Finite Group Databasebeta

← #13113363

Subgroups — #13113363

Order 1664.

326 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 63 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
1D13×#121C211yesmaximal, characteristic
2#11718387C211yesmaximal, characteristic, complemented
3#11718325C211yesmaximal, characteristic, complemented
4C13×#327C211yesmaximal, characteristic, complemented
5#11718129C211yesmaximal, characteristic, complemented
6#11718062C211yesmaximal, characteristic, complemented
7#11718043C211yesmaximal, characteristic, complemented
8C2×D4×D13—21no—
9C2×D4×D13C411yescharacteristic, complemented
10C22×C4×D13C2211yescharacteristic
11C13×#121C2211yescharacteristic
12#88193—21no—
13#88192C411yescharacteristic, complemented
14#88184C2211yescharacteristic
15C2×#6103—21no—
16C2×#6094—21no—
17#88149C411yescharacteristic, complemented
18C4⋊C4×D13C411yescharacteristic, complemented
19#88138—21no—
20C22⋊C4×D13—21no—
21C13×C22⋊C8C2211yescharacteristic, complemented
22C13×#95C2211yescharacteristic, complemented
23#88071—21no—
24#88071C2211yescharacteristic, complemented
25C22⋊#1055C2211yescharacteristic, complemented
26#88060—21no—
27C23×D13—21no—
28C23×D13D411yescharacteristic
29C2×D4×C13—21no—
30C2×D4×C13C2×C411yescharacteristic
31C22×C4×C13—21no—
32C22×C4×C13C2311yescharacteristic
33C2×C22⋊D13—21no—
34C2×C22⋊D13—21no—
35C2×C22⋊D13—21no—
36C22×Dic13—21no—
37C22×Dic13D411yescharacteristic
38D4×D13—42no—
39D4×D13—42no—
40D4×D13—42no—
41C2×D52—21no—
42C2×D52C2×C411yescharacteristic
43C2×C4×D13—21no—
44C2×C4×D13—42no—
45C2×C4×D13C2×C411yescharacteristic
46C2×C4×D13C2×C411yescharacteristic
47C2×C4×D13D411yescharacteristic
48C2×C4×D13D411yescharacteristic
49C2×C8×C13—21no—
50C13×C4⋊C4C2×C411yescharacteristic
51C13×C22⋊C4—21no—
52C22⋊Dic13—21no—
53#6103—21no—
54#6103—21no—
55#6103—42no—
56C4⋊Dic13C2×C411yescharacteristic
57#6101—21no—
58C2×#1055—21no—
59#6094—42no—
60#1510—131nomaximal, Sylow
61C23×C13—21no—
62C23×C13C2×D411yescharacteristic
63C22×D13—21no—
64C22×D13—21no—
65C22×D13—22no—
66C22×D13—21no—
67C22×D13—41no—
68C22×D13—42no—
69C22×D13—42no—
70C22×D13—42no—
71C22×D13C22⋊C411yescharacteristic
72C22×D13C22⋊C411yescharacteristic
73D4×C13—41no—
74D4×C13—41no—
75D4×C13—41no—
76C2×C4×C13—21no—
77C2×C4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13C22×C411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C22⋊D13—42no—
84C22⋊D13—42no—
85C22⋊D13—41no—
86C22⋊D13—41no—
87C2×Dic13—21no—
88C2×Dic13—41no—
89C2×Dic13—41no—
90C2×Dic13—41no—
91C2×Dic13—41no—
92C2×Dic13C22⋊C411yescharacteristic
93C2×Dic13C22⋊C411yescharacteristic
94D52—41no—
95D52—42no—
96C4×D13—22no—
97C4×D13—22no—
98C4×D13—41no—
99C4×D13—41no—
100C4×D13—42no—
101C8×C13—41no—
102#1055—41no—
103C2×#121—131no—
104#407—131no—
105#381—131no—
106#327—131no—
107#327—131no—
108#327—131no—
109#327D1311yescharacteristic, complemented
110C22×C13—21no—
111C22×C13—21no—
112C22×C13—41no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13C2×C22⋊C411yescharacteristic
116C22×C13AGL(1,ℤ/8)11yescharacteristic
117C22×C13AGL(1,ℤ/8)11yescharacteristic
118C2×D13—21no—
119C2×D13—21no—
120C2×D13—21no—
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—41no—
126C2×D13—41no—
127C2×D13—41no—
128C2×D13—84no—
129C2×D13#9912yes—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—41no—
133C4×C13—81no—
