Finite Group Databasebeta

← C2×#14271161 #16828001

Subgroups — C2×#14271161 #16828001

Order 3712.

816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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×#90807C211yesmaximal, characteristic
2C22×#90772C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D29C211yesmaximal, characteristic, complemented
4#14271161C218yesmaximal, direct product factor
5C2×#11745164C211yesmaximal, characteristic, complemented
6C2×#11745158C211yesmaximal, characteristic, complemented
7C2×#11745180C211yesmaximal, characteristic, complemented
8C2×C29×#102C211yesmaximal, characteristic, complemented
9C22×D4×C29C2211yescharacteristic
10C22×C22⋊D29—21no—
11C23×Dic29—21no—
12C2×#90807—22no—
13C2×#90807—24no—
14C2×#90807C418yescomplemented
15C2×#90807C2214yes—
16C22×C4×D29—21no—
17C22×C4×D29C2211yescharacteristic
18C22×Dic58C2211yescharacteristic
19C22×C8×C29C2211yescharacteristic
20C2×C4⋊C4×C29C2211yescharacteristic
21C2×C4⋊Dic29C2211yescharacteristic
22C2×#90779—21no—
23C22×#6597C2211yescharacteristic
24C2×#90772—24no—
25C2×#90772C2214yescomplemented
26C4⋊C4×D29—22no—
27C4⋊C4×D29C2214yescomplemented
28C29×#102C2214yescomplemented
29#11745180C2214yescomplemented
30#11745164C2214yescomplemented
31#11745158C2214yescomplemented
32C24×C29—21no—
33C23×D29D411yescharacteristic
34C2×D4×C29—21no—
35C2×D4×C29—22no—
36C2×D4×C29C2×C414yescomplemented
37C2×D4×C29C2312yes—
38C22×C4×C29—21no—
39C22×C4×C29C2311yescharacteristic
40C2×C22⋊D29—28no—
41C2×C22⋊D29—24no—
42C22×Dic29—21no—
43C22×Dic29—28no—
44C22×Dic29—24no—
45C22×Dic29—21no—
46C22×Dic29D411yescharacteristic
47#90807—216no—
48#90807—28no—
49#90807C2×C4116yescomplemented
50C2×C4×D29—24no—
51C2×C4×D29—44no—
52C2×C4×D29C2×C414yes—
53C2×C4×D29D412yes—
54C2×C4×D29D414yes—
55C2×C4×D29C2312yes—
56C2×Dic58—21no—
57C2×Dic58—22no—
58C2×Dic58C2×C414yescomplemented
59C2×Dic58C2312yes—
60C2×C8×C29—22no—
61C2×C8×C29C2312yes—
62C4⋊C4×C29—21no—
63C4⋊C4×C29C2312yes—
64C4⋊Dic29—21no—
65C4⋊Dic29C2312yes—
66#90779—24no—
67C2×#6597—22no—
68C2×#6597C2312yes—
69#90772—28no—
70C23×C29—24no—
71C23×C29—22no—
72C23×C29—42no—
73C23×C29—42no—
74C23×C29C2×D411yescharacteristic
75C22×D29—22no—
76C22×D29—22no—
77C22×D29C22⋊C414yes—
78C22×D29C2×D412yes—
79D4×C29—24no—
80D4×C29—22no—
81D4×C29C22×C414yescomplemented
82C2×C4×C29—22no—
83C2×C4×C29—42no—
84C2×C4×C29C22×C412yes—
85C2×C4×C29C2×D411yescharacteristic
86C2×C4×C29C2×D412yes—
87C2×C4×C29C2411yescharacteristic
88C22⋊D29—216no—
89C2×Dic29—24no—
90C2×Dic29—22no—
91C2×Dic29—216no—
92C2×Dic29—22no—
93C2×Dic29—42no—
94C2×Dic29C22⋊C414yes—
95C2×Dic29C2×D412yes—
96C4×D29—48no—
97C4×D29C22⋊C418yes—
98C4×D29C22×C414yes—
99C4×D29C2×D414yes—
100Dic58—24no—
101Dic58—22no—
102Dic58C22×C414yescomplemented
103C8×C29—22no—
104#6597—22no—
105C2×#417—291nomaximal, Sylow
106C22×C29—24no—
107C22×C29—42no—
108C22×C29—42no—
109C22×C29—48no—
110C22×C29C2×C22⋊C412yes—
111C22×C29AGL(1,ℤ/8)12yes—
112C22×C29#13712yes—
113C22×C29C22×D411yescharacteristic
114C2×D29—22no—
115C2×D29—22no—
116C2×D29—28no—
117C2×D29C2×C22⋊C414yes—
118C4×C29—42no—
119C4×C29C2×C22⋊C412yes—
120C4×C29C23×C411yescharacteristic
121C4×C29C22×D411yescharacteristic
122Dic29—24no—
123Dic29—42no—
124Dic29C2×C22⋊C414yes—
125C22×#41—291no—
126C22×M16—291no—
127C22×C4⋊C4—291no—
128#417—298no—
129C2×#103—291no—
130C2×#103—291no—
131C2×#102—291no—
132C2×#102D2911yescharacteristic, complemented
133C2×C29—44no—
134C2×C29#41714yescomplemented
135C2×C29C22×C22⋊C411yescharacteristic
