Finite Group Databasebeta

← #27181694

Subgroups — #27181694

Order 12928.

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

normal subgroups only

This group has 412 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
1#20265732C211yesmaximal, characteristic, complemented
2#20265728C211yesmaximal, characteristic
3#20265573C211yesmaximal, characteristic, complemented
4#20265551C211yesmaximal, characteristic, complemented
5#20265524C211yesmaximal, characteristic, complemented
6#20265409C214yesmaximal, complemented
7#20265262C214yesmaximal, complemented
8C4×C8×D101C211yesmaximal, characteristic, complemented
9#487×C101C211yesmaximal, characteristic, complemented
10C2×#13108075—21no—
11C2×#13108061C2214yes—
12C2×C8×D101C2212yes—
13#15692255C2211yescharacteristic
14#15692252C2211yescharacteristic
15#15692246—21no—
16#15692244—21no—
17#15692235—21no—
18#15692231C2212yes—
19#15692230—21no—
20#15692230C2212yes—
21Q8×Dic101C2212yes—
22#15692220—21no—
23#15692217—21no—
24#15692217C2212yes—
25#15692213—21no—
26C42×D101C2211yescharacteristic
27#15692186C2214yes—
28#15692177C2214yes—
29C4×#11717579C2211yescharacteristic
30C8×Dic101C2212yes—
31C4⋊Q8×C101C2211yescharacteristic
32C4⋊Q8×C101C2211yescharacteristic
33#103×C101C2214yes—
34C4×C8×C101C2211yescharacteristic
35#13108075—44no—
36C2×Dic202—21no—
37C2×D404—22no—
38C2×D404—21no—
39C2×D404—21no—
40C2×D404C2312yes—
41C2×C4×D101—22no—
42C2×C4×D101D411yescharacteristic
43C2×C4×D101D411yescharacteristic
44C2×C4×D101C2311yescharacteristic
45#13108061—28no—
46C2×#11717579C2312yes—
47C8×D101—24no—
48C4⋊Dic101—21no—
49C4⋊Dic101—22no—
50C4⋊Dic101C2312yes—
51#13108053—22no—
52#13108051—22no—
53#13108051—22no—
54#13108051—22no—
55C4×Dic101—22no—
56C4×Dic101D411yescharacteristic
57C4×Dic101D411yescharacteristic
58C4×Dic101C2311yescharacteristic
59C2×Q8×C101—21no—
60C2×Q8×C101C2312yes—
61C2×C8×C101C2312yes—
62C4⋊C4×C101—21no—
63C4⋊C4×C101—21no—
64C4⋊C4×C101—21no—
65C4⋊C4×C101C2312yes—
66C42×C101C2311yescharacteristic
67C22×D101—22no—
68C22×D101C2×D411yescharacteristic
69Q8×C101—24no—
70Q8×C101—42no—
71C2×C4×C101—22no—
72C2×C4×C101—22no—
73C2×C4×C101C2×D411yescharacteristic
74C2×C4×C101C2×D411yescharacteristic
75C2×C4×C101C2411yescharacteristic
76C2×Dic101—22no—
77C2×Dic101C2×D411yescharacteristic
78C2×Dic101C2×D411yescharacteristic
79C2×Dic101C2×D411yescharacteristic
80D404—24no—
81D404—44no—
82D404—42no—
83D404—42no—
84C4×D101—22no—
85C4×D101—22no—
86C4×D101—44no—
87C4×D101SD1614yescomplemented
88Dic202—42no—
89C8×C101—22no—
90#11717579#4114yescomplemented
91C22×C101C22×D411yescharacteristic
92C2×D101—21no—
93C2×D101—21no—
94C2×D101—42no—
95C2×D101—42no—
96C2×D101—42no—
97C2×D101C2×SD1612yes—
98C4×C101—42no—
99C4×C101—42no—
100C4×C101C2×SD1612yes—
101C4×C101#13512yes—
102C4×C101C2×#4112yes—
103Dic101—21no—
104Dic101—21no—
105Dic101—42no—
106Dic101C2×SD1612yes—
107C2×C101#53211yescharacteristic
108C2×C101C22×SD1611yescharacteristic
