Finite Group Databasebeta

← #27171561

Subgroups — #27171561

Order 12928.

432 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C23×#11717579C211yesmaximal, characteristic, complemented
2C2×#15692176C212yesmaximal, complemented
3#20265037C211yesmaximal, characteristic, complemented
4#20264939C212yesmaximal, complemented
5C2×#121×C101C211yesmaximal, characteristic
6C22×#11717579—24no—
7C22×#11717579—22no—
8C22×#11717579C2212yes—
9C2×C4⋊Dic101C2212yes—
10C2×C22⋊Dic101—21no—
11#15692176—24no—
12#15692162—21no—
13C22×D4×C101—21no—
14C22×D4×C101C2211yescharacteristic
15C23×C4×C101C2211yescharacteristic
16#121×C101—22no—
17#121×C101C414yescomplemented
18C2×C4⋊C4×C101C2211yescharacteristic
19C2×C22⋊C4×C101—21no—
20C22×Dic101—22no—
21C2×#11717579—28no—
22C2×#11717579—22no—
23C2×#11717579—22no—
24C2×#11717579D414yescomplemented
25C4⋊Dic101—22no—
26C4⋊Dic101—22no—
27C22⋊Dic101—42no—
28C24×C101—21no—
29C24×C101D411yescharacteristic
30C2×D4×C101—24no—
31C2×D4×C101—22no—
32C2×D4×C101—21no—
33C2×D4×C101—22no—
34C2×D4×C101—42no—
35C2×D4×C101—42no—
36C2×D4×C101C2×C412yes—
37C22×C4×C101—22no—
38C22×C4×C101—22no—
39C22×C4×C101—21no—
40C22×C4×C101C2×C412yes—
41C22×C4×C101D411yescharacteristic
42C22×C4×C101D412yes—
43C22×C4×C101C2311yescharacteristic
44C4⋊C4×C101—21no—
45C4⋊C4×C101C2×C412yes—
46C22⋊C4×C101—24no—
47C23×C101—22no—
48C23×C101—22no—
49C23×C101—22no—
50C23×C101—42no—
51C23×C101—41no—
52C23×C101—41no—
53C23×C101—42no—
54C23×C101C22⋊C412yes—
55C23×C101D812yes—
56C23×C101SD1612yes—
57C23×C101C2×D411yescharacteristic
58D4×C101—24no—
59D4×C101—48no—
60D4×C101—41no—
61D4×C101—41no—
62C2×C4×C101—22no—
63C2×C4×C101—24no—
64C2×C4×C101—22no—
65C2×C4×C101—22no—
66C2×C4×C101—22no—
67C2×C4×C101—41no—
68C2×C4×C101—41no—
69C2×C4×C101C22⋊C412yes—
70C2×C4×C101C22×C411yescharacteristic
71C2×C4×C101C2×D412yes—
72C2×C4×C101C2×D411yescharacteristic
73C2×C4×C101#4112yes—
74C2×Dic101—42no—
75C2×Dic101—42no—
76C2×Dic101—42no—
77#11717579—24no—
78C22×C101—22no—
79C22×C101—22no—
80C22×C101—24no—
81C22×C101—24no—
82C22×C101—42no—
83C22×C101—42no—
84C22×C101—42no—
85C22×C101—82no—
86C22×C101—82no—
87C22×C101#10214yescomplemented
88C22×C101C2×C22⋊C411yescharacteristic
89C22×C101#12112yes—
90C22×C101C2×D811yescharacteristic
91C22×C101C2×SD1611yescharacteristic
92C22×C101#13512yes—
93C4×C101—22no—
94C4×C101—42no—
95C4×C101C4×D412yes—
96C4×C101#12011yescharacteristic
97C4×C101#12311yescharacteristic
98Dic101—82no—
99C2×C101—24no—
100C2×C101—82no—
101C2×C101#38611yescharacteristic
102C2×C101C2×#10211yescharacteristic
103C2×C101#41611yescharacteristic
104C2×C101#46512yes—
105C2×C101#46612yes—
106#1893—1011nomaximal, Sylow
107C101#189311yescharacteristic, complemented, Sylow
108C23×C8—1011no—
