Finite Group Databasebeta

← #15783736

Subgroups — #15783736

Order 3328.

200 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 51 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#13117154C211yesmaximal, characteristic, complemented
2#13117151C211yesmaximal, characteristic
3#13117098C211yesmaximal, characteristic, complemented
4#13116716C211yesmaximal, characteristic, complemented
5#13113033C211yesmaximal, characteristic, complemented
6#13113025C211yesmaximal, characteristic, complemented
7C13×#1420C211yesmaximal, characteristic, complemented
8C2×C13×Q32C2211yescharacteristic
9#11718852—21no—
10C2×#88068—21no—
11#11718565C2211yescharacteristic
12C2×D208C2211yescharacteristic
13#11718556—21no—
14C13×M64C2211yescharacteristic
15C13×#368C2211yescharacteristic
16#11718114—21no—
17#11718113—21no—
18C16×Dic13C2211yescharacteristic
19#11718091C2211yescharacteristic
20#11718089—21no—
21#11718041—21no—
22D416—21no—
23C2×C13×Q16—21no—
24#88201—41no—
25C2×#6106—41no—
26#88161—41no—
27#88158—21no—
28C2×D104—21no—
29C13×Q32—21no—
30C13×Q32—21no—
31C2×C13×C16C2311yescharacteristic
32C13×#108—21no—
33#88068—42no—
34#88065—41no—
35C8×Dic13D411yescharacteristic
36C2×#6090D411yescharacteristic
37Dic104D411yescharacteristic
38#88040—21no—
39D208—21no—
40D208—21no—
41D208D411yescharacteristic
42C13×C32—21no—
43#88034—21no—
44#13691—131nomaximal, Sylow
45C2×Q8×C13—41no—
46#6127—41no—
47C2×D52—41no—
48C13×Q16—41no—
49C13×Q16—41no—
50C13×M16—41no—
51C2×C8×C13C2×D411yescharacteristic
52#6106—81no—
53#6106—81no—
54#6103—82no—
55C4×Dic13D811yescharacteristic
56C2×#1055D811yescharacteristic
57Dic52—21no—
58D104—21no—
59D104—41no—
60D104—41no—
61#6095—41no—
62#6094—81no—
63C8×D13—81no—
64C13×C16C2×D411yescharacteristic
65C13×C16#4111yescharacteristic
66#6090—21no—
67#2264—131no—
68#2263—131no—
69#2249—131no—
70#2178—131no—
71#1422—131no—
72#1420D1311yescharacteristic, complemented
73#1419—131no—
74C22×D13—81no—
75Q8×C13—81no—
76Q8×C13—81no—
77C2×C4×C13—81no—
78C2×C4×C13C2×D811yescharacteristic
79C22⋊D13—81no—
80C2×Dic13—21no—
81D52—41no—
82D52—81no—
83D52—81no—
84C4×D13—81no—
85Dic26—41no—
86C8×C13—81no—
87C8×C13#12111yescharacteristic
88C8×C13AGL(1,ℤ/8)11yescharacteristic
89#1055D1611yescharacteristic
90#1055D1611yescharacteristic
91#508—131no—
92C2×Q32C2×D1311yescharacteristic
93C2×SD32—261no—
94C2×D16—131no—
95#495—261no—
96#443—261no—
97Q64—261no—
98SD64—261no—
99SD64—261no—
100D32—261no—
101M64—131no—
102M64C2×D1311yescharacteristic
103#368C2×D1311yescharacteristic
104#359—261no—
105C4×C16—131no—
106C22×C13#50911yescharacteristic
107C2×D13—81no—
108C2×D13—162no—
109C2×D13—161no—
110C4×C13—161no—
111C4×C13#45911yescharacteristic
112C4×C13C2×D1611yescharacteristic
113Dic13—41no—
114Dic13—81no—
115#135—261no—
116C2×Q16—21no—
117C2×SD16—521no—
118C2×D8—261no—
119#131—521no—
120#124—521no—
121Q32—21no—
122Q32—21no—
123Q32—131no—
124SD32—261no—
125SD32—522no—
126D16—131no—
127D16—261no—
128D16—261no—
129C2×C16—131no—
130C2×C16C22×D1311yescharacteristic
131#108—21no—
132#104—521no—
133C4×C8—131no—
134C32—21no—
135C32—261no—
136C2×C13—21no—
137C2×C13#220611yescharacteristic
138D13—161no—
139D13—321no—
140#41—521no—
141C2×Q8—41no—
142C2×D4—521no—
143Q16—41no—
144Q16—41no—
145Q16—261no—
146SD16—521no—
147SD16—1041no—
148SD16—1041no—
149D8—261no—
150D8—521no—
151D8—521no—
152M16—41no—
153M16—1041no—
154C2×C8—131no—
155C2×C8—1041no—
156C2×C8D4×D1311yescharacteristic
157C22⋊C4—1042no—
158C42—131no—
159C16—261no—
160C16#612711yescharacteristic
161C16D4×D1311yescharacteristic
162C13#1369111yescharacteristic, complemented, Sylow
163C23—1041no—
164Q8—81no—
165Q8—81no—
166Q8—521no—
167D4—521no—
168D4—1041no—
169D4—1041no—
170D4—1041no—
171C2×C4—81no—
172C2×C4—261no—
173C2×C4—1041no—
174C2×C4D8×D1311yescharacteristic
175C8—81no—
176C8—131no—
177C8—131no—
178C8#8813811yescharacteristic
179C8#8816811yescharacteristic
180C22—1041no—
181C22—2082no—
182C22—2081no—
183C22#1171857511yescharacteristic
184C4—161no—
185C4—521no—
186C4—1041no—
187C4#1171844711yescharacteristic
188C4D13×D1611yescharacteristic
189C2—21no—
190C2—4161no—
191C2—2081no—
192C2#1311687011yescharacteristic
subgroupG/H
centerC2#13116870
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#1420C2
socleC2×C13#2206
prime radical#13117151C2
hypercenter#1420D13
hypocenterC13#13691
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1420

Complements

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

NH ≅ G/Ntype
1. #13117154C2semidirect
3. #13117098C2semidirect
4. #13116716C2semidirect
5. #13113033C2semidirect
6. #13113025C2semidirect
7. C13×#1420C2semidirect
72. #1420D13semidirect
162. C13#13691semidirect

Maximal subgroups

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

subgroupindex
#131171542
#131171512
#131170982
#131167162
#131130332
#131130252
C13×#14202
#1369113