Finite Group Databasebeta

← C2×#19127846 #24916664

Subgroups — C2×#19127846 #24916664

Order 10624.

812 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×#13050577C211yesmaximal, characteristic, complemented
2C22×#13050575C211yesmaximal, characteristic, complemented
3C2×#14581766C211yesmaximal, characteristic, complemented
4#19127846C218yesmaximal, direct product factor
5C2×#14581716C211yesmaximal, characteristic, complemented
6C2×#14581713C211yesmaximal, characteristic, complemented
7C2×C22⋊(C83⋊C8)C211yesmaximal, characteristic, complemented
8C22×#41×C83C211yesmaximal, characteristic, complemented
9C22×D332C2211yescharacteristic
10C22×C22⋊D83—21no—
11C2×#13050577—24no—
12C2×#13050577C2214yescomplemented
13C2×#13050575—24no—
14C2×#13050575C2214yescomplemented
15C22×C83⋊C8C2211yescharacteristic
16C22×C83⋊C8C2211yescharacteristic
17#14581766—22no—
18#14581766C2214yescomplemented
19C2×C4⋊Dic83C2211yescharacteristic
20C2×(C2×D83)⋊C4—21no—
21#14581716C2214yescomplemented
22#14581713C2214yescomplemented
23C22⋊(C83⋊C8)C2214yescomplemented
24C2×#41×C83—24no—
25C2×#41×C83—24no—
26C2×#41×C83—22no—
27C2×#41×C83C2214yescomplemented
28C22×Q8×C83C2211yescharacteristic
29C22×D4×C83—21no—
30C22×D4×C83C2211yescharacteristic
31C23×C4×C83—21no—
32C23×C4×C83C2211yescharacteristic
33C23×D83—21no—
34C2×D332—22no—
35C2×D332—22no—
36C2×D332—21no—
37C2×D332C2312yes—
38C2×C22⋊D83—24no—
39C2×C22⋊D83—44no—
40C22×Dic83—21no—
41#13050577—28no—
42#13050575—28no—
43C2×C83⋊C8—22no—
44C2×C83⋊C8—22no—
45C2×C83⋊C8C2312yes—
46C2×C83⋊C8C2312yes—
47C4⋊Dic83—21no—
48C4⋊Dic83C2312yes—
49(C2×D83)⋊C4—24no—
50C24×C83—21no—
51C24×C83D411yescharacteristic
52#41×C83—216no—
53#41×C83—28no—
54#41×C83—28no—
55C2×Q8×C83—22no—
56C2×Q8×C83—21no—
57C2×Q8×C83D414yescomplemented
58C2×Q8×C83C2312yes—
59C2×D4×C83—28no—
60C2×D4×C83—24no—
61C2×D4×C83—21no—
62C2×D4×C83—22no—
63C2×D4×C83D414yescomplemented
64C2×D4×C83C2312yes—
65C22×C4×C83—28no—
66C22×C4×C83—21no—
67C22×C4×C83—24no—
68C22×C4×C83—22no—
69C22×C4×C83—22no—
70C22×C4×C83D412yes—
71C22×C4×C83D411yescharacteristic
72C22×C4×C83C2312yes—
73C22×C4×C83C2311yescharacteristic
74C23×C83—22no—
75C23×C83—24no—
76C23×C83—22no—
77C23×C83—22no—
78C23×C83—22no—
79C23×C83—42no—
80C23×C83—42no—
81C23×C83C2×D412yes—
82C23×C83C2×D411yescharacteristic
83C22×D83—22no—
84C22×D83—42no—
85C22×D83—42no—
86C22×D83—42no—
87Q8×C83—24no—
88Q8×C83—22no—
89Q8×C83C2×D414yescomplemented
90D4×C83—216no—
91D4×C83—24no—
92D4×C83—22no—
93D4×C83C2×D414yescomplemented
94C2×C4×C83—216no—
95C2×C4×C83—22no—
96C2×C4×C83—24no—
97C2×C4×C83—22no—
98C2×C4×C83—24no—
99C2×C4×C83—22no—
100C2×C4×C83—22no—
101C2×C4×C83C2×D412yes—
102C2×C4×C83C2×D411yescharacteristic
103C2×C4×C83C2×D412yes—
104C2×C4×C83C2×D412yes—
105C2×C4×C83C2411yescharacteristic
106C22⋊D83—48no—
107C2×Dic83—22no—
108C2×Dic83—42no—
109D332—22no—
110D332—22no—
111D332—42no—
112C83⋊C8—22no—
113C83⋊C8—22no—
114C22×C83—22no—
115C22×C83—24no—
116C22×C83—22no—
117C22×C83—22no—
118C22×C83—42no—
119C22×C83—42no—
120C22×C83—44no—
121C22×C83—48no—
122C22×C83#12012yes—
123C22×C83#13512yes—
124C22×C83AGL(1,ℤ/8)12yes—
125C22×C83C22×D411yescharacteristic
126C2×D83—42no—
127C2×D83—42no—
128C2×D83—42no—
129C2×D83—84no—
130C4×C83—22no—
131C4×C83—24no—
132C4×C83#12012yes—
133C4×C83C22×D411yescharacteristic
134C4×C83C22×D411yescharacteristic
135Dic83—42no—
136C2×C83—42no—
137C2×C83—44no—
138C2×C83#44914yescomplemented
139C2×C83C2×#12011yescharacteristic
140C2×C83C2×#13511yescharacteristic
141C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
142D83—82no—
143C2×#449—831nomaximal, Sylow
144C83C2×#44911yescharacteristic, complemented, Sylow
145C22×#41D8311yescharacteristic, complemented
146C22×SD16—831no—
147C22×D8—831no—
