Finite Group Databasebeta

← #11790066

Subgroups — #11790066

Order 1152.

442 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C2×#63779C212yesmaximal
2C2×#63777C211yesmaximal, characteristic
3C2×C4⋊#622C211yesmaximal, characteristic
4#10592348C211yesmaximal, characteristic
5#10590207C212yesmaximal
6C22×#622C2212yes—
7C22×#622C2211yescharacteristic
8C22×#622C2211yescharacteristic
9C2×#3750C412yes—
10C2×C4×C3⋊Dic3C2212yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#63779—24no—
13#63777—22no—
14C4⋊#622—22no—
15C32×#95C411yescharacteristic
16#63658C411yescharacteristic
17#4649—62no—
18C22×C32×C4C2×C412yes—
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C412yes—
22C22×C3⋊Dic3C2311yescharacteristic
23C2×#622—21no—
24C2×#622—21no—
25C2×#622—21no—
26C2×#622—21no—
27C2×#622—22no—
28C2×#622—22no—
29C2×#622—22no—
30C2×#622D412yes—
31C2×#622Q812yes—
32#3750—24no—
33C4×C3⋊Dic3—22no—
34C4×C3⋊Dic3—22no—
35C4×C3⋊Dic3D412yes—
36C4×C3⋊Dic3Q812yes—
37#1940—91nomaximal, Sylow
38C2×Dic3⋊C4—64no—
39C2×C4×Dic3—62no—
40C2×C4×Dic3—64no—
41C3×#95—22no—
42C3⋊#95—62no—
43C23×C32C22×C411yescharacteristic
44C2×C32×C4—22no—
45C2×C32×C4—22no—
46C2×C32×C4—22no—
47C2×C32×C4—22no—
48C2×C32×C4C4⋊C412yes—
49C2×C3⋊Dic3—22no—
50C2×C3⋊Dic3—22no—
51C2×C3⋊Dic3—22no—
52C2×C3⋊Dic3C4⋊C412yes—
53C2×C3⋊Dic3M1614yes—
54C2×C3⋊Dic3C2×D411yescharacteristic
55C2×C3⋊Dic3C2×D411yescharacteristic
56C2×C3⋊Dic3C2×Q811yescharacteristic
57C2×C3⋊Dic3C2×Q811yescharacteristic
58C2×C3⋊Dic3#4111yescharacteristic
59C2×C3⋊Dic3#4111yescharacteristic
60#622—22no—
61#622—22no—
62#622—42no—
63C2×C4⋊C8—91no—
64C2×C4⋊C8—92no—
65C2×#97—91no—
66C4×C4⋊C4—91no—
67#336—92no—
68C22×C3×C4—22no—
69C22×C3×C4—24no—
70C22×Dic3—62no—
71C22×Dic3—62no—
72C22×Dic3—64no—
73Dic3⋊C4—616no—
74C4×Dic3—64no—
75C4×Dic3—64no—
76C4×Dic3—124no—
77C4×Dic3—124no—
78C22×C32C2×C4⋊C411yescharacteristic
79C22×C32C4×D411yescharacteristic
80C22×C32C4×Q811yescharacteristic
81C22×C32C2×M1612yes—
82C22×C32#13112yes—
83C32×C4—22no—
84C32×C4—42no—
85C3⋊Dic3—22no—
86C3⋊Dic3—24no—
87C3⋊Dic3#12111yescharacteristic
88C3⋊Dic3C22⋊Q811yescharacteristic
89C3⋊Dic3#12511yescharacteristic
90C3⋊Dic3C4⋊Q811yescharacteristic
91C22×C8—91no—
92C22×C8—91no—
93C22×C8—92no—
94C2×C4⋊C4—92no—
95C2×C42—91no—
96C2×C42—92no—
97C4⋊C8—182no—
98C4⋊C8—184no—
99#97—182no—
100#95—91no—
101#95#15711yescharacteristic
102C23×C3—22no—
103C2×C3×C4—28no—
104C2×C3×C4—24no—
105C2×C3×C4—44no—
106C2×C3×C4—44no—
107C2×C3×C4—44no—
108C2×Dic3—64no—
109C2×Dic3—62no—
110C2×Dic3—62no—
111C2×Dic3—62no—
112C2×Dic3—62no—
113C2×Dic3—62no—
114C2×Dic3—62no—
115C2×Dic3—68no—
116C2×Dic3—68no—
117C2×Dic3—124no—
118C2×Dic3—124no—
119C2×C32#38911yescharacteristic
120C2×C32#42311yescharacteristic
121C2×C32#42411yescharacteristic
122C2×C32#43512yes—
123C2×C32#44612yes—
124C22×C4—91no—
125C22×C4—92no—
126C22×C4—91no—
127C22×C4C2×#15712yes—
128C22×C4C2×#15711yescharacteristic
129C2×C8—92no—
130C2×C8—92no—
131C2×C8—181no—
132C2×C8—181no—
133C2×C8—181no—
134C2×C8—181no—
135C2×C8—182no—
136C2×C8—182no—
137C2×C8—182no—
138C4⋊C4—184no—
139C42—92no—
140C42—92no—
141C42—182no—
142C42—182no—
143C22×C3—24no—
144C22×C3—22no—
145C22×C3—24no—
146C22×C3—22no—
147C22×C3—22no—
148C3×C4—44no—
149C3×C4—48no—
150Dic3—62no—
151Dic3—62no—
152Dic3—62no—
153Dic3—62no—
154Dic3—68no—
155Dic3—128no—
156C32#194011yescharacteristic, complemented, Sylow
157C23C22×#15711yescharacteristic
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—94no—
169C2×C4—92no—
170C2×C4—182no—
171C2×C4—182no—
172C2×C4—182no—
173C2×C4C4⋊#15712yes—
174C8—182no—
175C8—182no—
176C8—362no—
177C2×C3—22no—
178C2×C3—24no—
179C2×C3—22no—
180C2×C3—24no—
181C2×C3—22no—
182C22#6428312yes—
183C22C2×C4⋊#15711yescharacteristic
184C22#6428712yes—
185C22D4×#15711yescharacteristic
186C22Q8×#15711yescharacteristic
187C4—22no—
188C4—42no—
189C4—91no—
190C4—91no—
191C4—91no—
192C4—91no—
193C4—182no—
194C4—184no—
195C3—22no—
196C2#1059372911yescharacteristic
197C2#1059374112yes—
198C2#1059374311yescharacteristic
199C2#1059375412yes—
200C2#1059375911yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socle, prime radicalC23×C32C22×C4
FittingC32×#95C4
cosocleC22×C3⋊Dic3C23
hypercenter#95#157
hypocenterC32#1940
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
156. C32#1940semidirect

Maximal subgroups

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

subgroupindex
C2×#637792
C2×#637772
C2×C4⋊#6222
#105923482
#105902072
#19409