Finite Group Databasebeta

← #24911459

Subgroups — #24911459

Order 10624.

668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14581770C212yesmaximal, complemented
2C2×C4×C22⋊D83C212yesmaximal, complemented
3#19127616C212yesmaximal, complemented
4#19127613C211yesmaximal, characteristic, complemented
5#19127610C211yesmaximal, characteristic
6#19127591C212yesmaximal, complemented
7#19127583C212yesmaximal, complemented
8#19127579C212yesmaximal, complemented
9#385×C83C211yesmaximal, characteristic, complemented
10C22×Dic166C2211yescharacteristic
11C22×D332C2211yescharacteristic
12C22×C22⋊D83C2212yes—
13C22×C4×D83C2212yes—
14#14581770—28no—
15C4×C22⋊D83—28no—
16C2×Dic83⋊C4C2212yes—
17C2×Dic83⋊C4C2212yes—
18C2×C22⋊Dic83C2212yes—
19C2×(C2×D83)⋊C4C2212yes—
20C2×(C2×D83)⋊C4C2212yes—
21C2×(C2×D83)⋊C4C2212yes—
22C2×(C2×D83)⋊C4C2212yes—
23C2×C4×Dic83C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2211yescharacteristic
26C83⋊#95C2212yes—
27C83⋊#95C2211yescharacteristic
28C23×C4×C83C2211yescharacteristic
29C2×C4⋊C4×C83C2212yes—
30C2×C22⋊C4×C83C2211yescharacteristic
31C2×C22⋊C4×C83C2211yescharacteristic
32#95×C83C2212yes—
33C23×D83C2312yes—
34C2×Dic166—24no—
35C2×Dic166—41no—
36C2×D332—24no—
37C2×D332—41no—
38C2×C22⋊D83—24no—
39C2×C22⋊D83—24no—
40C2×C22⋊D83—24no—
41C22×Dic83C2312yes—
42C22×Dic83C2312yes—
43C22×Dic83C2312yes—
44C2×C4×D83—24no—
45C2×C4×D83—24no—
46C2×C4×D83—42no—
47Dic83⋊C4—24no—
48Dic83⋊C4D418yescomplemented
49C22⋊Dic83—24no—
50(C2×D83)⋊C4—24no—
51(C2×D83)⋊C4—24no—
52(C2×D83)⋊C4—24no—
53(C2×D83)⋊C4—24no—
54C4×Dic83—24no—
55C24×C83C2311yescharacteristic
56C22×C4×C83—24no—
57C22×C4×C83—41no—
58C22×C4×C83C2311yescharacteristic
59C22×C4×C83C2311yescharacteristic
60C22×C4×C83C2312yes—
61C22×C4×C83C2312yes—
62C4⋊C4×C83—24no—
63C22⋊C4×C83—22no—
64C22⋊C4×C83—41no—
65C23×C83—22no—
66C23×C83—22no—
67C23×C83—21no—
68C23×C83—21no—
69C23×C83#4112yes—
70C23×C83C2411yescharacteristic
71C22×D83—22no—
72C22×D83—22no—
73C22×D83—22no—
74C22×D83—22no—
75C22×D83—22no—
76C22×D83—22no—
77C22×D83#4114yes—
78C2×C4×C83—22no—
79C2×C4×C83—22no—
80C2×C4×C83—22no—
81C2×C4×C83—22no—
82C2×C4×C83—22no—
83C2×C4×C83—22no—
84C2×C4×C83—22no—
85C2×C4×C83—21no—
86C2×C4×C83—21no—
87C2×C4×C83—44no—
88C2×C4×C83C2×D414yes—
89C22⋊D83—216no—
90C2×Dic83—22no—
91C2×Dic83—22no—
92C2×Dic83—22no—
93C2×Dic83—22no—
94C2×Dic83—22no—
95C2×Dic83—22no—
96C2×Dic83—22no—
97C2×Dic83C2×D414yes—
98C2×Dic83C2×D414yes—
99D332—44no—
100C4×D83—48no—
101Dic166—44no—
102C22×C83—24no—
103C22×C83—22no—
104C22×C83—41no—
105C22×C83—42no—
106C22×C83—41no—
107C22×C83C22×D412yes—
108C22×C83C2×#4112yes—
109C22×C83C2×#4111yescharacteristic
110C22×C83H(5,𝔽2)11yescharacteristic
111C22×C832−1+411yescharacteristic
112C2×D83—24no—
113C2×D83—24no—
114C2×D83—24no—
115C2×D83—42no—
116C2×D83—42no—
117C2×D83—42no—
118C2×D83—42no—
119C4×C83—24no—
120C4×C83—42no—
121C4×C83—41no—
122C4×C83—41no—
123Dic83—24no—
124Dic83—24no—
125Dic83—42no—
126C2×C83—42no—
127C2×C83#52512yes—
128C2×C83#53911yescharacteristic
129C2×C83D4211yescharacteristic
130C2×C83#54812yes—
