Finite Group Databasebeta

← #27179448

Subgroups — #27179448

Order 12928.

582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692249C211yesmaximal, characteristic, complemented
2C2×C42×D101C211yesmaximal, characteristic, complemented
3#20265069C213yesmaximal, complemented
4#20265062C213yesmaximal, complemented
5#20265055C213yesmaximal
6#20265051C213yesmaximal, complemented
7#383×C101C211yesmaximal, characteristic, complemented
8C22×D404C2211yescharacteristic
9C22×C4×D101C2213yes—
10#15692249—24no—
11C2×C4⋊Dic101C2213yes—
12C2×#13108053C2213yes—
13C2×#13108051C2213yes—
14C2×#13108051C2213yes—
15C2×#13108051C2213yes—
16C2×C4×Dic101C2213yes—
17C42×D101—24no—
18#15692162C2213yes—
19#15692162C2213yes—
20C2×C42×C101C2211yescharacteristic
21#95×C101C2213yes—
22#95×C101C2213yes—
23C23×D101C2311yescharacteristic
24C23×D101C2311yescharacteristic
25C2×D404—26no—
26C22×Dic101C2313yes—
27C22×Dic101C2313yes—
28C2×C4×D101—26no—
29C2×C4×D101—26no—
30C2×C4×D101—26no—
31C4⋊Dic101—26no—
32#13108053—26no—
33#13108051—26no—
34#13108051—26no—
35#13108051—26no—
36C4×Dic101—26no—
37C22×C4×C101C2311yescharacteristic
38C22×C4×C101C2313yes—
39C22×C4×C101C2313yes—
40C42×C101D414yescomplemented
41C23×C101C2411yescharacteristic
42C22×D101—21no—
43C22×D101—23no—
44C22×D101—21no—
45C22×D101—23no—
46C22×D101—23no—
47C22×D101#4116yes—
48C2×C4×C101—23no—
49C2×C4×C101—23no—
50C2×C4×C101—23no—
51C2×C4×C101—23no—
52C2×C4×C101—23no—
53C2×C4×C101—23no—
54C2×C4×C101C2×D416yes—
55C2×Dic101—23no—
56C2×Dic101—23no—
57C2×Dic101—23no—
58C2×Dic101—23no—
59C2×Dic101—23no—
60C2×Dic101#4116yes—
61D404—44no—
62C4×D101—224no—
63C22×C101C22×D411yescharacteristic
64C22×C101C2×#4113yes—
65C22×C101C2×#4113yes—
66C2×D101—26no—
67C2×D101—26no—
68C2×D101—43no—
69C2×D101—41no—
70C2×D101—43no—
71C2×D101#12614yescomplemented
72C4×C101—26no—
73C4×C101—41no—
74C4×C101—43no—
75Dic101—26no—
76Dic101—43no—
77C2×C101#52513yes—
78C2×C101C2×#12611yescharacteristic
79C2×C101#52913yes—
80D101—24no—
81D101—81no—
82#2852—1011nomaximal, Sylow
83C101#285211yescharacteristic, complemented, Sylow
84C2×#126—1011no—
85C22×C42—1011no—
86#388—1013no—
87#387—1013no—
88#386—1013no—
89#385—1013no—
90#383D10111yescharacteristic, complemented
91C22×D4—1011no—
92C23×C4—1013no—
93#126—2024no—
94C2×C4⋊C4—1013no—
95C2×C4⋊C4—1013no—
96C2×C22⋊C4—1013no—
97C2×C22⋊C4—1013no—
98C2×C22⋊C4—1013no—
99C2×C42—1013no—
100C2×C42—2024no—
101C2×C42C2×D10111yescharacteristic
102#95—1013no—
103#95—1013no—
104#95C2×D10113yes—
105#95C2×D10113yes—
106C24—1011no—
107C24—1011no—
108C2×D4—2026no—
109C22×C4—1013no—
110C22×C4—1013no—
111C22×C4—2026no—
112C22×C4—2026no—
113C22×C4—2026no—
114C22×C4C22×D10111yescharacteristic
115C22×C4C22×D10113yes—
116C22×C4C22×D10113yes—
117C4⋊C4—2026no—
118C4⋊C4—2026no—
119C22⋊C4—2026no—
120C22⋊C4—2026no—
121C22⋊C4—2026no—
122C42—2026no—
123C42D40414yescomplemented
124C23—1016no—
125C23—2021no—
126C23—2023no—
127C23—2023no—
128C23—2021no—
129C23—2023no—
130C23C23×D10111yescharacteristic
131D4—4044no—
132C2×C4—23no—
133C2×C4—23no—
134C2×C4—23no—
135C2×C4—23no—
136C2×C4—23no—
137C2×C4—23no—
138C2×C4—1016no—
139C2×C4—20224no—
140C2×C4—2023no—
141C2×C4—2023no—
142C2×C4—2023no—
143C2×C4—2023no—
144C2×C4—2023no—
145C2×C4C2×D40416yes—
146C22—1014no—
147C22—4043no—
148C22—4041no—
149C22—4043no—
150C22—2026no—
151C22—2026no—
152C22C22×D40411yescharacteristic
153C22#41×D10113yes—
154C22#41×D10113yes—
155C4—26no—
156C4—41no—
157C4—43no—
158C4—4043no—
159C4—2026no—
160C2—8081no—
161C2—2024no—
162C2#2026568913yes—
163C2#126×D10111yescharacteristic
164C2#2026571013yes—
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, cosocleC23×C101C24
Fitting#383×C101C2
prime radicalC22×D404C22
hypercenter#383D101
hypocenterC101#2852
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
1. C2×#15692249C2semidirect
2. C2×C42×D101C2semidirect
3. #20265069C2semidirect
4. #20265062C2semidirect
6. #20265051C2semidirect
7. #383×C101C2semidirect
40. C42×C101D4semidirect
71. C2×D101#126semidirect
83. C101#2852semidirect
90. #383D101semidirect
123. C42D404semidirect

Maximal subgroups

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

subgroupindex
C2×#156922492
C2×C42×D1012
#202650692
#202650622
#202650552
#202650512
#383×C1012
#2852101