Finite Group Databasebeta

← #16788440

Subgroups — #16788440

Order 3328.

274 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 60 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#13131205C212yesmaximal
2#13129843C212yesmaximal, complemented
3#13129842C212yesmaximal, complemented
4#13125218C211yesmaximal, characteristic
5C13×#533C411yescharacteristic
6C2×#88123C411yescharacteristic
7#11718754—22no—
8#11718730C411yescharacteristic
9#11718730C411yescharacteristic
10#11718730C2211yescharacteristic
11#11718730C2211yescharacteristic
12#11718665—22no—
13C4×#6099C2211yescharacteristic
14#11718284—22no—
15#11718233—22no—
16#11718232C2214yes—
17C22×Dic26—21no—
18C13×C4⋊Q8—21no—
19C13×#125C2×C411yescharacteristic
20C13×#125C2×C411yescharacteristic
21C13×C22⋊Q8—41no—
22C4×Q8×C13—41no—
23C13×#117—21no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C4⋊Dic13—41no—
26C2×#6099D412yes—
27#88123—21no—
28#88123—41no—
29#88123C2×C411yescharacteristic
30#88123C2×C411yescharacteristic
31#88106—24no—
32#88050—22no—
33#88050—22no—
34#88050—22no—
35#88050—22no—
36#88043C2×C411yescharacteristic
37#88043C2311yescharacteristic
38C4×#1055D412yes—
39#11916—131nomaximal, Sylow
40C2×Q8×C13—41no—
41C22×C4×C13—21no—
42C22×C4×C13C22⋊C411yescharacteristic
43C22×Dic13—41no—
44C2×Dic26—21no—
45C2×Dic26—21no—
46C2×Dic26—44no—
47C2×Dic26—41no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—41no—
51C13×C4⋊C4—41no—
52C13×C4⋊C4—41no—
53C13×C22⋊C4—41no—
54C42×C13—21no—
55C42×C13—41no—
56C42×C13C22⋊C411yescharacteristic
57C42×C13C22×C411yescharacteristic
58C4⋊Dic13—42no—
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61#6099—42no—
62C2×#1055C22⋊C412yes—
63C2×#1055C2×D412yes—
64#6092—44no—
65#3139—131no—
66#2165—132no—
67#1356—132no—
68#1356—132no—
69C23×C13#10011yescharacteristic
70Q8×C13—82no—
71C2×C4×C13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—42no—
75C2×C4×C13—41no—
76C2×C4×C13—41no—
77C2×C4×C13#10011yescharacteristic
78C2×C4×C13C2×C22⋊C411yescharacteristic
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13—82no—
82Dic26—42no—
83Dic26—42no—
84Dic26—82no—
85#1055—22no—
86#1055—22no—
87#533#26111yescharacteristic
88C2×C4⋊Q8—131no—
89#491—131no—
90#491—131no—
91#491—131no—
92#491—131no—
93#487—262no—
94#419—262no—
95C4×M16—131no—
96#364—262no—
97#349—262no—
98#347—134no—
99C22×C13—21no—
100C22×C13—41no—
101C22×C13C2×#10011yescharacteristic
102C4×C13—22no—
103C4×C13—21no—
104C4×C13—41no—
105C4×C13—81no—
106C4×C13—81no—
107C4×C13#42112yes—
108Dic13—81no—
109Dic13—81no—
110C22×Q8—261no—
111C2×M16—132no—
112C4⋊Q8—21no—
113C4⋊Q8—131no—
114C4⋊Q8—131no—
115C4⋊Q8—261no—
116C4⋊Q8—521no—
117#125C2×#26111yescharacteristic
118#125C2×#26111yescharacteristic
119C22⋊Q8—41no—
120C4×Q8—41no—
121#117—21no—
122C2×C4⋊C4—521no—
123C2×C42C2×#26111yescharacteristic
124M32—264no—
125#103—262no—
126#103—262no—
127#103—262no—
128#103—262no—
129#97—131no—
130#97—131no—
131C4×C8—132no—
132C2×C13—21no—
133C2×C13—41no—
134C2×C13#153311yescharacteristic
135C2×Q8—41no—
136C2×Q8—261no—
137C2×Q8—261no—
138C2×Q8—524no—
139C2×Q8—521no—
140C22×C4—21no—
141C22×C4—521no—
142C22×C4C22⋊#26111yescharacteristic
143M16—522no—
144C2×C8—132no—
145C2×C8—132no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—521no—
152C4⋊C4—521no—
153C4⋊C4—522no—
154C22⋊C4—41no—
155C42—21no—
156C42—41no—
157C42C22⋊#26111yescharacteristic
158C42C22×#26111yescharacteristic
159C16—524no—
160C13#1191611yescharacteristic, complemented, Sylow
161C23#8812111yescharacteristic
162Q8—82no—
163Q8—522no—
164Q8—522no—
165Q8—1042no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—521no—
173C2×C4—521no—
174C2×C4—1042no—
175C2×C4#8812111yescharacteristic
176C2×C4C2×C22⋊#26111yescharacteristic
177C8—262no—
178C8—262no—
179C22—21no—
180C22—41no—
181C22C2×#8812111yescharacteristic
182C4—22no—
183C4—21no—
184C4—41no—
185C4—81no—
186C4—81no—
187C4—1041no—
188C4—1041no—
189C4#1171915512yes—
190C2—21no—
191C2—41no—
192C2#1313031711yescharacteristic
subgroupG/H
centerC2#13130317
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#533C4
socleC2×C13#1533
prime radicalC23×C13#100
cosocle#88043C23
hypercenter#533#261
hypocenterC13#11916
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #13129843C2semidirect
3. #13129842C2semidirect
160. C13#11916semidirect

Maximal subgroups

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

subgroupindex
#131312052
#131298432
#131298422
#131252182
#1191613