109C2×C101C2×#13511yescharacteristic
110D101—22no—
111D101—82no—
112#3167—1011nomaximal, Sylow
113C101#316711yescharacteristic, complemented, Sylow
114#533—1011no—
115#532—1011no—
116#498—1011no—
117#492—1011no—
118#487D10111yescharacteristic, complemented
119#486—1011no—
120#465—1014no—
121C4×SD16—1014no—
122C2×C4×C8—1011no—
123C2×#41—2021no—
124C2×SD16—1014no—
125C22×C8—1012no—
126C4⋊Q8—1011no—
127C4⋊Q8C2×D10111yescharacteristic
128C4⋊Q8C2×D10111yescharacteristic
129#127—1011no—
130#125—2021no—
131#124—2021no—
132C22⋊Q8—1012no—
133C22⋊Q8—2021no—
134#121—1012no—
135#121—2021no—
136C4×Q8—1012no—
137C4×Q8—2021no—
138C4×D4—1012no—
139C4×D4—2021no—
140#117—2021no—
141C2×C42—1011no—
142#106—1014no—
143#103C2×D10114yes—
144#102—1014no—
145C4×C8—1012no—
146C4×C8—1011no—
147C4×C8C2×D10111yescharacteristic
148#41—4044no—
149C2×Q8—21no—
150C2×Q8—2021no—
151C2×Q8C22×D10112yes—
152C2×D4—1012no—
153C2×D4—2022no—
154C2×D4—2021no—
155C2×D4—2021no—
156C22×C4—1011no—
157C22×C4—1011no—
158C22×C4—1011no—
159C22×C4—2022no—
160SD16—2028no—
161C2×C8—1012no—
162C2×C8—2024no—
163C2×C8C22×D10112yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—1012no—
168C4⋊C4—2022no—
169C4⋊C4—2022no—
170C4⋊C4—2021no—
171C4⋊C4C22×D10112yes—
172C22⋊C4—2022no—
173C22⋊C4—2022no—
174C22⋊C4—2022no—
175C42—1011no—
176C42—1011no—
177C42—1011no—
178C42—2022no—
179C42C22×D10111yescharacteristic
180C23—1011no—
181C23—2022no—
182Q8—24no—
183Q8—42no—
184Q8—4042no—
185D4—4044no—
186D4—4042no—
187D4—4042no—
188D4—2024no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—1011no—
192C2×C4—1014no—
193C2×C4—1011no—
194C2×C4—1011no—
195C2×C4—4044no—
196C2×C4—2022no—
197C2×C4—2022no—
198C2×C4—2022no—
199C2×C4D4×D10111yescharacteristic
200C2×C4D4×D10111yescharacteristic
201C2×C4C23×D10111yescharacteristic
202C8—22no—
203C8—1014no—
204C22—1012no—
205C22—4042no—
206C22—4042no—
207C22—4042no—
208C22—2021no—
209C22—2021no—
210C22C2×D4×D10111yescharacteristic
211C4—42no—
212C4—42no—
213C4—1012no—
214C4—4042no—
215C4—2021no—
216C4—2021no—
217C4SD16×D10112yes—
218C4#1569227812yes—
219C4#41×D10112yes—
220C2—8082no—
221C2—2022no—
222C2#2026572611yescharacteristic
223C2C2×SD16×D10111yescharacteristic
224C2C2×#1569227811yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#487×C101C2
socleC22×C101C22×D4
prime radical#20265728C2
hypercenter#487D101
hypocenterC101#3167
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #20265732C2semidirect
3. #20265573C2semidirect
4. #20265551C2semidirect
5. #20265524C2semidirect
6. #20265409C2semidirect
7. #20265262C2semidirect
8. C4×C8×D101C2semidirect
9. #487×C101C2semidirect
87. C4×D101SD16semidirect
90. #11717579#41semidirect
113. C101#3167semidirect
118. #487D101semidirect

Maximal subgroups

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

subgroupindex
#202657322
#202657282
#202655732
#202655512
#202655242
#202654092
#202652622
C4×C8×D1012
#487×C1012
#3167101