Finite Group Databasebeta

← #13130787

Subgroups — #13130787

Order 1664.

316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C2×#88237C211yesmaximal, characteristic
2#11719136C211yesmaximal, characteristic
3C2×#88102C211yesmaximal, characteristic, complemented
4C2×#88101C211yesmaximal, characteristic, complemented
5D13×C22⋊C8C211yesmaximal, characteristic
6#11718265C211yesmaximal, characteristic, complemented
7#11718265C211yesmaximal, characteristic, complemented
8C22×C4×D13C2211yescharacteristic
9C2×C22⋊#261—21no—
10C2×C22⋊#261—21no—
11#88237—22no—
12#88237—22no—
13C2×C4⋊#261C2211yescharacteristic
14C2×C4⋊#261C2211yescharacteristic
15C2×C4⋊#261C2211yescharacteristic
16C2×C4⋊#261C2211yescharacteristic
17C2×C4×#261—21no—
18C2×C8×D13C2211yescharacteristic
19C2×C8×D13C2211yescharacteristic
20(C2×#261)⋊C4—21no—
21#88102—22no—
22#88101—22no—
23C13×C22⋊C8C411yescharacteristic, complemented
24C22⋊#1055C411yescharacteristic, complemented
25#88060C411yescharacteristic, complemented
26#88060C411yescharacteristic, complemented
27C23×D13D411yescharacteristic
28C22×#261—21no—
29C22×#261—21no—
30C22×#261—21no—
31C22×#261—21no—
32C22×C4×C13C2×C411yescharacteristic
33C22×Dic13Q811yescharacteristic
34C2×C4×D13—21no—
35C2×C4×D13—21no—
36C2×C4×D13—21no—
37C2×C4×D13—21no—
38C2×C4×D13C2×C411yescharacteristic
39C2×C4×D13D411yescharacteristic
40C2×C4×D13Q811yescharacteristic
41C2×C4×D13C2311yescharacteristic
42C22⋊#261—24no—
43C22⋊#261—42no—
44C4⋊#261—21no—
45C4⋊#261—21no—
46C4⋊#261—21no—
47C4⋊#261—21no—
48C4⋊#261—21no—
49C4⋊#261—21no—
50C4⋊#261D412yes—
51C4⋊#261D412yes—
52C4×#261—24no—
53C2×C8×C13C2×C411yescharacteristic
54C2×C8×C13C2×C411yescharacteristic
55C2×#1055C2×C411yescharacteristic
56C2×#1055C2×C411yescharacteristic
57C8×D13—21no—
58C8×D13—21no—
59C8×D13—21no—
60C8×D13—21no—
61#1854—131nomaximal, Sylow
62C23×C13C4⋊C411yescharacteristic
63C22×D13—21no—
64C22×D13—21no—
65C22×D13—21no—
66C22×D13—21no—
67C22×D13—21no—
68C22×D13—21no—
69C22×D13C4⋊C411yescharacteristic
70C22×D13C2×D411yescharacteristic
71C2×#261—22no—
72C2×#261—22no—
73C2×#261—41no—
74C2×#261—41no—
75C2×#261—41no—
76C2×#261—41no—
77C2×#261—41no—
78C2×#261—41no—
79C2×#261—41no—
80C2×#261—41no—
81C2×#261—41no—
82C2×#261—41no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13C4⋊C411yescharacteristic
86C2×C4×C13C22×C411yescharacteristic
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13C4⋊C411yescharacteristic
90C2×Dic13C2×Q811yescharacteristic
91C4×D13—21no—
92C4×D13—21no—
93C4×D13—21no—
94C4×D13—21no—
95C4×D13—21no—
96C4×D13—21no—
97C4×D13C2×D411yescharacteristic
98C4×D13C2×D411yescharacteristic
99C4×D13#4111yescharacteristic
100C4×D13#4111yescharacteristic
101C8×C13—21no—
102C8×C13—21no—
103#1055—21no—
104#1055—21no—
105C2×#117—131no—
106C2×#107—131no—
107C2×#106—131no—
108C2×C22⋊C8—131no—
109#380—131no—
110#340—131no—
111#340—131no—
112C22×C13—21no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13C2×C4⋊C411yescharacteristic
116C2×D13—21no—
117C2×D13—21no—
118C2×D13—21no—
119C2×D13—41no—
120C2×D13—41no—
121C2×D13—41no—
122C2×D13—41no—
123C2×D13#12011yescharacteristic
124C2×D13#12311yescharacteristic
125C2×D13#13511yescharacteristic
126C2×D13#13511yescharacteristic
127C2×D13AGL(1,ℤ/8)11yescharacteristic
128C2×D13#13711yescharacteristic
129#261—42no—
130#261—42no—
131#261—81no—
