Finite Group Databasebeta

← #392×D101 #27174326

Subgroups — #392×D101 #27174326

Order 12928.

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×D101C213yesmaximal, complemented
2C2×C22⋊C4×D101C213yesmaximal, complemented
3#20265087C211yesmaximal, characteristic, complemented
4#20265086C213yesmaximal, complemented
5#20265085C213yesmaximal, complemented
6#95×D101C211yesmaximal, characteristic, complemented
7#392×C101C211yesmaximal, characteristic, complemented
8C24×D101C2213yes—
9C22×D404C2213yescomplemented
10C22×C22⋊D101C2216yescomplemented
11C2×D4×D101—224no—
12C2×D4×D101—212no—
13C22×C4×D101C2211yescharacteristic
14C22×C4×D101C2213yes—
15C2×C22⋊Dic101C2213yescomplemented
16C2×#13108051C2213yescomplemented
17C2×#13108051C2213yescomplemented
18C22⋊C4×D101—212no—
19#15692162C2213yescomplemented
20C22×D4×C101C2213yescomplemented
21C2×C22⋊C4×C101C2213yescomplemented
22#95×C101C2211yescharacteristic, complemented
23C23×D101—212no—
24C23×D101—212no—
25C23×D101—26no—
26C23×D101—26no—
27C23×D101D4112yescomplemented
28C23×D101C2313yes—
29C23×D101C2311yescharacteristic
30C2×D404—212no—
31C2×D404—26no—
32C2×C22⋊D101—212no—
33C2×C22⋊D101—212no—
34C2×C22⋊D101—212no—
35D4×D101—296no—
36C22×Dic101C2311yescharacteristic
37C22×Dic101C2313yes—
38C2×C4×D101—212no—
39C2×C4×D101—26no—
40C2×C4×D101D4112yescomplemented
41C22⋊Dic101—26no—
42#13108051—26no—
43#13108051—26no—
44C24×C101C2313yes—
45C2×D4×C101—212no—
46C2×D4×C101—26no—
47C22×C4×C101C2311yescharacteristic
48C22×C4×C101C2313yes—
49C22⋊C4×C101—26no—
50C23×C101—23no—
51C23×C101—26no—
52C23×C101—26no—
53C23×C101—23no—
54C23×C101C2×D416yescomplemented
55C23×C101C2411yescharacteristic
56C22×D101—23no—
57C22×D101—26no—
58C22×D101—26no—
59C22×D101—23no—
60C22×D101—248no—
61C22×D101—224no—
62C22×D101—412no—
63C22×D101—424no—
64C22×D101—412no—
65C22×D101C2×D416yes—
66C22×D101C2×D416yes—
67C22×D101C2×D416yescomplemented
68C22×D101#4112yes—
69D4×C101—224no—
70C2×C4×C101—26no—
71C2×C4×C101—23no—
72C2×C4×C101C2×D416yescomplemented
73C22⋊D101—248no—
74C2×Dic101—26no—
75C2×Dic101—23no—
76C2×Dic101C2×D416yescomplemented
77D404—224no—
78C4×D101—224no—
79C4×D101—44no—
80C22×C101—212no—
81C22×C101—26no—
82C22×C101—43no—
83C22×C101—46no—
84C22×C101—43no—
85C22×C101C22×D413yes—
86C22×C101C22×D413yes—
87C22×C101C2×#4111yescharacteristic
88C2×D101—212no—
89C2×D101—26no—
90C2×D101—43no—
91C2×D101—46no—
92C2×D101—43no—
93C2×D101—448no—
94C2×D101#120112yes—
95C2×D101#121112yes—
96C2×D101#12714yes—
97C4×C101—26no—
98C4×C101—41no—
99Dic101—26no—
100Dic101—41no—
101C2×C101—46no—
102C2×C101C2×#12013yes—
103C2×C101C2×#12113yes—
104C2×C101C2×#12711yescharacteristic
105D101—46no—
106D101#39218yesdirect product factor
107C2×#392—1011nomaximal, Sylow
108C101C2×#39211yescharacteristic, complemented, Sylow
109C23×D4—1013no—
110C22×C22⋊C4—1013no—
111#392—1013no—
112#392—1013no—
113#392—1011no—
114#392D10111yescharacteristic, direct product factor
115C2×#95—1011no—
