Finite Group Databasebeta

← C2×#19127868 #24916786

Subgroups — C2×#19127868 #24916786

Order 10624.

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×#14581837C211yesmaximal, characteristic, complemented
2C2×#14581818C212yesmaximal, complemented
3#19127868C218yesmaximal, direct product factor
4C2×#14581720C212yesmaximal, complemented
5C2×#14581709C211yesmaximal, characteristic, complemented
6C2×#127×C83C211yesmaximal, characteristic, complemented
7#14581837—24no—
8#14581837—22no—
9#14581837C2214yescomplemented
10C2×#13050590C2212yes—
11C2×#13050589—22no—
12C22×C22⋊D83—22no—
13C2×D4×D83—22no—
14#14581818—24no—
15#14581818C2218yescomplemented
16C2×#13050578—22no—
17C2×#13050575—22no—
18C2×#13050574C2212yescomplemented
19#14581720C2218yescomplemented
20#14581709C2214yescomplemented
21C22×D4×C83—22no—
22C22×D4×C83C2211yescharacteristic
23C22×D4×C83C2211yescharacteristic, complemented
24#127×C83—22no—
25#127×C83C2214yescomplemented
26C2×C42×C83C2211yescharacteristic, complemented
27C23×D83—22no—
28#13050590—22no—
29#13050590—22no—
30#13050590D414yescomplemented
31#13050590C2314yes—
32#13050589—28no—
33#13050589—28no—
34C2×Dic166D412yescomplemented
35C2×D332D412yescomplemented
36C2×C22⋊D83—24no—
37C2×C22⋊D83—28no—
38C2×C22⋊D83—22no—
39C2×C22⋊D83—28no—
40D4×D83—28no—
41D4×D83—28no—
42C22×Dic83—22no—
43C2×C4×D83—22no—
44#13050578—28no—
45#13050575—28no—
46#13050574—22no—
47#13050574C2314yescomplemented
48C2×C83⋊C8—22no—
49C24×C83—21no—
50C24×C83D412yes—
51C2×D4×C83—28no—
52C2×D4×C83—22no—
53C2×D4×C83—22no—
54C2×D4×C83—22no—
55C2×D4×C83—22no—
56C2×D4×C83—21no—
57C2×D4×C83—48no—
58C2×D4×C83D412yes—
59C2×D4×C83C2312yes—
60C2×D4×C83C2312yescomplemented
61C22×C4×C83—21no—
62C22×C4×C83C2311yescharacteristic
63C42×C83—21no—
64C42×C83C2312yescomplemented
65C23×C83—22no—
66C23×C83—22no—
67C23×C83—22no—
68C23×C83—44no—
69C23×C83—44no—
70C23×C83—41no—
71C23×C83—41no—
72C23×C83C2×D411yescharacteristic
73C23×C83C2×D414yes—
74C22×D83—22no—
75C22×D83—28no—
76C22×D83—84no—
77D4×C83—24no—
78D4×C83—24no—
79D4×C83—24no—
80D4×C83—416no—
81D4×C83—42no—
82C2×C4×C83—24no—
83C2×C4×C83—22no—
84C2×C4×C83C2×D412yes—
85C2×C4×C83C2×D412yes—
86C2×C4×C83C2×D411yescharacteristic
87C2×C4×C83C2411yescharacteristic
88C22⋊D83—216no—
89C22⋊D83—24no—
90C22⋊D83—24no—
91C2×Dic83—28no—
92C2×Dic83—22no—
93D332—22no—
94D332C2×D414yescomplemented
95C4×D83—24no—
96C4×D83—24no—
97Dic166—22no—
98Dic166C2×D414yescomplemented
99C83⋊C8—24no—
100C22×C83—22no—
101C22×C83—24no—
102C22×C83—44no—
103C22×C83—44no—
104C22×C83—44no—
105C22×C83—42no—
106C22×C83—82no—
107C22×C83—82no—
108C22×C83—82no—
109C22×C83#12011yescharacteristic
110C22×C83#12011yescharacteristic
111C22×C83C22×D411yescharacteristic
112C2×D83—24no—
113C2×D83—44no—
114C2×D83—88no—
115C4×C83—24no—
116C4×C83#12012yes—
117C4×C83C22×D412yes—
118Dic83—24no—
119C2×C83—21no—
120C2×C83—21no—
121C2×C83—44no—
122C2×C83—82no—
123C2×C83#45312yescomplemented
124C2×C83C2×#12011yescharacteristic
125D83—44no—
126C2×#453—831nomaximal, Sylow
127C83C2×#45311yescharacteristic, complemented, Sylow
128C2×H(5,𝔽2)—831no—
129C2×AGL(1,ℤ/8)—832no—
130C2×#127D8311yescharacteristic, complemented
131#453—838no—
132C2×#104—832no—
133C2×#100—831no—
134H(5,𝔽2)—834no—
135H(5,𝔽2)—1664no—
136H(5,𝔽2)—1662no—