148C2×#121—831no—
149#449—838no—
150C2×#103—831no—
151C2×#102—831no—
152C2×C22⋊C8—831no—
153C2×#41—24no—
154C2×#41—24no—
155C2×#41—22no—
156C2×#41C2×D8314yescomplemented
157C22×Q8C2×D8311yescharacteristic
158C22×D4—21no—
159C22×D4—831no—
160C22×D4—1661no—
161C22×D4C2×D8311yescharacteristic
162C23×C4—21no—
163C23×C4C2×D8311yescharacteristic
164C2×SD16—834no—
165C2×SD16—1664no—
166C2×D8—834no—
167C2×D8—1664no—
168C22×C8—831no—
169C22×C8—831no—
170#121—834no—
171#121—1662no—
172C2×C4⋊C4—831no—
173C2×C22⋊C4—1661no—
174#103—834no—
175#102—834no—
176C22⋊C8—834no—
177C24—21no—
178C24—1661no—
179C24C22⋊D8311yescharacteristic
180#41—216no—
181#41—28no—
182#41—28no—
183C2×Q8—22no—
184C2×Q8—21no—
185C2×Q8C22⋊D8314yescomplemented
186C2×Q8C22×D8312yes—
187C2×D4—28no—
188C2×D4—24no—
189C2×D4—21no—
190C2×D4—22no—
191C2×D4—3324no—
192C2×D4—832no—
193C2×D4—1664no—
194C2×D4—1661no—
195C2×D4—1662no—
196C2×D4—1662no—
197C2×D4C22⋊D8314yescomplemented
198C2×D4C22×D8312yes—
199C22×C4—28no—
200C22×C4—21no—
201C22×C4—24no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—1661no—
205C22×C4C22⋊D8312yes—
206C22×C4C22⋊D8311yescharacteristic
207C22×C4C22×D8312yes—
208C22×C4C22×D8311yescharacteristic
209SD16—1668no—
210D8—1668no—
211C2×C8—832no—
212C2×C8—832no—
213C2×C8—1662no—
214C2×C8—1662no—
215C4⋊C4—832no—
216C4⋊C4—1661no—
217C22⋊C4—1664no—
218C23—22no—
219C23—24no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—42no—
224C23—42no—
225C23—3322no—
226C23—3322no—
227C23—3322no—
228C23—1662no—
229C23C2×C22⋊D8312yes—
230C23C2×C22⋊D8311yescharacteristic
231Q8—24no—
232Q8—22no—
233Q8C2×C22⋊D8314yescomplemented
234D4—216no—
235D4—24no—
236D4—22no—
237D4—3328no—
238D4—3322no—
239D4—1662no—
240D4—1662no—
241D4C2×C22⋊D8314yescomplemented
242C2×C4—216no—
243C2×C4—22no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—3322no—
250C2×C4—1662no—
251C2×C4C2×C22⋊D8312yes—
252C2×C4C2×C22⋊D8311yescharacteristic
253C2×C4C2×C22⋊D8312yes—
254C2×C4C2×C22⋊D8312yes—
255C2×C4C23×D8311yescharacteristic
256C8—1662no—
257C8—1662no—
258C22—22no—
259C22—24no—
260C22—22no—
261C22—22no—
262C22—44no—
263C22—48no—
264C22—42no—
265C22—42no—
266C22—3322no—
267C22—3322no—
268C22—3322no—
269C22—6644no—
270C22#1458176112yes—
271C22#1458181212yes—
272C22#1458181712yes—
273C22C22×C22⋊D8311yescharacteristic
274C4—22no—
275C4—24no—
276C4—3322no—
277C4#1458176112yes—
278C4C22×C22⋊D8311yescharacteristic
279C4C22×C22⋊D8311yescharacteristic
280C2—42no—
281C2—44no—
282C2—6642no—
283C2#1912784614yesdirect product factor
284C2C2×#1458176111yescharacteristic
285C2C2×#1458181211yescharacteristic
286C2C2×#1458181711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC22×#41×C83C2
socleC23×C83C2×D4
hypercenterC22×#41D83
hypocenterC83C2×#449
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#13050577C2semidirect
2. C22×#13050575C2semidirect
3. C2×#14581766C2semidirect
4. #19127846C2direct (N × H)
5. C2×#14581716C2semidirect
6. C2×#14581713C2semidirect
7. C2×C22⋊(C83⋊C8)C2semidirect
8. C22×#41×C83C2semidirect
12. C2×#13050577C22semidirect
14. C2×#13050575C22semidirect
18. #14581766C22semidirect
21. #14581716C22semidirect
22. #14581713C22semidirect
23. C22⋊(C83⋊C8)C22semidirect
27. C2×#41×C83C22semidirect
57. C2×Q8×C83D4semidirect
63. C2×D4×C83D4semidirect
89. Q8×C83C2×D4semidirect
93. D4×C83C2×D4semidirect
138. C2×C83#449semidirect
144. C83C2×#449semidirect
145. C22×#41D83semidirect
156. C2×#41C2×D83semidirect
185. C2×Q8C22⋊D83semidirect
197. C2×D4C22⋊D83semidirect
233. Q8C2×C22⋊D83semidirect
241. D4C2×C22⋊D83semidirect
283. C2#19127846direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130505772
C22×#130505752
C2×#145817662
#191278462
C2×#145817162
C2×#145817132
C2×C22⋊(C83⋊C8)2
C22×#41×C832
C2×#44983