Finite Group Databasebeta

← #15774114

Subgroups — #15774114

Order 3328.

274 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 61 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#13125215C211yesmaximal, characteristic
2#13116646C212yesmaximal
3#13112871C211yesmaximal, characteristic, complemented
4#13112870C212yesmaximal, complemented
5C13×#1356C211yesmaximal, characteristic, complemented
6D13×C4⋊Q8C411yescharacteristic
7#11719393C411yescharacteristic
8C13×#491C2211yescharacteristic
9#11718743C411yescharacteristic
10#11718730C411yescharacteristic
11#11718463—22no—
12#11718453—22no—
13#11718368C2211yescharacteristic
14#11718364C2211yescharacteristic
15C13×#347C2212yes—
16#11718106—22no—
17#11718103—22no—
18#11718058C2212yes—
19C2×Q8×D13—21no—
20C13×C4⋊Q8C2×C411yescharacteristic
21C13×#125C2×C411yescharacteristic
22#88198—21no—
23C2×#6094D412yes—
24#88150—41no—
25#88146—21no—
26C4⋊C4×D13—41no—
27#88142—21no—
28#88142—41no—
29#88141—41no—
30C42×D13C2×C411yescharacteristic
31#88124C2×C411yescharacteristic
32#88123C2×C411yescharacteristic
33C13×M32—22no—
34C13×#103—22no—
35C13×#97C2311yescharacteristic
36#88075—22no—
37#88056—22no—
38C8×Dic13D412yes—
39#88052—22no—
40#88050—22no—
41#88043C2×C411yescharacteristic
42#11916—131nomaximal, Sylow
43C2×Q8×C13—21no—
44Q8×D13—44no—
45C2×C4×D13—21no—
46C2×C4×D13—41no—
47C2×C4×D13C22⋊C411yescharacteristic
48C2×Dic26—21no—
49C2×Dic26—41no—
50C2×Dic26—41no—
51C2×C8×C13C2×D412yes—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—41no—
54C13×C4⋊C4—41no—
55C42×C13C22×C411yescharacteristic
56#6103—41no—
57C4⋊Dic13—21no—
58C4⋊Dic13—41no—
59#6101—41no—
60#6101—42no—
61#6101—41no—
62C4×Dic13—21no—
63C4×Dic13—41no—
64C4×Dic13C22⋊C411yescharacteristic
65C2×#1055C22⋊C412yes—
66#6094—42no—
67C13×C16—42no—
68#6090—42no—
69#3139—131no—
70#2165—132no—
71#1356—131no—
72#1356—132no—
73#1356D1311yescharacteristic, complemented
74C22×D13#10011yescharacteristic
75Q8×C13—42no—
76C2×C4×C13—21no—
77C2×C4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13C2×C22⋊C411yescharacteristic
80C2×Dic13—21no—
81C2×Dic13—41no—
82C2×Dic13—41no—
83C2×Dic13#10011yescharacteristic
84C4×D13—22no—
85C4×D13—42no—
86C4×D13—82no—
87Dic26—42no—
88Dic26—82no—
89Dic26—82no—
90C8×C13—22no—
91#1055—22no—
92#533—131no—
93C2×C4⋊Q8—131no—
94#491—131no—
95#491—131no—
96#491—131no—
97#491C2×D1311yescharacteristic
98#487—262no—
99#419—262no—
100C4×M16—131no—
101#364—262no—
102#349—262no—
103#347—132no—
104#347C2×D1312yes—
105C22×C13C2×#10011yescharacteristic
106C2×D13—21no—
107C2×D13—41no—
108C4×C13—41no—
109C4×C13—81no—
110C4×C13—81no—
111C4×C13#42112yes—
112Dic13—22no—
113Dic13—21no—
114Dic13—81no—
115Dic13—81no—
116C22×Q8—261no—
117C2×M16—132no—
118C4⋊Q8—131no—
119C4⋊Q8—261no—
120C4⋊Q8—261no—
121C4⋊Q8—521no—
122C4⋊Q8C4×D1311yescharacteristic
123#125—131no—
124#125C4×D1311yescharacteristic
125C22⋊Q8—521no—
126C4×Q8—521no—
127#117—261no—
128C2×C4⋊C4—521no—
129C2×C42—131no—
130M32—22no—
131M32—262no—
132#103—22no—
133#103—262no—
134#103—262no—
135#103—262no—
136#97—131no—
137#97C22×D1311yescharacteristic
138C4×C8—132no—
139C2×C13—21no—
140C2×C13#153311yescharacteristic
141D13—41no—
142C2×Q8—21no—
143C2×Q8—261no—
144C2×Q8—521no—
145C2×Q8—521no—
146C2×Q8—524no—
147C22×C4—131no—
148C22×C4—261no—
149C22×C4—521no—
150M16—522no—
151C2×C8—132no—
152C2×C8D4×D1312yes—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—261no—
157C4⋊C4—521no—
158C4⋊C4—521no—
159C4⋊C4—522no—
160C4⋊C4—521no—
161C22⋊C4—521no—
162C42—131no—
163C42—261no—
164C42—521no—
165C42C2×C4×D1311yescharacteristic
166C16—42no—
167C16—522no—
168C13#1191611yescharacteristic, complemented, Sylow
169C23—131no—
170Q8—42no—
171Q8—522no—
172Q8—1042no—
173Q8—1042no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—131no—
178C2×C4—261no—
179C2×C4—262no—
180C2×C4—522no—
181C2×C4—521no—
182C2×C4—521no—
183C2×C4—1042no—
184C2×C4C22⋊C4×D1311yescharacteristic
185C8—22no—
186C8—262no—
187C22—261no—
188C22—521no—
189C22D13×#10011yescharacteristic
190C4—41no—
191C4—81no—
192C4—81no—
193C4—262no—
194C4—261no—
195C4—1041no—
196C4—1041no—
197C4#1171848212yes—
198C2—21no—
199C2—521no—
200C2#1311345811yescharacteristic
subgroupG/H
centerC2#13113458
commutatorC42×C13C22×C4
Frattini#97C22×D13
FittingC13×#1356C2
socleC2×C13#1533
prime radicalC22×D13#100
cosocleC13×#97C23
hypercenter#1356D13
hypocenterC13#11916
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
3. #13112871C2semidirect
4. #13112870C2semidirect
5. C13×#1356C2semidirect
73. #1356D13semidirect
168. C13#11916semidirect

Maximal subgroups

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

subgroupindex
#131252152
#131166462
#131128712
#131128702
C13×#13562
#1191613