Finite Group Databasebeta

← Q8×#41⋊C9 #11919729

Subgroups — Q8×#41⋊C9 #11919729

Order 1152.

482 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 121 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
1Q8×Q8⋊C9C211yesmaximal, characteristic, complemented
2#557⋊C9C213yesmaximal, complemented
3C4×#41⋊C9C213yesmaximal
4C3×Q8×#41C311yesmaximal, characteristic
5C2×#41⋊C9C2211yescharacteristic
6C4×Q8×C9—41nomaximal
7C4×Q8⋊C9C2213yes—
8C4×Q8⋊C9C2213yes—
9C3×Q82C2×C311yescharacteristic
10C3×#557C2×C313yes—
11C3×#554—33no—
12C3×D4×Q8—31no—
13C3×#533—33no—
14C3×C4×#41C2×C313yes—
15C2×C3×C4×Q8—31no—
16C2×Q8×C9—41no—
17#41⋊C9Q812yesdirect product factor
18C2×Q8⋊C9C2311yescharacteristic
19C9×C4⋊C4—43no—
20C42×C9—43no—
21Q8×#41C911yescharacteristic, complemented, Sylow
22C2×C3×#41C22×C311yescharacteristic
23C22×C3×Q8—31no—
24C3×C4⋊Q8—33no—
25C3×C4⋊Q8—33no—
26C3×#125—36no—
27C3×C22⋊Q8—36no—
28C3×C22⋊Q8—36no—
29C3×C4×Q8—32no—
30C3×C4×Q8—31no—
31C3×C4×Q8—33no—
32C3×C4×Q8—33no—
33C3×C4×Q8A411yescharacteristic
34C3×C4×Q8C22×C313yes—
35C3×C4×Q8C22×C313yes—
36C3×C4×D4—33no—
37C3×C4×D4—33no—
38C3×#117—33no—
39C2×C3×C4⋊C4—33no—
40C2×C3×C42—33no—
41Q8×C9—44no—
42C2×C4×C9—43no—
43C2×C4×C9—43no—
44C2×C4×C9—41no—
45Q8⋊C9C2×Q811yescharacteristic, complemented
46Q82C2×C911yescharacteristic
47#557C2×C913yes—
48#554—33no—
49D4×Q8—31no—
50#533—33no—
51C4×#41C2×C913yes—
52C2×C4×Q8—31no—
53C3×#41—32no—
54C3×#41C3×Q812yes—
55C2×C3×Q8—32no—
56C2×C3×Q8—33no—
57C2×C3×Q8—64no—
58C2×C3×Q8C2×A411yescharacteristic
59C2×C3×Q8C23×C311yescharacteristic
60C2×C3×D4—31no—
61C22×C3×C4—31no—
62C22×C3×C4—33no—
63C22×C3×C4—33no—
64C3×C4⋊C4—33no—
65C3×C4⋊C4—33no—
66C3×C4⋊C4—36no—
67C3×C4⋊C4—36no—
68C3×C4⋊C4—33no—
69C3×C4⋊C4C2×A413yes—
70C3×C22⋊C4—36no—
71C3×C42—33no—
72C3×C42—33no—
73C3×C42—33no—
74C3×C42C2×A413yes—
75C22×C9—41no—
76C4×C9—42no—
77C4×C9—46no—
78C4×C9—83no—
79C2×#41C22×C911yescharacteristic
80C22×Q8—31no—
81C4⋊Q8—33no—
82C4⋊Q8—33no—
83#125—36no—
84C22⋊Q8—36no—
85C22⋊Q8—36no—
86C4×Q8—32no—
87C4×Q8—31no—
88C4×Q8—33no—
89C4×Q8—33no—
90C4×Q8C22⋊C911yescharacteristic
91C4×Q8C22×C913yes—
92C4×Q8C22×C913yes—
93C4×D4—33no—
94C4×D4—33no—
95#117—33no—
96C2×C4⋊C4—33no—
97C2×C42—33no—
98C23×C3—31no—
99C3×Q8—31no—
100C3×Q8—66no—
101C3×Q8—122no—
