dic3C2314yes—
46#2960—91nomaximal, Sylow
47C3×#125—22no—
48#896—68no—
49#892—64no—
50#888—64no—
51#887—68no—
52C42×D3—62no—
53#870—62no—
54C22×C3⋊D3C22×C411yescharacteristic
55C2×C32×C4C22×C412yes—
56C2×C32×C4C22×C414yes—
57C2×C32×C4C22×C411yescharacteristic
58C2×C3⋊Dic3C22×C414yes—
59C2×C3⋊Dic3C22×C412yes—
60C2×C3⋊Dic3C2411yescharacteristic
61C4×C3⋊D3—24no—
62C4×C3⋊D3C2×Q812yes—
63C4×C3⋊D3#4112yes—
64#634—28no—
65#622—22no—
66#622—24no—
67#622C2×Q812yes—
68#622C2×Q812yes—
69#533—91no—
70#446—94no—
71C8×Q8—94no—
72#424—92no—
73#423—91no—
74#405—92no—
75C2×C4×C8—91no—
76C2×C4×D3—62no—
77C2×C4×D3—64no—
78C2×Dic6—68no—
79C3×C4⋊C4—28no—
80C3×C4⋊C4—24no—
81C3×C42—22no—
82(C2×D3)⋊C4—68no—
83C4⋊Dic3—64no—
84Dic3⋊C4—68no—
85Dic3⋊C4—68no—
86C4×Dic3—64no—
87C4×Dic3—62no—
88C4×Dic3—68no—
89C22×C32C23×C411yescharacteristic
90C2×C3⋊D3—22no—
91C2×C3⋊D3C4×Q812yes—
92C32×C4—24no—
93C32×C4—22no—
94C32×C4C4×Q812yes—
95C3⋊Dic3—24no—
96C3⋊Dic3#13114yes—
97C3⋊Dic3C22×Q811yescharacteristic
98C3⋊Dic3C2×#4111yescharacteristic
99C2×M16—92no—
100C22×C8—91no—
101C22×C8—91no—
102C4⋊Q8—92no—
103#125—91no—
104#125#15711yescharacteristic
105C22⋊Q8—94no—
106C4×Q8—94no—
107#117—92no—
108C2×C42—91no—
109C4⋊C8—94no—
110C4⋊C8—94no—
111C4⋊C8—94no—
112#97—94no—
113C4×C8—92no—
114C4×C8—92no—
115C4×C8—94no—
116C22×D3—62no—
117C2×C3×C4—22no—
118C2×C3×C4—24no—
119C2×C3×C4—28no—
120C2×Dic3—64no—
121C2×Dic3—62no—
122C2×Dic3—68no—
123C4×D3—64no—
124C4×D3—64no—
125C4×D3—128no—
126Dic6—1216no—
127C2×C32C2×C4×Q811yescharacteristic
128C2×C32C2×#13112yes—
129C3⋊D3—22no—
130C2×Q8—94no—
131C22×C4—91no—
132C22×C4—92no—
133M16—184no—
134C2×C8—91no—
135C2×C8—91no—
136C2×C8—94no—
137C2×C8—92no—
138C2×C8—94no—
139C2×C8—182no—
140C4⋊C4—92no—
141C4⋊C4—94no—
142C4⋊C4—94no—
143C4⋊C4C2×#15712yes—
144C4⋊C4C2×#15714yes—
145C22⋊C4—94no—
146C42—92no—
147C42—94no—
148C42—91no—
149C42C2×#15711yescharacteristic
150C22×C3—22no—
151C2×D3—64no—
152C2×D3—124no—
153C3×C4—24no—
154C3×C4—48no—
155C3×C4—44no—
156Dic3—68no—
157Dic3—62no—
158Dic3—62no—
159Dic3—128no—
160C32#296011yescharacteristic, complemented, Sylow
161C23—91no—
162Q8—188no—
163C2×C4—91no—
164C2×C4—92no—
165C2×C4—92no—
166C2×C4—92no—
167C2×C4—94no—
168C2×C4—184no—
169C2×C4C22×#15712yes—
170C2×C4C22×#15714yes—
171C2×C4C22×#15711yescharacteristic
172C8—92no—
173C8—92no—
174C8—182no—
175C8—184no—
176C2×C3—22no—
177C2×C3—24no—
178D3—124no—
179C22—92no—
180C22—182no—
181C22C23×#15711yescharacteristic
182C4—22no—
183C4—24no—
184C4—91no—
185C4—91no—
186C4—94no—
187C4—184no—
188C4Q8×#15712yes—
189C3—22no—
190C2—182no—
191C2C2×Q8×#15711yescharacteristic
192C2#1059664712yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#125C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C3⋊Dic3C24
hypercenter#125#157
hypocenterC32#2960
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #10593754C2semidirect
4. #10593750C2semidirect
35. #3787Q8semidirect
160. C32#2960semidirect

Maximal subgroups

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

subgroupindex
#105961592
#105937552
#105937542
#105937502
#105937482
#105937292
C4×#37872
#29609