Finite Group Databasebeta

← C2×#20267958 #27204467

Subgroups — C2×#20267958 #27204467

Order 13184.

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

normal subgroups only

This group has 844 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×#15693066C211yesmaximal, characteristic, complemented
2C2×#15693047C212yesmaximal, complemented
3#20267958C218yesmaximal, direct product factor
4C2×#15692949C212yesmaximal, complemented
5C2×#15692938C211yesmaximal, characteristic, complemented
6C2×#127×C103C211yesmaximal, characteristic, complemented
7#15693066—24no—
8#15693066—22no—
9#15693066C2214yescomplemented
10C2×#13110105C2212yes—
11C2×#13110104—22no—
12C22×C22⋊D103—22no—
13C2×D4×D103—22no—
14#15693047—24no—
15#15693047C2218yescomplemented
16C2×#13110093—22no—
17C2×#13110090—22no—
18C2×#13110089C2212yescomplemented
19#15692949C2218yescomplemented
20#15692938C2214yescomplemented
21C22×D4×C103—22no—
22C22×D4×C103C2211yescharacteristic
23C22×D4×C103C2211yescharacteristic, complemented
24#127×C103—22no—
25#127×C103C2214yescomplemented
26C2×C42×C103C2211yescharacteristic, complemented
27C23×D103—22no—
28#13110105—22no—
29#13110105—22no—
30#13110105D414yescomplemented
31#13110105C2314yes—
32#13110104—28no—
33#13110104—28no—
34C2×Dic206D412yescomplemented
35C2×D412D412yescomplemented
36C2×C22⋊D103—24no—
37C2×C22⋊D103—28no—
38C2×C22⋊D103—22no—
39C2×C22⋊D103—28no—
40D4×D103—28no—
41D4×D103—28no—
42C22×Dic103—22no—
43C2×C4×D103—22no—
44#13110093—28no—
45#13110090—28no—
46#13110089—22no—
47#13110089C2314yescomplemented
48C2×C103⋊C8—22no—
49C24×C103—21no—
50C24×C103D412yes—
51C2×D4×C103—28no—
52C2×D4×C103—22no—
53C2×D4×C103—22no—
54C2×D4×C103—22no—
55C2×D4×C103—22no—
56C2×D4×C103—21no—
57C2×D4×C103—48no—
58C2×D4×C103D412yes—
59C2×D4×C103C2312yes—
60C2×D4×C103C2312yescomplemented
61C22×C4×C103—21no—
62C22×C4×C103C2311yescharacteristic
63C42×C103—21no—
64C42×C103C2312yescomplemented
65C23×C103—22no—
66C23×C103—22no—
67C23×C103—22no—
68C23×C103—44no—
69C23×C103—44no—
70C23×C103—41no—
71C23×C103—41no—
72C23×C103C2×D411yescharacteristic
73C23×C103C2×D414yes—
74C22×D103—22no—
75C22×D103—28no—
76C22×D103—84no—
77D4×C103—24no—
78D4×C103—24no—
79D4×C103—24no—
80D4×C103—416no—
81D4×C103—42no—
82C2×C4×C103—24no—
83C2×C4×C103—22no—
84C2×C4×C103C2×D412yes—
85C2×C4×C103C2×D412yes—
86C2×C4×C103C2×D411yescharacteristic
87C2×C4×C103C2411yescharacteristic
88C22⋊D103—216no—
89C22⋊D103—24no—
90C22⋊D103—24no—
91C2×Dic103—28no—
92C2×Dic103—22no—
93D412—22no—
94D412C2×D414yescomplemented
95C4×D103—24no—
96C4×D103—24no—
97Dic206—22no—
98Dic206C2×D414yescomplemented
99C103⋊C8—24no—
100C22×C103—22no—
101C22×C103—24no—
102C22×C103—44no—
103C22×C103—44no—
104C22×C103—44no—
105C22×C103—42no—
106C22×C103—82no—
107C22×C103—82no—
108C22×C103—82no—
109C22×C103#12011yescharacteristic
110C22×C103#12011yescharacteristic
111C22×C103C22×D411yescharacteristic
112C2×D103—24no—
113C2×D103—44no—
114C2×D103—88no—
115C4×C103—24no—
116C4×C103#12012yes—
117C4×C103C22×D412yes—
118Dic103—24no—
119C2×C103—21no—
120C2×C103—21no—
121C2×C103—44no—
122C2×C103—82no—
123C2×C103#45312yescomplemented
124C2×C103C2×#12011yescharacteristic
125D103—44no—
126C2×#453—1031nomaximal, Sylow
127C103C2×#45311yescharacteristic, complemented, Sylow
128C2×H(5,𝔽2)—1031no—
129C2×AGL(1,ℤ/8)—1032no—
130C2×#127D10311yescharacteristic, complemented
131#453—1038no—
