Finite Group Databasebeta

← #27179402

Subgroups — #27179402

Order 12928.

348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#20265118C212yesmaximal
2#20265111C212yesmaximal
3#20265109C212yesmaximal
4#20265107C212yesmaximal
5#20265098C212yesmaximal
6#20265097C211yesmaximal, characteristic
7#20265046C211yesmaximal, characteristic
8#20265044C212yesmaximal
9#400×C101C211yesmaximal, characteristic
10C22×Dic202C2211yescharacteristic
11C2×C4⋊Dic101C2211yescharacteristic
12C2×C4⋊Dic101C2212yes—
13C2×C4⋊Dic101C2212yes—
14C2×#13108053C2212yes—
15C2×#13108053C2212yes—
16C2×#13108053C2212yes—
17C2×#13108053C2212yes—
18C2×C4×Dic101C2211yescharacteristic
19#15692162C2212yes—
20#15692162C2212yes—
21#15692162C2212yes—
22#15692162C2212yes—
23#15692162C2212yes—
24#15692162C2211yescharacteristic
25#15692162C2212yes—
26C2×C4⋊C4×C101C2211yescharacteristic
27C2×C4⋊C4×C101C2211yescharacteristic
28#95×C101C2212yes—
29#95×C101C2212yes—
30#95×C101C2211yescharacteristic
31C2×Dic202—42no—
32C2×Dic202—41no—
33C22×Dic101C2312yes—
34C22×Dic101C2312yes—
35C22×Dic101C2312yes—
36C22×Dic101C2312yes—
37C4⋊Dic101—42no—
38C4⋊Dic101—41no—
39C4⋊Dic101—42no—
40#13108053—42no—
41#13108053—42no—
42#13108053—42no—
43#13108053—42no—
44C4×Dic101Q814yescomplemented
45C22×C4×C101C2311yescharacteristic
46C22×C4×C101C2312yes—
47C22×C4×C101C2312yes—
48C22×C4×C101C2311yescharacteristic
49C22×C4×C101C2311yescharacteristic
50C4⋊C4×C101—41no—
51C4⋊C4×C101—41no—
52C23×C101C2411yescharacteristic
53C2×C4×C101—21no—
54C2×C4×C101—21no—
55C2×C4×C101—21no—
56C2×C4×C101—22no—
57C2×C4×C101—21no—
58C2×C4×C101—22no—
59C2×C4×C101—22no—
60C2×C4×C101—22no—
61C2×C4×C101—22no—
62C2×C4×C101—22no—
63C2×C4×C101—24no—
64C2×C4×C101C2×Q812yes—
65C2×Dic101—22no—
66C2×Dic101—22no—
67C2×Dic101—22no—
68C2×Dic101—22no—
69C2×Dic101—22no—
70C2×Dic101—22no—
71C2×Dic101—22no—
72C2×Dic101—22no—
73C2×Dic101—22no—
74C2×Dic101—22no—
75C2×Dic101—22no—
76C2×Dic101C2×Q814yes—
77Dic202—44no—
78C22×C101C22×Q811yescharacteristic
79C22×C101H(5,𝔽2)11yescharacteristic
80C22×C101H(5,𝔽2)12yes—
81C22×C1012−1+411yescharacteristic
82C22×C1012−1+412yes—
83C4×C101—22no—
84C4×C101—41no—
85C4×C101—41no—
86C4×C101—42no—
87C4×C101—42no—
88Dic101—24no—
89Dic101—42no—
90Dic101—42no—
91Dic101—42no—
92C2×C101#54411yescharacteristic
93C2×C101#54412yes—
94C2×C101#56011yescharacteristic
95C2×C101#56311yescharacteristic
96C2×C101#56312yes—
97#2843—1011nomaximal, Sylow
98C101#284311yescharacteristic, complemented, Sylow
99#400—1012no—
100#400D10111yescharacteristic
101#398—1012no—
102#398—1012no—
103#398—1012no—
104#395—1011no—
105#395—1012no—
106#384—1011no—
107#383—1012no—
108C22×Q8—1011no—
109C2×C4⋊C4—1012no—
110C2×C4⋊C4—1012no—
111C2×C4⋊C4—1011no—
112C2×C4⋊C4—1012no—
113C2×C4⋊C4—1012no—
114C2×C4⋊C4—1012no—
115C2×C4⋊C4—1012no—
116C2×C4⋊C4C2×D10111yescharacteristic
117C2×C4⋊C4C2×D10111yescharacteristic
118C2×C42—1011no—
119#95—1012no—
120#95—1012no—
121#95—1012no—
122#95—1012no—
123#95—1012no—
124#95—1011no—
125#95—1012no—
126#95C2×D10112yes—
127#95C2×D10112yes—
128#95C2×D10111yescharacteristic
129C2×Q8—4041no—
130C2×Q8—4042no—
131C22×C4—1012no—
132C22×C4—1012no—
133C22×C4—1012no—
134C22×C4—1012no—
135C22×C4C22×D10112yes—
136C22×C4C22×D10112yes—
137C22×C4C22×D10111yescharacteristic
138C22×C4C22×D10111yescharacteristic
139C22×C4C22×D10111yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—4042no—
143C4⋊C4—4042no—
144C4⋊C4—4042no—
145C4⋊C4—4042no—
146C4⋊C4—4041no—
147C4⋊C4—4042no—
148C4⋊C4—4042no—
149C42—1014no—
150C23C23×D10111yescharacteristic
151Q8—4044no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—1014no—
164C2×C4—2022no—
165C2×C4—2022no—
166C2×C4—2022no—
167C2×C4—2022no—
168C2×C4—2022no—
169C2×C4—2022no—
170C2×C4—2022no—
171C2×C4—2022no—
172C2×C4—2022no—
173C2×C4—2022no—
174C2×C4—2022no—
175C2×C4Q8×D10112yes—
176C22C2×Q8×D10111yescharacteristic
177C22#1569230011yescharacteristic
178C22#1569230112yes—
179C22#1569230211yescharacteristic
180C22#1569230212yes—
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—4042no—
187C4—4042no—
188C4—4042no—
189C4—2024no—
190C2#2026580611yescharacteristic
191C2#2026580712yes—
192C2#2026591711yescharacteristic
193C2#2026592711yescharacteristic
194C2#2026592912yes—
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, prime radical, cosocleC23×C101C24
Fitting#400×C101C2
hypercenter#400D101
hypocenterC101#2843
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic101Q8semidirect
98. C101#2843semidirect

Maximal subgroups

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

subgroupindex
#202651182
#202651112
#202651092
#202651072
#202650982
#202650972
#202650462
#202650442
#400×C1012
#2843101