Finite Group Databasebeta

← #15750702

Subgroups — #15750702

Order 3328.

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

normal subgroups only

This group has 286 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#13116521C211yesmaximal, characteristic
2#13115665C211yesmaximal, characteristic
3C13×#2132C211yesmaximal, characteristic
4C13×#532C2211yescharacteristic
5C13×#413—21no—
6#11718898—21no—
7C2×#88077—21no—
8C2×#88077—21no—
9C42×Dic13C411yescharacteristic
10#11718585C411yescharacteristic
11C13×#356—21no—
12C13×#355C412yescomplemented
13#11718140—21no—
14#11718134C412yescomplemented
15C2×C13×#41D411yescharacteristic
16C2×C13×#41D411yescharacteristic
17C2×C13×M16—41no—
18C13×C4⋊Q8D411yescharacteristic
19C13×#127Q811yescharacteristic
20C13×#124C2×C411yescharacteristic
21C13×#124C2×C411yescharacteristic
22C13×#121—41no—
23C4×D4×C13—41no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C4×Dic13—21no—
26C2×C4×Dic13—41no—
27C2×#6099—21no—
28C2×#6099—41no—
29C13×#101—22no—
30C13×#100—41no—
31#88077—42no—
32#88077—42no—
33#88076—22no—
34#88073—41no—
35C4⋊#1055—41no—
36#7501—131nomaximal, Sylow
37C13×#41—41no—
38C13×#41—41no—
39C13×#41—41no—
40C13×#41—41no—
41C2×Q8×C13C22⋊C411yescharacteristic
42C2×Q8×C13C22⋊C411yescharacteristic
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—41no—
46C2×D4×C13C4⋊C411yescharacteristic
47C2×D4×C13C4⋊C411yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×Dic13—41no—
53C13×M16—42no—
54C13×M16—81no—
55C2×C8×C13—81no—
56C13×C4⋊C4—41no—
57C13×C22⋊C4—41no—
58C13×C22⋊C4—41no—
59C42×C13—21no—
60C42×C13C4211yescharacteristic
61C42×C13C4⋊C411yescharacteristic
62C4×Dic13—22no—
63C4×Dic13—41no—
64C4×Dic13—44no—
65#6099—42no—
66#6099—41no—
67#6099—41no—
68#6099—81no—
69C2×#1055—41no—
70C2×#1055—81no—
71#2132—131no—
72#2132D1311yescharacteristic
73#1962—131no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13#9911yescharacteristic
77Q8×C13—41no—
78Q8×C13—41no—
79D4×C13—41no—
80D4×C13—41no—
81D4×C13—82no—
82D4×C13—81no—
83D4×C13—81no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—42no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13#9511yescharacteristic
96C2×C4×C13#9911yescharacteristic
97C2×Dic13—42no—
98C2×Dic13—44no—
99C8×C13—82no—
100#1055—82no—
101#1055—81no—
102#532C2×D1311yescharacteristic
103#423—131no—
104C2×#104—261no—
105C2×#104—261no—
106#413—21no—
107#413—261no—
108C43—131no—
109#356—21no—
110#356—261no—
111#355—132no—
112#355Dic1312yescomplemented
113C22×C13—21no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—41no—
117C22×C13—81no—
118C22×C13—81no—
119C22×C13#34211yescharacteristic
120C4×C13—22no—
121C4×C13—21no—
122C4×C13—41no—
123C4×C13—41no—
124C4×C13—41no—
125C4×C13#35311yescharacteristic
126C4×C13#35411yescharacteristic
127Dic13—44no—
128C2×#41D5211yescharacteristic
129C2×#41C22⋊D1311yescharacteristic
130C2×M16—41no—
131C2×M16—261no—
132C2×M16—521no—
133C4⋊Q8C22⋊D1311yescharacteristic
134#127Dic2611yescharacteristic
135#124C4×D1311yescharacteristic
136#124C2×Dic1311yescharacteristic
137#121—41no—
138C4×D4—41no—
139C2×C42—261no—
140C2×C42—521no—
141C2×C42C4×D1311yescharacteristic
142C4⋊C8—521no—
143#104—522no—
144#104—522no—
145#101—22no—
146#101—262no—
147#100—41no—
148#100—521no—
149C2×C13—21no—
150C2×C13—41no—
151C2×C13—81no—
152C2×C13—81no—
153C2×C13#139311yescharacteristic
154#41—41no—
155#41—41no—
156#41—41no—
157#41—41no—
158C2×Q8#610311yescharacteristic
159C2×Q8C22⋊Dic1311yescharacteristic
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4#610111yescharacteristic
164C2×D4C4⋊Dic1311yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—521no—
169C22×C4#610311yescharacteristic
170M16—42no—
171M16—81no—
172M16—522no—
173M16—521no—
174M16—521no—
175M16—1041no—
176C2×C8—81no—
177C2×C8—521no—
178C2×C8—1041no—
179C4⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C42—21no—
183C42—262no—
184C42—521no—
185C42—524no—
186C42C4×Dic1311yescharacteristic
187C42#610111yescharacteristic
188C13#750111yescharacteristic, complemented, Sylow
189C23—21no—
190C23—21no—
191C23#8804611yescharacteristic
192Q8—41no—
193Q8—41no—
194D4—41no—
195D4—41no—
196D4—82no—
197D4—81no—
198D4—81no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—522no—
211C2×C4—524no—
212C2×C4#8804611yescharacteristic
213C2×C4#8807111yescharacteristic
214C8—82no—
215C8—1042no—
216C8—1041no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—81no—
222C22—81no—
223C22#1171811911yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—41no—
228C4—41no—
229C4—524no—
230C4#1171806511yescharacteristic
231C4#1171806611yescharacteristic
232C2—21no—
233C2—41no—
234C2—81no—
235C2—81no—
236C2#1311296011yescharacteristic
subgroupG/H
centerC4#11718065
commutatorC42×C13C42
Frattini#532C2×D13
FittingC13×#2132C2
socleC2×C13#1393
prime radical, cosocleC13×#532C22
hypercenter#2132D13
hypocenterC13#7501
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
12. C13×#355C4semidirect
14. #11718134C4semidirect
112. #355Dic13semidirect
188. C13#7501semidirect

Maximal subgroups

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

subgroupindex
#131165212
#131156652
C13×#21322
#750113