132C2×#104—1032no—
133C2×#100—1031no—
134H(5,𝔽2)—1034no—
135H(5,𝔽2)—2064no—
136H(5,𝔽2)—2062no—
137C2×#41—1032no—
138C2×#41—2062no—
139C22×D4—22no—
140C22×D4—2062no—
141C22×D4—2062no—
142C22×D4C2×D10311yescharacteristic
143C22×D4C2×D10311yescharacteristic, complemented
144AGL(1,ℤ/8)—1038no—
145AGL(1,ℤ/8)—2064no—
146C2×SD16—2062no—
147C2×D8—2062no—
148C2×M16—1032no—
149#127—22no—
150#127C2×D10314yescomplemented
151C2×C42C2×D10311yescharacteristic, complemented
152#104—1038no—
153#100—1034no—
154C24—21no—
155C24—2062no—
156C24C22⋊D10312yes—
157#41—1034no—
158#41—1034no—
159#41—2068no—
160#41—2068no—
161#41—2062no—
162#41—2062no—
163C2×Q8—1032no—
164C2×D4—28no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4—48no—
171C2×D4—1032no—
172C2×D4—2068no—
173C2×D4—2068no—
174C2×D4—2064no—
175C2×D4—2068no—
176C2×D4—2062no—
177C2×D4—2068no—
178C2×D4C22⋊D10312yes—
179C2×D4C22×D10312yes—
180C2×D4C22×D10312yescomplemented
181C22×C4—21no—
182C22×C4—2062no—
183C22×C4—2062no—
184C22×C4C22×D10311yescharacteristic
185SD16—2068no—
186D8—2068no—
187M16—1034no—
188M16—2062no—
189C2×C8—2062no—
190C42—21no—
191C42C22×D10312yescomplemented
192C23—22no—
193C23—22no—
194C23—22no—
195C23—44no—
196C23—44no—
197C23—41no—
198C23—41no—
199C23—8244no—
200C23—2068no—
201C23—2062no—
202C23C2×C22⋊D10311yescharacteristic
203C23C2×C22⋊D10314yes—
204Q8—1034no—
205Q8—2062no—
206D4—24no—
207D4—24no—
208D4—24no—
209D4—416no—
210D4—42no—
211D4—1034no—
212D4—20616no—
213D4—2064no—
214D4—2064no—
215D4—2062no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—2068no—
219C2×C4—2062no—
220C2×C4—2064no—
221C2×C4—2064no—
222C2×C4D4×D10312yes—
223C2×C4D4×D10312yes—
224C2×C4C2×C22⋊D10311yescharacteristic
225C2×C4C23×D10311yescharacteristic
226C8—2064no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—44no—
232C22—42no—
233C22—82no—
234C22—82no—
235C22—82no—
236C22—8248no—
237C22—4124no—
238C22—2064no—
239C22#1569298911yescharacteristic
240C22#1569298911yescharacteristic
241C22C22×C22⋊D10311yescharacteristic
242C4—24no—
243C4—2064no—
244C4#1569298912yes—
245C4C2×D4×D10312yes—
246C2—21no—
247C2—21no—
248C2—44no—
249C2—82no—
250C2—4124no—
251C2#2026795812yesdirect product factor
252C2C2×#1569298911yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#127×C103C2
socleC22×C103#120
hypercenterC2×#127D103
hypocenterC103C2×#453
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#15693066C2semidirect
2. C2×#15693047C2semidirect
3. #20267958C2direct (N × H)
4. C2×#15692949C2semidirect
5. C2×#15692938C2semidirect
6. C2×#127×C103C2semidirect
9. #15693066C22semidirect
15. #15693047C22semidirect
18. C2×#13110089C22semidirect
19. #15692949C22semidirect
20. #15692938C22semidirect
23. C22×D4×C103C22semidirect
25. #127×C103C22semidirect
26. C2×C42×C103C22semidirect
30. #13110105D4semidirect
34. C2×Dic206D4semidirect
35. C2×D412D4semidirect
47. #13110089C23semidirect
60. C2×D4×C103C23semidirect
64. C42×C103C23semidirect
94. D412C2×D4semidirect
98. Dic206C2×D4semidirect
123. C2×C103#453semidirect
127. C103C2×#453semidirect
130. C2×#127D103semidirect
143. C22×D4C2×D103semidirect
150. #127C2×D103semidirect
151. C2×C42C2×D103semidirect
180. C2×D4C22×D103semidirect
191. C42C22×D103semidirect
251. C2#20267958direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156930662
C2×#156930472
#202679582
C2×#156929492
C2×#156929382
C2×#127×C1032
C2×#453103