Finite Group Databasebeta

← #11796568

Subgroups — #11796568

Order 1152.

690 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 197 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
1C32×#536C211yesmaximal, characteristic
2#10592936C212yesmaximal
3#10589414C214yesmaximal, complemented
4#71873—34nomaximal
5C2×C32×#41C2211yescharacteristic
6C22×C32×Q8C411yescharacteristic
7C32×C4⋊Q8C2212yes—
8C32×#124C412yes—
9C32×#123—22no—
10C32×C22⋊Q8—22no—
11C32×#117C411yescharacteristic
12C2×#3748—22no—
13#63663C2214yes—
14#63660—22no—
15C3×#536D314yes—
16#5237—38no—
17#4548—316no—
18C32×#41—42no—
19C2×C32×Q8—21no—
20C2×C32×Q8—42no—
21C2×C32×Q8C2×C412yes—
22C2×C32×Q8C2311yescharacteristic
23C2×C32×D4C2×C411yescharacteristic
24C2×C32×D4D412yes—
25C22×C32×C4—21no—
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4D412yes—
28C32×C4⋊C4—21no—
29C32×C4⋊C4—24no—
30C32×C22⋊C4—21no—
31C32×C22⋊C4—24no—
32C32×C42C2×C412yes—
33#3748—24no—
34#3748—42no—
35C2×C3⋊(C3⋊C8)—42no—
36#2135—91noSylow
37C2×C3×#41C2×D314yes—
38C22×C3×Q8Dic314yes—
39C3×C4⋊Q8C2×D318yes—
40C3×#124Dic318yes—
41C3×#123—28no—
42C3×C22⋊Q8—28no—
43C3×#117Dic314yes—
44C2×#208—68no—
45#836—316no—
46#833—68no—
47C23×C32C22⋊C412yes—
48C23×C32C22⋊C411yescharacteristic
49C32×Q8—41no—
50C32×Q8—42no—
51C32×Q8—42no—
52C32×D4—41no—
53C32×D4—42no—
54C2×C32×C4—22no—
55C2×C32×C4—22no—
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—22no—
59C2×C32×C4—42no—
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4C22×C411yescharacteristic
62C2×C32×C4C2×D412yes—
63C3⋊(C3⋊C8)—44no—
64#536C3⋊D311yescharacteristic
65#413—92no—
66#356—94no—
67C3×#41—48no—
68C2×C3×Q8—24no—
69C2×C3×Q8—48no—
70C2×C3×Q8C2×Dic318yes—
71C2×C3×Q8C22×D314yes—
72C2×C3×D4C2×Dic314yes—
73C2×C3×D4#6718yes—
74C22×C3×C4—24no—
75C22×C3×C4C2×Dic314yes—
76C22×C3×C4#6718yes—
77C3×C4⋊C4—24no—
78C3×C4⋊C4—216no—
79C3×C22⋊C4—24no—
80C3×C22⋊C4—216no—
81C3×C42C2×Dic318yes—
82#208—616no—
83#208—128no—
84C2×C3⋊C8—128no—
85C22×C32—21no—
86C22×C32—22no—
87C22×C32—42no—
88C22×C32—41no—
89C22×C32C2×C22⋊C411yescharacteristic
90C32×C4—22no—
91C32×C4—21no—
92C32×C4—42no—
93C32×C4—42no—
94C32×C4#9912yes—
95C2×#41C2×C3⋊D311yescharacteristic
96C22×Q8C3⋊Dic311yescharacteristic
97C2×M16—182no—
98C4⋊Q8C2×C3⋊D312yes—
99#124C3⋊Dic312yes—
100#123—22no—
101C22⋊Q8—22no—
102#117C3⋊Dic311yescharacteristic
103#101—94no—
104#100—182no—
105C23×C3#21718yes—
106C23×C3#21714yes—
107C3×Q8—44no—
108C3×Q8—48no—
109C3×Q8—48no—
110C3×D4—44no—
111C3×D4—48no—
112C2×C3×C4—28no—
113C2×C3×C4—28no—
114C2×C3×C4—28no—
115C2×C3×C4—28no—
116C2×C3×C4—28no—
117C2×C3×C4—48no—
118C2×C3×C4#21714yes—
119C2×C3×C4C22×Dic314yes—
120C2×C3×C4C2×#6718yes—
121C3⋊C8—1216no—
122C2×C32—21no—
123C2×C32—41no—
124C2×C32—42no—
125C2×C32C2×#9911yescharacteristic
126#41—42no—
127C2×Q8—21no—
128C2×Q8—42no—
129C2×Q8C2×C3⋊Dic312yes—
130C2×Q8C22×C3⋊D311yescharacteristic
131C2×D4C2×C3⋊Dic311yescharacteristic
132C2×D4#63812yes—
133C22×C4—21no—
134C22×C4C2×C3⋊Dic311yescharacteristic
135C22×C4#63812yes—
136M16—184no—
137M16—362no—
138C2×C8—362no—
139C4⋊C4—21no—
140C4⋊C4—24no—
141C22⋊C4—21no—
142C22⋊C4—24no—
143C42C2×C3⋊Dic312yes—
144C22×C3—24no—
145C22×C3—28no—
146C22×C3—48no—
147C22×C3—44no—
148C22×C3C2×#21714yes—
149C3×C4—28no—
150C3×C4—24no—
151C3×C4—48no—
152C3×C4—48no—
153C3×C4#83418yes—
154C32#213511yescharacteristic, complemented, Sylow
155C23#375712yes—
156C23#375711yescharacteristic
157Q8—41no—
158Q8—42no—
159Q8—42no—
160D4—41no—
161D4—42no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4#375711yescharacteristic
169C2×C4C22×C3⋊Dic311yescharacteristic
170C2×C4C2×#63812yes—
171C8—364no—
172C2×C3—24no—
173C2×C3—44no—
174C2×C3—48no—
175C2×C3C2×#83414yes—
176C22—21no—
177C22—22no—
178C22—42no—
179C22—41no—
180C22C2×#375711yescharacteristic
181C4—22no—
182C4—21no—
183C4—42no—
184C4—42no—
185C4#6366112yes—
186C3#7187314yescomplemented
187C2—21no—
188C2—41no—
189C2—42no—
190C2C2×#6366111yescharacteristic
subgroupG/H
centerC2C2×#63661
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C22×C3⋊D3
FittingC32×#536C2
socleC2×C32C2×#99
prime radicalC2×C32×#41C22
cosocleC2×C32×Q8C23
hypercenter#536C3⋊D3
hypocenterC32#2135
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
3. #10589414C2semidirect
154. C32#2135semidirect
186. C3#71873semidirect

Maximal subgroups

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

subgroupindex
C32×#5362
#105929362
#105894142
#718733