Finite Group Databasebeta

← #11796548

Subgroups — #11796548

Order 1152.

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

normal subgroups only

This group has 786 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×#535C211yesmaximal, characteristic
2#10592936C212yesmaximal, complemented
3#10589408C214yesmaximal, complemented
4#71862—34nomaximal
5C2×C32×#41C2211yescharacteristic
6C22×C32×D4C411yescharacteristic
7C32×#127C412yes—
8C32×#124C2212yes—
9C32×#121—22no—
10C32×#120—22no—
11C32×#117C411yescharacteristic
12C2×#3748—22no—
13#63663C2214yescomplemented
14#63660—22no—
15C3×#535D314yes—
16#5237—38no—
17#4542—316no—
18C24×C32—21no—
19C32×#41—42no—
20C2×C32×Q8C2311yescharacteristic
21C2×C32×D4—24no—
22C2×C32×D4—21no—
23C2×C32×D4—42no—
24C2×C32×D4C2×C412yes—
25C2×C32×D4C2×C411yescharacteristic
26C2×C32×D4D412yes—
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4D412yes—
29C32×C4⋊C4—21no—
30C32×C22⋊C4—21no—
31C32×C22⋊C4—24no—
32C32×C42C2×C412yes—
33#3748—24no—
34#3748—42no—
35C2×C3⋊(C3⋊C8)—42no—
36#2134—91noSylow
37C2×C3×#41C2×D314yes—
38C22×C3×D4Dic314yes—
39C3×#127Dic318yes—
40C3×#124C2×D318yes—
41C3×#121—28no—
42C3×#120—28no—
43C3×#117Dic314yes—
44C2×#208—68no—
45#836—316no—
46#833—68no—
47C23×C32—22no—
48C23×C32—42no—
49C23×C32—82no—
50C23×C32C22⋊C411yescharacteristic
51C23×C32C22⋊C412yes—
52C32×Q8—41no—
53C32×D4—41no—
54C32×D4—42no—
55C32×D4—42no—
56C32×D4—42no—
57C32×D4—84no—
58C2×C32×C4—22no—
59C2×C32×C4—22no—
60C2×C32×C4—22no—
61C2×C32×C4—22no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22×C411yescharacteristic
64C2×C32×C4C2×D412yes—
65C3⋊(C3⋊C8)—44no—
66#535C3⋊D311yescharacteristic
67#413—92no—
68#355—94no—
69C24×C3—24no—
70C3×#41—48no—
71C2×C3×Q8C22×D314yes—
72C2×C3×D4—216no—
73C2×C3×D4—24no—
74C2×C3×D4—48no—
75C2×C3×D4C2×Dic318yes—
76C2×C3×D4C2×Dic314yes—
77C2×C3×D4#6718yes—
78C22×C3×C4C2×Dic314yes—
79C22×C3×C4#6718yes—
80C3×C4⋊C4—24no—
81C3×C22⋊C4—24no—
82C3×C22⋊C4—216no—
83C3×C42C2×Dic318yes—
84#208—616no—
85#208—128no—
86C2×C3⋊C8—128no—
87C22×C32—21no—
88C22×C32—22no—
89C22×C32—42no—
90C22×C32—41no—
91C22×C32—44no—
92C22×C32—42no—
93C22×C32—84no—
94C22×C32C2×C22⋊C411yescharacteristic
95C32×C4—22no—
96C32×C4—21no—
97C32×C4—42no—
98C32×C4#9912yes—
99C2×#41C2×C3⋊D311yescharacteristic
100C22×D4C3⋊Dic311yescharacteristic
101C2×M16—182no—
102#127C3⋊Dic312yes—
103#124C2×C3⋊D312yes—
104#121—22no—
105#120—22no—
106#117C3⋊Dic311yescharacteristic
107#101—94no—
108#100—182no—
109C23×C3—28no—
110C23×C3—48no—
111C23×C3—88no—
112C23×C3#21714yes—
113C23×C3#21718yes—
114C3×Q8—44no—
115C3×D4—44no—
116C3×D4—48no—
117C3×D4—48no—
118C3×D4—48no—
119C3×D4—816no—
120C2×C3×C4—28no—
121C2×C3×C4—28no—
122C2×C3×C4—28no—
123C2×C3×C4—28no—
124C2×C3×C4#21714yes—
125C2×C3×C4C22×Dic314yes—
126C2×C3×C4C2×#6718yes—
127C3⋊C8—1216no—
128C2×C32—21no—
129C2×C32—42no—
130C2×C32—41no—
131C2×C32—82no—
132C2×C32C2×#9911yescharacteristic
133C24—21no—
134#41—42no—
135C2×Q8C22×C3⋊D311yescharacteristic
136C2×D4—24no—
137C2×D4—21no—
138C2×D4—42no—
139C2×D4C2×C3⋊Dic312yes—
140C2×D4C2×C3⋊Dic311yescharacteristic
141C2×D4#63812yes—
142C22×C4C2×C3⋊Dic311yescharacteristic
143C22×C4#63812yes—
144M16—184no—
145M16—362no—
146C2×C8—362no—
147C4⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—24no—
150C42C2×C3⋊Dic312yes—
151C22×C3—24no—
152C22×C3—28no—
153C22×C3—48no—
154C22×C3—44no—
155C22×C3—416no—
156C22×C3—48no—
157C22×C3—816no—
158C22×C3C2×#21714yes—
159C3×C4—28no—
160C3×C4—24no—
161C3×C4—48no—
162C3×C4#83418yes—
163C32#213411yescharacteristic, complemented, Sylow
164C23—22no—
165C23—42no—
166C23—82no—
167C23#375711yescharacteristic
168C23#375712yes—
169Q8—41no—
170D4—41no—
171D4—42no—
172D4—42no—
173D4—42no—
174D4—84no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4#375711yescharacteristic
180C2×C4C22×C3⋊Dic311yescharacteristic
181C2×C4C2×#63812yes—
182C8—364no—
183C2×C3—24no—
184C2×C3—44no—
185C2×C3—48no—
186C2×C3—88no—
187C2×C3C2×#83414yes—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—41no—
192C22—44no—
193C22—42no—
194C22—84no—
195C22C2×#375711yescharacteristic
196C4—22no—
197C4—21no—
198C4—42no—
199C4#6366112yes—
200C3#7186214yescomplemented
201C2—21no—
202C2—41no—
203C2—42no—
204C2—82no—
205C2C2×#6366111yescharacteristic
subgroupG/H
centerC2C2×#63661
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C22×C3⋊D3
Fitting, prime radicalC32×#535C2
socleC2×C32C2×#99
cosocleC2×C32×Q8C23
hypercenter#535C3⋊D3
hypocenterC32#2134
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
2. #10592936C2semidirect
3. #10589408C2semidirect
13. #63663C22semidirect
163. C32#2134semidirect
200. C3#71862semidirect

Maximal subgroups

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

subgroupindex
C32×#5352
#105929362
#105894082
#718623