Finite Group Databasebeta

← #27181376

Subgroups — #27181376

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#20265782C211yesmaximal, characteristic, complemented
2#20265651C211yesmaximal, characteristic, complemented
3#20265502C212yesmaximal, complemented
4#20265478C212yesmaximal, complemented
5#20265373C212yesmaximal, complemented
6#20265313C212yesmaximal, complemented
7#20265290C212yesmaximal, complemented
8C4×D808C212yesmaximal, complemented
9#433×C101C211yesmaximal, characteristic, complemented
10C22×D404C2211yescharacteristic
11C2×D808C2212yes—
12C2×D808C2212yes—
13#15692252C2211yescharacteristic, complemented
14#15692247C2211yescharacteristic, complemented
15#15692240—22no—
16#15692229C2212yes—
17#15692228—22no—
18C4×D404C2212yes—
19C4×D404C2212yes—
20C4×D404C2212yescomplemented
21#15692217—22no—
22#15692214C2211yescharacteristic
23C22⋊C4×D101—22no—
24#15692189C2212yescomplemented
25#15692187C2212yescomplemented
26#15692177C2212yes—
27#15692177C2212yes—
28#15692177C2212yescomplemented
29#15692177C2212yescomplemented
30#117×C101C2211yescharacteristic
31C4⋊C8×C101C2212yescomplemented
32C22⋊C8×C101C2212yes—
33#97×C101C2211yescharacteristic, complemented
34C4×C8×C101C2211yescharacteristic, complemented
35C23×D101—21no—
36C2×D404—21no—
37C2×D404—24no—
38C2×D404—22no—
39C2×D404C2312yes—
40C2×D404C2312yes—
41C2×C22⋊D101—22no—
42C2×C4×D101—22no—
43C2×C4×D101—22no—
44C2×C4×D101—22no—
45D808—24no—
46D808—24no—
47C4⋊Dic101C2312yes—
48C4⋊Dic101C2312yes—
49#13108053—22no—
50C22⋊Dic101—21no—
51#13108051—22no—
52#13108051—22no—
53#13108051—22no—
54#13108051—22no—
55C4×Dic101—21no—
56C22×C4×C101C2311yescharacteristic
57C2×C8×C101C2312yes—
58C2×C8×C101C2312yes—
59C4⋊C4×C101D412yes—
60C22⋊C4×C101D412yes—
61C42×C101C2311yescharacteristic
62C42×C101C2311yescharacteristic
63C23×C101C2×D411yescharacteristic
64C22×D101—22no—
65C22×D101—24no—
66C22×D101—22no—
67C22×D101—82no—
68C2×C4×C101—22no—
69C2×C4×C101C2×D412yes—
70C2×C4×C101C2×D412yes—
71C2×C4×C101C2×D411yescharacteristic
72C2×C4×C101C2411yescharacteristic
73C22⋊D101—82no—
74C2×Dic101—22no—
75C2×Dic101—22no—
76D404—24no—
77D404—22no—
78D404—22no—
79D404—22no—
80D404—82no—
81D404#4114yes—
82C4×D101—82no—
83C4×D101—82no—
84C4×D101—82no—
85C8×C101—22no—
86C8×C101—22no—
87C22×C101—21no—
88C22×C101—22no—
89C22×C101C22×D411yescharacteristic
90C2×D101—24no—
91C2×D101—42no—
92C2×D101—42no—
93C2×D101—42no—
94C2×D101—42no—
95C2×D101—42no—
96C2×D101—84no—
97C4×C101—21no—
98C4×C101—22no—
99C4×C101—22no—
100C4×C101C2×#4112yes—
101Dic101—42no—
102Dic101—42no—
103C2×C101—41no—
104C2×C101#52511yescharacteristic
105C2×C101#57612yes—
106D101—44no—
107D101—82no—
108#3122—1011nomaximal, Sylow
109C101#312211yescharacteristic, complemented, Sylow
110#540—1011no—
111#518—1011no—
112#482—1012no—
113#478—1012no—
114#459—1012no—
115#447—1012no—