132#261—81no—
133C4×C13—21no—
134C4×C13C4×D411yescharacteristic
135C4×C13C4×D411yescharacteristic
136Dic13—21no—
137Dic13C22⋊Q811yescharacteristic
138Dic13C22⋊Q811yescharacteristic
139C23×C4—131no—
140C22×C8—131no—
141C22×C8—131no—
142#117—262no—
143#117—262no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4—131no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4—131no—
148C2×C22⋊C4—261no—
149C2×C22⋊C4—261no—
150C2×C42—261no—
151#107—262no—
152#106—262no—
153C22⋊C8—131no—
154C22⋊C8—131no—
155C22⋊C8—131no—
156C22⋊C8#26111yescharacteristic, complemented
157#95—261no—
158C2×C13—41no—
159C2×C13#38511yescharacteristic
160C2×C13#42711yescharacteristic
161C2×C13#42811yescharacteristic
162D13—41no—
163D13#44911yescharacteristic
164D13#45211yescharacteristic
165D13#48211yescharacteristic
166D13#48511yescharacteristic
167C24—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—131no—
171C22×C4—131no—
172C22×C4—131no—
173C22×C4—261no—
174C22×C4—261no—
175C22×C4—261no—
176C22×C4—261no—
177C22×C4—261no—
178C22×C4—261no—
179C22×C4—261no—
180C22×C4—261no—
181C22×C4C2×#26111yescharacteristic
182C2×C8—131no—
183C2×C8—131no—
184C2×C8—261no—
185C2×C8—261no—
186C2×C8—261no—
187C2×C8—261no—
188C2×C8C2×#26111yescharacteristic
189C2×C8C2×#26111yescharacteristic
190C4⋊C4—132no—
191C4⋊C4—132no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C22⋊C4—264no—
199C22⋊C4—522no—
200C42—264no—
201C13#185411yescharacteristic, complemented, Sylow
202C23—131no—
203C23—131no—
204C23—261no—
205C23—261no—
206C23—261no—
207C23—261no—
208C23—261no—
209C23—261no—
210C23C4⋊#26111yescharacteristic
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—131no—
214C2×C4—131no—
215C2×C4—131no—
216C2×C4—131no—
217C2×C4—131no—
218C2×C4—131no—
219C2×C4—261no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—521no—
230C2×C4—521no—
231C2×C4—521no—
232C2×C4—521no—
233C2×C4—521no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—521no—
237C2×C4—521no—
238C2×C4—521no—
239C2×C4C4⋊#26111yescharacteristic
240C2×C4C22×#26111yescharacteristic
241C8—21no—
242C8—21no—
243C8—261no—
244C8—261no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—131no—
249C22—131no—
250C22—131no—
251C22—131no—
252C22—131no—
253C22—131no—
254C22—261no—
255C22—261no—
256C22—261no—
257C22—521no—
258C22—521no—
259C22—521no—
260C22—521no—
261C22C2×C4⋊#26111yescharacteristic
262C4—21no—
263C4—131no—
264C4—131no—
265C4—261no—
266C4—522no—
267C4—522no—
268C4—1041no—
269C4—1041no—
270C4D4×#26111yescharacteristic
271C4D4×#26111yescharacteristic
272C2—41no—
273C2—131no—
274C2—131no—
275C2—131no—
276C2—131no—
277C2—521no—
278C2#1171907011yescharacteristic
279C2#1171909211yescharacteristic
280C2#1171909811yescharacteristic
subgroupG/H
centerC22C2×C4⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C22⋊C8C4
socleC22×C13C2×C4⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC22⋊C8#261
hypocenterC13#1854
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#88102C2semidirect
4. C2×#88101C2semidirect
6. #11718265C2semidirect
7. #11718265C2semidirect
23. C13×C22⋊C8C4semidirect
24. C22⋊#1055C4semidirect
25. #88060C4semidirect
26. #88060C4semidirect
156. C22⋊C8#261semidirect
201. C13#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#882372
#117191362
C2×#881022
C2×#881012
D13×C22⋊C82
#117182652
#185413