136C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C29C2×#13711yescharacteristic
138D29—24no—
139C2×#41—298no—
140C2×#41—294no—
141C2×#41—582no—
142C2×#41—584no—
143C22×Q8—291no—
144C22×D4—581no—
145C22×D4C2×D2911yescharacteristic
146C23×C4—291no—
147C23×C4—581no—
148C23×C4—581no—
149C2×M16—294no—
150C2×M16—584no—
151C22×C8—291no—
152C22×C8C2×D2911yescharacteristic
153C2×C4⋊C4—291no—
154C2×C4⋊C4—294no—
155C2×C4⋊C4—582no—
156C2×C4⋊C4—581no—
157C2×C4⋊C4C2×D2911yescharacteristic
158#103—294no—
159#103—294no—
160#102—294no—
161#102C2×D2914yescomplemented
162C29C2×#41711yescharacteristic, complemented, Sylow
163C24—21no—
164C24—291no—
165#41—2916no—
166#41—588no—
167#41—5816no—
168C2×Q8—294no—
169C2×Q8—292no—
170C2×Q8—581no—
171C2×Q8—582no—
172C2×D4—22no—
173C2×D4—21no—
174C2×D4—584no—
175C2×D4—588no—
176C2×D4C4×D2914yescomplemented
177C2×D4C22×D2912yes—
178C22×C4—21no—
179C22×C4—291no—
180C22×C4—294no—
181C22×C4—292no—
182C22×C4—294no—
183C22×C4—292no—
184C22×C4—584no—
185C22×C4—584no—
186C22×C4—588no—
187C22×C4—581no—
188C22×C4—581no—
189C22×C4—1164no—
190C22×C4C22×D2911yescharacteristic
191M16—588no—
192C2×C8—22no—
193C2×C8—292no—
194C2×C8—582no—
195C2×C8C22×D2912yes—
196C4⋊C4—21no—
197C4⋊C4—292no—
198C4⋊C4—584no—
199C4⋊C4—581no—
200C4⋊C4C22×D2912yes—
201C23—22no—
202C23—24no—
203C23—42no—
204C23—42no—
205C23—292no—
206C23—294no—
207C23—582no—
208C23—582no—
209C23D4×D2911yescharacteristic
210Q8—294no—
211Q8—582no—
212Q8—584no—
213D4—22no—
214D4—24no—
215D4—5816no—
216D4C2×C4×D2914yescomplemented
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—292no—
220C2×C4—294no—
221C2×C4—294no—
222C2×C4—294no—
223C2×C4—298no—
224C2×C4—5816no—
225C2×C4—582no—
226C2×C4—584no—
227C2×C4—582no—
228C2×C4—1168no—
229C2×C4—1162no—
230C2×C4C2×C4×D2912yes—
231C2×C4D4×D2912yes—
232C2×C4D4×D2911yescharacteristic
233C2×C4C23×D2911yescharacteristic
234C8—22no—
235C8—582no—
236C22—24no—
237C22—48no—
238C22—42no—
239C22—42no—
240C22—294no—
241C22—588no—
242C22—582no—
243C22—582no—
244C22C22⋊C4×D2912yes—
245C22#1174527312yes—
246C22#1174527712yes—
247C22C2×D4×D2911yescharacteristic
248C4—42no—
249C4—294no—
250C4—584no—
251C4—1162no—
252C4C22⋊C4×D2912yes—
253C4C22×C4×D2911yescharacteristic
254C4C2×D4×D2911yescharacteristic
255C2—44no—
256C2—584no—
257C2#1427116114yesdirect product factor
258C2C2×C22⋊C4×D2911yescharacteristic
259C2C2×#1174527311yescharacteristic
260C2C2×#1174527711yescharacteristic
subgroupG/H
centerC23D4×D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
FittingC2×C29×#102C2
socleC23×C29C2×D4
prime radicalC22×#90807C2
cosocleC2×C4×C29C24
hypercenterC2×#102D29
hypocenterC29C2×#417
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×#90772C2semidirect
3. C2×C4⋊C4×D29C2semidirect
4. #14271161C2direct (N × H)
5. C2×#11745164C2semidirect
6. C2×#11745158C2semidirect
7. C2×#11745180C2semidirect
8. C2×C29×#102C2semidirect
14. C2×#90807C4semidirect
25. C2×#90772C22semidirect
27. C4⋊C4×D29C22semidirect
28. C29×#102C22semidirect
29. #11745180C22semidirect
30. #11745164C22semidirect
31. #11745158C22semidirect
36. C2×D4×C29C2×C4semidirect
49. #90807C2×C4semidirect
58. C2×Dic58C2×C4semidirect
81. D4×C29C22×C4semidirect
102. Dic58C22×C4semidirect
132. C2×#102D29semidirect
134. C2×C29#417semidirect
161. #102C2×D29semidirect
162. C29C2×#417semidirect
176. C2×D4C4×D29semidirect
216. D4C2×C4×D29semidirect
257. C2#14271161direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#908072
C22×#907722
C2×C4⋊C4×D292
#142711612
C2×#117451642
C2×#117451582
C2×#117451802
C2×C29×#1022
C2×#41729