Finite Group Databasebeta

← C2×#20268128 #27205051

Subgroups — C2×#20268128 #27205051

Order 13184.

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×#15693001C211yesmaximal, characteristic
2C2×C4⋊C4×D103C211yesmaximal, characteristic
3#20268128C218yesmaximal, direct product factor
4C2×#15692954C211yesmaximal, characteristic, complemented
5C2×#15692946C211yesmaximal, characteristic, complemented
6C2×#15692944C211yesmaximal, characteristic, complemented
7C2×(C2×D103)⋊C8C211yesmaximal, characteristic
8C2×#107×C103C211yesmaximal, characteristic, complemented
9C22×Dic206C2211yescharacteristic
10C22×C4×D103—21no—
11C22×C4×D103C2211yescharacteristic
12C22×C103⋊C8C2211yescharacteristic
13#15693001—22no—
14#15693001C2214yes—
15C2×C4⋊Dic103—21no—
16C2×C4⋊Dic103C2211yescharacteristic
17C2×Dic103⋊C4—21no—
18C4⋊C4×D103—22no—
19C4⋊C4×D103C2214yes—
20C2×(C2×D103)⋊C4—21no—
21#15692954C2214yescomplemented
22#15692946C2214yescomplemented
23#15692944C2214yescomplemented
24(C2×D103)⋊C8C2214yes—
25C22×C8×C103C2211yescharacteristic
26C2×C4⋊C4×C103C2211yescharacteristic
27C2×C4⋊C4×C103C2211yescharacteristic
28#107×C103C2214yescomplemented
29C23×D103D411yescharacteristic
30C2×Dic206—22no—
31C2×Dic206—22no—
32C2×Dic206—21no—
33C2×Dic206C2312yes—
34C22×Dic103—21no—
35C22×Dic103—21no—
36C22×Dic103D411yescharacteristic
37C2×C4×D103—22no—
38C2×C4×D103—22no—
39C2×C4×D103—24no—
40C2×C4×D103—44no—
41C2×C4×D103D412yes—
42C2×C4×D103C2312yes—
43C2×C103⋊C8—22no—
44C2×C103⋊C8C2312yes—
45C4⋊Dic103—21no—
46C4⋊Dic103—24no—
47C4⋊Dic103C2312yes—
48Dic103⋊C4—24no—
49(C2×D103)⋊C4—24no—
50C22×C4×C103—21no—
51C22×C4×C103—21no—
52C22×C4×C103C2311yescharacteristic
53C2×C8×C103—22no—
54C2×C8×C103C2312yes—
55C4⋊C4×C103—21no—
56C4⋊C4×C103—21no—
57C4⋊C4×C103C2312yes—
58C4⋊C4×C103C2312yes—
59C23×C103C2×D411yescharacteristic
60C22×D103—22no—
61C22×D103—22no—
62C22×D103Q1614yes—
63C22×D103C2×D412yes—
64C2×C4×C103—22no—
65C2×C4×C103—22no—
66C2×C4×C103—42no—
67C2×C4×C103—42no—
68C2×C4×C103C2×D411yescharacteristic
69C2×C4×C103#4112yes—
70C2×C4×C103#4112yes—
71C2×C4×C103C2411yescharacteristic
72C2×Dic103—22no—
73C2×Dic103—22no—
74C2×Dic103—22no—
75C2×Dic103—42no—
76C2×Dic103—42no—
77C2×Dic103C2×D412yes—
78C4×D103—24no—
79C4×D103—22no—
80C4×D103—22no—
81C4×D103—48no—
82Dic206—22no—
83Dic206—22no—
84Dic206—42no—
85C8×C103—22no—
86C103⋊C8—22no—
87C22×C103#12312yes—
88C22×C103C2×Q1612yes—
89C22×C103AGL(1,ℤ/8)12yes—
90C22×C103C22×D411yescharacteristic
91C2×D103—22no—
92C2×D103—22no—
93C2×D103—28no—
94C2×D103C2×Q1614yes—
95C4×C103—42no—
96C4×C103—42no—
97C4×C103#12312yes—
98C4×C103C2×#4111yescharacteristic
99C4×C103C2×#4111yescharacteristic
100Dic103—22no—
101Dic103—42no—
102Dic103—42no—
103C2×C103#48414yescomplemented
104C2×C103C2×#12311yescharacteristic
105C2×C103C22×Q1611yescharacteristic
106C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
107D103—24no—
108C2×#484—1031nomaximal, Sylow
109C103C2×#48411yescharacteristic, complemented, Sylow
