Finite Group Databasebeta

← #15777701

Subgroups — #15777701

Order 3328.

284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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#13117091C211yesmaximal, characteristic
2#13117089C211yesmaximal, characteristic, complemented
3#13117065C211yesmaximal, characteristic, complemented
4#13114441C211yesmaximal, characteristic
5#13114434C211yesmaximal, characteristic, complemented
6#13112755C211yesmaximal, characteristic, complemented
7C13×#2240C211yesmaximal, characteristic
8C13×#500C2211yescharacteristic
9C13×#493C2211yescharacteristic
10C2×#88067—22no—
11#11718742—21no—
12#11718740—21no—
13#11718731—21no—
14#11718731—21no—
15C2×Dic104—22no—
16#11718360C2211yescharacteristic
17#11718360C2211yescharacteristic
18C13×#357—22no—
19C4×C13×C16C2211yescharacteristic
20#11718084—22no—
21C4×#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C13×C4⋊Q8—21no—
26C13×#127—21no—
27C2×Dic52—21no—
28C2×Dic52—21no—
29C2×Dic52—21no—
30C2×Dic52—21no—
31#88123—21no—
32#88123—21no—
33C2×C13×C16D412yes—
34C13×#107—21no—
35C13×#107—21no—
36C4×C8×C13C2311yescharacteristic
37#88075—42no—
38#88072—42no—
39#88072—42no—
40#88067—44no—
41C2×#6090D412yes—
42#88048—42no—
43C4×#1055D411yescharacteristic
44C4×#1055D411yescharacteristic
45Dic104—44no—
46#12530—131nomaximal, Sylow
47C2×Q8×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C2×Dic26—41no—
52C2×Dic26—41no—
53C13×D8—42no—
54C13×D8—42no—
55C2×C8×C13C2×D411yescharacteristic
56C2×C8×C13C2×D411yescharacteristic
57C13×C4⋊C4—41no—
58C13×C4⋊C4—41no—
59C42×C13C2×D411yescharacteristic
60C4⋊Dic13—41no—
61C4⋊Dic13—41no—
62C4⋊Dic13—41no—
63C4⋊Dic13—41no—
64C2×#1055D812yes—
65C2×#1055D812yes—
66Dic52—42no—
67Dic52—42no—
68Dic52—42no—
69Dic52—42no—
70C13×C16—22no—
71#6090—22no—
72#2248—131no—
73#2247—131no—
74#2241—131no—
75#2240D1311yescharacteristic
76#1709—131no—
77#1707—131no—
78#1312—131no—
79C23×C13—81no—
80Q8×C13—82no—
81D4×C13—81no—
82D4×C13—81no—
83D4×C13—82no—
84D4×C13—82no—
85C2×C4×C13—81no—
86C2×C4×C13#12711yescharacteristic
87C2×C4×C13C2×D811yescharacteristic
88C2×C4×C13C2×D811yescharacteristic
89C2×Dic13—81no—
90C2×Dic13—81no—
91Dic26—81no—
92Dic26—81no—
93Dic26—81no—
94Dic26—81no—
95C8×C13AGL(1,ℤ/8)12yes—
96C8×C13AGL(1,ℤ/8)12yes—
97#1055—22no—
98#1055—22no—
99C2×Q32—262no—
100C2×SD32—262no—
101#500C2×D1311yescharacteristic
102#498—261no—
103#494—131no—
104#494—131no—
105#493C2×D1311yescharacteristic
106#487—261no—
107#486—261no—
108#486—261no—
109#358—262no—
110#357—22no—
111C4×C16—131no—
112C4×C16C2×D1311yescharacteristic
113C82—131no—
114C22×C13—161no—
115C22×C13—161no—
116C22×C13—161no—
117C22×C13#49311yescharacteristic
118C4×C13—161no—
119C4×C13#49611yescharacteristic
120C4×C13#49611yescharacteristic
121C4×C13#50812yes—
122C4×C13#51012yes—
123Dic13—161no—
124Dic13—161no—
125C2×Q16—261no—
126C2×Q16—261no—
127C2×Q16—261no—
128C2×Q16—261no—
129C2×D8—21no—
130C2×D8—21no—
131C4⋊Q8—21no—
132C4⋊Q8—261no—
133C4⋊Q8—261no—
134#127—21no—
135Q32—524no—
136SD32—524no—
137C2×C16—132no—
138C2×C16C22⋊D1312yes—
139#107—21no—
140#107—21no—
141#106—522no—
142#103—522no—
143#102—522no—
144#102—522no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8C22×D1311yescharacteristic
148C2×C13—321no—
149C2×C13#172111yescharacteristic
150C2×C13#224911yescharacteristic
151C2×C13#225111yescharacteristic
152C2×Q8—41no—
153C2×Q8—521no—
154C2×Q8—521no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—41no—
158Q16—522no—
159Q16—522no—
160Q16—522no—
161Q16—522no—
162D8—42no—
163D8—42no—
164C2×C8—132no—
165C2×C8—132no—
166C2×C8D4×D1311yescharacteristic
167C2×C8C2×C22⋊D1311yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—521no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C4⋊C4—521no—
174C42D4×D1311yescharacteristic
175C16—22no—
176C16—262no—
177C13#1253011yescharacteristic, complemented, Sylow
178C23—81no—
179Q8—82no—
180Q8—1041no—
181Q8—1041no—
182Q8—1041no—
183Q8—1041no—
184D4—81no—
185D4—82no—
186D4—82no—
187D4—81no—
188C2×C4—81no—
189C2×C4—1041no—
190C2×C4—1041no—
191C2×C4D8×D1311yescharacteristic
192C2×C4D8×D1311yescharacteristic
193C2×C4#8819411yescharacteristic
194C8—262no—
195C8—262no—
196C8#8816812yes—
197C8#8820312yes—
198C22—161no—
199C22—161no—
200C22—161no—
201C22#1171881211yescharacteristic
202C4—161no—
203C4—2081no—
204C4—2081no—
205C4#1171857312yes—
206C4#1171857612yes—
207C4#1171871911yescharacteristic
208C4#1171883711yescharacteristic
209C2—321no—
210C2#1311450411yescharacteristic
211C2#1311709411yescharacteristic
212C2#1311710611yescharacteristic
subgroupG/H
centerC22#11718812
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2240C2
socleC22×C13#493
prime radicalC13×#493C22
hypercenter#2240D13
hypocenterC13#12530
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
2. #13117089C2semidirect
3. #13117065C2semidirect
5. #13114434C2semidirect
6. #13112755C2semidirect
177. C13#12530semidirect

Maximal subgroups

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

subgroupindex
#131170912
#131170892
#131170652
#131144412
#131144342
#131127552
C13×#22402
#1253013