Finite Group Databasebeta

← C2×#20292947 #28346362

Subgroups — C2×#20292947 #28346362

Order 13696.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812084C211yesmaximal, characteristic
2C2×C4⋊C4×D107C211yesmaximal, characteristic, complemented
3#20292947C218yesmaximal, direct product factor
4C2×#16812040C211yesmaximal, characteristic, complemented
5C2×#16812031C211yesmaximal, characteristic, complemented
6C2×#16812029C211yesmaximal, characteristic, complemented
7C2×(C2×D107)⋊C8C211yesmaximal, characteristic, complemented
8C2×#106×C107C211yesmaximal, characteristic, complemented
9C22×D428—21no—
10C22×D428C2211yescharacteristic
11C22×C4×D107—21no—
12C22×C4×D107C2211yescharacteristic
13C22×C107⋊C8C2211yescharacteristic
14#16812084—22no—
15#16812084C2214yes—
16C2×C4⋊Dic107C2211yescharacteristic
17C2×Dic107⋊C4—21no—
18C4⋊C4×D107—22no—
19C4⋊C4×D107C2214yescomplemented
20C2×(C2×D107)⋊C4—21no—
21#16812040C2214yescomplemented
22#16812031C2214yescomplemented
23#16812029C2214yescomplemented
24(C2×D107)⋊C8C2214yescomplemented
25C22×C8×C107C2211yescharacteristic
26C2×C4⋊C4×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28#106×C107C2214yescomplemented
29C23×D107—21no—
30C23×D107D411yescharacteristic
31C2×D428—22no—
32C2×D428—22no—
33C2×D428—24no—
34C2×D428—21no—
35C2×D428—44no—
36C2×D428C2312yes—
37C22×Dic107—21no—
38C22×Dic107D411yescharacteristic
39C2×C4×D107—22no—
40C2×C4×D107—22no—
41C2×C4×D107—24no—
42C2×C4×D107—44no—
43C2×C4×D107D412yes—
44C2×C4×D107C2312yes—
45C2×C107⋊C8—22no—
46C2×C107⋊C8C2312yes—
47C4⋊Dic107—21no—
48C4⋊Dic107C2312yes—
49Dic107⋊C4—24no—
50(C2×D107)⋊C4—24no—
51C22×C4×C107—21no—
52C22×C4×C107—21no—
53C22×C4×C107C2311yescharacteristic
54C2×C8×C107—22no—
55C2×C8×C107C2312yes—
56C4⋊C4×C107—21no—
57C4⋊C4×C107—21no—
58C4⋊C4×C107C2312yes—
59C4⋊C4×C107C2312yes—
60C23×C107C2×D411yescharacteristic
61C22×D107—22no—
62C22×D107—22no—
63C22×D107—22no—
64C22×D107—42no—
65C22×D107—42no—
66C22×D107—42no—
67C22×D107SD1614yes—
68C22×D107C2×D412yes—
69C2×C4×C107—22no—
70C2×C4×C107—22no—
71C2×C4×C107—42no—
72C2×C4×C107—42no—
73C2×C4×C107C2×D411yescharacteristic
74C2×C4×C107#4112yes—
75C2×C4×C107#4112yes—
76C2×C4×C107C2411yescharacteristic
77C2×Dic107—22no—
78C2×Dic107—22no—
79C2×Dic107—42no—
80C2×Dic107C2×D412yes—
81D428—22no—
82D428—22no—
83D428—48no—
84D428—42no—
85C4×D107—24no—
86C4×D107—22no—
87C4×D107—22no—
88C4×D107—48no—
89C8×C107—22no—
90C107⋊C8—22no—
91C22×C107#12312yes—
92C22×C107C2×SD1612yes—
93C22×C107AGL(1,ℤ/8)12yes—
94C22×C107C22×D411yescharacteristic
95C2×D107—22no—
96C2×D107—22no—
97C2×D107—28no—
98C2×D107—42no—
99C2×D107—42no—
100C2×D107—42no—
101C2×D107—84no—
102C2×D107C2×SD1614yes—
103C4×C107—42no—
104C4×C107—42no—
105C4×C107#12312yes—
106C4×C107C2×#4111yescharacteristic
107C4×C107C2×#4111yescharacteristic
108Dic107—22no—
109Dic107—42no—
110C2×C107#48114yescomplemented
111C2×C107C2×#12311yescharacteristic
112C2×C107C22×SD1611yescharacteristic
113C2×C107C2×AGL(1,ℤ/8)11yescharacteristic
114D107—24no—
115D107—82no—
116C2×#481—1071nomaximal, Sylow
117C107C2×#48111yescharacteristic, complemented, Sylow
118C2×#121—1071no—
