Finite Group Databasebeta

← C4⋊Q8×#1181 #16835963

Subgroups — C4⋊Q8×#1181 #16835963

Order 3712.

588 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 210 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×Q8×#1181C212yesmaximal
2(C2×#1181)⋊Q8C212yesmaximal
3#14272114C214yesmaximal
4#14272109C211yesmaximal, characteristic
5C4⋊C4×#1181C214yesmaximal
6C42×#1181C211yesmaximal, characteristic
7C4⋊Q8×D29C211yesmaximal, characteristic
8C2×Q8×D29C2212yes—
9Q8×#1181—28no—
10C2×C4⋊#1181C2214yes—
11C2×C4⋊#1181C2212yes—
12C2×C4⋊#1181C2214yes—
13C2×C4×#1181C2212yes—
14C2×C4×#1181C2211yescharacteristic
15C2×C4×#1181C2214yes—
16C2×C4×#1181C2211yescharacteristic
17C2×C4×#1181C2212yes—
18C29×C4⋊Q8C411yescharacteristic, complemented
19#11745306C412yescomplemented
20C4⋊C4×D29C2214yes—
21#11745250C414yescomplemented
22C42×D29C2211yescharacteristic
23#11745231C411yescharacteristic, complemented
24(C2×#1181)⋊C4C2218yes—
25C22×#1181C2314yes—
26C22×#1181C2311yescharacteristic
27C22×#1181C2312yes—
28C22×#1181C2311yescharacteristic
29C2×Q8×C29C2×C412yes—
30Q8×D29—24no—
31Q8×D29—24no—
32C2×C4×D29C2314yes—
33C2×C4×D29C2311yescharacteristic
34C2×C4×D29C2312yes—
35C2×Dic58C2×C412yes—
36C2×Dic58C2×C414yes—
37C4⋊#1181—28no—
38C4⋊#1181—24no—
39C4⋊#1181—28no—
40C4×#1181—28no—
41C4×#1181—22no—
42C4×#1181—24no—
43C4×#1181D414yes—
44C4×#1181Q818yescomplemented
45C4⋊C4×C29C2×C414yes—
46C42×C29C2×C411yescharacteristic
47C4⋊Dic29C2×C414yes—
48#90779C2×C418yes—
49C4×Dic29C2×C411yescharacteristic
50C4×Dic29C2×C412yes—
51C22×D29C2411yescharacteristic
52C2×#1181—22no—
53C2×#1181—22no—
54C2×#1181—22no—
55C2×#1181—24no—
56C2×#1181—28no—
57C2×#1181C2×D412yes—
58C2×#1181C2×D412yes—
59C2×#1181C2×Q814yes—
60C2×#1181C2×Q814yes—
61Q8×C29—24no—
62C2×C4×C29C22×C414yes—
63C2×C4×C29C22×C411yescharacteristic
64C2×C4×C29C22×C412yes—
65C2×Dic29C22×C414yes—
66C2×Dic29C22×C411yescharacteristic
67C2×Dic29C22×C412yes—
68C4×D29—24no—
69C4×D29—24no—
70C4×D29C2×D412yes—
71C4×D29C2×Q814yes—
72C4×D29#4112yes—
73C4×D29#4114yes—
74Dic58—24no—
75Dic58—28no—
76C4×C4⋊Q8—291nomaximal, Sylow
77C22×C29C23×C411yescharacteristic
78C2×D29C22×D411yescharacteristic
79C2×D29C22×Q812yes—
80C2×D29C2×#4112yes—
81C2×D29C2×#4111yescharacteristic
82#1181—22no—
83#1181—24no—
84#1181—44no—
85#1181C4⋊Q814yesdirect product factor
86C4×C29—24no—
87C4×C29C4×D412yes—
88C4×C29C4×Q814yescomplemented
89Dic29—24no—
90Dic29C4×D412yes—
91Dic29C4×Q814yescomplemented
92C2×C4⋊Q8—291no—
93C2×C4×Q8—292no—
