Finite Group Databasebeta

← #392×D83 #24910657

Subgroups — #392×D83 #24910657

Order 10624.

1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 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×D83C213yesmaximal, complemented
2C2×C22⋊C4×D83C213yesmaximal, complemented
3#19127611C211yesmaximal, characteristic, complemented
4#19127610C213yesmaximal, complemented
5#19127609C213yesmaximal, complemented
6#95×D83C211yesmaximal, characteristic, complemented
7#392×C83C211yesmaximal, characteristic, complemented
8C24×D83C2213yes—
9C22×D332C2213yescomplemented
10C22×C22⋊D83C2216yescomplemented
11C2×D4×D83—224no—
12C2×D4×D83—212no—
13C22×C4×D83C2211yescharacteristic
14C22×C4×D83C2213yes—
15C2×C22⋊Dic83C2213yescomplemented
16C2×(C2×D83)⋊C4C2213yescomplemented
17C2×(C2×D83)⋊C4C2213yescomplemented
18C22⋊C4×D83—212no—
19C83⋊#95C2213yescomplemented
20C22×D4×C83C2213yescomplemented
21C2×C22⋊C4×C83C2213yescomplemented
22#95×C83C2211yescharacteristic, complemented
23C23×D83—212no—
24C23×D83—212no—
25C23×D83—26no—
26C23×D83—26no—
27C23×D83D4112yescomplemented
28C23×D83C2313yes—
29C23×D83C2311yescharacteristic
30C2×D332—212no—
31C2×D332—26no—
32C2×C22⋊D83—212no—
33C2×C22⋊D83—212no—
34C2×C22⋊D83—212no—
35D4×D83—296no—
36C22×Dic83C2311yescharacteristic
37C22×Dic83C2313yes—
38C2×C4×D83—212no—
39C2×C4×D83—26no—
40C2×C4×D83D4112yescomplemented
41C22⋊Dic83—26no—
42(C2×D83)⋊C4—26no—
43(C2×D83)⋊C4—26no—
44C24×C83C2313yes—
45C2×D4×C83—212no—
46C2×D4×C83—26no—
47C22×C4×C83C2311yescharacteristic
48C22×C4×C83C2313yes—
49C22⋊C4×C83—26no—
50C23×C83—23no—
51C23×C83—26no—
52C23×C83—26no—
53C23×C83—23no—
54C23×C83C2×D416yescomplemented
55C23×C83C2411yescharacteristic
56C22×D83—23no—
57C22×D83—26no—
58C22×D83—26no—
59C22×D83—23no—
60C22×D83—248no—
61C22×D83—224no—
62C22×D83—412no—
63C22×D83—424no—
64C22×D83—412no—
65C22×D83C2×D416yes—
66C22×D83C2×D416yes—
67C22×D83C2×D416yescomplemented
68C22×D83#4112yes—
69D4×C83—224no—
70C2×C4×C83—26no—
71C2×C4×C83—23no—
72C2×C4×C83C2×D416yescomplemented
73C22⋊D83—248no—
74C2×Dic83—26no—
75C2×Dic83—23no—
76C2×Dic83C2×D416yescomplemented
77D332—224no—
78C4×D83—224no—
79C4×D83—44no—
80C22×C83—212no—
81C22×C83—26no—
82C22×C83—43no—
83C22×C83—46no—
84C22×C83—43no—
85C22×C83C22×D413yes—
86C22×C83C22×D413yes—
87C22×C83C2×#4111yescharacteristic
88C2×D83—212no—
89C2×D83—26no—
90C2×D83—43no—
91C2×D83—46no—
92C2×D83—43no—
93C2×D83—448no—
94C2×D83#120112yes—
95C2×D83#121112yes—
96C2×D83#12714yes—
97C4×C83—26no—
98C4×C83—41no—
99Dic83—26no—
100Dic83—41no—
101C2×C83—46no—
102C2×C83C2×#12013yes—
103C2×C83C2×#12113yes—
104C2×C83C2×#12711yescharacteristic
105D83—46no—
106D83#39218yesdirect product factor
107C2×#392—831nomaximal, Sylow
108C83C2×#39211yescharacteristic, complemented, Sylow
109C23×D4—833no—
110C22×C22⋊C4—833no—
111#392—833no—
112#392—833no—
113#392—831no—
114#392D8311yescharacteristic, direct product factor
