Finite Group Databasebeta

← #27181379

Subgroups — #27181379

Order 12928.

394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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#20265651C211yesmaximal, characteristic
2#20265515C212yesmaximal, complemented
3#20265474C212yesmaximal, complemented
4#20265379C212yesmaximal, complemented
5#20265327C212yesmaximal
6#20265275C212yesmaximal, complemented
7C4×#13108061C212yesmaximal, complemented
8#20265238C211yesmaximal, characteristic, complemented
9#541×C101C211yesmaximal, characteristic, complemented
10C22×D404C2211yescharacteristic
11C2×#13108061C2212yes—
12C2×#13108061C2212yes—
13C4×D404C2212yes—
14C4×D404C2212yes—
15#15692217—22no—
16#15692214C2211yescharacteristic
17C22⋊C4×D101—22no—
18#15692188C2212yescomplemented
19#15692186C2212yescomplemented
20C4⋊#11717579C2212yescomplemented
21#15692179C2212yescomplemented
22#15692179C2212yescomplemented
23#15692175C2212yes—
24#15692175C2212yes—
25C22⋊#11717579C2212yes—
26#15692166C2211yescharacteristic, complemented
27C4×#11717579C2211yescharacteristic, complemented
28C4⋊Q8×C101C2211yescharacteristic, complemented
29#126×C101—22no—
30#125×C101—22no—
31#125×C101C2211yescharacteristic, complemented
32C22⋊Q8×C101C2212yes—
33C4×Q8×C101C2212yescomplemented
34#117×C101C2211yescharacteristic
35C23×D101—21no—
36C2×D404—21no—
37C2×D404—24no—
38C2×D404C2312yes—
39C2×C4×D101—22no—
40C2×C4×D101—22no—
41#13108061—24no—
42#13108061—24no—
43C2×#11717579C2312yes—
44C2×#11717579C2312yes—
45C4⋊Dic101C2312yes—
46C22⋊Dic101—21no—
47#13108051—22no—
48#13108051—22no—
49C4×Dic101—21no—
50C2×Q8×C101C2312yes—
51C22×C4×C101C2311yescharacteristic
52C4⋊C4×C101—22no—
53C4⋊C4×C101—22no—
54C4⋊C4×C101—22no—
55C4⋊C4×C101—22no—
56C4⋊C4×C101D412yes—
57C4⋊C4×C101C2312yes—
58C22⋊C4×C101—22no—
59C22⋊C4×C101D412yes—
60C42×C101—22no—
61C42×C101C2311yescharacteristic
62C42×C101C2311yescharacteristic
63C23×C101C2×D411yescharacteristic
64C22×D101—22no—
65C22×D101—24no—
66C22×D101—82no—
67Q8×C101—22no—
68Q8×C101—22no—
69C2×C4×C101—22no—
70C2×C4×C101—22no—
71C2×C4×C101—22no—
72C2×C4×C101C2×D412yes—
73C2×C4×C101C2×D412yes—
74C2×C4×C101C2×D411yescharacteristic
75C2×C4×C101C2411yescharacteristic
76C2×Dic101—22no—
77D404—24no—
78D404—22no—
79D404#4114yes—
80C4×D101—82no—
81C4×D101—82no—
82#11717579—22no—
83#11717579—22no—
84C22×C101—21no—
85C22×C101—22no—
86C22×C101C22×D411yescharacteristic
87C2×D101—24no—
88C2×D101—42no—
89C2×D101—42no—
90C2×D101—84no—
91C4×C101—21no—
92C4×C101—22no—
93C4×C101—22no—
94C4×C101—42no—
95C4×C101—42no—
96C4×C101C2×#4112yes—
97Dic101—42no—
98C2×C101—41no—
99C2×C101#52511yescharacteristic
100C2×C101#57712yes—
101D101—44no—
102#3123—1011nomaximal, Sylow
103C101#312311yescharacteristic, complemented, Sylow
104#541D10111yescharacteristic, complemented
105#518—1011no—
106#485—1012no—
107#478—1012no—
108#461—1012no—
109#450—1012no—
110#440—1012no—
111C4×SD16—1012no—
112#433—1011no—
113C22×D4—1011no—
114C2×SD16—1012no—
115C2×SD16—1012no—
116C4⋊Q8C2×D10111yescharacteristic, complemented
117#126—22no—
118#125—22no—
119#125C2×D10111yescharacteristic, complemented
120C22⋊Q8C2×D10112yes—
121C4×Q8C2×D10112yescomplemented
122C4×D4—1012no—
123C4×D4—1012no—
124C4×D4—2022no—
125#117—1011no—
126#117C2×D10111yescharacteristic
127C2×C22⋊C4—2022no—
128#107—1012no—
129#106—1012no—
130C4⋊C8—1012no—
131#103—1012no—
132#103—1012no—
133#102—1012no—
134#102—1012no—
135C22⋊C8—1012no—
136#97—1011no—
137C4×C8—1011no—
138C24—2021no—
139C2×Q8C22×D10112yes—
140C2×D4—1012no—
141C2×D4—2024no—
142C2×D4—2021no—
143C22×C4—2022no—
144C22×C4—2022no—
145C22×C4C22×D10111yescharacteristic
146SD16—2024no—
147SD16—2024no—
148C2×C8—1012no—
149C2×C8—1012no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—1012no—
155C4⋊C4C22⋊D10112yes—
156C4⋊C4C22×D10112yes—
157C22⋊C4—22no—
158C22⋊C4—2021no—
159C22⋊C4—2022no—
160C22⋊C4—2022no—
161C22⋊C4C22⋊D10112yes—
162C42—22no—
163C42—2021no—
164C42C22×D10111yescharacteristic
165C42C22×D10111yescharacteristic
166C23—8082no—
167C23—2024no—
168C23—2022no—
169C23C2×C22⋊D10111yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—1014no—
173D4—2024no—
174D4—2022no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—8082no—
179C2×C4—8082no—
180C2×C4—2022no—
181C2×C4C2×C22⋊D10112yes—
182C2×C4C2×C22⋊D10111yescharacteristic
183C2×C4C2×C22⋊D10112yes—
184C2×C4C23×D10111yescharacteristic
185C8—2022no—
186C8—2022no—
187C22—22no—
188C22—21no—
189C22—8084no—
190C22—4042no—
191C22—4042no—
192C22—2024no—
193C22C22×C22⋊D10111yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—4042no—
200C4#41×D10112yes—
201C2—41no—
202C2—4044no—
203C2#2026568411yescharacteristic
204C2#2026598512yes—
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#541×C101C2
socleC22×C101C22×D4
prime radicalC22×D404C22
hypercenter#541D101
hypocenterC101#3123
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #20265515C2semidirect
3. #20265474C2semidirect
4. #20265379C2semidirect
6. #20265275C2semidirect
7. C4×#13108061C2semidirect
8. #20265238C2semidirect
9. #541×C101C2semidirect
18. #15692188C22semidirect
19. #15692186C22semidirect
20. C4⋊#11717579C22semidirect
21. #15692179C22semidirect
22. #15692179C22semidirect
26. #15692166C22semidirect
27. C4×#11717579C22semidirect
28. C4⋊Q8×C101C22semidirect
31. #125×C101C22semidirect
33. C4×Q8×C101C22semidirect
103. C101#3123semidirect
104. #541D101semidirect
116. C4⋊Q8C2×D101semidirect
119. #125C2×D101semidirect
121. C4×Q8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202656512
#202655152
#202654742
#202653792
#202653272
#202652752
C4×#131080612
#202652382
#541×C1012
#3123101