110C2×C22⋊Q8—1031no—
111C22×C4⋊C4—1031no—
112#484—1038no—
113C2×#107—1031no—
114C2×#107D10311yescharacteristic, complemented
115C2×#103—1031no—
116C2×#103—1031no—
117C2×C22⋊C8—1031no—
118C22×Q8—1031no—
119C23×C4—1031no—
120C23×C4—2061no—
121C22×C8—1031no—
122C22×C8C2×D10311yescharacteristic
123C22⋊Q8—1034no—
124C22⋊Q8—2062no—
125C2×C4⋊C4—1031no—
126C2×C4⋊C4—1034no—
127C2×C4⋊C4—2062no—
128C2×C4⋊C4—2061no—
129C2×C4⋊C4—2061no—
130C2×C4⋊C4C2×D10311yescharacteristic
131C2×C4⋊C4C2×D10311yescharacteristic
132C2×C22⋊C4—2061no—
133#107—1034no—
134#107C2×D10314yescomplemented
135#103—1034no—
136#103—1034no—
137C22⋊C8—1034no—
138C24—1031no—
139C2×Q8—1032no—
140C2×Q8—2062no—
141C2×Q8—2062no—
142C2×Q8—2061no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1031no—
146C22×C4—1032no—
147C22×C4—1032no—
148C22×C4—4124no—
149C22×C4—2064no—
150C22×C4—2061no—
151C22×C4—2061no—
152C22×C4—2062no—
153C22×C4—2062no—
154C22×C4C22×D10311yescharacteristic
155C2×C8—22no—
156C2×C8—1032no—
157C2×C8—2062no—
158C2×C8C22×D10312yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1032no—
162C4⋊C4—2064no—
163C4⋊C4—2064no—
164C4⋊C4—2061no—
165C4⋊C4C22×D10312yes—
166C4⋊C4C22×D10312yes—
167C22⋊C4—2064no—
168C23—1032no—
169C23—1034no—
170C23—2062no—
171C23—2062no—
172C23D4×D10311yescharacteristic
173Q8—4122no—
174Q8—2062no—
175Q8—2062no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—1032no—
181C2×C4—4128no—
182C2×C4—4122no—
183C2×C4—4122no—
184C2×C4—2062no—
185C2×C4—2062no—
186C2×C4—2062no—
187C2×C4—2062no—
188C2×C4—2062no—
189C2×C4—2064no—
190C2×C4D4×D10311yescharacteristic
191C2×C4#1311010512yes—
192C2×C4#1311010612yes—
193C2×C4C23×D10311yescharacteristic
194C8—22no—
195C8—2062no—
196C22—1034no—
197C22—2062no—
198C22—2062no—
199C22—2068no—
200C22#1569300612yes—
201C22Q16×D10312yes—
202C22#1569304512yes—
203C22C2×D4×D10311yescharacteristic
204C4—42no—
205C4—42no—
206C4—4122no—
207C4—4122no—
208C4—2062no—
209C4#1569300612yes—
210C4C2×#1311010511yescharacteristic
211C4C2×#1311010611yescharacteristic
212C2—2064no—
213C2#2026812814yesdirect product factor
214C2C2×#1569300611yescharacteristic
215C2C2×Q16×D10311yescharacteristic
216C2C2×#1569304511yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#107×C103C2
socleC23×C103C2×D4
prime radicalC23×D103D4
hypercenterC2×#107D103
hypocenterC103C2×#484
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #20268128C2direct (N × H)
4. C2×#15692954C2semidirect
5. C2×#15692946C2semidirect
6. C2×#15692944C2semidirect
8. C2×#107×C103C2semidirect
21. #15692954C22semidirect
22. #15692946C22semidirect
23. #15692944C22semidirect
28. #107×C103C22semidirect
103. C2×C103#484semidirect
109. C103C2×#484semidirect
114. C2×#107D103semidirect
134. #107C2×D103semidirect
213. C2#20268128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156930012
C2×C4⋊C4×D1032
#202681282
C2×#156929542
C2×#156929462
C2×#156929442
C2×(C2×D103)⋊C82
C2×#107×C1032
C2×#484103