Finite Group Databasebeta

← C2×#20292855 #28346020

Subgroups — C2×#20292855 #28346020

Order 13696.

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

normal subgroups only

This group has 564 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×#13133806C211yesmaximal, characteristic, complemented
2C22×C8×D107C211yesmaximal, characteristic, complemented
3C2×#16812089C211yesmaximal, characteristic, complemented
4C2×#16812080C211yesmaximal, characteristic
5#20292855C218yesmaximal, direct product factor
6C2×#16812040C211yesmaximal, characteristic, complemented
7C2×#16812034C211yesmaximal, characteristic, complemented
8C2×#102×C107C211yesmaximal, characteristic, complemented
9C22×Dic214C2211yescharacteristic
10C22×C22⋊D107—21no—
11C22×C4×D107C2211yescharacteristic
12C2×#13133806—24no—
13C2×#13133806C2214yescomplemented
14C22×C107⋊C8C2211yescharacteristic
15C2×C8×D107—24no—
16C2×C8×D107C2214yescomplemented
17#16812089—22no—
18#16812089C2214yescomplemented
19#16812080—22no—
20#16812080C2214yes—
21C2×C4⋊Dic107—21no—
22C2×C4⋊Dic107C2211yescharacteristic
23C2×C22⋊Dic107—21no—
24C2×(C2×D107)⋊C4—21no—
25#16812040C2214yescomplemented
26#16812034C2214yescomplemented
27C22×D4×C107C2211yescharacteristic
28C22×C8×C107C2211yescharacteristic
29C2×C4⋊C4×C107C2211yescharacteristic
30#102×C107C2214yescomplemented
31C23×D107D411yescharacteristic
32C2×Dic214—22no—
33C2×Dic214—22no—
34C2×Dic214—21no—
35C2×Dic214C2312yes—
36C2×C22⋊D107—24no—
37C2×C22⋊D107—44no—
38C22×Dic107—21no—
39C22×Dic107—21no—
40C22×Dic107D411yescharacteristic
41C2×C4×D107—22no—
42C2×C4×D107—22no—
43C2×C4×D107D412yes—
44C2×C4×D107C2312yes—
45#13133806—28no—
46C2×C107⋊C8D414yescomplemented
47C2×C107⋊C8C2312yes—
48C8×D107—28no—
49C4⋊Dic107—21no—
50C4⋊Dic107—24no—
51C4⋊Dic107C2312yes—
52C22⋊Dic107—24no—
53(C2×D107)⋊C4—24no—
54C24×C107—21no—
55C2×D4×C107—22no—
56C2×D4×C107—21no—
57C2×D4×C107—22no—
58C2×D4×C107C2312yes—
59C22×C4×C107—21no—
60C22×C4×C107C2311yescharacteristic
61C2×C8×C107—22no—
62C2×C8×C107C2312yes—
63C4⋊C4×C107—21no—
64C4⋊C4×C107C2312yes—
65C23×C107—22no—
66C23×C107—42no—
67C23×C107—42no—
68C23×C107—42no—
69C23×C107C2×D411yescharacteristic
70C22×D107—22no—
71C22×D107—22no—
72C22×D107SD1614yescomplemented
73C22×D107C2×D412yes—
74D4×C107—22no—
75D4×C107—22no—
76D4×C107—42no—
77C2×C4×C107—22no—
78C2×C4×C107—42no—
79C2×C4×C107C2×D411yescharacteristic
80C2×C4×C107C2×D412yes—
81C2×C4×C107#4112yes—
82C2×C4×C107C2411yescharacteristic
83C22⋊D107—48no—
84C2×Dic107—22no—
85C2×Dic107—22no—
86C2×Dic107—22no—
87C2×Dic107—42no—
88C2×Dic107—42no—
89C2×Dic107C2×D412yes—
90C4×D107—24no—
91C4×D107—22no—
92C4×D107—22no—
93Dic214—22no—
94Dic214—22no—
95Dic214—42no—
96C8×C107—22no—
97C107⋊C8C2×D414yescomplemented
98C22×C107—42no—
99C22×C107—42no—
100C22×C107—42no—
101C22×C107—84no—
102C22×C107#12112yes—
103C22×C107C2×SD1612yes—
104C22×C107#13512yes—
105C22×C107C22×D411yescharacteristic
106C2×D107—22no—
107C2×D107—22no—
108C2×D107—28no—
109C2×D107C2×SD1614yescomplemented
110C4×C107—42no—
111C4×C107#12112yes—
112C4×C107C22×D411yescharacteristic
113C4×C107C2×#4111yescharacteristic
114Dic107—22no—
115Dic107—42no—
116Dic107—42no—
117C2×C107—82no—
118C2×C107#46514yescomplemented
119C2×C107C2×#12111yescharacteristic
120C2×C107C22×SD1611yescharacteristic
121C2×C107C2×#13511yescharacteristic
122D107—24no—
123C2×#465—1071nomaximal, Sylow
