Finite Group Databasebeta

← #15783774

Subgroups — #15783774

Order 3328.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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×#11718039C211yesmaximal, characteristic, complemented
2#13116924C211yesmaximal, characteristic, complemented
3#13116919C211yesmaximal, characteristic
4#13113036C211yesmaximal, characteristic, complemented
5#13113017C211yesmaximal, characteristic, complemented
6#13113014C211yesmaximal, characteristic, complemented
7C2×C13×SD64C211yesmaximal, characteristic, complemented
8C2×C13×Q32C2211yescharacteristic
9C2×C13×D16C2211yescharacteristic
10#11718849—21no—
11#11718818—21no—
12C2×C16×D13C2211yescharacteristic
13C13×SD64—22no—
14C2×C13×C32C2211yescharacteristic
15#11718156—21no—
16#11718154—21no—
17#11718096C2211yescharacteristic
18#11718096C2211yescharacteristic
19C2×#88034C2211yescharacteristic
20#11718039—22no—
21C2×C13×Q16—21no—
22C2×C13×D8—21no—
23#88200—41no—
24#88192—41no—
25C2×C8×D13D411yescharacteristic
26C13×Q32—21no—
27C13×Q32—21no—
28C13×D16—21no—
29C13×D16—21no—
30C2×C13×C16C2311yescharacteristic
31#88075—41no—
32#88072—41no—
33#88058—21no—
34#88058—21no—
35C2×#6090D411yescharacteristic
36C16×D13—21no—
37C16×D13—21no—
38C13×C32D412yescomplemented
39#88034—21no—
40#13699—131nomaximal, Sylow
41C2×Q8×C13—41no—
42C2×D4×C13—41no—
43C2×C22⋊D13—81no—
44C2×C4×D13D811yescharacteristic
45C13×Q16—41no—
46C13×Q16—41no—
47C13×D8—41no—
48C13×D8—41no—
49C2×C8×C13C2×D411yescharacteristic
50C22⋊Dic13—81no—
51#6103—81no—
52C4⋊Dic13—41no—
53C4⋊Dic13—41no—
54#6101—81no—
55C2×#1055D811yescharacteristic
56C8×D13—21no—
57C8×D13—21no—
58C13×C16C2×D411yescharacteristic
59C13×C16#4111yescharacteristic
60#6090—21no—
61C2×SD64D1311yescharacteristic, complemented
62C2×M64—131no—
63#2216—131no—
64#2215—131no—
65#1423—131no—
66#1416—131no—
67#1415—131no—
68C23×C13—81no—
69C22×D13D1611yescharacteristic
70Q8×C13—81no—
71Q8×C13—81no—
72D4×C13—81no—
73D4×C13—81no—
74C2×C4×C13—81no—
75C2×C4×C13C2×D811yescharacteristic
76C22⋊D13—162no—
77C2×Dic13—81no—
78C2×Dic13—81no—
79C2×Dic13D1611yescharacteristic
80C4×D13—21no—
81C4×D13—21no—
82C8×C13#12111yescharacteristic
83C8×C13#13511yescharacteristic
84#1055—21no—
85C2×Q32C2×D1311yescharacteristic
86C2×D16C2×D1311yescharacteristic
87C22×C16—131no—
88#467—261no—
89#466—261no—
90SD64—22no—
91M64—262no—
92C2×C32—131no—
93C2×C32C2×D1311yescharacteristic
94#366—131no—
95#366—131no—
96#358—261no—
97#357—261no—
98C22×C13—161no—
99C22×C13—161no—
100C22×C13—161no—
101C22×C13C2×D1611yescharacteristic
102C2×D13—21no—
103C2×D13—21no—
104C2×D13—21no—
105C4×C13—161no—
106C4×C13#46611yescharacteristic
107C4×C13#50811yescharacteristic
108Dic13—21no—
109Dic13—161no—
110Dic13—161no—
111C2×Q16—21no—
112C2×D8—21no—
113C22×C8—131no—
114C22⋊Q8—521no—
115#121—521no—
116Q32—21no—
117Q32—21no—
118D16—21no—
119D16—21no—
120C2×C16—131no—
121C2×C16—261no—
122C2×C16—261no—
123C2×C16C22×D1311yescharacteristic
124#107—261no—
125#107—261no—
126#103—521no—
127#102—521no—
128C32—261no—
129C32C22⋊D1312yescomplemented
130C2×C13—321no—
131C2×C13#221511yescharacteristic
132C2×C13#226311yescharacteristic
133C2×C13#226411yescharacteristic
134D13—41no—
135C2×Q8—41no—
136C2×D4—41no—
137C2×D4—1041no—
138C22×C4—131no—
139Q16—41no—
140Q16—41no—
141D8—41no—
142D8—41no—
143C2×C8—131no—
144C2×C8—261no—
145C2×C8—261no—
146C2×C8D4×D1311yescharacteristic
147C4⋊C4—521no—
148C4⋊C4—521no—
149C4⋊C4—1041no—
150C22⋊C4—1041no—
151C22⋊C4—1041no—
152C16—261no—
153C16#612911yescharacteristic
154C16C2×C22⋊D1311yescharacteristic
155C13#1369911yescharacteristic, complemented, Sylow
156C23—81no—
157C23—131no—
158Q8—81no—
159Q8—81no—
160D4—81no—
161D4—81no—
162D4—2082no—
163C2×C4—81no—
164C2×C4—131no—
165C2×C4—261no—
166C2×C4—261no—
167C2×C4—1041no—
168C2×C4—1041no—
169C2×C4D8×D1311yescharacteristic
170C8—261no—
171C8#8816611yescharacteristic
172C8#8819211yescharacteristic
173C22—161no—
174C22—161no—
175C22—161no—
176C22—261no—
177C22—261no—
178C22—261no—
179C22D13×D1611yescharacteristic
180C4—161no—
181C4—261no—
182C4—2081no—
183C4—2081no—
184C4#1171857311yescharacteristic
185C4#1171881811yescharacteristic
186C2—321no—
187C2—521no—
188C2#1311691911yescharacteristic
189C2#1311715011yescharacteristic
190C2#1311715211yescharacteristic
subgroupG/H
centerC22D13×D16
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC2×C13×SD64C2
socleC22×C13C2×D16
prime radical#13116919C2
hypercenterC2×SD64D13
hypocenterC13#13699
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. C2×#11718039C2semidirect
2. #13116924C2semidirect
4. #13113036C2semidirect
5. #13113017C2semidirect
6. #13113014C2semidirect
7. C2×C13×SD64C2semidirect
38. C13×C32D4semidirect
61. C2×SD64D13semidirect
129. C32C22⋊D13semidirect
155. C13#13699semidirect

Maximal subgroups

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

subgroupindex
C2×#117180392
#131169242
#131169192
#131130362
#131130172
#131130142
C2×C13×SD642
#1369913