Finite Group Databasebeta

← #15783780

Subgroups — #15783780

Order 3328.

200 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×#11718113C211yesmaximal, characteristic, complemented
2C2×#11718039C211yesmaximal, characteristic, complemented
3#13116924C211yesmaximal, characteristic, complemented
4#13116923C211yesmaximal, characteristic
5#13113035C211yesmaximal, characteristic, complemented
6#13113015C211yesmaximal, characteristic, complemented
7C13×#1416C211yesmaximal, characteristic, complemented
8C2×C13×Q32C2211yescharacteristic
9#11718849—21no—
10C2×D208C2211yescharacteristic
11C2×C16×D13C2211yescharacteristic
12#11718544—21no—
13C2×C13×C32C2211yescharacteristic
14C13×#366C2211yescharacteristic
15#11718156—21no—
16#11718113—22no—
17#11718096C2211yescharacteristic
18C2×#88034C2211yescharacteristic
19#11718083—21no—
20#11718039—22no—
21C2×C13×Q16—21no—
22#88200—41no—
23C2×D104—21no—
24C2×C8×D13D411yescharacteristic
25#88149—41no—
26C13×Q32—21no—
27C13×Q32—21no—
28C2×C13×C16C2311yescharacteristic
29C13×#107—21no—
30#88075—41no—
31#88058—21no—
32C2×#6090D411yescharacteristic
33#88049—41no—
34D208—21no—
35D208—21no—
36C16×D13—21no—
37C16×D13—21no—
38C13×C32—21no—
39#88034D412yescomplemented
40#13699—131nomaximal, Sylow
41C2×Q8×C13—41no—
42C2×D52—41no—
43C2×D52—81no—
44C2×C4×D13D811yescharacteristic
45C13×Q16—41no—
46C13×Q16—41no—
47C2×C8×C13C2×D411yescharacteristic
48C13×C4⋊C4—41no—
49#6103—81no—
50#6103—81no—
51C4⋊Dic13—41no—
52#6101—81no—
53C2×#1055D811yescharacteristic
54D104—41no—
55D104—41no—
56C8×D13—21no—
57C8×D13—21no—
58C13×C16C2×D411yescharacteristic
59C13×C16#4111yescharacteristic
60#6090—21no—
61C2×SD64—131no—
62C2×M64—131no—
63#2216—131no—
64#2215—131no—
65#1423—131no—
66#1416D1311yescharacteristic, complemented
67#1415—131no—
68C22×D13—81no—
69C22×D13D1611yescharacteristic
70Q8×C13—81no—
71Q8×C13—81no—
72C2×C4×C13—81no—
73C2×C4×C13—81no—
74C2×C4×C13C2×D811yescharacteristic
75C2×Dic13—81no—
76C2×Dic13D1611yescharacteristic
77D52—81no—
78D52—81no—
79D52—162no—
80C4×D13—21no—
81C4×D13—21no—
82C8×C13#12111yescharacteristic
83C8×C13#13511yescharacteristic
84#1055—21no—
85C2×Q32C2×D1311yescharacteristic
86C2×D16—131no—
87C22×C16—131no—
88#467—261no—
89#466—261no—
90SD64—262no—
91M64—262no—
92C2×C32—131no—
93C2×C32C2×D1311yescharacteristic
94#366—131no—
95#366C2×D1311yescharacteristic
96#358—261no—
97#357—261no—
98C22×C13C2×D1611yescharacteristic
99C2×D13—21no—
100C2×D13—21no—
101C2×D13—21no—
102C2×D13—161no—
103C2×D13—161no—
104C2×D13—161no—
105C4×C13—161no—
106C4×C13—161no—
107C4×C13#46611yescharacteristic
108C4×C13#50811yescharacteristic
109Dic13—21no—
110Dic13—161no—
111C2×Q16—21no—
112C2×D8—261no—
113C22×C8—131no—
114C22⋊Q8—521no—
115#121—521no—
116Q32—21no—
117Q32—21no—
118D16—261no—
119D16—261no—
120C2×C16—131no—
121C2×C16—261no—
122C2×C16—261no—
123C2×C16C22×D1311yescharacteristic
124#107—21no—
125#107—261no—
126#103—521no—
127#102—521no—
128C32—21no—
129C32—132no—
130C2×C13#221511yescharacteristic
131C2×C13#226311yescharacteristic
132C2×C13#226411yescharacteristic
133D13—41no—
134D13—321no—
135C2×Q8—41no—
136C2×D4—521no—
137C2×D4—1041no—
138C22×C4—131no—
139Q16—41no—
140Q16—41no—
141D8—521no—
142D8—521no—
143C2×C8—131no—
144C2×C8—261no—
145C2×C8—261no—
146C2×C8D4×D1311yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—521no—
149C4⋊C4—1041no—
150C22⋊C4—1041no—
151C22⋊C4—1041no—
152C16—261no—
153C16#612711yescharacteristic
154C16D4×D1311yescharacteristic
155C13#1369911yescharacteristic, complemented, Sylow
156C23—131no—
157C23—1041no—
158Q8—81no—
159Q8—81no—
160D4—1041no—
161D4—1041no—
162D4—2082no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—131no—
166C2×C4—261no—
167C2×C4—261no—
168C2×C4—1041no—
169C2×C4D8×D1311yescharacteristic
170C8—261no—
171C8#8813811yescharacteristic
172C8#8817011yescharacteristic
173C22—261no—
174C22—261no—
175C22—261no—
176C22—2081no—
177C22—2081no—
178C22—2081no—
179C22D13×D1611yescharacteristic
180C4—161no—
181C4—161no—
182C4—261no—
183C4—2081no—
184C4#1171843611yescharacteristic
185C4#1171857711yescharacteristic
186C2—521no—
187C2—4161no—
188C2#1311692111yescharacteristic
189C2#1311715011yescharacteristic
190C2#1311715511yescharacteristic
subgroupG/H
centerC22D13×D16
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#1416C2
socleC22×C13C2×D16
prime radical#13116923C2
hypercenter#1416D13
hypocenterC13#13699
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1416

Complements

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

NH ≅ G/Ntype
1. C2×#11718113C2semidirect
2. C2×#11718039C2semidirect
3. #13116924C2semidirect
5. #13113035C2semidirect
6. #13113015C2semidirect
7. C13×#1416C2semidirect
39. #88034D4semidirect
66. #1416D13semidirect
155. C13#13699semidirect

Maximal subgroups

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

subgroupindex
C2×#117181132
C2×#117180392
#131169242
#131169232
#131130352
#131130152
C13×#14162
#1369913