Finite Group Databasebeta

← #11719397

Subgroups — #11719397

Order 832.

218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C13×#125C211yesmaximal, characteristic, complemented
2#88152C211yesmaximal, characteristic, complemented
3#88151C211yesmaximal, characteristic, complemented
4#88150C211yesmaximal, characteristic, complemented
5#88150C211yesmaximal, characteristic, complemented
6#88149C211yesmaximal, characteristic
7#88148C211yesmaximal, characteristic, complemented
8#88148C211yesmaximal, characteristic, complemented
9#88148C211yesmaximal, characteristic, complemented
10#88148C211yesmaximal, characteristic, complemented
11#88147C211yesmaximal, characteristic, complemented
12C4⋊C4×D13C211yesmaximal, characteristic, complemented
13#88143C211yesmaximal, characteristic, complemented
14#88130C211yesmaximal, characteristic, complemented
15C4×D52C211yesmaximal, characteristic, complemented
16C2×D52C2211yescharacteristic
17C2×D52C2211yescharacteristic
18C2×D52C2211yescharacteristic
19C2×C4×D13C2211yescharacteristic
20C2×C4×D13C2211yescharacteristic
21C2×C4×D13C2211yescharacteristic
22C2×C4×D13C2211yescharacteristic
23C2×C4×D13C2211yescharacteristic
24C2×Dic26C2211yescharacteristic
25C13×C4⋊C4C2211yescharacteristic
26C13×C4⋊C4C2211yescharacteristic
27C13×C4⋊C4C2211yescharacteristic
28C13×C4⋊C4C2211yescharacteristic
29C13×C4⋊C4C2211yescharacteristic
30C13×C4⋊C4C2211yescharacteristic
31C42×C13C2211yescharacteristic
32#6103C2211yescharacteristic
33#6103C2211yescharacteristic
34#6103C2211yescharacteristic
35#6103C2211yescharacteristic
36#6103C2211yescharacteristic
37#6103C2211yescharacteristic
38#6103C2211yescharacteristic
39#6103C2211yescharacteristic
40#6103C2211yescharacteristic
41#6103C2211yescharacteristic
42C4⋊Dic13C2211yescharacteristic
43C4⋊Dic13C2211yescharacteristic
44#6101C2211yescharacteristic
45#6101C2211yescharacteristic
46#6101C2211yescharacteristic
47#6101C2211yescharacteristic
48#6101C2211yescharacteristic
49#6101C2211yescharacteristic
50C4×Dic13C2211yescharacteristic
51C22×D13C2311yescharacteristic
52C22×D13C2311yescharacteristic
53C22×D13C2311yescharacteristic
54C2×C4×C13C2311yescharacteristic
55C2×C4×C13C2311yescharacteristic
56C2×C4×C13C2311yescharacteristic
57C2×C4×C13C2311yescharacteristic
58C2×C4×C13C2311yescharacteristic
59C2×C4×C13C2311yescharacteristic
60C2×C4×C13C2311yescharacteristic
61C2×Dic13C2311yescharacteristic
62C2×Dic13C2311yescharacteristic
63C2×Dic13C2311yescharacteristic
64C2×Dic13C2311yescharacteristic
65C2×Dic13C2311yescharacteristic
66D52—22no—
67D52—22no—
68D52—41no—
69C4×D13—22no—
70C4×D13—41no—
71C4×D13—41no—
72C4×D13—41no—
73C4×D13—41no—
74Dic26—41no—
75#539—131nomaximal, Sylow
76C22×C13C2411yescharacteristic
77C2×D13—21no—
78C2×D13—21no—
79C2×D13—21no—
80C2×D13—21no—
81C2×D13—21no—
82C2×D13—21no—
83C2×D13—21no—
84C2×D13—21no—
85C2×D13#4112yes—
86C4×C13—21no—
87C4×C13—21no—
88C4×C13—21no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13—21no—