109C2×#121D10111yescharacteristic
110C2×#102—1012no—
111#380—1011no—
112#340—1012no—
113C22×D4—21no—
114C22×D4C2×D10111yescharacteristic
115C23×C4C2×D10111yescharacteristic
116C22×C8—1012no—
117C22×C8—2024no—
118C22×C8—2022no—
119#121—22no—
120#121Dic10114yescomplemented
121C2×C4⋊C4—1012no—
122C2×C4⋊C4C2×D10111yescharacteristic
123C2×C22⋊C4—21no—
124C2×C22⋊C4—2021no—
125#102—2024no—
126#95—2021no—
127C24—21no—
128C24C22⋊D10111yescharacteristic
129C2×D4—24no—
130C2×D4—22no—
131C2×D4—21no—
132C2×D4—22no—
133C2×D4—42no—
134C2×D4—42no—
135C2×D4C2×Dic10112yes—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—21no—
139C22×C4—2022no—
140C22×C4C2×Dic10112yes—
141C22×C4C22⋊D10111yescharacteristic
142C22×C4C22⋊D10112yes—
143C22×C4C22×D10111yescharacteristic
144C2×C8—1014no—
145C2×C8—2028no—
146C2×C8—2022no—
147C2×C8—2022no—
148C4⋊C4—21no—
149C4⋊C4—2022no—
150C4⋊C4—2022no—
151C4⋊C4C2×Dic10112yes—
152C22⋊C4—24no—
153C22⋊C4—4042no—
154C23—22no—
155C23—22no—
156C23—22no—
157C23—42no—
158C23—41no—
159C23—41no—
160C23—42no—
161C23C22⋊Dic10112yes—
162C23#1310805912yes—
163C23#1310806212yes—
164C23C2×C22⋊D10111yescharacteristic
165D4—24no—
166D4—48no—
167D4—41no—
168D4—41no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—4042no—
177C2×C4—4042no—
178C2×C4—4042no—
179C2×C4C22⋊Dic10112yes—
180C2×C4C22×Dic10111yescharacteristic
181C2×C4D4×D10112yes—
182C2×C4C2×C22⋊D10111yescharacteristic
183C2×C4#1310807312yes—
184C8—2024no—
185C22—22no—
186C22—24no—
187C22—24no—
188C22—22no—
189C22—42no—
190C22—42no—
191C22—42no—
192C22—82no—
193C22—82no—
194C22#1569217614yescomplemented
195C22C2×C22⋊Dic10111yescharacteristic
196C22#1569222712yes—
197C22C2×#1310805911yescharacteristic
198C22C2×#1310806211yescharacteristic
199C22#1569227512yes—
200C4—22no—
201C4—42no—
202C4—8082no—
203C4D4×Dic10112yes—
204C4#1569222311yescharacteristic
205C4#1569223611yescharacteristic
206C2—24no—
207C2—82no—
208C2#2026505711yescharacteristic
209C2C2×#1569217611yescharacteristic
210C2#2026517311yescharacteristic
211C2#2026540412yes—
212C2#2026541112yes—
subgroupG/H
centerC23C2×C22⋊D101
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
Fitting, prime radicalC2×#121×C101C2
socleC23×C101C2×D4
cosocleC22×C4×C101C23
hypercenterC2×#121D101
hypocenterC101#1893
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C23×#11717579C2semidirect
2. C2×#15692176C2semidirect
3. #20265037C2semidirect
4. #20264939C2semidirect
17. #121×C101C4semidirect
24. C2×#11717579D4semidirect
87. C22×C101#102semidirect
107. C101#1893semidirect
120. #121Dic101semidirect
194. C22#15692176semidirect

Maximal subgroups

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

subgroupindex
C23×#117175792
C2×#156921762
#202650372
#202649392
C2×#121×C1012
#1893101