137C2×#41—832no—
138C2×#41—1662no—
139C22×D4—22no—
140C22×D4—1662no—
141C22×D4—1662no—
142C22×D4C2×D8311yescharacteristic
143C22×D4C2×D8311yescharacteristic, complemented
144AGL(1,ℤ/8)—838no—
145AGL(1,ℤ/8)—1664no—
146C2×SD16—1662no—
147C2×D8—1662no—
148C2×M16—832no—
149#127—22no—
150#127C2×D8314yescomplemented
151C2×C42C2×D8311yescharacteristic, complemented
152#104—838no—
153#100—834no—
154C24—21no—
155C24—1662no—
156C24C22⋊D8312yes—
157#41—834no—
158#41—834no—
159#41—1668no—
160#41—1668no—
161#41—1662no—
162#41—1662no—
163C2×Q8—832no—
164C2×D4—28no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4—48no—
171C2×D4—832no—
172C2×D4—1668no—
173C2×D4—1668no—
174C2×D4—1664no—
175C2×D4—1668no—
176C2×D4—1662no—
177C2×D4—1668no—
178C2×D4C22⋊D8312yes—
179C2×D4C22×D8312yes—
180C2×D4C22×D8312yescomplemented
181C22×C4—21no—
182C22×C4—1662no—
183C22×C4—1662no—
184C22×C4C22×D8311yescharacteristic
185SD16—1668no—
186D8—1668no—
187M16—834no—
188M16—1662no—
189C2×C8—1662no—
190C42—21no—
191C42C22×D8312yescomplemented
192C23—22no—
193C23—22no—
194C23—22no—
195C23—44no—
196C23—44no—
197C23—41no—
198C23—41no—
199C23—6644no—
200C23—1668no—
201C23—1662no—
202C23C2×C22⋊D8311yescharacteristic
203C23C2×C22⋊D8314yes—
204Q8—834no—
205Q8—1662no—
206D4—24no—
207D4—24no—
208D4—24no—
209D4—416no—
210D4—42no—
211D4—834no—
212D4—16616no—
213D4—1664no—
214D4—1664no—
215D4—1662no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—1668no—
219C2×C4—1662no—
220C2×C4—1664no—
221C2×C4—1664no—
222C2×C4D4×D8312yes—
223C2×C4D4×D8312yes—
224C2×C4C2×C22⋊D8311yescharacteristic
225C2×C4C23×D8311yescharacteristic
226C8—1664no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—44no—
232C22—42no—
233C22—82no—
234C22—82no—
235C22—82no—
236C22—3324no—
237C22—6648no—
238C22—1664no—
239C22#1458176011yescharacteristic
240C22#1458176011yescharacteristic
241C22C22×C22⋊D8311yescharacteristic
242C4—24no—
243C4—1664no—
244C4#1458176012yes—
245C4C2×D4×D8312yes—
246C2—21no—
247C2—21no—
248C2—44no—
249C2—82no—
250C2—3324no—
251C2#1912786812yesdirect product factor
252C2C2×#1458176011yescharacteristic
subgroupG/H
centerC22#14581760
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×#127×C83C2
socleC22×C83#120
hypercenterC2×#127D83
hypocenterC83C2×#453
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#14581837C2semidirect
2. C2×#14581818C2semidirect
3. #19127868C2direct (N × H)
4. C2×#14581720C2semidirect
5. C2×#14581709C2semidirect
6. C2×#127×C83C2semidirect
9. #14581837C22semidirect
15. #14581818C22semidirect
18. C2×#13050574C22semidirect
19. #14581720C22semidirect
20. #14581709C22semidirect
23. C22×D4×C83C22semidirect
25. #127×C83C22semidirect
26. C2×C42×C83C22semidirect
30. #13050590D4semidirect
34. C2×Dic166D4semidirect
35. C2×D332D4semidirect
47. #13050574C23semidirect
60. C2×D4×C83C23semidirect
64. C42×C83C23semidirect
94. D332C2×D4semidirect
98. Dic166C2×D4semidirect
123. C2×C83#453semidirect
127. C83C2×#453semidirect
130. C2×#127D83semidirect
143. C22×D4C2×D83semidirect
150. #127C2×D83semidirect
151. C2×C42C2×D83semidirect
180. C2×D4C22×D83semidirect
191. C42C22×D83semidirect
251. C2#19127868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145818372
C2×#145818182
#191278682
C2×#145817202
C2×#145817092
C2×#127×C832
C2×#45383