Finite Group Databasebeta

← #15777699

Subgroups — #15777699

Order 3328.

284 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 83 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#13117092C211yesmaximal, characteristic
2#13117089C211yesmaximal, characteristic, complemented
3#13117064C211yesmaximal, characteristic, complemented
4#13117060C211yesmaximal, characteristic
5#13114442C211yesmaximal, characteristic
6#13114433C211yesmaximal, characteristic, complemented
7C13×#1312C211yesmaximal, characteristic, complemented
8C2×Dic104—22no—
9C2×#88040—22no—
10#11718360C2211yescharacteristic
11#11718360C2211yescharacteristic
12#11718356C2211yescharacteristic
13#11718355—21no—
14#11718355—21no—
15#11718343C2211yescharacteristic
16#11718342—21no—
17#11718341—21no—
18C4×C13×C16C2211yescharacteristic
19C4×C13×C16C2211yescharacteristic
20C82×C13C2211yescharacteristic
21#11718101—22no—
22#11718095—22no—
23C2×Dic52—21no—
24C2×Dic52—21no—
25C2×Dic52—21no—
26C2×Dic52—21no—
27C2×D104—21no—
28C2×D104—21no—
29#88128—21no—
30#88123—21no—
31#88123—21no—
32#88123—21no—
33C2×C13×C16D412yes—
34C2×C13×C16D412yes—
35C4×C8×C13D411yescharacteristic
36C4×C8×C13D411yescharacteristic
37C4×C8×C13C2311yescharacteristic
38#88061—42no—
39#88061—42no—
40#88058—21no—
41#88058—21no—
42#88057—42no—
43#88056—42no—
44Dic104—44no—
45#88040—44no—
46#12530—131nomaximal, Sylow
47C2×D52—41no—
48C2×D52—41no—
49C2×D52—41no—
50C2×Dic26—41no—
51C2×Dic26—41no—
52C2×Dic26—41no—
53C2×C8×C13D812yes—
54C2×C8×C13D812yes—
55C2×C8×C13C2×D411yescharacteristic
56C2×C8×C13C2×D411yescharacteristic
57C42×C13C2×D411yescharacteristic
58C4⋊Dic13—41no—
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61C4⋊Dic13—41no—
62C4⋊Dic13—41no—
63C4⋊Dic13—41no—
64Dic52—42no—
65Dic52—42no—
66Dic52—42no—
67Dic52—42no—
68D104—42no—
69D104—42no—
70C13×C16—22no—
71C13×C16—22no—
72#2248—131no—
73#2247—131no—
74#2241—131no—
75#2240—131no—
76#1709—131no—
77#1707—131no—
78#1312D1311yescharacteristic, complemented
79C22×D13—81no—
80C2×C4×C13#12711yescharacteristic
81C2×C4×C13C2×D811yescharacteristic
82C2×C4×C13C2×D811yescharacteristic
83C2×Dic13—81no—
84C2×Dic13—81no—
85C2×Dic13—81no—
86D52—81no—
87D52—81no—
88D52—82no—
89D52—82no—
90Dic26—81no—
91Dic26—81no—
92Dic26—81no—
93Dic26—81no—
94Dic26—82no—
95C8×C13—22no—
96C8×C13—22no—
97C8×C13AGL(1,ℤ/8)12yes—
98C8×C13AGL(1,ℤ/8)12yes—
99C2×Q32—262no—
100C2×SD32—262no—
101#500—131no—
102#498—261no—
103#494—131no—
104#494—131no—
105#493—131no—
106#487—261no—
107#486—261no—
108#486—261no—
109#358—262no—
110#357—262no—
111C4×C16C2×D1311yescharacteristic
112C4×C16C2×D1311yescharacteristic
113C82C2×D1311yescharacteristic
114C22×C13#49311yescharacteristic
115C2×D13—161no—
116C2×D13—161no—
117C2×D13—161no—
118C4×C13#49611yescharacteristic
119C4×C13#49611yescharacteristic
120C4×C13#50812yes—
121C4×C13#51012yes—
122Dic13—161no—
123Dic13—161no—
124Dic13—161no—
125C2×Q16—261no—
126C2×Q16—261no—
127C2×Q16—261no—
128C2×Q16—261no—
129C2×D8—261no—
130C2×D8—261no—
131C4⋊Q8—261no—
132C4⋊Q8—261no—
133C4⋊Q8—261no—
134#127—261no—
135Q32—524no—
136SD32—524no—
137C2×C16D5212yes—
138C2×C16D5212yes—
139#107—261no—
140#107—261no—
141#106—522no—
142#103—522no—
143#102—522no—
144#102—522no—
145C4×C8D5211yescharacteristic
146C4×C8D5211yescharacteristic
147C4×C8C22×D1311yescharacteristic
148C2×C13#172111yescharacteristic
149C2×C13#224911yescharacteristic
150C2×C13#225111yescharacteristic
151D13—321no—
152C2×Q8—521no—
153C2×Q8—521no—
154C2×Q8—521no—
155C2×D4—521no—
156C2×D4—521no—
157C2×D4—521no—
158Q16—522no—
159Q16—522no—
160Q16—522no—
161Q16—522no—
162D8—522no—
163D8—522no—
164C2×C8D10412yes—
165C2×C8D10412yes—
166C2×C8C2×D5211yescharacteristic
167C2×C8C2×D5211yescharacteristic
168C4⋊C4—521no—
169C4⋊C4—521no—
170C4⋊C4—521no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C4⋊C4—521no—
174C42C2×D5211yescharacteristic
175C16—22no—
176C16—22no—
177C13#1253011yescharacteristic, complemented, Sylow
178C23—1041no—
179Q8—1042no—
180Q8—1041no—
181Q8—1041no—
182Q8—1041no—
183Q8—1041no—
184D4—1042no—
185D4—1042no—
186D4—1041no—
187D4—1041no—
188C2×C4—1041no—
189C2×C4—1041no—
190C2×C4—1041no—
191C2×C4#8812811yescharacteristic
192C2×C4C2×D10411yescharacteristic
193C2×C4C2×D10411yescharacteristic
194C8—22no—
195C8—22no—
196C8#8816212yes—
197C8#8816212yes—
198C22—2081no—
199C22—2081no—
200C22—2081no—
201C22#1171835611yescharacteristic
202C4—2081no—
203C4—2081no—
204C4—2081no—
205C4#1171837311yescharacteristic
206C4#1171837311yescharacteristic
207C4#1171856512yes—
208C4#1171857012yes—
209C2—4161no—
210C2#1311450211yescharacteristic
211C2#1311709711yescharacteristic
212C2#1311710711yescharacteristic
subgroupG/H
centerC22#11718356
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1312C2
socleC22×C13#493
prime radical#11718356C22
hypercenter#1312D13
hypocenterC13#12530
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1312

Complements

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

NH ≅ G/Ntype
2. #13117089C2semidirect
3. #13117064C2semidirect
6. #13114433C2semidirect
7. C13×#1312C2semidirect
78. #1312D13semidirect
177. C13#12530semidirect

Maximal subgroups

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

subgroupindex
#131170922
#131170892
#131170642
#131170602
#131144422
#131144332
C13×#13122
#1253013