Finite Group Databasebeta

← C2×#14271410 #16829081

Subgroups — C2×#14271410 #16829081

Order 3712.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×#90773C211yesmaximal, characteristic, complemented
2C22×#90772C211yesmaximal, characteristic, complemented
3C2×#11745259C211yesmaximal, characteristic, complemented
4C2×#11745257C211yesmaximal, characteristic
5#14271410C218yesmaximal, direct product factor
6C2×#11745158C211yesmaximal, characteristic, complemented
7C2×#11745157C211yesmaximal, characteristic, complemented
8C2×C29×#107C211yesmaximal, characteristic, complemented
9C22×D116—21no—
10C22×D116C2211yescharacteristic
11C22×C4×D29C2211yescharacteristic
12C22×Dic58C2211yescharacteristic
13C22×C8×C29C2211yescharacteristic
14C2×C4⋊C4×C29C2211yescharacteristic
15C2×C4⋊C4×C29C2211yescharacteristic
16C2×#90781—21no—
17C2×#90781—21no—
18C2×C4⋊Dic29—21no—
19C22×#6597C2211yescharacteristic
20C2×#90773—24no—
21C2×#90773C2214yescomplemented
22C2×#90772—24no—
23C2×#90772C2214yescomplemented
24#11745259—22no—
25#11745259C2214yescomplemented
26#11745257—22no—
27#11745257C2214yes—
28C29×#107C2214yescomplemented
29#11745158C2214yescomplemented
30#11745157C2214yescomplemented
31C23×D29—21no—
32C23×D29D411yescharacteristic
33C22×C4×C29—21no—
34C22×C4×C29—21no—
35C22×C4×C29C2311yescharacteristic
36C22×Dic29—21no—
37C22×Dic29D411yescharacteristic
38C2×D116—22no—
39C2×D116—22no—
40C2×D116—24no—
41C2×D116—21no—
42C2×D116—44no—
43C2×D116C2312yes—
44C2×C4×D29—22no—
45C2×C4×D29—22no—
46C2×C4×D29D412yes—
47C2×C4×D29C2312yes—
48C2×Dic58—22no—
49C2×Dic58—22no—
50C2×Dic58—21no—
51C2×Dic58C2312yes—
52C2×C8×C29D414yescomplemented
53C2×C8×C29C2312yes—
54C4⋊C4×C29—21no—
55C4⋊C4×C29—21no—
56C4⋊C4×C29C2312yes—
57C4⋊C4×C29C2312yes—
58#90781—24no—
59#90781—24no—
60C4⋊Dic29—24no—
61C2×#6597—22no—
62C2×#6597C2312yes—
63#90773—28no—
64#90772—28no—
65C23×C29C2×D411yescharacteristic
66C22×D29—22no—
67C22×D29—22no—
68C22×D29—22no—
69C22×D29—22no—
70C22×D29—42no—
71C22×D29—42no—
72C22×D29—42no—
73C22×D29C2×D412yes—
74C2×C4×C29—22no—
75C2×C4×C29—22no—
76C2×C4×C29—42no—
77C2×C4×C29—42no—
78C2×C4×C29C2×D412yes—
79C2×C4×C29C2×D411yescharacteristic
80C2×C4×C29#4112yes—
81C2×C4×C29C2411yescharacteristic
82C2×Dic29—22no—
83C2×Dic29—22no—
84C2×Dic29—42no—
85C2×Dic29C2×D412yes—
86D116—22no—
87D116—22no—
88D116—48no—
89D116—42no—
90C4×D29—24no—
91C4×D29—22no—
92C4×D29—22no—
93Dic58—22no—
94Dic58—22no—
95Dic58—42no—
96C8×C29C2×D414yescomplemented
97#6597—22no—
98C2×#468—291nomaximal, Sylow
99C22×C29#12112yes—
100C22×C29AGL(1,ℤ/8)12yes—
101C22×C29#13712yes—
102C22×C29C22×D411yescharacteristic
103C2×D29—22no—
104C2×D29—22no—
105C2×D29—22no—
106C2×D29—44no—
107C2×D29—42no—
108C2×D29—42no—
109C2×D29—42no—
110C2×D29—84no—
111C4×C29—42no—
112C4×C29—42no—
113C4×C29#12112yes—
114C4×C29C22×D411yescharacteristic
115C4×C29C2×#4111yescharacteristic
116Dic29—22no—
117Dic29—42no—
118C22×SD16—291no—
119C22×M16—291no—
120C2×C22⋊Q8—291no—
121C2×#121—291no—
122#468—298no—
123C2×#107D2911yescharacteristic, complemented
124C2×#103—291no—
125C2×#102—291no—
126C2×C29#46814yescomplemented
127C2×C29C2×#12111yescharacteristic
128C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C29C2×#13711yescharacteristic
