Finite Group Databasebeta

← C2×#20292956 #28346337

Subgroups — C2×#20292956 #28346337

Order 13696.

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

normal subgroups only

This group has 460 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×#16812085C211yesmaximal, characteristic
2C2×C4⋊C4×D107C211yesmaximal, characteristic
3#20292956C218yesmaximal, direct product factor
4C2×#16812041C211yesmaximal, characteristic, complemented
5C2×#16812040C211yesmaximal, characteristic, complemented
6C2×#16812033C211yesmaximal, characteristic, complemented
7C2×(C2×D107)⋊C8C211yesmaximal, characteristic
8C2×#103×C107C211yesmaximal, characteristic, complemented
9C22×C4×D107—21no—
10C22×C4×D107C2211yescharacteristic
11C22×C107⋊C8C2211yescharacteristic
12#16812085—22no—
13#16812085C2214yes—
14C2×C4⋊Dic107C2211yescharacteristic
15C2×C4⋊Dic107C2211yescharacteristic
16C2×Dic107⋊C4—21no—
17C2×Dic107⋊C4—21no—
18C4⋊C4×D107—22no—
19C4⋊C4×D107C2214yes—
20C2×(C2×D107)⋊C4—21no—
21#16812041C2214yescomplemented
22#16812040C2214yescomplemented
23#16812033C2214yescomplemented
24(C2×D107)⋊C8C2214yes—
25C22×Q8×C107C2211yescharacteristic
26C22×C8×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28#103×C107C2214yescomplemented
29C23×D107D411yescharacteristic
30C22×Dic107—21no—
31C22×Dic107—21no—
32C22×Dic107D411yescharacteristic
33C2×C4×D107—22no—
34C2×C4×D107—22no—
35C2×C4×D107—24no—
36C2×C4×D107—44no—
37C2×C4×D107D412yes—
38C2×C4×D107C2312yes—
39C2×C107⋊C8—22no—
40C2×C107⋊C8C2312yes—
41C4⋊Dic107—21no—
42C4⋊Dic107—21no—
43C4⋊Dic107C2312yes—
44C4⋊Dic107C2312yes—
45Dic107⋊C4—24no—
46Dic107⋊C4—24no—
47(C2×D107)⋊C4—24no—
48C2×Q8×C107—21no—
49C2×Q8×C107—22no—
50C2×Q8×C107—22no—
51C2×Q8×C107C2312yes—
52C22×C4×C107—21no—
53C22×C4×C107—21no—
54C22×C4×C107C2311yescharacteristic
55C2×C8×C107—22no—
56C2×C8×C107C2312yes—
57C4⋊C4×C107—21no—
58C4⋊C4×C107C2312yes—
59C23×C107C2×D411yescharacteristic
60C22×D107—22no—
61C22×D107—22no—
62C22×D107SD1614yes—
63C22×D107C2×D412yes—
64Q8×C107—22no—
65Q8×C107—22no—
66Q8×C107—42no—
67C2×C4×C107—22no—
68C2×C4×C107—22no—
69C2×C4×C107—42no—
70C2×C4×C107—42no—
71C2×C4×C107C2×D411yescharacteristic
72C2×C4×C107#4112yes—
73C2×C4×C107#4112yes—
74C2×C4×C107C2411yescharacteristic
75C2×Dic107—22no—
76C2×Dic107—22no—
77C2×Dic107—22no—
78C2×Dic107—42no—
79C2×Dic107—42no—
80C2×Dic107C2×D412yes—
81C4×D107—24no—
82C4×D107—22no—
83C4×D107—22no—
84C4×D107—48no—
85C8×C107—22no—
86C107⋊C8—22no—
87C22×C107#12312yes—
88C22×C107C2×SD1612yes—
89C22×C107#13712yes—
90C22×C107C22×D411yescharacteristic
91C2×D107—22no—
92C2×D107—22no—
93C2×D107—28no—
94C2×D107C2×SD1614yes—
95C4×C107—42no—
96C4×C107—42no—
97C4×C107#12312yes—
98C4×C107C2×#4111yescharacteristic
99C4×C107C2×#4111yescharacteristic
100Dic107—22no—
101Dic107—42no—
102Dic107—42no—
103C2×C107#48314yescomplemented
104C2×C107C2×#12311yescharacteristic
105C2×C107C22×SD1611yescharacteristic
106C2×C107C2×#13711yescharacteristic
107D107—24no—
108C2×#483—1071nomaximal, Sylow