131C2×C83#55111yescharacteristic
132D83—44no—
133#2463—831nomaximal, Sylow
134C83#246311yescharacteristic, complemented, Sylow
135C2×C22⋊Q8—832no—
136C2×C4×D4—832no—
137#394—832no—
138#393—831no—
139#392—831no—
140#388—832no—
141#387—832no—
142#386—832no—
143#385D8311yescharacteristic, complemented
144C22×Q8—831no—
145C22×D4—832no—
146C22×D4—831no—
147C23×C4—832no—
148C23×C4C2×D8311yescharacteristic
149C22⋊Q8—1668no—
150C4×D4—1668no—
151C2×C4⋊C4—832no—
152C2×C4⋊C4—832no—
153C2×C4⋊C4C2×D8312yes—
154C2×C22⋊C4—832no—
155C2×C22⋊C4—832no—
156C2×C22⋊C4—832no—
157C2×C22⋊C4—832no—
158C2×C22⋊C4—832no—
159C2×C22⋊C4C2×D8311yescharacteristic
160C2×C22⋊C4C2×D8311yescharacteristic
161C2×C42—832no—
162#95—832no—
163#95—831no—
164#95—832no—
165#95—831no—
166#95C2×D8312yes—
167C24—832no—
168C24C22×D8311yescharacteristic
169C2×Q8—3321no—
170C2×Q8—1664no—
171C2×D4—3321no—
172C2×D4—1664no—
173C2×D4—1664no—
174C2×D4—1664no—
175C2×D4—1664no—
176C22×C4—24no—
177C22×C4—41no—
178C22×C4—3322no—
179C22×C4—832no—
180C22×C4—832no—
181C22×C4—832no—
182C22×C4—1664no—
183C22×C4—1664no—
184C22×C4C22×D8311yescharacteristic
185C22×C4C22×D8312yes—
186C22×C4C22×D8311yescharacteristic
187C22×C4C22×D8312yes—
188C4⋊C4—24no—
189C4⋊C4—838no—
190C4⋊C4—1664no—
191C22⋊C4—22no—
192C22⋊C4—41no—
193C22⋊C4—1664no—
194C22⋊C4—1664no—
195C22⋊C4—1664no—
196C22⋊C4—1664no—
197C22⋊C4—1664no—
198C42—1664no—
199C23—22no—
200C23—22no—
201C23—21no—
202C23—21no—
203C23—834no—
204C23—1662no—
205C23—1662no—
206C23—1662no—
207C23—1662no—
208C23—1662no—
209C23—1662no—
210C23#1305059012yes—
211C23C23×D8311yescharacteristic
212Q8—3324no—
213D4—3324no—
214D4—16616no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—44no—
225C2×C4—3328no—
226C2×C4—834no—
227C2×C4—834no—
228C2×C4—1662no—
229C2×C4—1662no—
230C2×C4—1662no—
231C2×C4—1662no—
232C2×C4—1662no—
233C2×C4—1662no—
234C2×C4—1662no—
235C2×C4D4×D8314yes—
236C22—24no—
237C22—22no—
238C22—41no—
239C22—42no—
240C22—41no—
241C22—3322no—
242C22—3322no—
243C22—3322no—
244C22—3322no—
245C22—1664no—
246C22—1664no—
247C22—1664no—
248C22C2×D4×D8312yes—
249C22#41×D8312yes—
250C22C2×#1305059011yescharacteristic
251C22#1458183711yescharacteristic
252C22#1458184011yescharacteristic
253C4—24no—
254C4—41no—
255C4—41no—
256C4—42no—
257C4—3322no—
258C4—1664no—
259C4—1664no—
260C2—42no—
261C2—3324no—
262C2#1912821012yes—
263C2#1912829811yescharacteristic
264C2#1912833311yescharacteristic
265C2#1912836112yes—
266C2#1912837911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#385×C83C2
prime radical#19127610C2
hypercenter#385D83
hypocenterC83#2463
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14581770C2semidirect
2. C2×C4×C22⋊D83C2semidirect
3. #19127616C2semidirect
4. #19127613C2semidirect
6. #19127591C2semidirect
7. #19127583C2semidirect
8. #19127579C2semidirect
9. #385×C83C2semidirect
48. Dic83⋊C4D4semidirect
134. C83#2463semidirect
143. #385D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817702
C2×C4×C22⋊D832
#191276162
#191276132
#191276102
#191275912
#191275832
#191275792
#385×C832
#246383