Finite Group Databasebeta

← #13118243

Subgroups — #13118243

Order 1664.

610 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×C13×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#88183C211yesmaximal, characteristic
3C2×#88183C211yesmaximal, characteristic
4C2×#88180C211yesmaximal, characteristic, complemented
5#11718874C211yesmaximal, characteristic
6#11718872C211yesmaximal, characteristic, complemented
7#11718871C211yesmaximal, characteristic, complemented
8#11718655C212yesmaximal, complemented
9#11718651C212yesmaximal, complemented
10#11718645C212yesmaximal, complemented
11#11718633C212yesmaximal, complemented
12C23×C4×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C23×C4×C13C2211yescharacteristic
15C22×C22⋊D13C2211yescharacteristic
16C2×C13×C4⋊C4—24no—
17C2×C13×C4⋊C4C2212yes—
18C2×C13×C4⋊C4C2212yes—
19C2×C22⋊Dic13C2211yescharacteristic
20C2×C22⋊Dic13C2211yescharacteristic
21C2×C22⋊Dic13C2211yescharacteristic
22#88183—24no—
23#88183—24no—
24C2×#6103C2211yescharacteristic
25C2×#6103C2212yes—
26C2×#6103C2211yescharacteristic
27C2×#6103C2212yes—
28#88180—24no—
29C2×C4⋊Dic13C2212yes—
30C2×#6101C2211yescharacteristic
31C2×#6101C2212yes—
32C2×#6101C2211yescharacteristic
33C2×#6101C2212yes—
34C2×C4×Dic13C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37#88071C2212yes—
38#88071C2212yes—
39C24×C13C2311yescharacteristic
40C23×D13C2311yescharacteristic
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—24no—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13D414yes—
49C22×C4×C13C2312yes—
50C22×C4×C13C2311yescharacteristic
51C22×C4×C13C2311yescharacteristic
52C22×C4×C13C2312yes—
53C2×C22⋊D13—22no—
54C2×C22⋊D13—22no—
55C2×C22⋊D13—22no—
56C22×Dic13C2311yescharacteristic
57C22×Dic13C2312yes—
58C22×Dic13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C22×Dic13C2312yes—
61C13×C4⋊C4—24no—
62C13×C4⋊C4—24no—
63C22⋊Dic13—22no—
64C22⋊Dic13—22no—
65C22⋊Dic13D414yes—
66#6103—22no—
67#6103—22no—
68#6103—24no—
69#6103—24no—
70C4⋊Dic13—24no—
71#6101—22no—
72#6101—22no—
73#6101—24no—
74#6101—24no—
75C4×Dic13—24no—
76#2413—131nomaximal, Sylow
77C23×C13—22no—
78C23×C13—22no—
79C23×C13C2×D412yes—
80C23×C13C2×D412yes—
81C23×C13#4112yes—
82C23×C13C2411yescharacteristic
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—22no—
86C22×D13—21no—
87C22×D13—22no—
88C2×C4×C13—28no—
89C2×C4×C13—28no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—44no—
100C2×C4×C13C2×D412yes—
101C2×C4×C13C2×D412yes—
102C2×C4×C13#4114yes—
103C22⋊D13—44no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—21no—
114C2×Dic13—22no—
115C2×Dic13—22no—
116C2×Dic13C2×D414yes—
117C2×#123—131no—
118C2×#123—131no—
119C2×#117—131no—
120C22×C4⋊C4D1311yescharacteristic, complemented
121#398—132no—
122#396—132no—
123#389—132no—
124#388—132no—
125#386—131no—
126#385—131no—
127#381—131no—
128C22×C13—22no—
129C22×C13—22no—
130C22×C13—24no—
131C22×C13—24no—
132C22×C13#12114yes—
133C22×C13C22×D411yescharacteristic
134C22×C13C22×D411yescharacteristic
135C22×C13C2×#4112yes—
136C22×C13C2×#4111yescharacteristic
137C22×C132−1+412yes—
138C2×D13—41no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—42no—
