Finite Group Databasebeta

← #27179405

Subgroups — #27179405

Order 12928.

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

normal subgroups only

This group has 356 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#20265117C212yesmaximal
3#20265116C211yesmaximal, characteristic
4#20265098C212yesmaximal
5#20265098C212yesmaximal
6#20265097C212yesmaximal
7#20265042C211yesmaximal, characteristic
8#20265041C212yesmaximal
9#400×C101C211yesmaximal, characteristic
10C22×Dic202C2212yes—
11C2×C4⋊Dic101C2211yescharacteristic
12C2×C4⋊Dic101C2211yescharacteristic
13C2×C4⋊Dic101C2212yes—
14C2×#13108053C2212yes—
15C2×#13108053C2212yes—
16C2×#13108053C2212yes—
17C2×C4×Dic101C2211yescharacteristic
18#15692162C2212yes—
19#15692162C2212yes—
20#15692162C2212yes—
21#15692162C2212yes—
22#15692162C2212yes—
23#15692162C2212yes—
24#15692162C2212yes—
25#15692162C2211yescharacteristic
26C2×C4⋊C4×C101C2211yescharacteristic
27C2×C4⋊C4×C101C2211yescharacteristic
28#95×C101C2212yes—
29#95×C101C2212yes—
30#95×C101C2211yescharacteristic
31C2×Dic202—42no—
32C2×Dic202—42no—
33C2×Dic202—42no—
34C22×Dic101C2312yes—
35C22×Dic101C2312yes—
36C22×Dic101C2312yes—
37C22×Dic101C2312yes—
38C4⋊Dic101—41no—
39C4⋊Dic101—41no—
40C4⋊Dic101—42no—
41#13108053—42no—
42#13108053—42no—
43#13108053—42no—
44C4×Dic101Q814yescomplemented
45C22×C4×C101C2312yes—
46C22×C4×C101C2312yes—
47C22×C4×C101C2311yescharacteristic
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—21no—
57C2×C4×C101—22no—
58C2×C4×C101—22no—
59C2×C4×C101—22no—
60C2×C4×C101—22no—
61C2×C4×C101—22no—
62C2×C4×C101—22no—
63C2×C4×C101—22no—
64C2×C4×C101—22no—
65C2×C4×C101C2×Q812yes—
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×Dic101—22no—
77C2×Dic101C2×Q814yes—
78Dic202—48no—
79C22×C101C22×Q811yescharacteristic
80C22×C101H(5,𝔽2)11yescharacteristic
81C22×C101H(5,𝔽2)12yes—
82C22×C1012−1+411yescharacteristic
83C22×C1012−1+412yes—
84C4×C101—22no—
85C4×C101—42no—
86C4×C101—42no—
87C4×C101—41no—
88C4×C101—41no—
89Dic101—24no—
90Dic101—42no—
91Dic101—42no—
92Dic101—42no—
93C2×C101#54411yescharacteristic
94C2×C101#54412yes—
95C2×C101H(3,𝔽4)11yescharacteristic
96C2×C101#56312yes—
97C2×C101#56311yescharacteristic
98#2844—1011nomaximal, Sylow
99C101#284411yescharacteristic, complemented, Sylow
100#400—1011no—
101#400—1012no—
102#400—1012no—
103#400D10111yescharacteristic
104#395—1012no—
105#395—1012no—
106#395—1012no—
107#382—1011no—
108#382—1012no—
109C22×Q8—1012no—
110C2×C4⋊C4—1012no—
111C2×C4⋊C4—1011no—
112C2×C4⋊C4—1012no—
113C2×C4⋊C4—1012no—
114C2×C4⋊C4—1011no—
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—1012no—
125#95—1012no—
126#95—1011no—
127#95C2×D10112yes—
128#95C2×D10112yes—
129#95C2×D10111yescharacteristic
130C2×Q8—4042no—
131C2×Q8—4042no—
132C2×Q8—4042no—
133C22×C4—1012no—
134C22×C4—1012no—
135C22×C4—1012no—
136C22×C4—1012no—
137C22×C4C22×D10111yescharacteristic
138C22×C4C22×D10111yescharacteristic
139C22×C4C22×D10112yes—
140C22×C4C22×D10112yes—
141C22×C4C22×D10111yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—4042no—
145C4⋊C4—4042no—
146C4⋊C4—4042no—
147C4⋊C4—4041no—
148C4⋊C4—4041no—
149C4⋊C4—4042no—
150C42—1014no—
151C23C23×D10111yescharacteristic
152Q8—4048no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—1014no—
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×C4—2022no—
176C2×C4—2022no—
177C2×C4Q8×D10112yes—
178C22C2×Q8×D10111yescharacteristic
179C22#1569230011yescharacteristic
180C22#1569230112yes—
181C22#1569230211yescharacteristic
182C22#1569230212yes—
183C4—22no—
184C4—42no—
185C4—42no—
186C4—41no—
187C4—41no—
188C4—4042no—
189C4—4042no—
190C4—4042no—
191C4—2024no—
192C2#2026580611yescharacteristic
193C2#2026580712yes—
194C2#2026591911yescharacteristic
195C2#2026592912yes—
196C2#2026593011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, prime radical, cosocleC23×C101C24
Fitting#400×C101C2
hypercenter#400D101
hypocenterC101#2844
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic101Q8semidirect
99. C101#2844semidirect

Maximal subgroups

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

subgroupindex
#202651182
#202651172
#202651162
#202650982
#202650972
#202650422
#202650412
#400×C1012
#2844101