Finite Group Databasebeta

← C22×D4×#1181 #16836466

Subgroups — C22×D4×#1181 #16836466

Order 3712.

2528 conjugacy classes of subgroups; only the 850 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 850 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
1C24×#1181C212yesmaximal, complemented
2C2×D4×#1181C2124yesmaximal, direct product factor
3C22×C4⋊#1181C211yesmaximal, characteristic, complemented
4C22×C22⋊#1181C212yesmaximal, complemented
5C22×C4×#1181C211yesmaximal, characteristic, complemented
6C22×D4×D29C211yesmaximal, characteristic
7C24×D29C2212yes—
8C23×#1181—216no—
9C23×#1181C2211yescharacteristic
10C23×#1181C2212yes—
11C23×#1181C2211yescharacteristic
12C23×#1181C22124yescomplemented
13C22×D4×C29C411yescharacteristic, complemented
14C22×C22⋊D29C412yescomplemented
15C2×D4×D29C4112yescomplemented
16C2×D4×D29C22112yes—
17C22×D116C411yescharacteristic, complemented
18C22×C4×D29C2211yescharacteristic
19C2×C22⋊#1181C22124yescomplemented
20D4×#1181C22164yesdirect product factor
21C2×C4⋊#1181C22112yescomplemented
22C2×C4×#1181C22112yescomplemented
23C24×C29C2×C412yescomplemented
24C23×D29—28no—
25C23×D29—28no—
26C23×D29C2×C4112yescomplemented
27C23×D29C2×C412yescomplemented
28C23×D29C23112yes—
29C23×D29C2311yescharacteristic
30C22×#1181—28no—
31C22×#1181—24no—
32C22×#1181—296no—
33C22×#1181D418yesdirect product factor
34C22×#1181C2316yes—
35C22×#1181C23112yes—
36C22×#1181C2316yes—
37C22×#1181C23132yescomplemented
38C2×D4×C29C2×C4112yescomplemented
39C22×C4×C29C2×C411yescharacteristic, complemented
40C2×C22⋊D29C2×C4124yescomplemented
41C22×Dic29C2×C411yescharacteristic, complemented
42D4×D29C2×C4148yescomplemented
43D4×D29C23116yes—
44C2×D116C2×C4112yescomplemented
45C2×C4×D29C2×C416yescomplemented
46C2×C4×D29C2316yes—
47C22⋊#1181C23132yescomplemented
48C4⋊#1181C23116yescomplemented
49C4×#1181C23116yescomplemented
50C23×C29—28no—
51C23×C29C22×C411yescharacteristic
52C23×C29C22×C4112yescomplemented
53C22×D29—28no—
54C22×D29—248no—
55C22×D29—224no—
56C22×D29—224no—
57C22×D29C22×C413yes—
58C22×D29C22×C4124yescomplemented
59C22×D29C22×C4112yescomplemented
60C22×D29C2×D414yes—
61C22×D29#4114yes—
62C22×D29C2418yes—
63C22×D29C2413yes—
64C2×#1181—224no—
65C2×#1181—212no—
66C2×#1181—264no—
67C2×#1181C2×D4124yesdirect product factor
68C2×#1181C2414yes—
69C2×#1181C2418yes—
70C2×#1181C2414yes—
71D4×C29C22×C4116yescomplemented
72C2×C4×C29C22×C416yescomplemented
73C22⋊D29C22×C4132yescomplemented
74C2×Dic29C22×C416yescomplemented
75D116C22×C4116yescomplemented
76C4×D29C22×C4112yescomplemented
77C4×D29C2414yes—
78C22×C4×D4—291nomaximal, Sylow
79C22×C29—224no—
80C22×C29C4×D414yescomplemented
81C22×C29C23×C413yes—
82C22×C29C23×C418yescomplemented
83C2×D29—224no—
84C2×D29—248no—
85C2×D29—28no—
86C2×D29—28no—
87C2×D29C4×D4112yescomplemented
88C2×D29C23×C413yes—
89C2×D29C23×C418yescomplemented
90C2×D29C22×D416yes—
91C2×D29C2×#4116yes—
92C2×D29C2511yescharacteristic
93#1181—28no—
94#1181—24no—
95#1181C22×D418yesdirect product factor
96C4×C29C23×C414yescomplemented
97Dic29C23×C414yescomplemented
98C23×D4—291no—
99C24×C4—292no—
100C2×C4×D4—2924no—
101C22×C4⋊C4—291no—
102C22×C22⋊C4—292no—
103C22×C42—291no—
104C2×C29—28no—
105C2×C29C2×C4×D416yescomplemented
106C2×C29C24×C411yescharacteristic
107D29—28no—
108D29C2×C4×D416yescomplemented
109D29C23×D411yescharacteristic
110D29C22×#4111yescharacteristic
111C25—292no—
112C22×D4—292no—
113C22×D4—2912no—
114C22×D4—2912no—
115C22×D4—291no—
116C22×D4#118111yescharacteristic, direct product factor
117C23×C4—291no—
118C23×C4—291no—
119C23×C4—291no—
120C23×C4—292no—
121C23×C4—2924no—
122C23×C4—5816no—
123C4×D4—2964no—
124C2×C4⋊C4—2912no—
125C2×C22⋊C4—2924no—