142C2×D13—42no—
143C4×C13—22no—
144C4×C13—22no—
145C4×C13—24no—
146C4×C13—42no—
147Dic13—24no—
148Dic13—41no—
149Dic13—41no—
150Dic13—41no—
151Dic13—42no—
152C22×D4—131no—
153C23×C4C2×D1311yescharacteristic
154C23×C4C2×D1311yescharacteristic
155C23×C4C2×D1311yescharacteristic
156#123—264no—
157#123—264no—
158#117—264no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—132no—
165C2×C4⋊C4C2×D1312yes—
166C2×C4⋊C4C2×D1312yes—
167C2×C22⋊C4—131no—
168C2×C22⋊C4—131no—
169C2×C22⋊C4—131no—
170C2×C22⋊C4—131no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4—131no—
173C2×C22⋊C4—132no—
174C2×C42—132no—
175#95—132no—
176#95—132no—
177#95—132no—
178#95—132no—
179C2×C13—24no—
180C2×C13C2×#12111yescharacteristic
181C2×C13#52511yescharacteristic
182C2×C13#53611yescharacteristic
183C2×C13#54712yes—
184C2×C13#55212yes—
185D13—81no—
186C24—131no—
187C24C22×D1311yescharacteristic
188C2×D4—262no—
189C2×D4—262no—
190C2×D4—262no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—132no—
199C22×C4—131no—
200C22×C4—132no—
201C22×C4—131no—
202C22×C4—131no—
203C22×C4C22⋊D1314yes—
204C22×C4C22×D1312yes—
205C22×C4C22×D1312yes—
206C22×C4C22×D1311yescharacteristic
207C22×C4C22×D1311yescharacteristic
208C4⋊C4—24no—
209C4⋊C4—24no—
210C4⋊C4—264no—
211C4⋊C4—264no—
212C4⋊C4—264no—
213C4⋊C4—262no—
214C4⋊C4—262no—
215C22⋊C4—134no—
216C22⋊C4—264no—
217C22⋊C4—262no—
218C22⋊C4—262no—
219C22⋊C4—264no—
220C22⋊C4—262no—
221C22⋊C4—262no—
222C42—264no—
223C13#241311yescharacteristic, complemented, Sylow
224C23—22no—
225C23—22no—
226C23—262no—
227C23—261no—
228C23—261no—
229C23—262no—
230C23—261no—
231C23D4×D1312yes—
232C23#612912yes—
233C23C2×C22⋊D1312yes—
234C23C23×D1311yescharacteristic
235D4—524no—
236C2×C4—28no—
237C2×C4—28no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—44no—
248C2×C4—134no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4#612714yes—
262C2×C4C2×C22⋊D1312yes—
263C2×C4C2×C22⋊D1312yes—
264C22—24no—
265C22—24no—
266C22—22no—
267C22—22no—
268C22—522no—
269C22—522no—
270C22—521no—
271C22—521no—
272C22—521no—
273C22#8819314yes—
274C22C2×#612712yes—
275C22C2×D4×D1311yescharacteristic
276C22C2×#612911yescharacteristic
277C22#8825412yes—
278C22C22×C22⋊D1311yescharacteristic
279C4—24no—
280C4—22no—
281C4—22no—
282C4—42no—
283C4—264no—
284C4—522no—
285C4—521no—
286C4—521no—
287C4—521no—
288C2—24no—
289C2—1041no—
290C2#1171921212yes—
291C2#1171921812yes—
292C2#1171949611yescharacteristic
293C2C2×#8819311yescharacteristic
294C2#1171952111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC22×C13×C4⋊C4C2
prime radicalC22×C22⋊D13C22
hypercenterC22×C4⋊C4D13
hypocenterC13#2413
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C13×C4⋊C4C2semidirect
4. C2×#88180C2semidirect
6. #11718872C2semidirect
7. #11718871C2semidirect
8. #11718655C2semidirect
9. #11718651C2semidirect
10. #11718645C2semidirect
11. #11718633C2semidirect
120. C22×C4⋊C4D13semidirect
223. C13#2413semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C4⋊C42
C2×#881832
C2×#881802
#117188742
#117188722
#117188712
#117186552
#117186512
#117186452
#117186332
#241313