Finite Group Databasebeta

← #15783731

Subgroups — #15783731

Order 3328.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#13117153C211yesmaximal, characteristic, complemented
2#13117094C211yesmaximal, characteristic, complemented
3#13116717C211yesmaximal, characteristic, complemented
4#13113033C211yesmaximal, characteristic, complemented
5#13113030C211yesmaximal, characteristic, complemented
6#13113026C211yesmaximal, characteristic, complemented
7C13×#2263C211yesmaximal, characteristic
8C13×#508C2211yescharacteristic
9C2×C13×D16C2211yescharacteristic
10#11718857—21no—
11#11718816—21no—
12C2×#88067—21no—
13C2×Dic104C2211yescharacteristic
14C13×SD64—21no—
15C13×D32—21no—
16C13×M64C2211yescharacteristic
17#11718159—21no—
18#11718114—21no—
19#11718112—21no—
20#11718098C2211yescharacteristic
21C16×Dic13C2211yescharacteristic
22#11718091C2211yescharacteristic
23C13×#135—21no—
24C2×C13×D8—21no—
25#88202—41no—
26#88190—41no—
27C2×#6105—41no—
28C2×Dic52—21no—
29C13×Q32D411yescharacteristic
30C13×SD32—21no—
31C13×D16—21no—
32C13×D16—21no—
33C13×D16D411yescharacteristic
34C2×C13×C16C2311yescharacteristic
35#88077—41no—
36#88067—42no—
37#88059—21no—
38C8×Dic13D411yescharacteristic
39C2×#6090D411yescharacteristic
40Dic104—21no—
41Dic104—21no—
42C13×C32—21no—
43#88034—21no—
44#13691—131nomaximal, Sylow
45C13×#41—41no—
46C2×D4×C13—41no—
47C2×Dic26—41no—
48C13×Q16—21no—
49C13×SD16—41no—
50C13×D8—21no—
51C13×D8—41no—
52C13×D8—41no—
53C2×C8×C13C2×D411yescharacteristic
54C22⋊Dic13—82no—
55#6105—81no—
56#6105—81no—
57C4×Dic13D811yescharacteristic
58#6099—41no—
59#6099—81no—
60C2×#1055—81no—
61C2×#1055D811yescharacteristic
62Dic52—41no—
63Dic52—41no—
64C13×C16C2×D411yescharacteristic
65C13×C16#4111yescharacteristic
66#6090—21no—
67#2264—131no—
68#2263D1311yescharacteristic
69#2249—131no—
70#2178—131no—
71#1422—131no—
72#1420—131no—
73#1419—131no—
74C23×C13—81no—
75Q8×C13—41no—
76D4×C13—41no—
77D4×C13—81no—
78D4×C13—81no—
79D4×C13—81no—
80C2×C4×C13—81no—
81C2×C4×C13C2×D811yescharacteristic
82C2×Dic13—21no—
83C2×Dic13—81no—
84Dic26—81no—
85Dic26—81no—
86C8×C13#12111yescharacteristic
87C8×C13AGL(1,ℤ/8)11yescharacteristic
88#1055—81no—
89#1055D1611yescharacteristic
90#1055D1611yescharacteristic
91#508C2×D1311yescharacteristic
92C2×Q32—131no—
93C2×SD32—261no—
94C2×D16C2×D1311yescharacteristic
95#495—261no—
96#443—261no—
97Q64—261no—
98SD64—21no—
99SD64—261no—
100D32—21no—
101M64—131no—
102M64C2×D1311yescharacteristic
103#368—131no—
104#359—261no—
105C4×C16—131no—
106C22×C13—81no—
107C22×C13—162no—
108C22×C13—161no—
109C22×C13#50911yescharacteristic
110C4×C13—81no—
111C4×C13#45911yescharacteristic
112C4×C13C2×D1611yescharacteristic
113Dic13—41no—
114Dic13—161no—
115#135—21no—
116C2×Q16—261no—
117C2×SD16—521no—
118C2×D8—21no—
119#131—521no—
120#124—521no—
121Q32—261no—
122Q32—261no—
123Q32C22⋊D1311yescharacteristic
124SD32—21no—
125SD32—522no—
126D16—21no—
127D16—21no—
128D16C22⋊D1311yescharacteristic
129C2×C16—131no—
130C2×C16C22×D1311yescharacteristic
131#108—261no—
132#104—521no—
133C4×C8—131no—
134C32—21no—
135C32—261no—
136C2×C13—21no—
137C2×C13—161no—
138C2×C13—321no—
139C2×C13#220611yescharacteristic
140#41—41no—
141C2×Q8—521no—
142C2×D4—41no—
143Q16—21no—
144Q16—521no—
145Q16—521no—
146SD16—41no—
147SD16—1041no—
148SD16—1041no—
149D8—21no—
150D8—41no—
151D8—41no—
152M16—521no—
153M16—1041no—
154C2×C8—131no—
155C2×C8—1041no—
156C2×C8D4×D1311yescharacteristic
157C22⋊C4—1042no—
158C42—131no—
159C16—261no—
160C16#612911yescharacteristic
161C16C2×C22⋊D1311yescharacteristic
162C13#1369111yescharacteristic, complemented, Sylow
163C23—81no—
164Q8—41no—
165Q8—1041no—
166Q8—1041no—
167D4—41no—
168D4—81no—
169D4—81no—
170D4—81no—
171C2×C4—81no—
172C2×C4—261no—
173C2×C4—1041no—
174C2×C4D8×D1311yescharacteristic
175C8—131no—
176C8—131no—
177C8—1041no—
178C8#8816511yescharacteristic
179C8#8819311yescharacteristic
180C22—81no—
181C22—162no—
182C22—161no—
183C22#1171857211yescharacteristic
184C4—81no—
185C4—521no—
186C4—2081no—
187C4D13×D1611yescharacteristic
188C4#1171881111yescharacteristic
189C2—21no—
190C2—161no—
191C2—321no—
192C2#1311686911yescharacteristic
subgroupG/H
centerC2#13116869
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
Fitting, prime radicalC13×#2263C2
socleC2×C13#2206
hypercenter#2263D13
hypocenterC13#13691
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2263

Complements

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

NH ≅ G/Ntype
1. #13117153C2semidirect
2. #13117094C2semidirect
3. #13116717C2semidirect
4. #13113033C2semidirect
5. #13113030C2semidirect
6. #13113026C2semidirect
162. C13#13691semidirect

Maximal subgroups

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

subgroupindex
#131171532
#131170942
#131167172
#131130332
#131130302
#131130262
C13×#22632
#1369113