Finite Group Databasebeta

← #27174237

Subgroups — #27174237

Order 12928.

448 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 185 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#20265062C212yesmaximal
3#20265061C212yesmaximal
4#20265060C212yesmaximal
5#20265059C212yesmaximal
6C4×#13108053C212yesmaximal
7#20265028C212yesmaximal
8#20265023C211yesmaximal, characteristic
9#376×C101C211yesmaximal, characteristic
10#15692247C418yescomplemented
11C2×C4⋊Dic101C2211yescharacteristic
12C2×C4⋊Dic101C2211yescharacteristic
13C2×#13108053C2212yes—
14C2×#13108053C2212yes—
15C2×#13108053C2212yes—
16C2×#13108053C2212yes—
17C2×C4×Dic101C2212yes—
18C2×C4×Dic101C2212yes—
19C2×C4×Dic101C2212yes—
20#15692162C2211yescharacteristic
21#15692162C2212yes—
22#15692162C2211yescharacteristic
23#15692162C2212yes—
24#15692162C2212yes—
25#15692162C2212yes—
26#15692162C2212yes—
27C2×C42×C101C2212yes—
28C2×C42×C101C2211yescharacteristic
29#95×C101C2211yescharacteristic
30#95×C101C2211yescharacteristic
31#95×C101C2212yes—
32C22×Dic101C2312yes—
33C22×Dic101C2312yes—
34C22×Dic101C2312yes—
35C22×Dic101C2312yes—
36C4⋊Dic101C2×C414yes—
37C4⋊Dic101C2×C414yes—
38#13108053—24no—
39#13108053—24no—
40#13108053C2×C418yes—
41#13108053C2×C418yes—
42C4×Dic101—24no—
43C4×Dic101—24no—
44C4×Dic101—24no—
45C22×C4×C101C2312yes—
46C22×C4×C101C2311yescharacteristic
47C22×C4×C101C2311yescharacteristic
48C22×C4×C101C2311yescharacteristic
49C22×C4×C101C2312yes—
50C42×C101—24no—
51C42×C101C2×C414yes—
52C23×C101C2411yescharacteristic
53C2×C4×C101—22no—
54C2×C4×C101—22no—
55C2×C4×C101—22no—
56C2×C4×C101—21no—
57C2×C4×C101—21no—
58C2×C4×C101—22no—
59C2×C4×C101—22no—
60C2×C4×C101—22no—
61C2×C4×C101—22no—
62C2×C4×C101C22×C412yes—
63C2×C4×C101C22×C412yes—
64C2×C4×C101C22×C412yes—
65C2×C4×C101#4114yes—
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×Dic101C22×C414yes—
76C2×Dic101C22×C414yes—
77C2×Dic101#4114yes—
78C22×C101C23×C411yescharacteristic
79C22×C101C2×#4112yes—
80C22×C101C2×#4112yes—
81C22×C1012−1+411yescharacteristic
82C22×C1012−1+411yescharacteristic
83C4×C101—22no—
84C4×C101—22no—
85C4×C101—22no—
86C4×C101—24no—
87C4×C101—42no—
88Dic101—24no—
89Dic101—24no—
90Dic101—24no—
91Dic101—42no—
92C2×C101C4×#4111yescharacteristic
93C2×C101C4×#4111yescharacteristic
94C2×C101#51911yescharacteristic
95C2×C101#55212yes—
96C2×C101#55212yes—
97#2371—1011nomaximal, Sylow
98C101#237111yescharacteristic, complemented, Sylow
99C2×#125—1011no—
100#387—1012no—
101#387—1012no—
102#387—1012no—
103#387—1012no—
104C4×C4⋊C4—1012no—
105C4×C4⋊C4—1012no—
106#376—1011no—
107#376D10111yescharacteristic
108#125—1018no—
109C2×C4⋊C4—1012no—
110C2×C4⋊C4—1012no—
111C2×C4⋊C4—1011no—
112C2×C4⋊C4—1011no—
113C2×C4⋊C4—1012no—
114C2×C4⋊C4—1012no—
115C2×C42—1012no—
116C2×C42—1012no—
117C2×C42—1012no—
118C2×C42C2×D10112yes—
119C2×C42C2×D10111yescharacteristic
120#95—1011no—
121#95—1012no—
122#95—1011no—
123#95—1012no—
124#95—1012no—
125#95—1012no—
126#95—1012no—
127#95C2×D10111yescharacteristic
128#95C2×D10111yescharacteristic
129#95C2×D10112yes—
130C22×C4—1012no—
131C22×C4—1012no—
132C22×C4—1012no—
133C22×C4—1012no—
134C22×C4C22×D10112yes—
135C22×C4C22×D10111yescharacteristic
136C22×C4C22×D10111yescharacteristic
137C22×C4C22×D10111yescharacteristic
138C22×C4C22×D10112yes—
139C4⋊C4—1018no—
140C4⋊C4—1018no—
141C4⋊C4—1014no—
142C4⋊C4—1014no—
143C4⋊C4—2024no—
144C4⋊C4—2024no—
145C42—24no—
146C42—2024no—
147C42—2024no—
148C42—2024no—
149C42C4×D10114yes—
150C23C23×D10111yescharacteristic
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—1014no—
161C2×C4—1014no—
162C2×C4—1014no—
163C2×C4—2022no—
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×C4C2×C4×D10112yes—
173C2×C4C2×C4×D10112yes—
174C2×C4C2×C4×D10112yes—
175C2×C4#1310807414yes—
176C22C22×C4×D10111yescharacteristic
177C22#41×D10112yes—
178C22C2×#1310807412yes—
179C22#1569230211yescharacteristic
180C22#1569230211yescharacteristic
181C4—24no—
182C4—22no—
183C4—22no—
184C4—22no—
185C4—42no—
186C4—4042no—
187C4—2024no—
188C4—2024no—
189C4—2024no—
190C2#2026564511yescharacteristic
191C2C4×#1310807411yescharacteristic
192C2#2026565411yescharacteristic
193C2#2026586012yes—
194C2#2026586612yes—
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#376×C101C2
socle, prime radical, cosocleC23×C101C24
hypercenter#376D101
hypocenterC101#2371
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
10. #15692247C4semidirect
98. C101#2371semidirect

Maximal subgroups

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

subgroupindex
C2×#156922472
#202650622
#202650612
#202650602
#202650592
C4×#131080532
#202650282
#202650232
#376×C1012
#2371101