115C2×#95—831no—
116C25—833no—
117C22×D4—836no—
118C22×D4—833no—
119C22×D4—16612no—
120C22×D4—16624no—
121C22×D4C2×D8313yescomplemented
122C23×C4—833no—
123C23×C4—831no—
124C2×C22⋊C4—833no—
125C2×C22⋊C4—833no—
126C2×C22⋊C4—833no—
127C2×C22⋊C4—16612no—
128C2×C22⋊C4C2×D8313yescomplemented
129#95—833no—
130#95C2×D8311yescharacteristic, complemented
131C24—831no—
132C24—8312no—
133C24—833no—
134C24—1666no—
135C24—16612no—
136C24—16612no—
137C24—1666no—
138C24C22×D8313yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—16612no—
142C2×D4—16612no—
143C2×D4—16696no—
144C2×D4—16612no—
145C2×D4—16612no—
146C2×D4—1666no—
147C22×C4—833no—
148C22×C4—8312no—
149C22×C4—831no—
150C22×C4—1666no—
151C22×C4—16612no—
152C22×C4C22×D8311yescharacteristic
153C22×C4C22×D8313yes—
154C22⋊C4—26no—
155C22⋊C4—1666no—
156C22⋊C4—1666no—
157C22⋊C4—1666no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—33212no—
163C23—33224no—
164C23—33212no—
165C23—836no—
166C23—836no—
167C23—832no—
168C23—836no—
169C23—16648no—
170C23—16624no—
171C23—1663no—
172C23—1666no—
173C23—1666no—
174C23—1663no—
175C23D4×D8316yescomplemented
176C23C23×D8311yescharacteristic
177D4—224no—
178D4—16624no—
179D4—16648no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—3324no—
183C2×C4—836no—
184C2×C4—16624no—
185C2×C4—1663no—
186C2×C4—1666no—
187C2×C4D4×D8316yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—46no—
192C22—43no—
193C22—33248no—
194C22—3323no—
195C22—3326no—
196C22—3323no—
197C22—8312no—
198C22—8312no—
199C22—834no—
200C22—16612no—
201C22—1666no—
202C22C2×D4×D8313yes—
203C22C2×D4×D8313yes—
204C22#41×D8311yescharacteristic
205C4—26no—
206C4—41no—
207C4—3321no—
208C4—1666no—
209C2—46no—
210C2—3326no—
211C2—838no—
212C2#120×D8313yes—
213C2#121×D8313yes—
214C2#127×D8311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#392×C83C2
hypercenter#392D83
hypocenterC83C2×#392
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D83C2semidirect
2. C2×C22⋊C4×D83C2semidirect
3. #19127611C2semidirect
4. #19127610C2semidirect
5. #19127609C2semidirect
6. #95×D83C2semidirect
7. #392×C83C2semidirect
9. C22×D332C22semidirect
10. C22×C22⋊D83C22semidirect
15. C2×C22⋊Dic83C22semidirect
16. C2×(C2×D83)⋊C4C22semidirect
17. C2×(C2×D83)⋊C4C22semidirect
19. C83⋊#95C22semidirect
20. C22×D4×C83C22semidirect
21. C2×C22⋊C4×C83C22semidirect
22. #95×C83C22semidirect
27. C23×D83D4semidirect
40. C2×C4×D83D4semidirect
54. C23×C83C2×D4semidirect
67. C22×D83C2×D4semidirect
72. C2×C4×C83C2×D4semidirect
76. C2×Dic83C2×D4semidirect
106. D83#392direct (N × H)
108. C83C2×#392semidirect
114. #392D83direct (N × H)
121. C22×D4C2×D83semidirect
128. C2×C22⋊C4C2×D83semidirect
130. #95C2×D83semidirect
175. C23D4×D83semidirect
187. C2×C4D4×D83semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D832
C2×C22⋊C4×D832
#191276112
#191276102
#191276092
#95×D832
#392×C832
C2×#39283