Finite Group Databasebeta

← C2×#19127850 #24916643

Subgroups — C2×#19127850 #24916643

Order 10624.

996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×D83C211yesmaximal, characteristic
2C22×#13050577C211yesmaximal, characteristic, complemented
3C2×#14581768C211yesmaximal, characteristic, complemented
4#19127850C218yesmaximal, direct product factor
5C2×#14581714C211yesmaximal, characteristic, complemented
6C2×#14581713C211yesmaximal, characteristic, complemented
7C2×(C2×D83)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C83C211yesmaximal, characteristic, complemented
9C24×D83—21no—
10C22×D332C2211yescharacteristic
11C22×C22⋊D83—21no—
12C2×D4×D83—24no—
13C2×D4×D83—22no—
14C2×D4×D83—24no—
15C2×D4×D83C2214yes—
16C22×C4×D83C2211yescharacteristic
17C2×#13050577—24no—
18C2×#13050577C2214yescomplemented
19C22×C83⋊C8C2211yescharacteristic, complemented
20#14581768—22no—
21#14581768C2214yescomplemented
22C2×C4⋊Dic83C2211yescharacteristic, complemented
23C2×Dic83⋊C4—21no—
24C2×(C2×D83)⋊C4—21no—
25#14581714C2214yescomplemented
26#14581713C2214yescomplemented
27(C2×D83)⋊C8C2214yescomplemented
28C22×Q8×C83C2211yescharacteristic, complemented
29C22×D4×C83C2211yescharacteristic
30C2×SD16×C83—24no—
31C2×SD16×C83C2214yescomplemented
32C22×C8×C83C2211yescharacteristic, complemented
33C23×D83—28no—
34C23×D83—21no—
35C23×D83—24no—
36C23×D83—44no—
37C23×D83—44no—
38C23×D83D411yescharacteristic
39C2×D332—21no—
40C2×D332—22no—
41C2×D332D414yes—
42C2×D332C2312yes—
43C2×C22⋊D83—28no—
44C2×C22⋊D83—24no—
45D4×D83—216no—
46D4×D83—28no—
47D4×D83—28no—
48C22×Dic83—21no—
49C22×Dic83D411yescharacteristic
50C2×C4×D83—22no—
51C2×C4×D83—22no—
52C2×C4×D83D412yes—
53C2×C4×D83C2312yes—
54#13050577—28no—
55C2×C83⋊C8—22no—
56C2×C83⋊C8C2312yescomplemented
57C4⋊Dic83—21no—
58C4⋊Dic83C2312yescomplemented
59Dic83⋊C4—24no—
60(C2×D83)⋊C4—24no—
61C24×C83—21no—
62C2×Q8×C83—21no—
63C2×Q8×C83—22no—
64C2×Q8×C83—22no—
65C2×Q8×C83C2312yescomplemented
66C2×D4×C83—21no—
67C2×D4×C83—22no—
68C2×D4×C83D414yes—
69C2×D4×C83C2312yes—
70C22×C4×C83—21no—
71C22×C4×C83C2311yescharacteristic
72SD16×C83—28no—
73C2×C8×C83—22no—
74C2×C8×C83C2312yescomplemented
75C23×C83—24no—
76C23×C83—22no—
77C23×C83—42no—
78C23×C83—42no—
79C23×C83C2×D411yescharacteristic
80C22×D83—22no—
81C22×D83—22no—
82C22×D83—216no—
83C22×D83—24no—
84C22×D83—22no—
85C22×D83—48no—
86C22×D83—432no—
87C22×D83—42no—
88C22×D83—42no—
89C22×D83—48no—
90C22×D83SD1614yescomplemented
91C22×D83C2×D412yes—
92Q8×C83—22no—
93Q8×C83—22no—
94Q8×C83—42no—
95D4×C83—24no—
96D4×C83—22no—
97D4×C83C2×D414yes—
98C2×C4×C83—22no—
99C2×C4×C83—42no—
100C2×C4×C83C2×D411yescharacteristic
101C2×C4×C83C2×D412yes—
102C2×C4×C83C2×D412yes—
103C2×C4×C83C2411yescharacteristic
104C22⋊D83—216no—
105C2×Dic83—22no—
106C2×Dic83—22no—
107C2×Dic83—42no—
108C2×Dic83C2×D412yes—
109D332—24no—
110D332—22no—
111D332C2×D414yes—
112C4×D83—24no—
113C4×D83—22no—
114C4×D83—22no—
115C8×C83—22no—
116C83⋊C8—22no—
117C22×C83—24no—
118C22×C83—42no—
119C22×C83—42no—
120C22×C83—48no—
121C22×C83#12012yes—
122C22×C83C2×SD1612yes—
123C22×C83AGL(1,ℤ/8)12yes—
124C22×C83C22×D411yescharacteristic
125C2×D83—22no—
126C2×D83—22no—
127C2×D83—28no—
128C2×D83—24no—
129C2×D83—432no—
130C2×D83—42no—
131C2×D83—42no—
132C2×D83—48no—
133C2×D83C2×SD1614yescomplemented
134C4×C83—42no—
135C4×C83#12012yes—
136C4×C83C22×D411yescharacteristic
137C4×C83C22×D411yescharacteristic
138Dic83—22no—
139Dic83—42no—
140C2×C83—44no—
141C2×C83#45014yescomplemented
142C2×C83C2×#12011yescharacteristic
143C2×C83C22×SD1611yescharacteristic
144C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
145D83—24no—
146D83—44no—
147C2×#450—831nomaximal, Sylow
148C83C2×#45011yescharacteristic, complemented, Sylow
149C23×D4—831no—
150C22×SD16—831no—
151C22×SD16D8311yescharacteristic, complemented
152C2×C22⋊Q8—831no—
153#450—838no—
154C2×#102—831no—
155C2×#102—831no—
156C2×C22⋊C8—831no—
