Finite Group Databasebeta

← #16788441

Subgroups — #16788441

Order 3328.

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

normal subgroups only

This group has 280 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, complemented
2#13129841C212yesmaximal, complemented
3#13129838C212yesmaximal, complemented
4#13125236C211yesmaximal, characteristic
5C13×#532C411yescharacteristic
6C2×#88124C411yescharacteristic
7#11718893—22no—
8#11718743C411yescharacteristic
9#11718743C2211yescharacteristic
10#11718732C411yescharacteristic
11#11718732C2211yescharacteristic
12#11718717—22no—
13C4×#6099C2211yescharacteristic
14#11718284—22no—
15#11718233—22no—
16#11718232C2214yes—
17C2×C13×#41—21no—
18C13×C4⋊Q8C2×C411yescharacteristic
19C13×#127C2×C411yescharacteristic
20C13×#124—21no—
21C13×#121—41no—
22C4×D4×C13—41no—
23C2×C42×C13C2×C411yescharacteristic
24C2×C4⋊Dic13—21no—
25C2×#6101—41no—
26C2×#6099D412yes—
27#88124—21no—
28#88124—41no—
29#88124C2×C411yescharacteristic
30#88124C2×C411yescharacteristic
31#88106—24no—
32#88075—22no—
33#88075—22no—
34#88072—22no—
35#88072—22no—
36#88043C2×C411yescharacteristic
37#88043C2311yescharacteristic
38C4×#1055D412yes—
39#11917—131nomaximal, Sylow
40C13×#41—44no—
41C2×Q8×C13—21no—
42C2×D4×C13—21no—
43C2×D4×C13—41no—
44C2×D4×C13—41no—
45C22×C4×C13—21no—
46C22×C4×C13—41no—
47C22×C4×C13C22⋊C411yescharacteristic
48C22×Dic13—41no—
49C13×C4⋊C4—41no—
50C13×C22⋊C4—42no—
51C42×C13—21no—
52C42×C13C22⋊C411yescharacteristic
53C42×C13C22×C411yescharacteristic
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56C4⋊Dic13—41no—
57#6101—42no—
58#6101—41no—
59#6101—41no—
60#6099—42no—
61C2×#1055C22⋊C412yes—
62C2×#1055C2×D412yes—
63#6092—44no—
64#3142—131no—
65#2165—132no—
66#1356—132no—
67#1355—132no—
68C23×C13—41no—
69C23×C13#10011yescharacteristic
70Q8×C13—42no—
71D4×C13—42no—
72D4×C13—82no—
73D4×C13—82no—
74C2×C4×C13—22no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—41no—
78C2×C4×C13—82no—
79C2×C4×C13—81no—
80C2×C4×C13#10011yescharacteristic
81C2×C4×C13C2×C22⋊C411yescharacteristic
82C2×Dic13—41no—
83C2×Dic13—41no—
84C2×Dic13—82no—
85#1055—22no—
86#1055—22no—
87#532#26111yescharacteristic
88C2×#125—131no—
89#491—131no—
90#491—131no—
91#490—131no—
92#490—131no—
93#488—262no—
94#417—262no—
95C4×M16—131no—
96#364—262no—
97#349—262no—
98#347—134no—
99C22×C13—21no—
100C22×C13—41no—
101C22×C13—82no—
102C22×C13—81no—
103C22×C13C2×#10011yescharacteristic
104C4×C13—21no—
105C4×C13—41no—
106C4×C13—41no—
107C4×C13—81no—
108C4×C13#42112yes—
109Dic13—81no—
110Dic13—81no—
111C2×#41—21no—
112C2×M16—132no—
113C4⋊Q8C2×#26111yescharacteristic
114#127C2×#26111yescharacteristic
115#125—131no—
116#125—131no—
117#125—261no—
118#125—521no—
119#124—21no—
120#121—41no—
121C4×D4—41no—
122C2×C4⋊C4—261no—
123C2×C4⋊C4—521no—
124C2×C42C2×#26111yescharacteristic
125M32—264no—
126#103—262no—
127#103—262no—
128#102—262no—
129#102—262no—
130#97—131no—
131#97—131no—
132C4×C8—132no—
133C2×C13—21no—
134C2×C13—41no—
135C2×C13—161no—
136C2×C13#153311yescharacteristic
137#41—44no—
138C2×Q8—21no—
139C2×D4—21no—
140C2×D4—41no—
141C2×D4—41no—
142C22×C4—21no—
143C22×C4—41no—
144C22×C4—521no—
145C22×C4C22⋊#26111yescharacteristic
146M16—522no—
147C2×C8—132no—
148C2×C8—132no—
149C4⋊C4—41no—
150C4⋊C4—261no—
151C4⋊C4—261no—
152C4⋊C4—521no—
153C4⋊C4—521no—
154C4⋊C4—522no—
155C4⋊C4—521no—
156C22⋊C4—42no—
157C42—21no—
158C42C22⋊#26111yescharacteristic
159C42C22×#26111yescharacteristic
160C16—524no—
161C13#1191711yescharacteristic, complemented, Sylow
162C23—41no—
163C23#8812111yescharacteristic
164Q8—42no—
165D4—42no—
166D4—82no—
167D4—82no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—82no—
173C2×C4—81no—
174C2×C4—521no—
175C2×C4—521no—
176C2×C4—1042no—
177C2×C4#8812111yescharacteristic
178C2×C4C2×C22⋊#26111yescharacteristic
179C8—262no—
180C8—262no—
181C22—21no—
182C22—41no—
183C22—82no—
184C22—81no—
185C22C2×#8812111yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—81no—
190C4—1041no—
191C4—1041no—
192C4#1171914012yes—
193C2—21no—
194C2—41no—
195C2—161no—
196C2#1313031511yescharacteristic
subgroupG/H
centerC2#13130315
commutatorC42×C13C22×C4
FrattiniC42C22×#261
Fitting, prime radicalC13×#532C4
socleC2×C13#1533
cosocle#88043C23
hypercenter#532#261
hypocenterC13#11917
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #13131205C2semidirect
2. #13129841C2semidirect
3. #13129838C2semidirect
161. C13#11917semidirect

Maximal subgroups

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

subgroupindex
#131312052
#131298412
#131298382
#131252362
#1191713