Finite Group Databasebeta

← C2×#20268115 #27205028

Subgroups — C2×#20268115 #27205028

Order 13184.

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

normal subgroups only

This group has 468 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×#15692995C211yesmaximal, characteristic
2#20268115C218yesmaximal, direct product factor
3C2×#15692954C211yesmaximal, characteristic, complemented
4C2×#15692952C211yesmaximal, characteristic, complemented
5C2×#15692941C211yesmaximal, characteristic, complemented
6C2×#15692941C211yesmaximal, characteristic, complemented
7C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
8C2×#117×C103C211yesmaximal, characteristic, complemented
9C22×D412C2211yescharacteristic
10C22×C22⋊D103—21no—
11C22×C103⋊C8C2211yescharacteristic
12C22×C103⋊C8C2211yescharacteristic
13#15692995—22no—
14#15692995C2214yes—
15C2×C4⋊Dic103C2211yescharacteristic
16C2×(C2×D103)⋊C4—21no—
17#15692954C2214yescomplemented
18#15692952C2214yescomplemented
19#15692941C2214yescomplemented
20#15692941C2214yescomplemented
21C22⋊(C103⋊C8)C2214yescomplemented
22C23×C4×C103C2211yescharacteristic
23#117×C103—22no—
24#117×C103C2214yescomplemented
25C2×C4⋊C4×C103C2211yescharacteristic
26C2×C4⋊C4×C103C2211yescharacteristic
27C2×C22⋊C4×C103—21no—
28C2×C42×C103—21no—
29C23×D103—21no—
30C2×D412—22no—
31C2×D412—22no—
32C2×D412—21no—
33C2×D412C2312yes—
34C2×C22⋊D103—24no—
35C2×C22⋊D103—44no—
36C22×Dic103—21no—
37C2×C103⋊C8—22no—
38C2×C103⋊C8—22no—
39C2×C103⋊C8C2312yes—
40C2×C103⋊C8C2312yes—
41C4⋊Dic103—21no—
42C4⋊Dic103C2312yes—
43(C2×D103)⋊C4—24no—
44C24×C103D411yescharacteristic
45C22×C4×C103—22no—
46C22×C4×C103—22no—
47C22×C4×C103—21no—
48C22×C4×C103—21no—
49C22×C4×C103D411yescharacteristic
50C22×C4×C103D412yes—
51C22×C4×C103C2312yes—
52C22×C4×C103C2311yescharacteristic
53C4⋊C4×C103—21no—
54C4⋊C4×C103—21no—
55C4⋊C4×C103C2312yes—
56C4⋊C4×C103C2312yes—
57C22⋊C4×C103—24no—
58C42×C103—24no—
59C23×C103—22no—
60C23×C103—22no—
61C23×C103—22no—
62C23×C103C2×D412yes—
63C23×C103C2×D411yescharacteristic
64C22×D103—22no—
65C22×D103—42no—
66C22×D103—42no—
67C22×D103—42no—
68C2×C4×C103—22no—
69C2×C4×C103—24no—
70C2×C4×C103—22no—
71C2×C4×C103—22no—
72C2×C4×C103—22no—
73C2×C4×C103—22no—
74C2×C4×C103—42no—
75C2×C4×C103—42no—
76C2×C4×C103C2×D412yes—
77C2×C4×C103C2×D411yescharacteristic
78C2×C4×C103#4112yes—
79C2×C4×C103#4112yes—
80C2×C4×C103C2411yescharacteristic
81C22⋊D103—48no—
82C2×Dic103—22no—
83C2×Dic103—42no—
84D412—22no—
85D412—22no—
86D412—42no—
87C103⋊C8—22no—
88C103⋊C8—22no—
89C22×C103—22no—
90C22×C103—22no—
91C22×C103—22no—
92C22×C103—44no—
93C22×C103#12312yes—
94C22×C103#13512yes—
95C22×C103AGL(1,ℤ/8)12yes—
96C22×C103C22×D411yescharacteristic
97C2×D103—42no—
98C2×D103—42no—
99C2×D103—42no—
100C2×D103—84no—
101C4×C103—22no—
102C4×C103—42no—
103C4×C103—42no—
104C4×C103#12312yes—
105C4×C103C2×#4111yescharacteristic
106C4×C103C2×#4111yescharacteristic
107Dic103—42no—
108C2×C103—42no—
109C2×C103#48214yescomplemented
110C2×C103C2×#12311yescharacteristic
111C2×C103C2×#13511yescharacteristic
112C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
113D103—82no—