92C4×C13—21no—
93Dic13—21no—
94Dic13—21no—
95Dic13—21no—
96Dic13—21no—
97Dic13—21no—
98#126—131no—
99#126—131no—
100#125—131no—
101#125D1311yescharacteristic, complemented
102#123—131no—
103#123—131no—
104#123—131no—
105#123—131no—
106C22⋊Q8—131no—
107C22⋊Q8—131no—
108C22⋊Q8—131no—
109#121—131no—
110C4×D4—131no—
111C4×D4—131no—
112C2×C4⋊C4—131no—
113C2×C13C2×#4111yescharacteristic
114C2×C13H(5,𝔽2)11yescharacteristic
115C2×C132−1+411yescharacteristic
116D13—22no—
117D13—41no—
118D13—41no—
119C2×Q8—131no—
120C2×D4—131no—
121C2×D4—131no—
122C2×D4—131no—
123C22×C4—131no—
124C22×C4—131no—
125C22×C4—131no—
126C22×C4—131no—
127C22×C4—131no—
128C4⋊C4—131no—
129C4⋊C4—131no—
130C4⋊C4—131no—
131C4⋊C4—131no—
132C4⋊C4—131no—
133C4⋊C4—131no—
134C4⋊C4—131no—
135C4⋊C4—131no—
136C4⋊C4C2×D1311yescharacteristic
137C4⋊C4C2×D1311yescharacteristic
138C4⋊C4C2×D1311yescharacteristic
139C4⋊C4C2×D1311yescharacteristic
140C4⋊C4C2×D1311yescharacteristic
141C4⋊C4C2×D1311yescharacteristic
142C22⋊C4—131no—
143C22⋊C4—131no—
144C22⋊C4—131no—
145C22⋊C4—131no—
146C22⋊C4—131no—
147C22⋊C4—131no—
148C22⋊C4—131no—
149C22⋊C4—131no—
150C22⋊C4—131no—
151C22⋊C4—131no—
152C42—131no—
153C42C2×D1311yescharacteristic
154C13#53911yescharacteristic, complemented, Sylow
155C23—131no—
156C23—131no—
157C23—131no—
158Q8—521no—
159D4—262no—
160D4—262no—
161D4—521no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—131no—
165C2×C4—131no—
166C2×C4—131no—
167C2×C4—262no—
168C2×C4—521no—
169C2×C4—521no—
170C2×C4—521no—
171C2×C4—521no—
172C2×C4C22×D1311yescharacteristic
173C2×C4C22×D1311yescharacteristic
174C2×C4C22×D1311yescharacteristic
175C2×C4C22×D1311yescharacteristic
176C2×C4C22×D1311yescharacteristic
177C2×C4C22×D1311yescharacteristic
178C2×C4C22×D1311yescharacteristic
179C22—132no—
180C22—261no—
181C22—261no—
182C22—261no—
183C22—261no—
184C22—261no—
185C22—261no—
186C22—261no—
187C22—261no—
188C22C23×D1311yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—261no—
197C4—261no—
198C4—261no—
199C4—261no—
200C4—261no—
201C2—262no—
202C2—521no—
203C2—521no—
204C2#8825411yescharacteristic
205C2#41×D1311yescharacteristic
206C2#8825611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D13
commutator, socle, cosocleC22×C13C24
FittingC13×#125C2
prime radical#88149C2
hypercenter#125D13
hypocenterC13#539
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C13×#125C2semidirect
2. #88152C2semidirect
3. #88151C2semidirect
4. #88150C2semidirect
5. #88150C2semidirect
7. #88148C2semidirect
8. #88148C2semidirect
9. #88148C2semidirect
10. #88148C2semidirect
11. #88147C2semidirect
12. C4⋊C4×D13C2semidirect
13. #88143C2semidirect
14. #88130C2semidirect
15. C4×D52C2semidirect
101. #125D13semidirect
154. C13#539semidirect

Maximal subgroups

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

subgroupindex
C13×#1252
#881522
#881512
#881502
#881492
#881482
#881472
C4⋊C4×D132
#881432
#881302
C4×D522
#53913