130D29—42no—
131D29—82no—
132C22×Q8—291no—
133C22×D4—291no—
134C22×D4—581no—
135C23×C4—291no—
136C2×SD16—294no—
137C2×SD16—584no—
138C2×M16—294no—
139C2×M16—584no—
140C22×C8—291no—
141C22×C8C2×D2911yescharacteristic
142C22⋊Q8—294no—
143C22⋊Q8—582no—
144#121—294no—
145#121—582no—
146C2×C4⋊C4—581no—
147C2×C4⋊C4C2×D2911yescharacteristic
148C2×C4⋊C4C2×D2911yescharacteristic
149C2×C22⋊C4—581no—
150C2×C22⋊C4—581no—
151#107C2×D2914yescomplemented
152#103—294no—
153#102—294no—
154C29C2×#46811yescharacteristic, complemented, Sylow
155C24—291no—
156C24—581no—
157C2×Q8—292no—
158C2×Q8—581no—
159C2×Q8—582no—
160C2×Q8—582no—
161C2×D4—292no—
162C2×D4—584no—
163C2×D4—582no—
164C2×D4—581no—
165C2×D4—582no—
166C2×D4—1164no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—291no—
170C22×C4—292no—
171C22×C4—292no—
172C22×C4—582no—
173C22×C4—582no—
174C22×C4—581no—
175C22×C4C22×D2911yescharacteristic
176SD16—588no—
177M16—588no—
178C2×C8—292no—
179C2×C8—582no—
180C2×C8D11614yescomplemented
181C2×C8C22×D2912yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—584no—
185C4⋊C4C22×D2912yes—
186C4⋊C4C22×D2912yes—
187C22⋊C4—584no—
188C22⋊C4—584no—
189C23—292no—
190C23—582no—
191C23—582no—
192C23—582no—
193C23—582no—
194C23—1162no—
195C23—1162no—
196C23—1162no—
197C23D4×D2911yescharacteristic
198Q8—582no—
199Q8—582no—
200Q8—1162no—
201D4—582no—
202D4—582no—
203D4—1168no—
204D4—1162no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—292no—
210C2×C4—582no—
211C2×C4—582no—
212C2×C4—582no—
213C2×C4—584no—
214C2×C4—582no—
215C2×C4—1162no—
216C2×C4C2×D11612yes—
217C2×C4D4×D2911yescharacteristic
218C2×C4#9080912yes—
219C2×C4C23×D2911yescharacteristic
220C8—582no—
221C8C2×D11614yescomplemented
222C22—582no—
223C22—582no—
224C22—582no—
225C22—1164no—
226C22—1162no—
227C22—1162no—
228C22—1162no—
229C22—2324no—
230C22#1174525712yes—
231C22#1174527312yes—
232C22#1174528012yes—
233C22C2×D4×D2911yescharacteristic
234C4—42no—
235C4—42no—
236C4—582no—
237C4—1162no—
238C4#1174525712yes—
239C4C22×D11611yescharacteristic
240C4C2×#9080911yescharacteristic
241C2—1162no—
242C2—2322no—
243C2#1427141014yesdirect product factor
244C2C2×#1174525711yescharacteristic
245C2C2×#1174527311yescharacteristic
246C2C2×#1174528011yescharacteristic
subgroupG/H
centerC23D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#107C2
socleC23×C29C2×D4
prime radicalC2×#11745257C2
hypercenterC2×#107D29
hypocenterC29C2×#468
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#90773C2semidirect
2. C22×#90772C2semidirect
3. C2×#11745259C2semidirect
5. #14271410C2direct (N × H)
6. C2×#11745158C2semidirect
7. C2×#11745157C2semidirect
8. C2×C29×#107C2semidirect
21. C2×#90773C22semidirect
23. C2×#90772C22semidirect
25. #11745259C22semidirect
28. C29×#107C22semidirect
29. #11745158C22semidirect
30. #11745157C22semidirect
52. C2×C8×C29D4semidirect
96. C8×C29C2×D4semidirect
123. C2×#107D29semidirect
126. C2×C29#468semidirect
151. #107C2×D29semidirect
154. C29C2×#468semidirect
180. C2×C8D116semidirect
221. C8C2×D116semidirect
243. C2#14271410direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#907732
C22×#907722
C2×#117452592
C2×#117452572
#142714102
C2×#117451582
C2×#117451572
C2×C29×#1072
C2×#46829