126C2×C42—2912no—
127C29C22×C4×D411yescharacteristic, complemented, Sylow
128C24—291no—
129C24—292no—
130C24—2912no—
131C24—2912no—
132C24—588no—
133C24—588no—
134C24C2×#118112yescomplemented
135C2×D4—2924no—
136C2×D4—2916no—
137C2×D4—2948no—
138C2×D4—2912no—
139C2×D4C2×#1181112yesdirect product factor
140C22×C4—296no—
141C22×C4—298no—
142C22×C4—291no—
143C22×C4—296no—
144C22×C4—296no—
145C22×C4—296no—
146C22×C4—2912no—
147C22×C4—2932no—
148C22×C4—5896no—
149C22×C4—588no—
150C22×C4—584no—
151C22×C4C2×#118111yescharacteristic, complemented
152C4⋊C4—2916no—
153C22⋊C4—2932no—
154C42—2916no—
155C23—28no—
156C23—294no—
157C23—294no—
158C23—293no—
159C23—293no—
160C23—2912no—
161C23—298no—
162C23—2924no—
163C23—5824no—
164C23—5824no—
165C23—5848no—
166C23—588no—
167C23C22×#118111yescharacteristic
168C23C22×#1181112yescomplemented
169D4—2932no—
170D4—2916no—
171D4C22×#1181116yesdirect product factor
172C2×C4—294no—
173C2×C4—2924no—
174C2×C4—296no—
175C2×C4—294no—
176C2×C4—2912no—
177C2×C4—294no—
178C2×C4—298no—
179C2×C4—5864no—
180C2×C4—5824no—
181C2×C4—5812no—
182C2×C4C22×#118116yescomplemented
183C22—224no—
184C22—296no—
185C22—296no—
186C22—2912no—
187C22—291no—
188C22—293no—
189C22—298no—
190C22—588no—
191C22—588no—
192C22—5848no—
193C22—5824no—
194C22D4×#118114yesdirect product factor
195C22C23×#118113yes—
196C22C23×#118118yescomplemented
197C4—298no—
198C4—294no—
199C4—588no—
200C4—584no—
201C4C23×#118114yescomplemented
202C2—28no—
203C2—291no—
204C2—291no—
205C2—296no—
206C2—588no—
207C2C2×D4×#118116yesdirect product factor
208C2C24×#118111yescharacteristic
subgroupG/H
centerC23C22×#1181
commutatorC2×C29C24×C4
FrattiniC2C24×#1181
FittingC22×D4×C29C4
socleC23×C29C22×C4
prime radicalC22×D4×D29C2
cosocleC2×D29C25
hypercenterC22×D4#1181
hypocenterC29C22×C4×D4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×#1181C2semidirect
2. C2×D4×#1181C2direct (N × H)
3. C22×C4⋊#1181C2semidirect
4. C22×C22⋊#1181C2semidirect
5. C22×C4×#1181C2semidirect
12. C23×#1181C22semidirect
13. C22×D4×C29C4semidirect
14. C22×C22⋊D29C4semidirect
15. C2×D4×D29C4semidirect
17. C22×D116C4semidirect
19. C2×C22⋊#1181C22semidirect
20. D4×#1181C22direct (N × H)
21. C2×C4⋊#1181C22semidirect
22. C2×C4×#1181C22semidirect
23. C24×C29C2×C4semidirect
26. C23×D29C2×C4semidirect
27. C23×D29C2×C4semidirect
33. C22×#1181D4direct (N × H)
37. C22×#1181C23semidirect
38. C2×D4×C29C2×C4semidirect
39. C22×C4×C29C2×C4semidirect
40. C2×C22⋊D29C2×C4semidirect
41. C22×Dic29C2×C4semidirect
42. D4×D29C2×C4semidirect
44. C2×D116C2×C4semidirect
45. C2×C4×D29C2×C4semidirect
47. C22⋊#1181C23semidirect
48. C4⋊#1181C23semidirect
49. C4×#1181C23semidirect
52. C23×C29C22×C4semidirect
58. C22×D29C22×C4semidirect
59. C22×D29C22×C4semidirect
67. C2×#1181C2×D4direct (N × H)
71. D4×C29C22×C4semidirect
72. C2×C4×C29C22×C4semidirect
73. C22⋊D29C22×C4semidirect
74. C2×Dic29C22×C4semidirect
75. D116C22×C4semidirect
76. C4×D29C22×C4semidirect
80. C22×C29C4×D4semidirect
82. C22×C29C23×C4semidirect
87. C2×D29C4×D4semidirect
89. C2×D29C23×C4semidirect
95. #1181C22×D4direct (N × H)
96. C4×C29C23×C4semidirect
97. Dic29C23×C4semidirect
105. C2×C29C2×C4×D4semidirect
108. D29C2×C4×D4semidirect
116. C22×D4#1181direct (N × H)
127. C29C22×C4×D4semidirect
134. C24C2×#1181semidirect
139. C2×D4C2×#1181direct (N × H)
151. C22×C4C2×#1181semidirect
168. C23C22×#1181semidirect
171. D4C22×#1181direct (N × H)
182. C2×C4C22×#1181semidirect
194. C22D4×#1181direct (N × H)
196. C22C23×#1181semidirect
201. C4C23×#1181semidirect
207. C2C2×D4×#1181direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#11812
C2×D4×#11812
C22×C4⋊#11812
C22×C22⋊#11812
C22×C4×#11812
C22×D4×D292
C22×C4×D429