Finite Group Databasebeta

← #27173933

Subgroups — #27173933

Order 12928.

428 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 177 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×#15692247C211yesmaximal, characteristic
2#20265074C212yesmaximal
3#20265064C212yesmaximal
4#20265062C212yesmaximal
5#20265060C212yesmaximal
6#20265059C212yesmaximal
7C4×C4⋊Dic101C211yesmaximal, characteristic
8#20265028C212yesmaximal
9#383×C101C211yesmaximal, characteristic
10#15692247C418yescomplemented
11C2×C4⋊Dic101C2212yes—
12C2×C4⋊Dic101C2211yescharacteristic
13C2×C4⋊Dic101C2211yescharacteristic
14C2×#13108053C2212yes—
15C2×#13108053C2212yes—
16C2×#13108053C2212yes—
17C2×#13108053C2212yes—
18C2×C4×Dic101C2212yes—
19C2×C4×Dic101C2211yescharacteristic
20C2×C4×Dic101C2212yes—
21C2×C4×Dic101C2211yescharacteristic
22#15692162C2212yes—
23#15692162C2212yes—
24#15692162C2212yes—
25#15692162C2212yes—
26#15692162C2212yes—
27C2×C42×C101C2211yescharacteristic
28#95×C101C2212yes—
29#95×C101C2212yes—
30#95×C101C2211yescharacteristic
31#95×C101C2211yescharacteristic
32C22×Dic101C2312yes—
33C22×Dic101C2312yes—
34C22×Dic101C2312yes—
35C22×Dic101C2312yes—
36C4⋊Dic101—24no—
37C4⋊Dic101C2×C414yes—
38C4⋊Dic101C2×C414yes—
39#13108053—24no—
40#13108053—42no—
41#13108053C2×C418yes—
42#13108053C2×C418yes—
43C4×Dic101—24no—
44C4×Dic101—41no—
45C4×Dic101—42no—
46C4×Dic101—41no—
47C22×C4×C101C2312yes—
48C22×C4×C101C2312yes—
49C22×C4×C101C2311yescharacteristic
50C22×C4×C101C2311yescharacteristic
51C22×C4×C101C2311yescharacteristic
52C42×C101C2×C414yes—
53C23×C101C2411yescharacteristic
54C2×C4×C101—22no—
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—22no—
64C2×C4×C101C22×C412yes—
65C2×C4×C101C22×C412yes—
66C2×C4×C101C22×C412yes—
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×Dic101C22×C414yes—
77C2×Dic101C22×C414yes—
78C2×Dic101#4114yes—
79C22×C101C23×C411yescharacteristic
80C22×C101C2×#4112yes—
81C22×C101H(5,𝔽2)11yescharacteristic
82C22×C1012−1+412yes—
83C22×C1012−1+411yescharacteristic
84C4×C101—22no—
85C4×C101—22no—
86C4×C101—22no—
87C4×C101—42no—
88C4×C101—42no—
89Dic101—24no—
90Dic101—24no—
91Dic101—24no—
92Dic101—42no—
93C2×C101C4×#4111yescharacteristic
94C2×C101#51911yescharacteristic
95C2×C101#52011yescharacteristic
96C2×C101#53912yes—
97C2×C101#54112yes—
98#2336—1011nomaximal, Sylow
99C101#233611yescharacteristic, complemented, Sylow
100C2×#125—1011no—
101#389—1012no—
102#387—1012no—
103#387—1012no—
104#387—1012no—
105#387—1012no—
106#383D10111yescharacteristic
107C4×C4⋊C4—1011no—
108C4×C4⋊C4—1012no—
109#125—1018no—
110C2×C4⋊C4—1012no—
111C2×C4⋊C4—1011no—
112C2×C4⋊C4—1011no—
113C2×C4⋊C4—1012no—
114C2×C4⋊C4—1012no—
115C2×C4⋊C4—1012no—
116C2×C4⋊C4—1012no—
117C2×C42—1011no—
118C2×C42—1011no—
119C2×C42—1012no—
120C2×C42—1012no—
121C2×C42C2×D10111yescharacteristic
122#95—1012no—
123#95—1012no—
124#95—1012no—
125#95—1012no—
126#95—1012no—
127#95C2×D10112yes—
128#95C2×D10111yescharacteristic
129#95C2×D10112yes—
130#95C2×D10111yescharacteristic
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—1018no—
141C4⋊C4—1018no—
142C4⋊C4—1014no—
143C4⋊C4—1014no—
144C4⋊C4—4042no—
145C4⋊C4—2024no—
146C4⋊C4—2024no—
147C42—4041no—
148C42—4041no—
149C42—4042no—
150C42—2024no—
151C42C4×D10114yes—
152C23C23×D10111yescharacteristic
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—1014no—
164C2×C4—1014no—
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×C4C2×C4×D10112yes—
176C2×C4C2×C4×D10112yes—
177C2×C4C2×C4×D10112yes—
178C22C22×C4×D10111yescharacteristic
179C22#41×D10112yes—
180C22#1569230111yescharacteristic
181C22#1569230212yes—
182C22#1569230211yescharacteristic
183C4—22no—
184C4—22no—
185C4—22no—
186C4—42no—
187C4—42no—
188C4—4042no—
189C4—2024no—
190C4—2024no—
191C4—2024no—
192C2#2026564511yescharacteristic
193C2#2026565411yescharacteristic
194C2#2026565711yescharacteristic
195C2#2026576812yes—
196C2#2026578412yes—
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#383×C101C2
socle, prime radical, cosocleC23×C101C24
hypercenter#383D101
hypocenterC101#2336
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
10. #15692247C4semidirect
99. C101#2336semidirect

Maximal subgroups

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

subgroupindex
C2×#156922472
#202650742
#202650642
#202650622
#202650602
#202650592
C4×C4⋊Dic1012
#202650282
#383×C1012
#2336101