119C22×C4⋊C4—1071no—
120#481—1078no—
121C2×#106—1071no—
122C2×#106D10711yescharacteristic, complemented
123C2×#102—1071no—
124C2×#102—1071no—
125C2×C22⋊C8—1071no—
126C22×D4—1071no—
127C22×D4—2141no—
128C23×C4—1071no—
129C23×C4—2141no—
130C22×C8—1071no—
131C22×C8C2×D10711yescharacteristic
132#121—1074no—
133#121—2142no—
134C2×C4⋊C4—1071no—
135C2×C4⋊C4—1074no—
136C2×C4⋊C4—2142no—
137C2×C4⋊C4—2141no—
138C2×C4⋊C4C2×D10711yescharacteristic
139C2×C4⋊C4C2×D10711yescharacteristic
140C2×C22⋊C4—2141no—
141#106—1074no—
142#106C2×D10714yescomplemented
143#102—1074no—
144#102—1074no—
145C22⋊C8—1074no—
146C24—1071no—
147C24—2141no—
148C2×D4—1072no—
149C2×D4—4284no—
150C2×D4—2144no—
151C2×D4—2141no—
152C2×D4—2142no—
153C2×D4—2142no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—1071no—
157C22×C4—1072no—
158C22×C4—1072no—
159C22×C4—4284no—
160C22×C4—2144no—
161C22×C4—2141no—
162C22×C4—2142no—
163C22×C4—2142no—
164C22×C4C22×D10711yescharacteristic
165C2×C8—22no—
166C2×C8—1072no—
167C2×C8—2142no—
168C2×C8C22×D10712yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—1072no—
172C4⋊C4—2144no—
173C4⋊C4—2141no—
174C4⋊C4C22×D10712yes—
175C4⋊C4C22×D10712yes—
176C22⋊C4—2144no—
177C23—1074no—
178C23—1072no—
179C23—4282no—
180C23—4282no—
181C23—4282no—
182C23—2142no—
183C23—2142no—
184C23—2142no—
185C23D4×D10711yescharacteristic
186D4—4288no—
187D4—4282no—
188D4—2142no—
189D4—2142no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—1072no—
195C2×C4—4288no—
196C2×C4—4282no—
197C2×C4—2142no—
198C2×C4—2142no—
199C2×C4—2144no—
200C2×C4—2142no—
201C2×C4—2142no—
202C2×C4D4×D10711yescharacteristic
203C2×C4#1313381812yes—
204C2×C4#1313381912yes—
205C2×C4C23×D10711yescharacteristic
206C8—22no—
207C8—2142no—
208C22—8564no—
209C22—1074no—
210C22—4282no—
211C22—4282no—
212C22—4282no—
213C22—2142no—
214C22—2142no—
215C22—2148no—
216C22#1681209412yes—
217C22SD16×D10712yes—
218C22#1681213612yes—
219C22C2×D4×D10711yescharacteristic
220C4—42no—
221C4—42no—
222C4—4282no—
223C4—2142no—
224C4#1681209412yes—
225C4C2×#1313381811yescharacteristic
226C4C2×#1313381911yescharacteristic
227C2—8562no—
228C2—2144no—
229C2#2029294714yesdirect product factor
230C2C2×#1681209411yescharacteristic
231C2C2×SD16×D10711yescharacteristic
232C2C2×#1681213611yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#106×C107C2
socleC23×C107C2×D4
prime radicalC2×#16812084C2
hypercenterC2×#106D107
hypocenterC107C2×#481
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D107C2semidirect
3. #20292947C2direct (N × H)
4. C2×#16812040C2semidirect
5. C2×#16812031C2semidirect
6. C2×#16812029C2semidirect
7. C2×(C2×D107)⋊C8C2semidirect
8. C2×#106×C107C2semidirect
19. C4⋊C4×D107C22semidirect
21. #16812040C22semidirect
22. #16812031C22semidirect
23. #16812029C22semidirect
24. (C2×D107)⋊C8C22semidirect
28. #106×C107C22semidirect
110. C2×C107#481semidirect
117. C107C2×#481semidirect
122. C2×#106D107semidirect
142. #106C2×D107semidirect
229. C2#20292947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168120842
C2×C4⋊C4×D1072
#202929472
C2×#168120402
C2×#168120312
C2×#168120292
C2×(C2×D107)⋊C82
C2×#106×C1072
C2×#481107