134Dic13—21no—
135Dic13—21no—
136Dic13—41no—
137Dic13—81no—
138C22×D4—131no—
139C22×D4—261no—
140C23×C4—131no—
141C2×M16—261no—
142#121—131no—
143#121—131no—
144#121—131no—
145#121—261no—
146#121—261no—
147#121C2×D1311yescharacteristic
148C2×C4⋊C4—131no—
149C2×C22⋊C4—261no—
150C2×C22⋊C4—261no—
151C22⋊C8—131no—
152C22⋊C8—261no—
153C22⋊C8C2×D1311yescharacteristic, complemented
154#95—131no—
155#95—261no—
156#95C2×D1311yescharacteristic, complemented
157C2×C13—21no—
158C2×C13—21no—
159C2×C13—81no—
160C2×C13C2×#9911yescharacteristic
161C2×C13#41811yescharacteristic
162C2×C13#42111yescharacteristic
163D13—22no—
164D13—41no—
165D13—81no—
166C24—131no—
167C24—261no—
168C2×D4—21no—
169C2×D4—131no—
170C2×D4—261no—
171C2×D4—261no—
172C2×D4—261no—
173C2×D4—261no—
174C2×D4—522no—
175C2×D4—522no—
176C2×D4—522no—
177C2×D4C4×D1311yescharacteristic
178C22×C4—21no—
179C22×C4—131no—
180C22×C4—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—261no—
185C22×C4—261no—
186C22×C4—522no—
187C22×C4C22×D1311yescharacteristic
188M16—522no—
189C2×C8—21no—
190C2×C8—261no—
191C4⋊C4—131no—
192C4⋊C4—261no—
193C4⋊C4C4×D1311yescharacteristic
194C22⋊C4—21no—
195C22⋊C4—261no—
196C22⋊C4—261no—
197C22⋊C4—261no—
198C22⋊C4—522no—
199C13#151011yescharacteristic, complemented, Sylow
200C23—21no—
201C23—131no—
202C23—131no—
203C23—262no—
204C23—261no—
205C23—261no—
206C23—261no—
207C23—521no—
208C23—522no—
209C23—522no—
210C23—522no—
211C23D4×D1311yescharacteristic
212D4—41no—
213D4—41no—
214D4—41no—
215D4—521no—
216D4—522no—
217D4—522no—
218D4—522no—
219D4—521no—
220D4—521no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—131no—
227C2×C4—131no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—261no—
231C2×C4—521no—
232C2×C4—521no—
233C2×C4—522no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—521no—
237C2×C4—521no—
238C2×C4C2×C4×D1311yescharacteristic
239C2×C4D4×D1311yescharacteristic
240C8—41no—
241C8—521no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—132no—
248C22—261no—
249C22—261no—
250C22—261no—
251C22—261no—
252C22—261no—
253C22—522no—
254C22—522no—
255C22—521no—
256C22—521no—
257C22—521no—
258C22—1044no—
259C22C22⋊C4×D1311yescharacteristic
260C22#8816511yescharacteristic
261C22#8816811yescharacteristic
262C4—21no—
263C4—21no—
264C4—41no—
265C4—81no—
266C4—261no—
267C4—261no—
268C4—521no—
269C4—1041no—
270C2—21no—
271C2—21no—
272C2—81no—
273C2—262no—
274C2—521no—
275C2—1041no—
276C2D13×#9911yescharacteristic
277C2#1171843111yescharacteristic
278C2#1171848211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#327C2
socleC22×C13C2×C22⋊C4
prime radicalD13×#121C2
cosocleC22×C4×C13C23
hypercenter#327D13
hypocenterC13#1510
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #11718387C2semidirect
3. #11718325C2semidirect
4. C13×#327C2semidirect
5. #11718129C2semidirect
6. #11718062C2semidirect
7. #11718043C2semidirect
9. C2×D4×D13C4semidirect
13. #88192C4semidirect
17. #88149C4semidirect
18. C4⋊C4×D13C4semidirect
21. C13×C22⋊C8C22semidirect
22. C13×#95C22semidirect
24. #88071C22semidirect
25. C22⋊#1055C22semidirect
109. #327D13semidirect
153. C22⋊C8C2×D13semidirect
156. #95C2×D13semidirect
199. C13#1510semidirect

Maximal subgroups

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

subgroupindex
D13×#1212
#117183872
#117183252
C13×#3272
#117181292
#117180622
#117180432
#151013