Finite Group Databasebeta

← #15750691

Subgroups — #15750691

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#13116521C211yesmaximal, characteristic
2#13113571C211yesmaximal, characteristic
3C13×#1884C211yesmaximal, characteristic
4C13×#568C411yescharacteristic
5C13×#532C2211yescharacteristic
6C13×#421—21no—
7C13×#410C411yescharacteristic
8#11718898—21no—
9#11718585—21no—
10C13×#339—21no—
11#11718140—21no—
12#11718138—21no—
13#11718136C412yescomplemented
14#11718134C412yescomplemented
15C2×C13×#41C2×C411yescharacteristic
16C2×C13×#41D411yescharacteristic
17C13×#131—42no—
18C2×C13×M16—21no—
19C2×C13×M16—41no—
20C13×C4⋊Q8D411yescharacteristic
21C13×#127C2×C411yescharacteristic
22C13×#124C2×C411yescharacteristic
23C13×#124Q811yescharacteristic
24C13×#121—41no—
25C4×D4×C13—41no—
26C13×#117—21no—
27C2×C42×C13D411yescharacteristic
28C2×#6099—41no—
29C2×#6099—41no—
30C13×#104—42no—
31C13×#99—41no—
32#88076—22no—
33#88073—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—22no—
53C13×M16—41no—
54C13×M16—42no—
55C2×C8×C13—41no—
56C2×C8×C13—42no—
57C13×C4⋊C4—41no—
58C13×C4⋊C4—41no—
59C13×C22⋊C4—41no—
60C13×C22⋊C4—41no—
61C13×C22⋊C4—41no—
62C42×C13—21no—
63C42×C13—41no—
64C42×C13C22⋊C411yescharacteristic
65C42×C13C4⋊C411yescharacteristic
66#6099—42no—
67#6099—82no—
68#6099—81no—
69C2×#1055—42no—
70C2×#1055—81no—
71#2132—131no—
72#1884D1311yescharacteristic
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—81no—
98C2×C4×C13#9511yescharacteristic
99C2×C4×C13#9911yescharacteristic
100C8×C13—42no—
101#1055—82no—
102#1055—82no—
103#568Dic1311yescharacteristic
104#532C2×D1311yescharacteristic
105#423—261no—
106#421—21no—
107#413—261no—
108#410Dic1311yescharacteristic
109#356—261no—
110#355—132no—
111#339—21no—
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×C13—161no—
128C4×C13AΣL(1,𝔽16)11yescharacteristic
129C4×C13#35211yescharacteristic
130C2×#41C2×Dic1311yescharacteristic
131C2×#41C22⋊D1311yescharacteristic
132#131—42no—
133C2×M16—21no—
134C2×M16—41no—
135C2×M16—521no—
136C2×M16—521no—
137C4⋊Q8D5211yescharacteristic
138#127C4×D1311yescharacteristic
139#124Dic2611yescharacteristic
140#124C4×D1311yescharacteristic
141#121—41no—
142C4×D4—41no—
143#117—21no—
144C2×C42C22⋊D1311yescharacteristic
145C4⋊C8—262no—
146C4⋊C8—521no—
147#104—42no—
148#101—262no—
149#100—521no—
150#99—41no—
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×Q8C4⋊Dic1311yescharacteristic
161C2×Q8#610311yescharacteristic
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×C4C22⋊Dic1311yescharacteristic
171M16—22no—
172M16—41no—
173M16—42no—
174M16—522no—
175M16—1042no—
176M16—1041no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—522no—
180C2×C8—1041no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C42—21no—
187C42—41no—
188C42#610111yescharacteristic
189C42#610311yescharacteristic
190C13#749611yescharacteristic, complemented, Sylow
191C23—21no—
192C23—21no—
193C23#8807411yescharacteristic
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—81no—
215C2×C4#8807111yescharacteristic
216C2×C4#8807411yescharacteristic
217C8—42no—
218C8—1042no—
219C8—1042no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22#1171811811yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—161no—
234C4#1171812811yescharacteristic
235C4#1171813111yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—81no—
240C2#1311295411yescharacteristic
subgroupG/H
centerC2#13112954
commutatorC2×D4×C13C42
Frattini#532C2×D13
FittingC13×#1884C2
socleC2×C13#1390
prime radical, cosocleC13×#532C22
hypercenter#1884D13
hypocenterC13#7496
LCSG ▷ C2×D4×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1884

Complements

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

NH ≅ G/Ntype
13. #11718136C4semidirect
14. #11718134C4semidirect
190. C13#7496semidirect

Maximal subgroups

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

subgroupindex
#131165212
#131135712
C13×#18842
#749613