157C25—1661no—
158C22×Q8C2×D8311yescharacteristic, complemented
159C22×D4—834no—
160C22×D4—831no—
161C22×D4—1662no—
162C22×D4—1661no—
163C22×D4—1664no—
164C22×D4—1664no—
165C22×D4C2×D8311yescharacteristic
166C23×C4—831no—
167C2×SD16—24no—
168C2×SD16—834no—
169C2×SD16—1664no—
170C2×SD16C2×D8314yescomplemented
171C22×C8—831no—
172C22×C8C2×D8311yescharacteristic, complemented
173C22⋊Q8—834no—
174C22⋊Q8—1662no—
175C2×C4⋊C4—831no—
176C2×C4⋊C4—1661no—
177C2×C22⋊C4—1661no—
178#102—834no—
179#102—834no—
180C22⋊C8—834no—
181C24—21no—
182C24—3324no—
183C24—3324no—
184C24—831no—
185C24—1664no—
186C24—1668no—
187C24—1661no—
188C2×Q8—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8C22×D8312yescomplemented
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—834no—
195C2×D4—832no—
196C2×D4—1664no—
197C2×D4—1668no—
198C2×D4—16616no—
199C2×D4—1668no—
200C2×D4—1668no—
201C2×D4—1661no—
202C2×D4—1662no—
203C2×D4C22⋊D8314yes—
204C2×D4C22×D8312yes—
205C22×C4—21no—
206C22×C4—831no—
207C22×C4—832no—
208C22×C4—832no—
209C22×C4—1661no—
210C22×C4—1662no—
211C22×C4—1662no—
212C22×C4C22×D8311yescharacteristic
213SD16—28no—
214SD16—1668no—
215C2×C8—22no—
216C2×C8—832no—
217C2×C8—1662no—
218C2×C8C22×D8312yescomplemented
219C4⋊C4—832no—
220C4⋊C4—1664no—
221C4⋊C4—1661no—
222C22⋊C4—1664no—
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—3328no—
228C23—33232no—
229C23—3328no—
230C23—3322no—
231C23—3322no—
232C23—834no—
233C23—832no—
234C23—16616no—
235C23—1664no—
236C23—1662no—
237C23—1662no—
238C23—1662no—
239C23D4×D8311yescharacteristic
240Q8—22no—
241Q8—22no—
242Q8—42no—
243D4—24no—
244D4—22no—
245D4—834no—
246D4—16616no—
247D4—1664no—
248D4—1662no—
249D4C2×C22⋊D8314yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—3322no—
253C2×C4—832no—
254C2×C4—1662no—
255C2×C4—1662no—
256C2×C4—1664no—
257C2×C4—1662no—
258C2×C4—1662no—
259C2×C4D4×D8311yescharacteristic
260C2×C4D4×D8312yes—
261C2×C4C2×C22⋊D8312yes—
262C2×C4C23×D8311yescharacteristic
263C8—22no—
264C8—1662no—
265C22—24no—
266C22—48no—
267C22—42no—
268C22—42no—
269C22—33232no—
270C22—3328no—
271C22—3322no—
272C22—3322no—
273C22—834no—
274C22—1664no—
275C22—1668no—
276C22—1662no—
277C22—1662no—
278C22#1458176012yes—
279C22SD16×D8312yes—
280C22#1458181912yes—
281C22C2×D4×D8311yescharacteristic
282C4—42no—
283C4—3322no—
284C4—1662no—
285C4#1458176012yes—
286C4C2×D4×D8311yescharacteristic
287C4C22×C22⋊D8311yescharacteristic
288C2—44no—
289C2—3324no—
290C2—1664no—
291C2#1912785014yesdirect product factor
292C2C2×#1458176011yescharacteristic
293C2C2×SD16×D8311yescharacteristic
294C2C2×#1458181911yescharacteristic
subgroupG/H
centerC23D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC22×SD16×C83C2
socleC23×C83C2×D4
prime radicalC22×D4×D83C2
hypercenterC22×SD16D83
hypocenterC83C2×#450
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C22×#13050577C2semidirect
3. C2×#14581768C2semidirect
4. #19127850C2direct (N × H)
5. C2×#14581714C2semidirect
6. C2×#14581713C2semidirect
7. C2×(C2×D83)⋊C8C2semidirect
8. C22×SD16×C83C2semidirect
18. C2×#13050577C22semidirect
19. C22×C83⋊C8C22semidirect
21. #14581768C22semidirect
22. C2×C4⋊Dic83C22semidirect
25. #14581714C22semidirect
26. #14581713C22semidirect
27. (C2×D83)⋊C8C22semidirect
28. C22×Q8×C83C22semidirect
31. C2×SD16×C83C22semidirect
32. C22×C8×C83C22semidirect
56. C2×C83⋊C8C23semidirect
58. C4⋊Dic83C23semidirect
65. C2×Q8×C83C23semidirect
74. C2×C8×C83C23semidirect
90. C22×D83SD16semidirect
133. C2×D83C2×SD16semidirect
141. C2×C83#450semidirect
148. C83C2×#450semidirect
151. C22×SD16D83semidirect
158. C22×Q8C2×D83semidirect
170. C2×SD16C2×D83semidirect
172. C22×C8C2×D83semidirect
191. C2×Q8C22×D83semidirect
218. C2×C8C22×D83semidirect
291. C2#19127850direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D832
C22×#130505772
C2×#145817682
#191278502
C2×#145817142
C2×#145817132
C2×(C2×D83)⋊C82
C22×SD16×C832
C2×#45083