Finite Group Databasebeta

← #27179506

Subgroups — #27179506

Order 12928.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C2×#15692246C211yesmaximal, characteristic, complemented
2C2×#15692244C211yesmaximal, characteristic
3#20265084C211yesmaximal, characteristic, complemented
4#20265079C211yesmaximal, characteristic
5#20265078C211yesmaximal, characteristic
6#20265069C214yesmaximal, complemented
7#20265066C214yesmaximal, complemented
8C42×Dic101C211yesmaximal, characteristic, complemented
9#391×C101C211yesmaximal, characteristic, complemented
10C22×D404C2211yescharacteristic
11#15692246—24no—
12#15692244—24no—
13C2×C4⋊Dic101C2212yes—
14C2×C4⋊Dic101C2211yescharacteristic
15C2×#13108053C2212yes—
16C2×#13108051C2212yes—
17C2×#13108051C2214yes—
18C2×#13108051C2214yes—
19C2×#13108051C2212yes—
20C2×C4×Dic101C2212yes—
21C2×C4×Dic101C2212yes—
22C2×C4×Dic101C2211yescharacteristic
23C2×C4×Dic101C2211yescharacteristic
24#15692162C2214yes—
25C22×Q8×C101C2211yescharacteristic
26C2×C4⋊C4×C101C2211yescharacteristic
27C2×C42×C101C2211yescharacteristic
28#95×C101C2214yes—
29C23×D101C2312yes—
30C2×D404—22no—
31C2×D404—22no—
32C2×D404—22no—
33C22×Dic101C2312yes—
34C22×Dic101C2311yescharacteristic
35C22×Dic101C2311yescharacteristic
36C22×Dic101C2312yes—
37C4⋊Dic101—22no—
38C4⋊Dic101—24no—
39#13108053—24no—
40#13108051—28no—
41#13108051—24no—
42#13108051—24no—
43#13108051—28no—
44C4×Dic101—22no—
45C4×Dic101—24no—
46C4×Dic101—24no—
47C4×Dic101D414yes—
48C2×Q8×C101—22no—
49C2×Q8×C101—22no—
50C2×Q8×C101—22no—
51C22×C4×C101C2312yes—
52C22×C4×C101C2312yes—
53C22×C4×C101C2312yes—
54C22×C4×C101C2311yescharacteristic
55C4⋊C4×C101—22no—
56C42×C101—22no—
57C23×C101C2411yescharacteristic
58C22×D101—22no—
59C22×D101—24no—
60C22×D101—24no—
61C22×D101—22no—
62C22×D101—22no—
63Q8×C101—44no—
64C2×C4×C101—22no—
65C2×C4×C101—22no—
66C2×C4×C101—22no—
67C2×C4×C101—22no—
68C2×C4×C101—22no—
69C2×C4×C101—22no—
70C2×C4×C101—24no—
71C2×C4×C101C2×D412yes—
72C2×C4×C101#4112yes—
73C2×C4×C101#4112yes—
74C2×C4×C101#4114yes—
75C2×Dic101—22no—
76C2×Dic101—22no—
77C2×Dic101—22no—
78C2×Dic101—22no—
79C2×Dic101—22no—
80C2×Dic101—24no—
81C2×Dic101C2×D412yes—
82C2×Dic101C2×D412yes—
83C2×Dic101#4114yes—
84D404—44no—
85C22×C101C22×D411yescharacteristic
86C22×C101C2×#4112yes—
87C22×C101C2×#4111yescharacteristic
88C22×C101C2×#4111yescharacteristic
89C22×C101C2×#4112yes—
90C2×D101—42no—
91C2×D101—44no—
92C2×D101—44no—
93C2×D101—42no—
94C2×D101—42no—
95C4×C101—24no—
96C4×C101—42no—
97C4×C101—42no—
98C4×C101#12414yes—
99Dic101—24no—
100Dic101—22no—
101Dic101—22no—
102Dic101—42no—
103C2×C101C2×#12411yescharacteristic
104C2×C101#52912yes—
105C2×C101#52912yes—
106C2×C101#53211yescharacteristic
107C2×C101#53211yescharacteristic
108D101—82no—
