Finite Group Databasebeta

← C2×#19127878 #24916792

Subgroups — C2×#19127878 #24916792

Order 10624.

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

normal subgroups only

This group has 760 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
2C2×#14581823C212yesmaximal, complemented
3#19127878C218yesmaximal, direct product factor
4C2×#14581720C212yesmaximal, complemented
5C2×#14581709C211yesmaximal, characteristic, complemented
6C2×#124×C83C211yesmaximal, characteristic, complemented
7#14581837—24no—
8#14581837—22no—
9#14581837C2214yes—
10C2×#13050590C2212yes—
11C2×#13050589—22no—
12C22×C22⋊D83—22no—
13C2×D4×D83—22no—
14#14581823—24no—
15#14581823C2218yescomplemented
16C2×#13050580—22no—
17C2×#13050577—22no—
18C2×#13050574C2212yescomplemented
19#14581720C2218yescomplemented
20#14581709C2214yescomplemented
21C22×Q8×C83C2211yescharacteristic, complemented
22C22×D4×C83C2211yescharacteristic
23#124×C83—22no—
24#124×C83C2214yescomplemented
25C2×C22⋊C4×C83—22no—
26C2×C42×C83C2211yescharacteristic, complemented
27C23×D83—22no—
28#13050590—22no—
29#13050590—22no—
30#13050590D414yes—
31#13050590C2314yes—
32#13050589—28no—
33#13050589—28no—
34C2×Dic166D412yes—
35C2×D332D412yes—
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#13050580—28no—
45#13050577—28no—
46#13050574—22no—
47#13050574C2314yescomplemented
48C2×C83⋊C8—22no—
49C24×C83D412yes—
50C2×Q8×C83—21no—
51C2×Q8×C83—22no—
52C2×Q8×C83—22no—
53C2×Q8×C83C2312yescomplemented
54C2×D4×C83—22no—
55C2×D4×C83—22no—
56C2×D4×C83D412yes—
57C2×D4×C83C2312yes—
58C22×C4×C83—21no—
59C22×C4×C83—21no—
60C22×C4×C83C2311yescharacteristic
61C22⋊C4×C83—28no—
62C42×C83—21no—
63C42×C83C2312yescomplemented
64C23×C83—22no—
65C23×C83—22no—
66C23×C83—44no—
67C23×C83C2×D411yescharacteristic
68C23×C83C2×D414yes—
69C22×D83—22no—
70C22×D83—28no—
71C22×D83—84no—
72Q8×C83—24no—
73Q8×C83—42no—
74D4×C83—24no—
75D4×C83—24no—
76C2×C4×C83—22no—
77C2×C4×C83—22no—
78C2×C4×C83—42no—
79C2×C4×C83—41no—
80C2×C4×C83—41no—
81C2×C4×C83C2×D412yes—
82C2×C4×C83C2×D412yes—
83C2×C4×C83C2×D411yescharacteristic
84C2×C4×C83C2411yescharacteristic
85C22⋊D83—216no—
86C22⋊D83—24no—
87C22⋊D83—24no—
88C2×Dic83—28no—
89C2×Dic83—22no—
90D332—22no—
91D332C2×D414yes—
92C4×D83—24no—
93C4×D83—24no—
94Dic166—22no—
95Dic166C2×D414yes—
96C83⋊C8—24no—
97C22×C83—22no—
98C22×C83—24no—
99C22×C83—44no—
100C22×C83—44no—
101C22×C83—82no—
102C22×C83#12011yescharacteristic
103C22×C83#12011yescharacteristic
104C22×C83C22×D411yescharacteristic
105C2×D83—24no—
106C2×D83—44no—
107C2×D83—88no—
108C4×C83—42no—
109C4×C83—42no—
110C4×C83#12012yes—
111C4×C83C22×D412yes—
112Dic83—24no—
113C2×C83—21no—
114C2×C83—21no—
115C2×C83—44no—
116C2×C83#45512yescomplemented
117C2×C83C2×#12011yescharacteristic
118D83—44no—
119C2×#455—831nomaximal, Sylow
120C83C2×#45511yescharacteristic, complemented, Sylow
121C2×H(5,𝔽2)—831no—
122C2×#137—832no—
123C2×#124D8311yescharacteristic, complemented
124#455—838no—
125C2×#104—832no—
126C2×#100—831no—
127H(5,𝔽2)—834no—
128H(5,𝔽2)—1664no—
129H(5,𝔽2)—1662no—