116C25—1013no—
117C22×D4—1016no—
118C22×D4—1013no—
119C22×D4—20212no—
120C22×D4—20224no—
121C22×D4C2×D10113yescomplemented
122C23×C4—1013no—
123C23×C4—1011no—
124C2×C22⋊C4—1013no—
125C2×C22⋊C4—1013no—
126C2×C22⋊C4—1013no—
127C2×C22⋊C4—20212no—
128C2×C22⋊C4C2×D10113yescomplemented
129#95—1013no—
130#95C2×D10111yescharacteristic, complemented
131C24—1011no—
132C24—10112no—
133C24—1013no—
134C24—2026no—
135C24—20212no—
136C24—20212no—
137C24—2026no—
138C24C22×D10113yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—20212no—
142C2×D4—20212no—
143C2×D4—20296no—
144C2×D4—20212no—
145C2×D4—20212no—
146C2×D4—2026no—
147C22×C4—1013no—
148C22×C4—10112no—
149C22×C4—1011no—
150C22×C4—2026no—
151C22×C4—20212no—
152C22×C4C22×D10111yescharacteristic
153C22×C4C22×D10113yes—
154C22⋊C4—26no—
155C22⋊C4—2026no—
156C22⋊C4—2026no—
157C22⋊C4—2026no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—1016no—
163C23—1016no—
164C23—1012no—
165C23—1016no—
166C23—40412no—
167C23—40424no—
168C23—40412no—
169C23—20248no—
170C23—20224no—
171C23—2023no—
172C23—2026no—
173C23—2026no—
174C23—2023no—
175C23D4×D10116yescomplemented
176C23C23×D10111yescharacteristic
177D4—224no—
178D4—20224no—
179D4—20248no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—1016no—
183C2×C4—4044no—
184C2×C4—20224no—
185C2×C4—2023no—
186C2×C4—2026no—
187C2×C4D4×D10116yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—46no—
192C22—43no—
193C22—10112no—
194C22—10112no—
195C22—1014no—
196C22—40448no—
197C22—4043no—
198C22—4046no—
199C22—4043no—
200C22—20212no—
201C22—2026no—
202C22C2×D4×D10113yes—
203C22C2×D4×D10113yes—
204C22#41×D10111yescharacteristic
205C4—26no—
206C4—41no—
207C4—4041no—
208C4—2026no—
209C2—46no—
210C2—1018no—
211C2—4046no—
212C2#120×D10113yes—
213C2#121×D10113yes—
214C2#127×D10111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, cosocleC23×C101C24
Fitting#392×C101C2
hypercenter#392D101
hypocenterC101C2×#392
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D101C2semidirect
2. C2×C22⋊C4×D101C2semidirect
3. #20265087C2semidirect
4. #20265086C2semidirect
5. #20265085C2semidirect
6. #95×D101C2semidirect
7. #392×C101C2semidirect
9. C22×D404C22semidirect
10. C22×C22⋊D101C22semidirect
15. C2×C22⋊Dic101C22semidirect
16. C2×#13108051C22semidirect
17. C2×#13108051C22semidirect
19. #15692162C22semidirect
20. C22×D4×C101C22semidirect
21. C2×C22⋊C4×C101C22semidirect
22. #95×C101C22semidirect
27. C23×D101D4semidirect
40. C2×C4×D101D4semidirect
54. C23×C101C2×D4semidirect
67. C22×D101C2×D4semidirect
72. C2×C4×C101C2×D4semidirect
76. C2×Dic101C2×D4semidirect
106. D101#392direct (N × H)
108. C101C2×#392semidirect
114. #392D101direct (N × H)
121. C22×D4C2×D101semidirect
128. C2×C22⋊C4C2×D101semidirect
130. #95C2×D101semidirect
175. C23D4×D101semidirect
187. C2×C4D4×D101semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1012
C2×C22⋊C4×D1012
#202650872
#202650862
#202650852
#95×D1012
#392×C1012
C2×#392101