Finite Group Databasebeta

← #15750690

Subgroups — #15750690

Order 3328.

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

normal subgroups only

This group has 274 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#13115220C211yesmaximal, characteristic
2#13113571C211yesmaximal, characteristic
3C13×#2132C211yesmaximal, characteristic
4C13×#532C2211yescharacteristic
5#11719524C411yescharacteristic
6C13×#413—21no—
7#11718901C411yescharacteristic
8#11718897—21no—
9#11718585—21no—
10C13×#356—21no—
11C13×#355C412yescomplemented
12#11718138—21no—
13#11718136C412yescomplemented
14#11718115—21no—
15C2×C13×#41C2×C411yescharacteristic
16C2×C13×#41D411yescharacteristic
17C2×C13×M16—41no—
18C13×C4⋊Q8D411yescharacteristic
19C13×#127C2×C411yescharacteristic
20C13×#124C2×C411yescharacteristic
21C13×#124Q811yescharacteristic
22C13×#121—41no—
23C4×D4×C13—41no—
24C2×C42×C13D411yescharacteristic
25#88202—42no—
26#88180—21no—
27C2×#6099—21no—
28C2×#6099—41no—
29C2×#6099—41no—
30C13×#101—22no—
31C13×#100—41no—
32#88077—42no—
33#88074—41no—
34C4⋊#1055—22no—
35C4⋊#1055—41no—
36#7496—131nomaximal, Sylow
37C13×#41—41no—
38C13×#41—41no—
39C13×#41—41no—
40C13×#41—41no—
41C2×Q8×C13C22⋊C411yescharacteristic
42C2×Q8×C13C4⋊C411yescharacteristic
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—41no—
46C2×D4×C13C4211yescharacteristic
47C2×D4×C13C4⋊C411yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C22⋊C411yescharacteristic
52C13×M16—42no—
53C13×M16—81no—
54C2×C8×C13—81no—
55C13×C4⋊C4—41no—
56C13×C22⋊C4—41no—
57C13×C22⋊C4—41no—
58C42×C13—21no—
59C42×C13C22⋊C411yescharacteristic
60C42×C13C4⋊C411yescharacteristic
61C22⋊Dic13—41no—
62C4⋊Dic13—41no—
63C4×Dic13—41no—
64#6099—22no—
65#6099—41no—
66#6099—42no—
67#6099—82no—
68C2×#1055—41no—
69C2×#1055—42no—
70C2×#1055—42no—
71#2132D1311yescharacteristic
72#1884—131no—
73#1560—131no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13#9911yescharacteristic
77Q8×C13—41no—
78Q8×C13—41no—
79D4×C13—41no—
80D4×C13—41no—
81D4×C13—42no—
82D4×C13—81no—
83D4×C13—81no—
84D4×C13—81no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13#9511yescharacteristic
98C2×C4×C13#9911yescharacteristic
99C2×Dic13—81no—
100C8×C13—82no—
101#1055—42no—
102#1055—82no—
103#568—131no—
104#532C2×D1311yescharacteristic
105#423—261no—
106#421—261no—
107#413—21no—
108#410—131no—
109#356—21no—
110#355Dic1312yescomplemented
111#339—261no—
112#333—261no—
113#331—132no—
114C22×C13—21no—
115C22×C13—41no—
116C22×C13—41no—
117C22×C13—41no—
118C22×C13—81no—
119C22×C13—81no—
120C22×C13#34211yescharacteristic
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—41no—
125C4×C13—41no—
126C4×C13—41no—
127C4×C13AΣL(1,𝔽16)11yescharacteristic
128C4×C13#35211yescharacteristic
129Dic13—161no—
130C2×#41C4×D1311yescharacteristic
131C2×#41C22⋊D1311yescharacteristic
132#131—522no—
133C2×M16—41no—
134C2×M16—261no—
135C2×M16—521no—
136C2×M16—521no—
137C4⋊Q8C22⋊D1311yescharacteristic
138#127C4×D1311yescharacteristic
139#124Dic2611yescharacteristic
140#124C2×Dic1311yescharacteristic
141#121—41no—
142C4×D4—41no—
143#117—261no—
144C2×C42D5211yescharacteristic
145C4⋊C8—262no—
146C4⋊C8—521no—
147#104—522no—
148#101—22no—
149#100—41no—
150#99—521no—
151C2×C13—21no—
152C2×C13—41no—
153C2×C13—81no—
154C2×C13—81no—
155C2×C13#139011yescharacteristic
156#41—41no—
157#41—41no—
158#41—41no—
159#41—41no—
160C2×Q8#610111yescharacteristic
161C2×Q8C22⋊Dic1311yescharacteristic
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—41no—
165C2×D4C4×Dic1311yescharacteristic
166C2×D4#610111yescharacteristic
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4#610311yescharacteristic
171M16—42no—
172M16—81no—
173M16—262no—
174M16—521no—
175M16—522no—
176M16—1042no—
177C2×C8—81no—
178C2×C8—521no—
179C2×C8—522no—
180C2×C8—522no—
181C4⋊C4—41no—
182C4⋊C4—521no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—521no—
186C42—21no—
187C42—521no—
188C42C4⋊Dic1311yescharacteristic
189C42#610311yescharacteristic
190C13#749611yescharacteristic, complemented, Sylow
191C23—21no—
192C23—21no—
193C23#8804611yescharacteristic
194Q8—41no—
195Q8—41no—
196D4—41no—
197D4—41no—
198D4—42no—
199D4—81no—
200D4—81no—
201D4—81no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1041no—
215C2×C4#8804611yescharacteristic
216C2×C4#8807111yescharacteristic
217C8—82no—
218C8—522no—
219C8—1042no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22#1171811911yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—2081no—
234C4#1171806311yescharacteristic
235C4#1171806411yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—81no—
240C2#1311295311yescharacteristic
subgroupG/H
centerC2#13112953
commutatorC2×D4×C13C42
Frattini#532C2×D13
FittingC13×#2132C2
socleC2×C13#1390
prime radical, cosocleC13×#532C22
hypercenter#2132D13
hypocenterC13#7496
LCSG ▷ C2×D4×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
11. C13×#355C4semidirect
13. #11718136C4semidirect
110. #355Dic13semidirect
190. C13#7496semidirect

Maximal subgroups

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

subgroupindex
#131152202
#131135712
C13×#21322
#749613