Finite Group Databasebeta

← #27181370

Subgroups — #27181370

Order 12928.

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

normal subgroups only

This group has 418 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, complemented
2#20265498C212yesmaximal, complemented
3#20265474C212yesmaximal, complemented
4#20265369C212yesmaximal, complemented
5#20265310C212yesmaximal, complemented
6#20265287C212yesmaximal, complemented
7C4×#13108059C212yesmaximal, complemented
8#20265238C211yesmaximal, characteristic, complemented
9#540×C101C211yesmaximal, characteristic, complemented
10C22×D404C2211yescharacteristic
11C2×#13108059C2212yes—
12C2×#13108059C2212yes—
13C4×D404C2212yes—
14C4×D404C2212yes—
15#15692217—22no—
16#15692214C2211yescharacteristic
17C22⋊C4×D101—22no—
18#15692188C2212yescomplemented
19#15692186C2212yescomplemented
20C4⋊#11717579C2212yescomplemented
21#15692176C2212yescomplemented
22#15692176C2212yescomplemented
23#15692175C2212yes—
24#15692175C2212yes—
25C22⋊#11717579C2212yes—
26#15692166C2211yescharacteristic, complemented
27C4×#11717579C2211yescharacteristic, complemented
28#127×C101C2211yescharacteristic, complemented
29#125×C101C2211yescharacteristic, complemented
30#123×C101—22no—
31#121×C101—22no—
32#121×C101C2212yes—
33C4×D4×C101C2212yescomplemented
34#117×C101C2211yescharacteristic
35C23×D101—21no—
36C2×D404—21no—
37C2×D404—24no—
38C2×D404C2312yes—
39C2×C4×D101—22no—
40C2×C4×D101—22no—
41#13108059—24no—
42#13108059—24no—
43C2×#11717579C2312yes—
44C2×#11717579C2312yes—
45C4⋊Dic101C2312yes—
46C22⋊Dic101—21no—
47#13108051—22no—
48#13108051—22no—
49C4×Dic101—21no—
50C2×D4×C101—22no—
51C2×D4×C101—22no—
52C2×D4×C101C2312yes—
53C22×C4×C101—22no—
54C22×C4×C101C2311yescharacteristic
55C4⋊C4×C101—22no—
56C4⋊C4×C101D412yes—
57C4⋊C4×C101C2312yes—
58C22⋊C4×C101—22no—
59C22⋊C4×C101—22no—
60C22⋊C4×C101D412yes—
61C42×C101C2311yescharacteristic
62C42×C101C2311yescharacteristic
63C23×C101—22no—
64C23×C101C2×D411yescharacteristic
65C22×D101—22no—
66C22×D101—24no—
67C22×D101—82no—
68D4×C101—22no—
69D4×C101—22no—
70D4×C101—82no—
71D4×C101—82no—
72C2×C4×C101—22no—
73C2×C4×C101—22no—
74C2×C4×C101—82no—
75C2×C4×C101C2×D412yes—
76C2×C4×C101C2×D412yes—
77C2×C4×C101C2×D411yescharacteristic
78C2×C4×C101C2411yescharacteristic
79C2×Dic101—22no—
80D404—24no—
81D404—22no—
82D404#4114yes—
83C4×D101—82no—
84C4×D101—82no—
85#11717579—22no—
86#11717579—22no—
87C22×C101—21no—
88C22×C101—22no—
89C22×C101—42no—
90C22×C101—42no—
91C22×C101—42no—
92C22×C101C22×D411yescharacteristic
93C2×D101—24no—
94C2×D101—42no—
95C2×D101—42no—
96C2×D101—84no—
97C4×C101—21no—
98C4×C101—22no—
99C4×C101—22no—
100C4×C101—42no—
101C4×C101C2×#4112yes—
102Dic101—42no—
103C2×C101—41no—
104C2×C101—82no—
105C2×C101#52511yescharacteristic
106C2×C101#57612yes—
107D101—44no—
108#3122—1011nomaximal, Sylow
109C101#312211yescharacteristic, complemented, Sylow
110#540D10111yescharacteristic, complemented
111#518—1011no—
112#482—1012no—
113#478—1012no—
114#459—1012no—
115#447—1012no—
116#442—1012no—
117C4×D8—1012no—
118#433—1011no—
119C22×D4—1011no—
120C2×D8—1012no—
121C2×D8—1012no—
122#127C2×D10111yescharacteristic, complemented
123#125C2×D10111yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D10112yes—
127C4×D4—1012no—
128C4×D4—1012no—
129C4×D4—2022no—
130C4×D4C2×D10112yescomplemented
131#117—1011no—
132#117C2×D10111yescharacteristic
133C2×C22⋊C4—2022no—
134#107—1012no—
135#106—1012no—
136C4⋊C8—1012no—
137#102—1012no—
138#102—1012no—
139#102—1012no—
140#102—1012no—
141C22⋊C8—1012no—
142#97—1011no—
143C4×C8—1011no—
144C24—2021no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—1012no—
148C2×D4—2024no—
149C2×D4—2021no—
150C2×D4C22×D10112yes—
151C22×C4—22no—
152C22×C4—2022no—
153C22×C4—2022no—
154C22×C4C22×D10111yescharacteristic
155D8—2024no—
156D8—2024no—
157C2×C8—1012no—
158C2×C8—1012no—
159C4⋊C4—22no—
160C4⋊C4—1012no—
161C4⋊C4C22⋊D10112yes—
162C4⋊C4C22×D10112yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—2021no—
166C22⋊C4—2022no—
167C22⋊C4—2022no—
168C22⋊C4C22⋊D10112yes—
169C42—2021no—
170C42C22×D10111yescharacteristic
171C42C22×D10111yescharacteristic
172C23—22no—
173C23—8082no—
174C23—2024no—
175C23—2022no—
176C23C2×C22⋊D10111yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—1014no—
182D4—2024no—
183D4—2022no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—8082no—
188C2×C4—8082no—
189C2×C4—2022no—
190C2×C4C2×C22⋊D10111yescharacteristic
191C2×C4C2×C22⋊D10112yes—
192C2×C4C2×C22⋊D10112yes—
193C2×C4C23×D10111yescharacteristic
194C8—2022no—
195C8—2022no—
196C22—21no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—8084no—
202C22—4042no—
203C22—4042no—
204C22—2024no—
205C22C22×C22⋊D10111yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—4042no—
211C4#41×D10112yes—
212C2—41no—
213C2—82no—
214C2—4044no—
215C2#2026568411yescharacteristic
216C2#2026598012yes—
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#540×C101C2
socleC22×C101C22×D4
hypercenter#540D101
hypocenterC101#3122
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20265651C2semidirect
2. #20265498C2semidirect
3. #20265474C2semidirect
4. #20265369C2semidirect
5. #20265310C2semidirect
6. #20265287C2semidirect
7. C4×#13108059C2semidirect
8. #20265238C2semidirect
9. #540×C101C2semidirect
18. #15692188C22semidirect
19. #15692186C22semidirect
20. C4⋊#11717579C22semidirect
21. #15692176C22semidirect
22. #15692176C22semidirect
26. #15692166C22semidirect
27. C4×#11717579C22semidirect
28. #127×C101C22semidirect
29. #125×C101C22semidirect
33. C4×D4×C101C22semidirect
109. C101#3122semidirect
110. #540D101semidirect
122. #127C2×D101semidirect
123. #125C2×D101semidirect
130. C4×D4C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202656512
#202654982
#202654742
#202653692
#202653102
#202652872
C4×#131080592
#202652382
#540×C1012
#3122101