114C2×#482—1031nomaximal, Sylow
115C103C2×#48211yescharacteristic, complemented, Sylow
116C2×#121—1031no—
117C2×#117D10311yescharacteristic, complemented
118#482—1038no—
119C2×#107—1031no—
120C2×#106—1031no—
121C2×#102—1031no—
122C2×#102—1031no—
123C2×C22⋊C8—1031no—
124C22×D4—1031no—
125C22×D4—2061no—
126C23×C4C2×D10311yescharacteristic
127C22×C8—1031no—
128C22×C8—1031no—
129#121—1034no—
130#121—2062no—
131#117—22no—
132#117C2×D10314yescomplemented
133C2×C4⋊C4—1031no—
134C2×C4⋊C4C2×D10311yescharacteristic
135C2×C4⋊C4C2×D10311yescharacteristic
136C2×C22⋊C4—21no—
137C2×C22⋊C4—2061no—
138C2×C42—21no—
139#107—1034no—
140#106—1034no—
141#102—1034no—
142#102—1034no—
143C22⋊C8—1034no—
144C24—2061no—
145C24C22⋊D10311yescharacteristic
146C2×D4—1032no—
147C2×D4—4124no—
148C2×D4—2064no—
149C2×D4—2061no—
150C2×D4—2062no—
151C2×D4—2062no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—2061no—
157C22×C4C22⋊D10312yes—
158C22×C4C22⋊D10311yescharacteristic
159C22×C4C22×D10312yes—
160C22×C4C22×D10311yescharacteristic
161C2×C8—1032no—
162C2×C8—1032no—
163C2×C8—2062no—
164C2×C8—2062no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—1032no—
168C4⋊C4—2061no—
169C4⋊C4C22×D10312yes—
170C4⋊C4C22×D10312yes—
171C22⋊C4—24no—
172C22⋊C4—2064no—
173C42—24no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—4122no—
178C23—4122no—
179C23—4122no—
180C23—2062no—
181C23C2×C22⋊D10312yes—
182C23C2×C22⋊D10311yescharacteristic
183D4—4128no—
184D4—4122no—
185D4—2062no—
186D4—2062no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—4122no—
196C2×C4—2062no—
197C2×C4C2×C22⋊D10312yes—
198C2×C4C2×C22⋊D10311yescharacteristic
199C2×C4#1311010512yes—
200C2×C4#1311010512yes—
201C2×C4C23×D10311yescharacteristic
202C8—2062no—
203C8—2062no—
204C22—22no—
205C22—22no—
206C22—22no—
207C22—44no—
208C22—8244no—
209C22—4122no—
210C22—4122no—
211C22—4122no—
212C22#1569300412yes—
213C22#1569304112yes—
214C22#1569304612yes—
215C22C22×C22⋊D10311yescharacteristic
216C4—22no—
217C4—42no—
218C4—42no—
219C4—4122no—
220C4#1569300412yes—
221C4C2×#1311010511yescharacteristic
222C4C2×#1311010511yescharacteristic
223C2—42no—
224C2—8242no—
225C2#2026811514yesdirect product factor
226C2C2×#1569300411yescharacteristic
227C2C2×#1569304111yescharacteristic
228C2C2×#1569304611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#117×C103C2
socleC23×C103C2×D4
prime radicalC2×#15692995C2
hypercenterC2×#117D103
hypocenterC103C2×#482
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #20268115C2direct (N × H)
3. C2×#15692954C2semidirect
4. C2×#15692952C2semidirect
5. C2×#15692941C2semidirect
6. C2×#15692941C2semidirect
7. C2×C22⋊(C103⋊C8)C2semidirect
8. C2×#117×C103C2semidirect
17. #15692954C22semidirect
18. #15692952C22semidirect
19. #15692941C22semidirect
20. #15692941C22semidirect
21. C22⋊(C103⋊C8)C22semidirect
24. #117×C103C22semidirect
109. C2×C103#482semidirect
115. C103C2×#482semidirect
117. C2×#117D103semidirect
132. #117C2×D103semidirect
225. C2#20268115direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156929952
#202681152
C2×#156929542
C2×#156929522
C2×#156929412
C2×C22⋊(C103⋊C8)2
C2×#117×C1032
C2×#482103