Finite Group Databasebeta

← #27182568

Subgroups — #27182568

Order 12928.

370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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#20265780C212yesmaximal, complemented
2#20265479C212yesmaximal, complemented
3#20265476C212yesmaximal, complemented
4#20265430C211yesmaximal, characteristic, complemented
5#20265411C212yesmaximal, complemented
6#20265371C212yesmaximal, complemented
7#20265370C212yesmaximal, complemented
8#20265205C211yesmaximal, characteristic, complemented
9#469×C101C211yesmaximal, characteristic, complemented
10C2×D808C2211yescharacteristic
11C2×#13108059C2212yes—
12C22×#11717579C2211yescharacteristic
13#15692251C2212yes—
14#15692246C2212yes—
15#15692239—22no—
16#15692237—22no—
17#15692229C2212yes—
18#15692227—22no—
19#15692226—22no—
20D4×Dic101C2212yes—
21#15692217C2212yes—
22#15692214C2211yescharacteristic
23#15692188C2212yes—
24#15692187C2211yescharacteristic
25#15692184C2212yes—
26#15692184C2212yes—
27#15692177C2212yes—
28#15692176C2212yes—
29#15692175C2212yes—
30C2×D8×C101C2211yescharacteristic
31C2×M16×C101C2211yescharacteristic
32#121×C101C2212yes—
33#106×C101C2211yescharacteristic
34#102×C101C2212yes—
35C2×D404C2312yes—
36C2×C22⋊D101—22no—
37C2×C22⋊D101—22no—
38C2×C22⋊D101—22no—
39C22×Dic101—22no—
40C2×C4×D101—22no—
41D808—41no—
42#13108059—42no—
43C2×#11717579—41no—
44C2×#11717579C2312yes—
45C4⋊Dic101—22no—
46C4⋊Dic101D412yes—
47C4⋊Dic101C2312yes—
48#13108053—22no—
49C22⋊Dic101—22no—
50C22⋊Dic101D411yescharacteristic
51C22⋊Dic101D411yescharacteristic
52#13108051—22no—
53#13108051—22no—
54C4×Dic101C2312yes—
55C2×D4×C101—22no—
56C2×D4×C101C2312yes—
57C22×C4×C101C2311yescharacteristic
58D8×C101—41no—
59M16×C101—41no—
60C2×C8×C101C2311yescharacteristic
61C2×C8×C101C2311yescharacteristic
62C4⋊C4×C101C2312yes—
63C22⋊C4×C101—22no—
64C23×C101—22no—
65C23×C101C2×D411yescharacteristic
66C22×D101—22no—
67D4×C101—22no—
68D4×C101—22no—
69D4×C101—82no—
70C2×C4×C101—21no—
71C2×C4×C101—21no—
72C2×C4×C101—22no—
73C2×C4×C101C2×D411yescharacteristic
74C2×C4×C101C2411yescharacteristic
75C22⋊D101—82no—
76C22⋊D101—82no—
77C22⋊D101—82no—
78C2×Dic101—22no—
79C2×Dic101—82no—
80C2×Dic101C2×D412yes—
81C2×Dic101C2×D412yes—
82D404—22no—
83D404—22no—
84C4×D101—82no—
85C8×C101—21no—
86C8×C101—21no—
87#11717579—22no—
88C22×C101—21no—
89C22×C101—22no—
90C22×C101—42no—
91C22×C101—42no—
92C22×C101—42no—
93C22×C101C22×D411yescharacteristic
94C2×D101—42no—
95C2×D101—42no—
96C2×D101—42no—
97C4×C101—21no—
98C4×C101—42no—
99C4×C101H(5,𝔽2)11yescharacteristic
100C4×C1012−1+411yescharacteristic
101Dic101—22no—
102Dic101—22no—
103Dic101—42no—
104C2×C101—41no—
105C2×C101—82no—
106C2×C101#53711yescharacteristic
107C2×C101#57612yes—
108D101—82no—
109#3259—1011nomaximal, Sylow
110C101#325911yescharacteristic, complemented, Sylow
111#540—1012no—
112#478—1012no—
113#478—1012no—
114#469—1011no—
115#469D10111yescharacteristic, complemented
116#466—1012no—
117#459—1012no—
118#459—1012no—
119#424—1011no—
120C2×D8—1012no—
121C2×D8—1011no—
122C2×D8C2×D10111yescharacteristic
123C2×M16C2×D10111yescharacteristic
124C22×C8—1011no—
125#127—1012no—
126#125—1012no—
127#123—2022no—
128#123—2022no—
129#121—1012no—
130#121—2022no—
131#121—2022no—
132#121C2×D10112yes—
133C4×D4—1012no—
134C4×D4—1012no—
135#117—1011no—
136#107—1012no—
137#106—1011no—
138#106C2×D10111yescharacteristic
139C4⋊C8—1012no—
140C4⋊C8—1012no—
141#102—1012no—
142#102—1012no—
143#102—1012no—
144#102C2×D10112yes—
145C2×D4—22no—
146C2×D4—1012no—
147C2×D4—2022no—
148C2×D4—2022no—
149C2×D4—2022no—
150C2×D4C22×D10112yes—
151C22×C4—2022no—
152C22×C4—2022no—
153C22×C4C22×D10111yescharacteristic
154D8—41no—
155D8—4041no—
156D8—4042no—
157M16—41no—
158C2×C8—1012no—
159C2×C8—4041no—
160C2×C8C22×D10111yescharacteristic
161C2×C8C22×D10111yescharacteristic
162C4⋊C4—1012no—
163C4⋊C4—1012no—
164C4⋊C4—2022no—
165C4⋊C4—2022no—
166C4⋊C4C22×D10112yes—
167C22⋊C4—22no—
168C22⋊C4—1011no—
169C22⋊C4—1011no—
170C22⋊C4—2022no—
171C22⋊C4—2022no—
172C22⋊C4—2022no—
173C42—1012no—
174C23—22no—
175C23—2022no—
176C23D4×D10111yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—8082no—
181D4—8082no—
182D4—8082no—
183D4—2022no—
184D4—2022no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—8082no—
189C2×C4—8082no—
190C2×C4—1012no—
191C2×C4—1012no—
192C2×C4—2022no—
193C2×C4D4×D10111yescharacteristic
194C2×C4C23×D10111yescharacteristic
195C8—21no—
196C8—21no—
197C8—2022no—
198C22—21no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—4042no—
204C22—4042no—
205C22—4042no—
206C22C2×D4×D10111yescharacteristic
207C4—21no—
208C4—42no—
209C4—4042no—
210C4—2022no—
211C4—2022no—
212C4#1569230011yescharacteristic
213C4#1569230211yescharacteristic
214C2—41no—
215C2—82no—
216C2—8082no—
217C2#2026575411yescharacteristic
218C2#2026598112yes—
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#469×C101C2
socleC22×C101C22×D4
hypercenter#469D101
hypocenterC101#3259
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20265780C2semidirect
2. #20265479C2semidirect
3. #20265476C2semidirect
4. #20265430C2semidirect
5. #20265411C2semidirect
6. #20265371C2semidirect
7. #20265370C2semidirect
8. #20265205C2semidirect
9. #469×C101C2semidirect
110. C101#3259semidirect
115. #469D101semidirect

Maximal subgroups

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

subgroupindex
#202657802
#202654792
#202654762
#202654302
#202654112
#202653712
#202653702
#202652052
#469×C1012
#3259101