Finite Group Databasebeta

← #15777625

Subgroups — #15777625

Order 3328.

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

normal subgroups only

This group has 246 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#13117065C211yesmaximal, characteristic
2#13117064C211yesmaximal, characteristic
3#13117063C211yesmaximal, characteristic
4#13114452C211yesmaximal, characteristic
5#13114445C211yesmaximal, characteristic
6#13112752C211yesmaximal, characteristic
7C13×#2241C211yesmaximal, characteristic
8C13×#500C2211yescharacteristic
9C13×#494C2211yescharacteristic
10#11718754—21no—
11#11718742—21no—
12#11718739—21no—
13#11718739—21no—
14#11718360C2211yescharacteristic
15#11718343C2211yescharacteristic
16C13×#358—22no—
17C4×C13×C16C2211yescharacteristic
18#11718156—22no—
19#11718095—22no—
20#11718084—22no—
21C4×#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26C13×C4⋊Q8—21no—
27C2×Dic52—21no—
28C2×Dic52—21no—
29#88123—21no—
30#88123—21no—
31C2×C13×C16D412yes—
32C13×#107—21no—
33C13×#107—21no—
34C4×C8×C13C2311yescharacteristic
35#88075—42no—
36#88058—21no—
37#88058—21no—
38C2×#6090D412yes—
39#88050—42no—
40#88047—42no—
41#88047—42no—
42C4×#1055D411yescharacteristic
43C4×#1055D411yescharacteristic
44#12514—131nomaximal, Sylow
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Dic26—41no—
48C2×Dic26—41no—
49C13×Q16—42no—
50C13×Q16—42no—
51C2×C8×C13C2×D411yescharacteristic
52C2×C8×C13C2×D411yescharacteristic
53C13×C4⋊C4—41no—
54C13×C4⋊C4—41no—
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C42×C13C2×D411yescharacteristic
58C4⋊Dic13—41no—
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61C4⋊Dic13—41no—
62C2×#1055D812yes—
63C2×#1055D812yes—
64Dic52—42no—
65Dic52—42no—
66C13×C16—22no—
67#6090—22no—
68#2241—131no—
69#2241—131no—
70#2241—131no—
71#2241D1311yescharacteristic
72#1713—131no—
73#1710—131no—
74#1311—131no—
75Q8×C13—81no—
76Q8×C13—81no—
77Q8×C13—82no—
78C2×C4×C13—81no—
79C2×C4×C13—81no—
80C2×C4×C13#12711yescharacteristic
81C2×C4×C13C2×D811yescharacteristic
82C2×C4×C13C2×D811yescharacteristic
83C2×Dic13—81no—
84C2×Dic13—81no—
85Dic26—81no—
86Dic26—81no—
87Dic26—82no—
88C8×C13#13512yes—
89C8×C13#13512yes—
90#1055—22no—
91#1055—22no—
92#500—131no—
93#500—261no—
94#500—261no—
95#500C2×D1311yescharacteristic
96#494—131no—
97#494C2×D1311yescharacteristic
98#487—261no—
99#487—261no—
100#358—22no—
101#358—262no—
102#358—262no—
103#358—262no—
104C4×C16—131no—
105C4×C16C2×D1311yescharacteristic
106C82—131no—
107C22×C13#49311yescharacteristic
108C4×C13—161no—
109C4×C13—161no—
110C4×C13#49511yescharacteristic
111C4×C13#49511yescharacteristic
112C4×C13#51012yes—
113C4×C13#51012yes—
114Dic13—161no—
115Dic13—161no—
116C2×Q16—21no—
117C2×Q16—21no—
118C2×Q16—261no—
119C2×Q16—261no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—261no—
123C4⋊Q8—261no—
124C2×C16—132no—
125C2×C16C22⋊D1312yes—
126#107—21no—
127#107—21no—
128#107—261no—
129#107—261no—
130#107—522no—
131#107—522no—
132#103—522no—
133#103—522no—
134C4×C8—131no—
135C4×C8—131no—
136C4×C8C22×D1311yescharacteristic
137C2×C13#170911yescharacteristic
138C2×C13#225111yescharacteristic
139C2×C13#225111yescharacteristic
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—521no—
143C2×Q8—521no—
144Q16—42no—
145Q16—42no—
146Q16—522no—
147Q16—522no—
148C2×C8—132no—
149C2×C8—132no—
150C2×C8D4×D1311yescharacteristic
151C2×C8C2×C22⋊D1311yescharacteristic
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—521no—
157C4⋊C4—521no—
158C4⋊C4—521no—
159C4⋊C4—521no—
160C42D4×D1311yescharacteristic
161C16—22no—
162C16—262no—
163C13#1251411yescharacteristic, complemented, Sylow
164Q8—81no—
165Q8—81no—
166Q8—82no—
167Q8—1041no—
168Q8—1041no—
169Q8—1042no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—1041no—
173C2×C4—1041no—
174C2×C4D8×D1311yescharacteristic
175C2×C4D8×D1311yescharacteristic
176C2×C4#8819411yescharacteristic
177C8—262no—
178C8—262no—
179C8#8817012yes—
180C8#8820412yes—
181C22#1171881211yescharacteristic
182C4—161no—
183C4—161no—
184C4—2081no—
185C4—2081no—
186C4#1171857612yes—
187C4#1171857912yes—
188C4#1171872011yescharacteristic
189C4#1171882911yescharacteristic
190C2#1311444011yescharacteristic
191C2#1311710411yescharacteristic
192C2#1311710611yescharacteristic
subgroupG/H
centerC22#11718812
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2241C2
socle, prime radicalC22×C13#493
hypercenter#2241D13
hypocenterC13#12514
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
163. C13#12514semidirect

Maximal subgroups

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

subgroupindex
#131170652
#131170642
#131170632
#131144522
#131144452
#131127522
C13×#22412
#1251413