94#391—292no—
95#389—294no—
96#384—291no—
97C4×C4⋊C4—294no—
98C43—291no—
99C2×C29C2×C4×D411yescharacteristic
100C2×C29C2×C4×Q812yes—
101D29C2×C4⋊Q811yescharacteristic
102D29#53211yescharacteristic
103D29#53312yes—
104C22×Q8—292no—
105C4⋊Q8—292no—
106C4⋊Q8—294no—
107C4⋊Q8—291no—
108C4⋊Q8#118111yescharacteristic, direct product factor
109C4×Q8—588no—
110C2×C4⋊C4—294no—
111C2×C4⋊C4—292no—
112C2×C4⋊C4—294no—
113C2×C4⋊C4—294no—
114C2×C42—291no—
115C2×C42—292no—
116C2×C42—291no—
117C2×C42—294no—
118C2×C42—292no—
119C2×C42—291no—
120#95—298no—
121C29C4×C4⋊Q811yescharacteristic, complemented, Sylow
122C2×Q8—294no—
123C2×Q8—292no—
124C2×Q8—584no—
125C2×Q8—584no—
126C2×Q8C2×#118112yes—
127C22×C4—291no—
128C22×C4—292no—
129C22×C4—291no—
130C22×C4—292no—
131C22×C4—291no—
132C22×C4—294no—
133C22×C4—294no—
134C4⋊C4—298no—
135C4⋊C4—294no—
136C4⋊C4—584no—
137C4⋊C4—588no—
138C4⋊C4—588no—
139C4⋊C4C2×#118114yes—
140C42—294no—
141C42—298no—
142C42—291no—
143C42—292no—
144C42—588no—
145C42—582no—
146C42—584no—
147C42C2×#118111yescharacteristic
148C23—291no—
149Q8—24no—
150Q8—588no—
151Q8—584no—
152C2×C4—292no—
153C2×C4—294no—
154C2×C4—292no—
155C2×C4—291no—
156C2×C4—292no—
157C2×C4—292no—
158C2×C4—294no—
159C2×C4—294no—
160C2×C4—292no—
161C2×C4—294no—
162C2×C4—294no—
163C2×C4—584no—
164C2×C4—584no—
165C2×C4—582no—
166C2×C4—582no—
167C2×C4—582no—
168C2×C4—584no—
169C2×C4—588no—
170C2×C4C22×#118114yes—
171C2×C4C22×#118111yescharacteristic
172C2×C4C22×#118112yes—
173C22—291no—
174C22—291no—
175C22—292no—
176C22—292no—
177C22C23×#118111yescharacteristic
178C4—24no—
179C4—294no—
180C4—292no—
181C4—294no—
182C4—582no—
183C4—584no—
184C4—584no—
185C4—1164no—
186C4D4×#118112yes—
187C4Q8×#118114yescomplemented
188C2—291no—
189C2—291no—
190C2—292no—
191C2C2×D4×#118111yescharacteristic
192C2C2×Q8×#118112yes—
subgroupG/H
center, FrattiniC22C23×#1181
commutator, socleC22×C29C23×C4
FittingC29×C4⋊Q8C4
prime radical, cosocleC22×D29C24
hypercenterC4⋊Q8#1181
hypocenterC29C4×C4⋊Q8
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
18. C29×C4⋊Q8C4semidirect
19. #11745306C4semidirect
21. #11745250C4semidirect
23. #11745231C4semidirect
44. C4×#1181Q8semidirect
85. #1181C4⋊Q8direct (N × H)
88. C4×C29C4×Q8semidirect
91. Dic29C4×Q8semidirect
108. C4⋊Q8#1181direct (N × H)
121. C29C4×C4⋊Q8semidirect
187. C4Q8×#1181semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#11812
(C2×#1181)⋊Q82
#142721142
#142721092
C4⋊C4×#11812
C42×#11812
C4⋊Q8×D292
C4×C4⋊Q829