124C107C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—1071no—
126C23×C8—1071no—
127C2×C22⋊Q8—1071no—
128C2×#121—1071no—
129#465—1078no—
130C2×#106—1071no—
131C2×#103—1071no—
132C2×#102D10711yescharacteristic, complemented
133C22×Q8—1071no—
134C22×D4—2141no—
135C22×D4C2×D10711yescharacteristic
136C23×C4—1071no—
137C2×SD16—1074no—
138C2×SD16—2144no—
139C22×C8—1071no—
140C22×C8—1074no—
141C22×C8—2144no—
142C22×C8C2×D10711yescharacteristic
143C22⋊Q8—1074no—
144C22⋊Q8—2142no—
145#121—1074no—
146#121—2142no—
147C2×C4⋊C4—1071no—
148C2×C4⋊C4—2141no—
149C2×C4⋊C4C2×D10711yescharacteristic
150C2×C22⋊C4—2141no—
151C2×C22⋊C4—2141no—
152#106—1074no—
153#103—1074no—
154#102C2×D10714yescomplemented
155C24—21no—
156C24—1071no—
157C2×Q8—1072no—
158C2×Q8—2142no—
159C2×Q8—2142no—
160C2×Q8—2141no—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—4284no—
165C2×D4—2144no—
166C2×D4C22×D10712yes—
167C22×C4—21no—
168C22×C4—1071no—
169C22×C4—1072no—
170C22×C4—1072no—
171C22×C4—2141no—
172C22×C4—2141no—
173C22×C4—2142no—
174C22×C4—2142no—
175C22×C4C22×D10711yescharacteristic
176SD16—2148no—
177C2×C8—22no—
178C2×C8—1074no—
179C2×C8—1072no—
180C2×C8—2148no—
181C2×C8C22×D10712yes—
182C4⋊C4—21no—
183C4⋊C4—1072no—
184C4⋊C4—2144no—
185C4⋊C4—2141no—
186C4⋊C4C22×D10712yes—
187C22⋊C4—2144no—
188C22⋊C4—2144no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—1074no—
194C23—1072no—
195C23—2142no—
196C23—2142no—
197C23D4×D10711yescharacteristic
198Q8—4282no—
199Q8—2142no—
200Q8—2142no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—4288no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—1072no—
208C2×C4—4282no—
209C2×C4—4282no—
210C2×C4—2142no—
211C2×C4—2142no—
212C2×C4—2142no—
213C2×C4—2144no—
214C2×C4—2142no—
215C2×C4—2142no—
216C2×C4D4×D10711yescharacteristic
217C2×C4D4×D10712yes—
218C2×C4#1313381812yes—
219C2×C4C23×D10711yescharacteristic
220C8—22no—
221C8—1074no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—1074no—
227C22—2142no—
228C22—2148no—
229C22—2142no—
230C22#1681208212yes—
231C22SD16×D10712yes—
232C22#1681212812yes—
233C22C2×D4×D10711yescharacteristic
234C4—42no—
235C4—4282no—
236C4—4282no—
237C4—2142no—
238C4#1681208212yes—
239C4C2×D4×D10711yescharacteristic
240C4C2×#1313381811yescharacteristic
241C2—82no—
242C2—2144no—
243C2#2029285514yesdirect product factor
244C2C2×#1681208211yescharacteristic
245C2C2×SD16×D10711yescharacteristic
246C2C2×#1681212811yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#102×C107C2
socleC23×C107C2×D4
prime radicalC2×#16812080C2
hypercenterC2×#102D107
hypocenterC107C2×#465
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#13133806C2semidirect
2. C22×C8×D107C2semidirect
3. C2×#16812089C2semidirect
5. #20292855C2direct (N × H)
6. C2×#16812040C2semidirect
7. C2×#16812034C2semidirect
8. C2×#102×C107C2semidirect
13. C2×#13133806C22semidirect
16. C2×C8×D107C22semidirect
18. #16812089C22semidirect
25. #16812040C22semidirect
26. #16812034C22semidirect
30. #102×C107C22semidirect
46. C2×C107⋊C8D4semidirect
72. C22×D107SD16semidirect
97. C107⋊C8C2×D4semidirect
109. C2×D107C2×SD16semidirect
118. C2×C107#465semidirect
124. C107C2×#465semidirect
132. C2×#102D107semidirect
154. #102C2×D107semidirect
243. C2#20292855direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131338062
C22×C8×D1072
C2×#168120892
C2×#168120802
#202928552
C2×#168120402
C2×#168120342
C2×#102×C1072
C2×#465107