102C3×Q8#41⋊C314yes—
103C3×Q8C2×C3×Q811yescharacteristic
104C3×D4—32no—
105C3×D4—32no—
106C2×C3×C4—31no—
107C2×C3×C4—32no—
108C2×C3×C4—32no—
109C2×C3×C4—33no—
110C2×C3×C4—33no—
111C2×C3×C4—66no—
112C2×C3×C4—123no—
113C2×C3×C4C22×A413yes—
114C2×C3×C4C22×A413yes—
115C2×C3×C4C22×A411yescharacteristic
116C2×C9—41no—
117C2×C9—41no—
118C2×C9—41no—
119#41—32no—
120#41Q8×C912yescomplemented
121C2×Q8—32no—
122C2×Q8—33no—
123C2×Q8—64no—
124C2×Q8C2×C22⋊C911yescharacteristic
125C2×Q8C23×C911yescharacteristic
126C2×D4—31no—
127C22×C4—31no—
128C22×C4—33no—
129C22×C4—33no—
130C4⋊C4—33no—
131C4⋊C4—33no—
132C4⋊C4—36no—
133C4⋊C4—36no—
134C4⋊C4—33no—
135C4⋊C4C2×C22⋊C913yes—
136C22⋊C4—36no—
137C42—33no—
138C42—33no—
139C42—33no—
140C42C2×C22⋊C913yes—
141C22×C3—32no—
142C22×C3—61no—
143C22×C3—61no—
144C22×C3C23×A411yescharacteristic
145C3×C4—23no—
146C3×C4—31no—
147C3×C4—31no—
148C3×C4—63no—
149C3×C4—63no—
150C3×C4Q8×A412yes—
151C3×C4C2×#41⋊C316yes—
152C9—41noSylow
153C23—31no—
154Q8—31no—
155Q8—66no—
156Q8—122no—
157Q8#41⋊C914yesdirect product factor
158Q8C2×Q8×C911yescharacteristic
159D4—32no—
160D4—32no—
161C2×C4—31no—
162C2×C4—32no—
163C2×C4—32no—
164C2×C4—33no—
165C2×C4—33no—
166C2×C4—66no—
167C2×C4—123no—
168C2×C4C22×C22⋊C913yes—
169C2×C4C22×C22⋊C911yescharacteristic
170C2×C4C22×C22⋊C913yes—
171C2×C3—62no—
172C2×C3C2×Q8×A411yescharacteristic
173C2×C3C22×#41⋊C311yescharacteristic
174C2×C3#594511yescharacteristic
175C22—32no—
176C22—61no—
177C22—61no—
178C22C23×C22⋊C911yescharacteristic
179C4—23no—
180C4—31no—
181C4—31no—
182C4—63no—
183C4—63no—
184C4Q8×C22⋊C912yes—
185C4C2×#41⋊C916yes—
186C3Q8×#41⋊C311yescharacteristic
187C2—62no—
188C2C2×Q8×C22⋊C911yescharacteristic
189C2C22×#41⋊C911yescharacteristic
190C2#1059312011yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutatorC2×Q8C23×C9
Frattini, socleC22×C3C23×A4
FittingC3×Q8×#41C3
prime radicalC2×C3×#41C22×C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×C4×Q8A4
hypocenterQ8C2×Q8×C9
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×Q8⋊C9C2semidirect
2. #557⋊C9C2semidirect
17. #41⋊C9Q8direct (N × H)
21. Q8×#41C9semidirect
45. Q8⋊C9C2×Q8semidirect
120. #41Q8×C9semidirect
157. Q8#41⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×Q8⋊C92
#557⋊C92
C4×#41⋊C92
C3×Q8×#413
C4×Q8×C94