116#442—1012no—
117C4×D8—1012no—
118#433D10111yescharacteristic, complemented
119C22×D4—1011no—
120C2×D8—1012no—
121C2×D8—1012no—
122#127—1011no—
123#125—1011no—
124#123—2022no—
125#121—1012no—
126#121—2022no—
127C4×D4—1012no—
128C4×D4—1012no—
129C4×D4—1012no—
130C4×D4—2022no—
131#117—1011no—
132#117C2×D10111yescharacteristic
133C2×C22⋊C4—2022no—
134#107—1012no—
135#106—1012no—
136C4⋊C8C2×D10112yescomplemented
137#102—1012no—
138#102—1012no—
139#102—1012no—
140#102—1012no—
141C22⋊C8C2×D10112yes—
142#97C2×D10111yescharacteristic, complemented
143C4×C8C2×D10111yescharacteristic, complemented
144C24—2021no—
145C2×D4—1012no—
146C2×D4—1012no—
147C2×D4—2024no—
148C2×D4—2022no—
149C2×D4—2022no—
150C2×D4—2021no—
151C22×C4—2022no—
152C22×C4—2022no—
153C22×C4—2022no—
154C22×C4C22×D10111yescharacteristic
155D8—2024no—
156D8—2024no—
157C2×C8C22×D10112yes—
158C2×C8C22×D10112yes—
159C4⋊C4—1012no—
160C4⋊C4—1012no—
161C4⋊C4—2022no—
162C4⋊C4D40412yes—
163C22⋊C4—2021no—
164C22⋊C4—2022no—
165C22⋊C4—2022no—
166C22⋊C4—2022no—
167C22⋊C4—2022no—
168C22⋊C4D40412yes—
169C42—2021no—
170C42C22×D10111yescharacteristic
171C42C22×D10111yescharacteristic
172C23—8082no—
173C23—2024no—
174C23—2022no—
175C23—2022no—
176C23C2×D40411yescharacteristic
177D4—8082no—
178D4—8082no—
179D4—1014no—
180D4—2024no—
181D4—2022no—
182D4—2022no—
183D4—2022no—
184C2×C4—22no—
185C2×C4—8082no—
186C2×C4—8082no—
187C2×C4—8082no—
188C2×C4—2022no—
189C2×C4—2022no—
190C2×C4C2×D40411yescharacteristic
191C2×C4C2×D40412yes—
192C2×C4C2×D40412yes—
193C2×C4C23×D10111yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—8084no—
199C22—4042no—
200C22—4042no—
201C22—4042no—
202C22—4042no—
203C22—4042no—
204C22—2024no—
205C22C22×D40411yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—4042no—
210C4—4042no—
211C4#41×D10112yes—
212C2—41no—
213C2—8082no—
214C2—4044no—
215C2#2026568911yescharacteristic
216C2#2026598212yes—
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#433×C101C2
socleC22×C101C22×D4
hypercenter#433D101
hypocenterC101#3122
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20265782C2semidirect
2. #20265651C2semidirect
3. #20265502C2semidirect
4. #20265478C2semidirect
5. #20265373C2semidirect
6. #20265313C2semidirect
7. #20265290C2semidirect
8. C4×D808C2semidirect
9. #433×C101C2semidirect
13. #15692252C22semidirect
14. #15692247C22semidirect
20. C4×D404C22semidirect
24. #15692189C22semidirect
25. #15692187C22semidirect
28. #15692177C22semidirect
29. #15692177C22semidirect
31. C4⋊C8×C101C22semidirect
33. #97×C101C22semidirect
34. C4×C8×C101C22semidirect
109. C101#3122semidirect
118. #433D101semidirect
136. C4⋊C8C2×D101semidirect
142. #97C2×D101semidirect
143. C4×C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202657822
#202656512
#202655022
#202654782
#202653732
#202653132
#202652902
C4×D8082
#433×C1012
#3122101