Finite Group Databasebeta

← #15776295

Subgroups — #15776295

Order 3328.

318 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 59 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#13117048C212yesmaximal, complemented
2#13116411C211yesmaximal, characteristic, complemented
3#13112821C212yesmaximal, complemented
4#13112787C211yesmaximal, characteristic, complemented
5C13×#3253C211yesmaximal, characteristic
6C13×#532—21no—
7C13×#476—22no—
8C13×#469—21no—
9C13×#469C2212yes—
10C13×#459—22no—
11C13×#423C2211yescharacteristic
12#11718786C2211yescharacteristic
13#11718155—22no—
14#11718151—21no—
15#11718149C2211yescharacteristic
16#11718145C2212yes—
17#11718115—21no—
18#11718079—22no—
19C2×C13×#41—41no—
20C2×C13×D8—21no—
21C2×C13×D8D412yes—
22C2×C13×M16D411yescharacteristic
23C2×C13×M16C2311yescharacteristic
24C13×C4⋊Q8—21no—
25C13×#127—21no—
26C13×#124—41no—
27C13×#121—22no—
28C13×#121—41no—
29C4×D4×C13—22no—
30C4×D4×C13—41no—
31C2×C42×C13D411yescharacteristic
32#88180—21no—
33C2×#6099—21no—
34C13×#106—21no—
35C13×#106D412yes—
36C13×C4⋊C8—22no—
37C13×#102—22no—
38C13×#102—22no—
39#88059—22no—
40#88052—22no—
41#12307—131nomaximal, Sylow
42C13×#41—84no—
43C2×Q8×C13—41no—
44C2×D4×C13—22no—
45C2×D4×C13—41no—
46C2×D4×C13—41no—
47C2×D4×C13—42no—
48C22×C4×C13—21no—
49C22×C4×C13—42no—
50C22×C4×C13C2×D411yescharacteristic
51C13×D8—42no—
52C13×D8—81no—
53C13×M16—41no—
54C13×M16—41no—
55C2×C8×C13—21no—
56C2×C8×C13C2×D412yes—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—41no—
59C13×C22⋊C4—42no—
60C13×C22⋊C4—42no—
61C42×C13—21no—
62C42×C13SD1611yescharacteristic
63C42×C13SD1611yescharacteristic
64C22⋊Dic13—41no—
65C4⋊Dic13—41no—
66C4×Dic13—41no—
67#6099—41no—
68#6099—41no—
69C2×#1055—41no—
70#6090—42no—
71#3253D1311yescharacteristic
72#2238—132no—
73#2102—131no—
74#1339—132no—
75#1327—131no—
76C23×C13—42no—
77C23×C13AGL(1,ℤ/8)11yescharacteristic
78Q8×C13—82no—
79D4×C13—42no—
80D4×C13—42no—
81D4×C13—82no—
82D4×C13—82no—
83D4×C13—84no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—84no—
91C2×C4×C13#12011yescharacteristic
92C2×C4×C13C2×SD1611yescharacteristic
93C2×Dic13—81no—
94C8×C13—22no—
95C8×C13—41no—
96#1055—81no—
97#532—21no—
98#476—22no—
99#469—21no—
100#469C2×D1312yes—
101#459—22no—
102#430—131no—
103#423C2×D1311yescharacteristic
104#365—262no—
105#361—262no—
106#349—132no—
107#344—261no—
108#339—261no—
109H(3,ℤ/4)—131no—
110C22×C13—21no—
111C22×C13—41no—
112C22×C13—82no—
113C22×C13—82no—
114C22×C13—82no—
115C22×C13#45011yescharacteristic
116C4×C13—22no—
117C4×C13—21no—
118C4×C13—41no—
119C4×C13—82no—
120C4×C13#45411yescharacteristic
121C4×C13#45811yescharacteristic
122Dic13—161no—
123C2×#41—41no—
124C2×D8—21no—
125C2×D8C22⋊D1312yes—
126C2×M16—261no—
127C2×M16C22⋊D1311yescharacteristic
128C2×M16C22×D1311yescharacteristic
129C4⋊Q8—21no—
130#127—21no—
131#124—41no—
132#121—22no—
133#121—41no—
134C4×D4—22no—
135C4×D4—41no—
136#117—261no—
137C2×C42C22⋊D1311yescharacteristic
138M32—262no—
139#108—262no—
140#106—21no—
141#106C22⋊D1312yes—
142C4⋊C8—22no—
143#102—22no—
144#102—22no—
145C2×C13—21no—
146C2×C13—41no—
147C2×C13—162no—
148C2×C13#161611yescharacteristic
149#41—84no—
150C2×Q8—41no—
151C2×D4—22no—
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—42no—
155C22×C4—21no—
156C22×C4—42no—
157C22×C4C2×C22⋊D1311yescharacteristic
158D8—42no—
159D8—81no—
160M16—41no—
161M16—41no—
162M16—521no—
163M16—521no—
164C2×C8—21no—
165C2×C8—521no—
166C2×C8C2×C22⋊D1312yes—
167C4⋊C4—22no—
168C4⋊C4—41no—
169C4⋊C4—521no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C22⋊C4—521no—
173C42—21no—
174C42—521no—
175C42#610511yescharacteristic
176C42#610511yescharacteristic
177C16—522no—
178C13#1230711yescharacteristic, complemented, Sylow
179C23—42no—
180C23#8818611yescharacteristic
181Q8—82no—
182D4—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—84no—
194C2×C4—1041no—
195C2×C4C2×#610511yescharacteristic
196C2×C4#8820711yescharacteristic
197C8—22no—
198C8—41no—
199C8—1041no—
200C22—21no—
201C22—41no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#1171887911yescharacteristic
206C4—22no—
207C4—21no—
208C4—41no—
209C4—82no—
210C4—2081no—
211C4#1171890411yescharacteristic
212C4#1171890611yescharacteristic
213C2—21no—
214C2—41no—
215C2—162no—
216C2#1311387311yescharacteristic
subgroupG/H
centerC2#13113873
commutator, cosocleC2×C13×M16C23
FrattiniC2×M16C22×D13
Fitting, prime radicalC13×#3253C2
socleC2×C13#1616
hypercenter#3253D13
hypocenterC13#12307
LCSG ▷ C2×C13×M16 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #13117048C2semidirect
2. #13116411C2semidirect
3. #13112821C2semidirect
4. #13112787C2semidirect
178. C13#12307semidirect

Maximal subgroups

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

subgroupindex
#131170482
#131164112
#131128212
#131127872
C13×#32532
#1230713