109#2861—1011nomaximal, Sylow
110C101#286111yescharacteristic, complemented, Sylow
111C2×#125—1011no—
112C2×#124—1011no—
113#391—1011no—
114#391D10111yescharacteristic, complemented
115#390—1011no—
116#390—1011no—
117#388—1014no—
118#388—1014no—
119C43—1011no—
120C22×Q8C2×D10111yescharacteristic
121C22×D4—1011no—
122#125—2024no—
123#124—2024no—
124C2×C4⋊C4—1012no—
125C2×C4⋊C4—1012no—
126C2×C4⋊C4—1011no—
127C2×C4⋊C4C2×D10111yescharacteristic
128C2×C22⋊C4—1012no—
129C2×C22⋊C4—1012no—
130C2×C22⋊C4—1014no—
131C2×C22⋊C4—1014no—
132C2×C42—1011no—
133C2×C42—1012no—
134C2×C42—1012no—
135C2×C42—1011no—
136C2×C42C2×D10111yescharacteristic
137#95—1014no—
138#95C2×D10114yes—
139C24—1012no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×D4—2022no—
144C2×D4—2022no—
145C2×D4—2022no—
146C22×C4—1012no—
147C22×C4—1011no—
148C22×C4—1011no—
149C22×C4—1012no—
150C22×C4C22×D10112yes—
151C22×C4C22×D10112yes—
152C22×C4C22×D10112yes—
153C22×C4C22×D10111yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—2024no—
156C4⋊C4—2024no—
157C4⋊C4—2022no—
158C22⋊C4—2028no—
159C22⋊C4—2024no—
160C22⋊C4—2024no—
161C22⋊C4—2028no—
162C42—22no—
163C42—1014no—
164C42—2024no—
165C42—2022no—
166C42—2024no—
167C23—2022no—
168C23—2024no—
169C23—2022no—
170C23—2022no—
171C23—2024no—
172C23C23×D10111yescharacteristic
173Q8—44no—
174D4—4044no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—1012no—
183C2×C4—1012no—
184C2×C4—1014no—
185C2×C4—2022no—
186C2×C4—2024no—
187C2×C4—2022no—
188C2×C4—2022no—
189C2×C4—2022no—
190C2×C4—2022no—
191C2×C4D4×D10112yes—
192C2×C4#1310807312yes—
193C2×C4#1310807412yes—
194C2×C4#1310807514yes—
195C22—4042no—
196C22—4042no—
197C22—4044no—
198C22—4044no—
199C22—4042no—
200C22C2×D4×D10111yescharacteristic
201C22#41×D10112yes—
202C22C2×#1310807311yescharacteristic
203C22C2×#1310807411yescharacteristic
204C22C2×#1310807512yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—4042no—
209C4—2022no—
210C4—2024no—
211C4—2022no—
212C4#1569224114yes—
213C2—8082no—
214C2C2×#1569224111yescharacteristic
215C2#2026571312yes—
216C2#2026571412yes—
217C2#2026572611yescharacteristic
218C2#2026572811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, cosocleC23×C101C24
Fitting#391×C101C2
prime radicalC22×D404C22
hypercenter#391D101
hypocenterC101#2861
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#15692246C2semidirect
3. #20265084C2semidirect
6. #20265069C2semidirect
7. #20265066C2semidirect
8. C42×Dic101C2semidirect
9. #391×C101C2semidirect
110. C101#2861semidirect
114. #391D101semidirect

Maximal subgroups

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

subgroupindex
C2×#156922462
C2×#156922442
#202650842
#202650792
#202650782
#202650692
#202650662
C42×Dic1012
#391×C1012
#2861101