Finite Group Databasebeta

← #27174311

Subgroups — #27174311

Order 12928.

424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 173 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×#15692253C211yesmaximal, characteristic
2#20265084C211yesmaximal, characteristic
3#20265081C212yesmaximal
4#20265064C212yesmaximal
5#20265061C212yesmaximal
6#20265059C212yesmaximal
7#20265058C212yesmaximal
8#20265044C212yesmaximal
9#391×C101C211yesmaximal, characteristic
10C22×Dic202C2211yescharacteristic
11#15692253C418yescomplemented
12C2×C4⋊Dic101C2211yescharacteristic
13C2×#13108053C2212yes—
14C2×#13108053C2212yes—
15C2×#13108053C2212yes—
16C2×C4×Dic101C2212yes—
17C2×C4×Dic101C2211yescharacteristic
18C2×C4×Dic101C2211yescharacteristic
19#15692162C2212yes—
20#15692162C2212yes—
21#15692162C2212yes—
22#15692162C2212yes—
23#15692162C2212yes—
24#15692162C2212yes—
25#15692162C2212yes—
26#15692162C2212yes—
27C22×Q8×C101C2211yescharacteristic
28C2×C4⋊C4×C101C2211yescharacteristic
29C2×C42×C101C2211yescharacteristic
30#95×C101C2212yes—
31#95×C101C2212yes—
32C2×Dic202—41no—
33C2×Dic202—41no—
34C2×Dic202C2×C414yes—
35C22×Dic101C2312yes—
36C22×Dic101C2312yes—
37C22×Dic101C2312yes—
38C22×Dic101C2312yes—
39C4⋊Dic101—41no—
40#13108053—42no—
41#13108053C2×C418yes—
42#13108053C2×C418yes—
43C4×Dic101—42no—
44C4×Dic101—41no—
45C4×Dic101C2×C414yes—
46C2×Q8×C101—41no—
47C2×Q8×C101—41no—
48C2×Q8×C101C2×C414yes—
49C22×C4×C101C2312yes—
50C22×C4×C101C2312yes—
51C22×C4×C101C2311yescharacteristic
52C22×C4×C101C2311yescharacteristic
53C22×C4×C101C2311yescharacteristic
54C4⋊C4×C101—41no—
55C42×C101—41no—
56C23×C101C2411yescharacteristic
57Q8×C101—44no—
58C2×C4×C101—21no—
59C2×C4×C101—21no—
60C2×C4×C101—21no—
61C2×C4×C101—21no—
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101—22no—
65C2×C4×C101—22no—
66C2×C4×C101—22no—
67C2×C4×C101—24no—
68C2×C4×C101—22no—
69C2×C4×C101C22×C412yes—
70C2×C4×C101C22×C412yes—
71C2×C4×C101C22×C412yes—
72C2×Dic101—22no—
73C2×Dic101—22no—
74C2×Dic101—22no—
75C2×Dic101—22no—
76C2×Dic101—22no—
77C2×Dic101—22no—
78C2×Dic101—22no—
79C2×Dic101—22no—
80C2×Dic101—24no—
81C2×Dic101C22×C414yes—
82C2×Dic101C22×C414yes—
83Dic202—44no—
84C22×C101C23×C411yescharacteristic
85C22×C101H(5,𝔽2)11yescharacteristic
86C22×C101H(5,𝔽2)11yescharacteristic
87C22×C1012−1+412yes—
88C22×C1012−1+412yes—
89C4×C101—22no—
90C4×C101—22no—
91C4×C101—22no—
92C4×C101—42no—
93C4×C101—42no—
94Dic101—24no—
95Dic101—24no—
96Dic101—42no—
97Dic101—42no—
98C2×C101#51811yescharacteristic
99C2×C101#51912yes—
100C2×C101#56311yescharacteristic
101C2×C101#56311yescharacteristic
102C2×C101#56312yes—
103#2381—1011nomaximal, Sylow
104C101#238111yescharacteristic, complemented, Sylow
105C2×C4⋊Q8—1011no—
106#391—1011no—
107#391—1012no—
108#391D10111yescharacteristic
109#387—1012no—
110#387—1012no—
111#387—1012no—
112#387—1012no—
113#383—1012no—
114C22×Q8—1011no—
115C22×Q8C2×D10111yescharacteristic
116C4⋊Q8—1018no—
117C2×C4⋊C4—1012no—
118C2×C4⋊C4—1012no—
119C2×C4⋊C4—1012no—
120C2×C4⋊C4—1011no—
121C2×C4⋊C4C2×D10111yescharacteristic
122C2×C42—1011no—
123C2×C42—1012no—
124C2×C42—1011no—
125C2×C42C2×D10111yescharacteristic
126#95—1012no—
127#95—1012no—
128#95—1012no—
129#95—1012no—
130#95—1012no—
131#95—1012no—
132#95—1012no—
133#95—1012no—
134#95C2×D10112yes—
135#95C2×D10112yes—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—1014no—
139C2×Q8—4041no—
140C2×Q8—4041no—
141C2×Q8C4×D10114yes—
142C22×C4—1012no—
143C22×C4—1012no—
144C22×C4—1012no—
145C22×C4—1012no—
146C22×C4C22×D10112yes—
147C22×C4C22×D10112yes—
148C22×C4C22×D10111yescharacteristic
149C22×C4C22×D10111yescharacteristic
150C22×C4C22×D10111yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—1018no—
153C4⋊C4—1018no—
154C4⋊C4—4042no—
155C4⋊C4—4041no—
156C42—41no—
157C42—1014no—
158C42—4041no—
159C42—4042no—
160C23C23×D10111yescharacteristic
161Q8—44no—
162Q8—4044no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—1014no—
175C2×C4—1014no—
176C2×C4—2022no—
177C2×C4—2022no—
178C2×C4—2022no—
179C2×C4—2024no—
180C2×C4—2022no—
181C2×C4—2022no—
182C2×C4—2022no—
183C2×C4—2022no—
184C2×C4—2022no—
185C2×C4C2×C4×D10112yes—
186C2×C4C2×C4×D10112yes—
187C2×C4C2×C4×D10112yes—
188C22C22×C4×D10111yescharacteristic
189C22#1569230011yescharacteristic
190C22#1569230011yescharacteristic
191C22#1569230212yes—
192C22#1569230312yes—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—4042no—
199C4—4042no—
200C4—2024no—
201C4—2024no—
202C2#2026565011yescharacteristic
203C2#2026565312yes—
204C2#2026592611yescharacteristic
205C2#2026592711yescharacteristic
206C2#2026592812yes—
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#391×C101C2
socle, prime radical, cosocleC23×C101C24
hypercenter#391D101
hypocenterC101#2381
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #15692253C4semidirect
104. C101#2381semidirect

Maximal subgroups

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

subgroupindex
C2×#156922532
#202650842
#202650812
#202650642
#202650612
#202650592
#202650582
#202650442
#391×C1012
#2381101