109C107C2×#48311yescharacteristic, complemented, Sylow
110C2×C22⋊Q8—1071no—
111C22×C4⋊C4—1071no—
112#483—1078no—
113C2×#106—1071no—
114C2×#106—1071no—
115C2×#103—1071no—
116C2×#103D10711yescharacteristic, complemented
117C2×C22⋊C8—1071no—
118C22×Q8C2×D10711yescharacteristic
119C23×C4—1071no—
120C23×C4—2141no—
121C22×C8—1071no—
122C22×C8C2×D10711yescharacteristic
123C22⋊Q8—1074no—
124C22⋊Q8—2142no—
125C2×C4⋊C4—1071no—
126C2×C4⋊C4—1071no—
127C2×C4⋊C4—1074no—
128C2×C4⋊C4—2142no—
129C2×C4⋊C4—2141no—
130C2×C4⋊C4—2141no—
131C2×C4⋊C4C2×D10711yescharacteristic
132C2×C22⋊C4—2141no—
133#106—1074no—
134#106—1074no—
135#103—1074no—
136#103C2×D10714yescomplemented
137C22⋊C8—1074no—
138C24—1071no—
139C2×Q8—21no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8C22×D10712yes—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1071no—
146C22×C4—1072no—
147C22×C4—1072no—
148C22×C4—4284no—
149C22×C4—2144no—
150C22×C4—2141no—
151C22×C4—2141no—
152C22×C4—2142no—
153C22×C4—2142no—
154C22×C4C22×D10711yescharacteristic
155C2×C8—22no—
156C2×C8—1072no—
157C2×C8—2142no—
158C2×C8C22×D10712yes—
159C4⋊C4—21no—
160C4⋊C4—1072no—
161C4⋊C4—1072no—
162C4⋊C4—2144no—
163C4⋊C4—2144no—
164C4⋊C4—2141no—
165C4⋊C4—2141no—
166C4⋊C4C22×D10712yes—
167C22⋊C4—2144no—
168C23—1074no—
169C23—1072no—
170C23—2142no—
171C23—2142no—
172C23D4×D10711yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—42no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—1072no—
181C2×C4—4288no—
182C2×C4—4282no—
183C2×C4—4282no—
184C2×C4—2142no—
185C2×C4—2142no—
186C2×C4—2142no—
187C2×C4—2144no—
188C2×C4—2142no—
189C2×C4—2142no—
190C2×C4D4×D10711yescharacteristic
191C2×C4#1313381712yes—
192C2×C4#1313381812yes—
193C2×C4C23×D10711yescharacteristic
194C8—22no—
195C8—2142no—
196C22—1074no—
197C22—2142no—
198C22—2142no—
199C22—2148no—
200C22#1681209112yes—
201C22SD16×D10712yes—
202C22#1681214112yes—
203C22C2×D4×D10711yescharacteristic
204C4—42no—
205C4—42no—
206C4—4282no—
207C4—4282no—
208C4—2142no—
209C4#1681209112yes—
210C4C2×#1313381711yescharacteristic
211C4C2×#1313381811yescharacteristic
212C2—2144no—
213C2#2029295614yesdirect product factor
214C2C2×#1681209111yescharacteristic
215C2C2×SD16×D10711yescharacteristic
216C2C2×#1681214111yescharacteristic
subgroupG/H
centerC23D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#103×C107C2
socleC23×C107C2×D4
prime radicalC23×D107D4
hypercenterC2×#103D107
hypocenterC107C2×#483
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #20292956C2direct (N × H)
4. C2×#16812041C2semidirect
5. C2×#16812040C2semidirect
6. C2×#16812033C2semidirect
8. C2×#103×C107C2semidirect
21. #16812041C22semidirect
22. #16812040C22semidirect
23. #16812033C22semidirect
28. #103×C107C22semidirect
103. C2×C107#483semidirect
109. C107C2×#483semidirect
116. C2×#103D107semidirect
136. #103C2×D107semidirect
213. C2#20292956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168120852
C2×C4⋊C4×D1072
#202929562
C2×#168120412
C2×#168120402
C2×#168120332
C2×(C2×D107)⋊C82
C2×#103×C1072
C2×#483107