Finite Group Databasebeta

← #15777729

Subgroups — #15777729

Order 3328.

250 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 79 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#13117118C211yesmaximal, characteristic
2#13117116C211yesmaximal, characteristic
3#13117063C211yesmaximal, characteristic
4#13114453C211yesmaximal, characteristic
5#13114430C211yesmaximal, characteristic
6#13112755C211yesmaximal, characteristic
7C13×#2241C211yesmaximal, characteristic
8C13×#500C2211yescharacteristic
9C13×#494C2211yescharacteristic
10#11718754—21no—
11#11718753—21no—
12#11718740—21no—
13#11718739—21no—
14#11718343C2211yescharacteristic
15#11718343C2211yescharacteristic
16C13×#358—22no—
17C4×C13×C16C2211yescharacteristic
18#11718156—22no—
19#11718097—22no—
20#11718082—22no—
21C4×#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26C13×C4⋊Q8—21no—
27C2×#6107—42no—
28#88123—21no—
29#88123—21no—
30C2×C13×C16D412yes—
31C13×#107—21no—
32C13×#107—21no—
33C4×C8×C13C2311yescharacteristic
34#88058—21no—
35#88058—21no—
36#88058—21no—
37#88058—21no—
38C2×#6090D412yes—
39#88050—42no—
40#88048—42no—
41#88047—42no—
42C4×#1055D411yescharacteristic
43C4×#1055D411yescharacteristic
44#12535—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
58#6107—84no—
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61C4⋊Dic13—41no—
62C4⋊Dic13—41no—
63C2×#1055D812yes—
64C2×#1055D812yes—
65C13×C16—22no—
66#6090—22no—
67#2254—131no—
68#2254—131no—
69#2241—131no—
70#2241D1311yescharacteristic
71#1713—131no—
72#1707—131no—
73#1312—131no—
74Q8×C13—81no—
75Q8×C13—81no—
76Q8×C13—82no—
77C2×C4×C13—81no—
78C2×C4×C13—81no—
79C2×C4×C13#12711yescharacteristic
80C2×C4×C13C2×D811yescharacteristic
81C2×C4×C13C2×D811yescharacteristic
82C2×Dic13—81no—
83C2×Dic13—81no—
84Dic26—82no—
85Dic26—82no—
86C8×C13#13712yes—
87C8×C13#13712yes—
88#1055—22no—
89#1055SD3214yes—
90#500—131no—
91#500—131no—
92#500—261no—
93#500C2×D1311yescharacteristic
94#498—261no—
95#494—261no—
96#494C2×D1311yescharacteristic
97#487—261no—
98#367—262no—
99#367—262no—
100#358—22no—
101#358—262no—
102C4×C16—131no—
103C4×C16C2×D1311yescharacteristic
104C82—131no—
105C22×C13#49311yescharacteristic
106C4×C13—161no—
107C4×C13—161no—
108C4×C13#49711yescharacteristic
109C4×C13#49711yescharacteristic
110C4×C13C2×SD3212yes—
111C4×C13#51012yes—
112Dic13—161no—
113Dic13—161no—
114C2×Q16—21no—
115C2×Q16—21no—
116C2×Q16—522no—
117C4⋊Q8—21no—
118C4⋊Q8—21no—
119C4⋊Q8—261no—
120C4⋊Q8—261no—
121C2×C16—132no—
122C2×C16C22⋊D1312yes—
123#107—21no—
124#107—21no—
125#107—261no—
126#107—261no—
127#107—261no—
128#107—261no—
129#107—522no—
130#106—522no—
131#103—522no—
132C4×C8—131no—
133C4×C8—131no—
134C4×C8C22×D1311yescharacteristic
135C2×C13#172211yescharacteristic
136C2×C13#224811yescharacteristic
137C2×C13#225111yescharacteristic
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—521no—
141C2×Q8—521no—
142Q16—42no—
143Q16—42no—
144Q16—1044no—
145C2×C8—132no—
146C2×C8—132no—
147C2×C8D4×D1311yescharacteristic
148C2×C8C2×C22⋊D1311yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—521no—
154C4⋊C4—521no—
155C4⋊C4—521no—
156C4⋊C4—521no—
157C42D4×D1311yescharacteristic
158C16—22no—
159C16—262no—
160C13#1253511yescharacteristic, complemented, Sylow
161Q8—81no—
162Q8—81no—
163Q8—82no—
164Q8—1042no—
165Q8—1042no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—1041no—
169C2×C4—1041no—
170C2×C4D8×D1311yescharacteristic
171C2×C4D8×D1311yescharacteristic
172C2×C4#8819411yescharacteristic
173C8—134no—
174C8—262no—
175C8#8816912yes—
176C8#8820512yes—
177C22#1171881211yescharacteristic
178C4—161no—
179C4—161no—
180C4—2081no—
181C4—2081no—
182C4D13×SD3212yes—
183C4#1171857912yes—
184C4#1171872111yescharacteristic
185C4#1171882811yescharacteristic
186C2#1311450911yescharacteristic
187C2#1311709011yescharacteristic
188C2#1311710411yescharacteristic
subgroupG/H
centerC22#11718812
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2241C2
socle, prime radicalC22×C13#493
hypercenter#2241D13
hypocenterC13#12535
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
160. C13#12535semidirect

Maximal subgroups

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

subgroupindex
#131171182
#131171162
#131170632
#131144532
#131144302
#131127552
C13×#22412
#1253513