130C2×#41—832no—
131C2×#41—1662no—
132C22×Q8C2×D8311yescharacteristic, complemented
133C22×D4—1662no—
134C22×D4—1662no—
135C22×D4C2×D8311yescharacteristic
136#137—838no—
137#137—1664no—
138C2×Q16—1662no—
139C2×SD16—1662no—
140C2×M16—832no—
141#124—22no—
142#124C2×D8314yescomplemented
143C2×C22⋊C4—22no—
144C2×C42C2×D8311yescharacteristic, complemented
145#104—838no—
146#100—834no—
147C24—1662no—
148C24C22⋊D8312yes—
149#41—834no—
150#41—834no—
151#41—1668no—
152#41—1668no—
153#41—1662no—
154#41—1662no—
155C2×Q8—21no—
156C2×Q8—22no—
157C2×Q8—22no—
158C2×Q8—832no—
159C2×Q8C22×D8312yescomplemented
160C2×D4—22no—
161C2×D4—22no—
162C2×D4—832no—
163C2×D4—1668no—
164C2×D4—1668no—
165C2×D4—1664no—
166C2×D4—1668no—
167C2×D4—1662no—
168C2×D4—1668no—
169C2×D4C22⋊D8312yes—
170C2×D4C22×D8312yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—1662no—
174C22×C4—1662no—
175C22×C4C22×D8311yescharacteristic
176Q16—1668no—
177SD16—1668no—
178M16—834no—
179M16—1662no—
180C2×C8—1662no—
181C22⋊C4—28no—
182C42—21no—
183C42C22×D8312yescomplemented
184C23—22no—
185C23—22no—
186C23—44no—
187C23—6644no—
188C23—1668no—
189C23—1662no—
190C23C2×C22⋊D8311yescharacteristic
191C23C2×C22⋊D8314yes—
192Q8—24no—
193Q8—42no—
194Q8—834no—
195Q8—1662no—
196D4—24no—
197D4—24no—
198D4—834no—
199D4—16616no—
200D4—1664no—
201D4—1664no—
202D4—1662no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—1668no—
209C2×C4—1662no—
210C2×C4—1664no—
211C2×C4—1664no—
212C2×C4D4×D8312yes—
213C2×C4D4×D8312yes—
214C2×C4C2×C22⋊D8311yescharacteristic
215C2×C4C23×D8311yescharacteristic
216C8—1664no—
217C22—22no—
218C22—24no—
219C22—44no—
220C22—44no—
221C22—82no—
222C22—3324no—
223C22—6648no—
224C22—1664no—
225C22#1458176011yescharacteristic
226C22#1458176011yescharacteristic
227C22C22×C22⋊D8311yescharacteristic
228C4—42no—
229C4—42no—
230C4—1664no—
231C4#1458176012yes—
232C4C2×D4×D8312yes—
233C2—21no—
234C2—21no—
235C2—44no—
236C2—3324no—
237C2#1912787812yesdirect product factor
238C2C2×#1458176011yescharacteristic
subgroupG/H
centerC22#14581760
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×#124×C83C2
socleC22×C83#120
prime radicalC2×#14581837C2
hypercenterC2×#124D83
hypocenterC83C2×#455
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×#14581823C2semidirect
3. #19127878C2direct (N × H)
4. C2×#14581720C2semidirect
5. C2×#14581709C2semidirect
6. C2×#124×C83C2semidirect
15. #14581823C22semidirect
18. C2×#13050574C22semidirect
19. #14581720C22semidirect
20. #14581709C22semidirect
21. C22×Q8×C83C22semidirect
24. #124×C83C22semidirect
26. C2×C42×C83C22semidirect
47. #13050574C23semidirect
53. C2×Q8×C83C23semidirect
63. C42×C83C23semidirect
116. C2×C83#455semidirect
120. C83C2×#455semidirect
123. C2×#124D83semidirect
132. C22×Q8C2×D83semidirect
142. #124C2×D83semidirect
144. C2×C42C2×D83semidirect
159. C2×Q8C22×D83semidirect
183. C42C22×D83semidirect
237. C2#19127878direct (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×#145818232
#191278782
C2×#145817202
C2×#145817092
C2×#124×C832
C2×#45583