Finite Group Databasebeta

← #13113402

Subgroups — #13113402

Order 1664.

340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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
2D13×C22⋊C8C211yesmaximal, characteristic, complemented
3#11718328C211yesmaximal, 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×#6101—21no—
17C2×C8×D13—21no—
18#88149C411yescharacteristic, complemented
19C4⋊C4×D13C411yescharacteristic, complemented
20#88138—21no—
21C22⋊C4×D13—21no—
22C13×C22⋊C8C2211yescharacteristic, complemented
23C13×#95C2211yescharacteristic, complemented
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—
58#6101—42no—
59C2×#1055—21no—
60C8×D13—42no—
61#1519—131nomaximal, Sylow
62C23×C13—21no—
63C23×C13C2×D411yescharacteristic
64C22×D13—21no—
65C22×D13—41no—
66C22×D13—41no—
67C22×D13—42no—
68C22×D13—42no—
69C22×D13—42no—
70C22×D13C22⋊C411yescharacteristic
71C22×D13C22⋊C411yescharacteristic
72C22×D13D812yes—
73C22×D13SD1612yes—
74D4×C13—41no—
75D4×C13—41no—
76D4×C13—41no—
77C2×C4×C13—21no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13—41no—
82C2×C4×C13C22×C411yescharacteristic
83C2×C4×C13C2×D411yescharacteristic
84C22⋊D13—41no—
85C22⋊D13—41no—
86C22⋊D13—42no—
87C22⋊D13—42no—
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13—41no—
91C2×Dic13—41no—
92C2×Dic13—41no—
93C2×Dic13C22⋊C411yescharacteristic
94C2×Dic13C22⋊C411yescharacteristic
95D52—41no—
96D52—42no—
97C4×D13—22no—
98C4×D13—22no—
99C4×D13—41no—
100C4×D13—41no—
101C4×D13—42no—
102C8×C13—41no—
103#1055—41no—
104C2×#121—131no—
105C2×C22⋊C8—131no—
106#380—131no—
107#327—131no—
108#327—131no—
109#327—131no—
110#327D1311yescharacteristic, complemented
111C22×C13—21no—
112C22×C13—21no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13C2×C22⋊C411yescharacteristic
117C22×C13C2×D811yescharacteristic
118C22×C13C2×SD1611yescharacteristic
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#10212yes—
130C2×D13#10212yes—
131C4×C13—21no—
132C4×C13—21no—
133C4×C13—41no—
134C4×C13—81no—
135Dic13—21no—
136Dic13—41no—
137Dic13—81no—
138Dic13#9912yes—
139C22×D4—131no—
140C22×D4—261no—
141C23×C4—131no—
142C22×C8—261no—
143#121—131no—
144#121—131no—
145#121—131no—
146#121—261no—
147#121—261no—
148#121C2×D1311yescharacteristic
149C2×C4⋊C4—131no—
150C2×C4⋊C4—261no—
151C2×C22⋊C4—261no—
152C2×C22⋊C4—261no—
153C22⋊C8—131no—
154C22⋊C8—261no—
155C22⋊C8C2×D1311yescharacteristic, complemented
156#95—131no—
157#95C2×D1311yescharacteristic, complemented
158C2×C13—21no—
159C2×C13—21no—
160C2×C13—81no—
161C2×C13C2×#9911yescharacteristic
162C2×C13C2×#10211yescharacteristic
163C2×C13#42111yescharacteristic
164D13—22no—
165D13—22no—
166D13—81no—
167C24—131no—
168C24—261no—
169C2×D4—21no—
170C2×D4—131no—
171C2×D4—261no—
172C2×D4—261no—
173C2×D4—261no—
174C2×D4—261no—
175C2×D4—522no—
176C2×D4—522no—
177C2×D4—522no—
178C2×D4C4×D1311yescharacteristic
179C22×C4—21no—
180C22×C4—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—261no—
186C22×C4—261no—
187C22×C4—522no—
188C22×C4C22×D1311yescharacteristic
189C2×C8—21no—
190C2×C8—261no—
191C2×C8—522no—
192C4⋊C4—131no—
193C4⋊C4—261no—
194C4⋊C4—522no—
195C4⋊C4C4×D1311yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—261no—
198C22⋊C4—261no—
199C22⋊C4—261no—
200C22⋊C4—522no—
201C13#151911yescharacteristic, complemented, Sylow
202C23—21no—
203C23—131no—
204C23—131no—
205C23—132no—
206C23—132no—
207C23—261no—
208C23—521no—
209C23—521no—
210C23—522no—
211C23—522no—
212C23—522no—
213C23D4×D1311yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—521no—
218D4—522no—
219D4—522no—
220D4—522no—
221D4—521no—
222D4—521no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—131no—
229C2×C4—131no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—261no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—522no—
237C2×C4—521no—
238C2×C4—521no—
239C2×C4—521no—
240C2×C4C2×C4×D1311yescharacteristic
241C2×C4D4×D1311yescharacteristic
242C8—41no—
243C8—521no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—132no—
250C22—132no—
251C22—261no—
252C22—261no—
253C22—261no—
254C22—261no—
255C22—522no—
256C22—522no—
257C22—521no—
258C22—521no—
259C22—521no—
260C22—1044no—
261C22C22⋊C4×D1311yescharacteristic
262C22D8×D1311yescharacteristic
263C22SD16×D1311yescharacteristic
264C4—21no—
265C4—21no—
266C4—41no—
267C4—81no—
268C4—132no—
269C4—261no—
270C4—521no—
271C4—1041no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—262no—
276C2—262no—
277C2—1041no—
278C2D13×#9911yescharacteristic
279C2D13×#10211yescharacteristic
280C2#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#1519
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. D13×C22⋊C8C2semidirect
3. #11718328C2semidirect
4. C13×#327C2semidirect
5. #11718129C2semidirect
6. #11718062C2semidirect
7. #11718043C2semidirect
9. C2×D4×D13C4semidirect
13. #88192C4semidirect
18. #88149C4semidirect
19. C4⋊C4×D13C4semidirect
22. C13×C22⋊C8C22semidirect
23. C13×#95C22semidirect
24. #88071C22semidirect
25. C22⋊#1055C22semidirect
110. #327D13semidirect
155. C22⋊C8C2×D13semidirect
157. #95C2×D13semidirect
201. C13#1519semidirect

Maximal subgroups

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

subgroupindex
D13×#1212
D13×C22⋊C82
#117183282
C13×#3272
#117181292
#117180622
#117180432
#151913