Finite Group Databasebeta

← #3567⋊C9 #11919851

Subgroups — #3567⋊C9 #11919851

Order 1152.

354 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 32 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#564⋊C9C211yesmaximal, characteristic, complemented
2C3×#3567C311yesmaximal, characteristic
3#127⋊C9—42nomaximal
4#126⋊C9—42nomaximal
5C2×C42⋊C9—41nomaximal
6C3×#564C2×C311yescharacteristic
7C3×#562—31no—
8C3×#553—32no—
9C3×#552—32no—
10C3×#540—32no—
11C3×#539—32no—
12C3×#529—31no—
13C42⋊C9—41no—
14C42⋊C9—42no—
15C42⋊C9—42no—
16#3567C911yescharacteristic, complemented, Sylow
17C3×#127A412yes—
18C3×#126—32no—
19C3×#126—32no—
20C3×#126A412yes—
21C3×#125—32no—
22C3×#125—31no—
23C3×#125—32no—
24C3×#125—32no—
25C3×#124—31no—
26C3×#123—32no—
27C3×#123—32no—
28C3×#123—32no—
29C3×#123—32no—
30C3×#123—32no—
31C3×C22⋊Q8—32no—
32C3×C22⋊Q8—32no—
33C3×C22⋊Q8—31no—
34C3×#121—32no—
35C3×#121—32no—
36C3×#121—31no—
37C3×#121—32no—
38C3×#121—32no—
39C3×C4×Q8—31no—
40C3×C4×D4—32no—
41C3×C4×D4—31no—
42C3×C4×D4—32no—
43C3×C4×D4—32no—
44C3×#117—32no—
45C3×#117—32no—
46C2×C3×C4⋊C4—32no—
47C2×C3×C42A411yescharacteristic
48C2×C22⋊C9—161no—
49#564C2×C911yescharacteristic, complemented
50#562—31no—
51#553—32no—
52#552—32no—
53#540—32no—
54#539—32no—
55#529—31no—
56C2×C3×Q8—31no—
57C2×C3×D4—32no—
58C2×C3×D4—32no—
59C2×C3×D4—31no—
60C2×C3×D4—32no—
61C22×C3×C4—32no—
62C22×C3×C4—32no—
63C22×C3×C4—32no—
64C22×C3×C4—31no—
65C3×C4⋊C4—32no—
66C3×C4⋊C4—32no—
67C3×C4⋊C4—32no—
68C3×C4⋊C4—32no—
69C3×C4⋊C4—32no—
70C3×C4⋊C4—32no—
71C3×C4⋊C4—32no—
72C3×C4⋊C4—32no—
73C3×C4⋊C4—31no—
74C3×C4⋊C4—31no—
75C3×C22⋊C4—32no—
76C3×C22⋊C4—32no—
77C3×C22⋊C4—32no—
78C3×C22⋊C4—32no—
79C3×C22⋊C4—32no—
80C3×C22⋊C4—32no—
81C3×C22⋊C4—32no—
82C3×C42—31no—
83C3×C42—32no—
84C3×C42C2×A411yescharacteristic
85C3×C42C2×A412yes—
86C3×C42C2×A412yes—
87C22⋊C9—161no—
88#127C22⋊C912yes—
89#126—32no—
90#126—32no—
91#126C22⋊C912yes—
92#125—32no—
93#125—31no—
94#125—32no—
95#125—32no—
96#124—31no—
97#123—32no—
98#123—32no—
99#123—32no—
100#123—32no—
101#123—32no—
102C22⋊Q8—31no—
103C22⋊Q8—32no—
104C22⋊Q8—32no—
105#121—31no—
106#121—32no—
107#121—32no—
108#121—32no—
109#121—32no—
110C4×Q8—31no—
111C4×D4—32no—
112C4×D4—31no—
113C4×D4—32no—
114C4×D4—32no—
115#117—32no—
116#117—32no—
117C2×C4⋊C4—32no—
118C2×C42C22⋊C911yescharacteristic
119C23×C3—32no—
120C23×C3C22⋊A411yescharacteristic
121C3×Q8—121no—
122C3×D4—122no—
123C3×D4—122no—
124C3×D4—122no—
125C3×D4—121no—
126C2×C3×C4—31no—
127C2×C3×C4—31no—
128C2×C3×C4—32no—
129C2×C3×C4—32no—
130C2×C3×C4—32no—
131C2×C3×C4—122no—
132C2×C3×C4—121no—
133C2×C3×C4—122no—
134C2×C3×C4—122no—
135C2×C9—641no—
136C2×Q8—31no—
137C2×D4—32no—
138C2×D4—32no—
139C2×D4—31no—
140C2×D4—32no—
141C22×C4—32no—
142C22×C4—32no—
143C22×C4—32no—
144C22×C4—31no—
145C4⋊C4—32no—
146C4⋊C4—32no—
147C4⋊C4—32no—
148C4⋊C4—32no—
149C4⋊C4—32no—
150C4⋊C4—32no—
151C4⋊C4—32no—
152C4⋊C4—32no—
153C4⋊C4—31no—
154C4⋊C4—31no—
155C22⋊C4—32no—
156C22⋊C4—32no—
157C22⋊C4—32no—
158C22⋊C4—32no—
159C22⋊C4—32no—
160C22⋊C4—32no—
161C22⋊C4—32no—
162C42—31no—
163C42—32no—
164C42C2×C22⋊C911yescharacteristic
165C42C2×C22⋊C912yes—
166C42C2×C22⋊C912yes—
167C22×C3—61no—
168C22×C3—62no—
169C22×C3—62no—
170C22×C3—62no—
171C22×C3C2×C22⋊A411yescharacteristic
172C3×C4—61no—
173C3×C4—62no—
174C3×C4—62no—
175C3×C4—62no—
176C3×C4—61no—
177C9—641noSylow
178C23—32no—
179C23C22⋊(C22⋊C9)11yescharacteristic
180Q8—121no—
181D4—122no—
182D4—122no—
183D4—122no—
184D4—121no—
185C2×C4—31no—
186C2×C4—31no—
187C2×C4—32no—
188C2×C4—32no—
189C2×C4—32no—
190C2×C4—122no—
191C2×C4—121no—
192C2×C4—122no—
193C2×C4—122no—
194C2×C3—31no—
195C2×C3—41no—
196C2×C3—122no—
197C22—61no—
198C22—62no—
199C22—62no—
200C22—62no—
201C22C2×C22⋊(C22⋊C9)11yescharacteristic
202C4—61no—
203C4—62no—
204C4—62no—
205C4—62no—
206C4—61no—
207C3#3567⋊C311yescharacteristic
208C2—31no—
209C2—41no—
210C2—122no—
subgroupG/H
center, hypercenterC3#3567⋊C3
commutator, hypocenter#564C2×C9
Frattini, socleC22×C3C2×C22⋊A4
Fitting, prime radicalC3×#3567C3
cosocleC3×#564C2×C3
LCSG ▷ #564
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #564⋊C9C2semidirect
16. #3567C9semidirect
49. #564C2×C9semidirect

Maximal subgroups

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

subgroupindex
#564⋊C92
C3×#35673
#127⋊C94
#126⋊C94
C2×C42⋊C94