Finite Group Databasebeta

← #13120405

Subgroups — #13120405

Order 1664.

604 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 135 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×#88147C211yesmaximal, characteristic, complemented
2C2×#88146C211yesmaximal, characteristic, complemented
3C13×#400C211yesmaximal, characteristic, complemented
4#11718653C211yesmaximal, characteristic, complemented
5#11718652C211yesmaximal, characteristic, complemented
6#11718332C211yesmaximal, characteristic
7#11718330C212yesmaximal, complemented
8#11718329C212yesmaximal, complemented
9#11718326C212yesmaximal, complemented
10#11718326C212yesmaximal, complemented
11#11718312C211yesmaximal, characteristic, complemented
12C22×D52C2211yescharacteristic
13C22×D52C2212yes—
14C22×C4×D13C2211yescharacteristic
15C22×C4×D13C2212yes—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×#6103C2211yescharacteristic
19C2×#6103C2211yescharacteristic
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×#6101C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28C2×C4×Dic13C2211yescharacteristic
29#88147—24no—
30#88146—24no—
31C13×#95C2211yescharacteristic
32C13×#95C2212yes—
33C13×#95C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2211yescharacteristic
37C23×D13C2311yescharacteristic
38C23×D13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C2×D52—24no—
49C2×D52—22no—
50C2×D52—24no—
51C2×D52—24no—
52C2×D52—42no—
53C2×C4×D13—22no—
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—24no—
57C2×C4×D13—42no—
58C2×C4×D13—42no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—22no—
61#6103—24no—
62#6103—22no—
63#6103—24no—
64#6103—22no—
65#6103—24no—
66#6103—42no—
67#6103—42no—
68C4⋊Dic13—22no—
69#6101—42no—
70C4×Dic13—22no—
71C4×Dic13D414yescomplemented
72#2598—131nomaximal, Sylow
73C23×C13C2411yescharacteristic
74C22×D13—21no—
75C22×D13—22no—
76C22×D13—22no—
77C22×D13—21no—
78C22×D13—22no—
79C22×D13—22no—
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—22no—
84C22×D13#4114yes—
85C22×D13#4112yes—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13C2×D412yes—
98C2×C4×C13#4112yes—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13C2×D412yes—
108C2×Dic13C2×D412yes—
109D52—28no—
110D52—48no—
111C4×D13—28no—
112C4×D13—48no—
113C2×C4×D4—131no—
114C2×#117—131no—
115#400D1311yescharacteristic, complemented
116#399—131no—
117#394—131no—
118#392—131no—
119#388—132no—
120#386—132no—
121#386—132no—
122#385—132no—
123#383—131no—
124C22×C13C22×D411yescharacteristic
125C22×C13C2×#4111yescharacteristic
126C22×C13C2×#4111yescharacteristic
127C22×C13C2×#4112yes—
128C22×C13H(5,𝔽2)12yes—
129C2×D13—22no—
130C2×D13—24no—
131C2×D13—24no—
132C2×D13—24no—
133C2×D13—24no—
134C2×D13—42no—
135C2×D13—41no—
136C2×D13—42no—
137C2×D13—41no—
138C2×D13—42no—
139C2×D13—42no—
140C2×D13—42no—
141C4×C13—22no—
142C4×C13—22no—
143C4×C13—41no—
144C4×C13—42no—
145C4×C13—42no—
146Dic13—22no—
147Dic13—22no—
148Dic13—41no—
149Dic13—42no—
150C22×D4—131no—
151C22×D4—132no—
152C23×C4—131no—
153C23×C4—132no—
154C4×D4—264no—
155#117—264no—
156C2×C4⋊C4—131no—
157C2×C4⋊C4—132no—
158C2×C4⋊C4C2×D1311yescharacteristic
159C2×C4⋊C4C2×D1311yescharacteristic
160C2×C22⋊C4—131no—
161C2×C22⋊C4—131no—
162C2×C22⋊C4—132no—
163C2×C22⋊C4—132no—
164C2×C22⋊C4—132no—
165C2×C22⋊C4—132no—
166C2×C22⋊C4—132no—
167C2×C42—131no—
168C2×C42—131no—
169#95—132no—
170#95—132no—
171#95—131no—
172#95C2×D1311yescharacteristic
173#95C2×D1312yes—
174#95C2×D1312yes—
175C2×C13#52511yescharacteristic
176C2×C13#52511yescharacteristic
177C2×C13#53511yescharacteristic
178C2×C13#55112yes—
179C2×C13#55312yes—
180D13—42no—
181D13—44no—
182C24—132no—
183C24—131no—
184C2×D4—264no—
185C2×D4—264no—
186C2×D4—264no—
187C2×D4—262no—
188C2×D4—522no—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—132no—
192C22×C4—131no—
193C22×C4—262no—
194C22×C4—264no—
195C22×C4—262no—
196C22×C4—262no—
197C22×C4—522no—
198C22×C4—522no—
199C22×C4C22×D1312yes—
200C22×C4C22×D1311yescharacteristic
201C22×C4C22×D1312yes—
202C22×C4C22×D1311yescharacteristic
203C22×C4C22×D1311yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—262no—
207C4⋊C4—522no—
208C22⋊C4—262no—
209C22⋊C4—264no—
210C22⋊C4—264no—
211C22⋊C4—262no—
212C22⋊C4—264no—
213C22⋊C4—522no—
214C22⋊C4—522no—
215C42—134no—
216C42—262no—
217C13#259811yescharacteristic, complemented, Sylow
218C23—134no—
219C23—132no—
220C23—261no—
221C23—262no—
222C23—262no—
223C23—261no—
224C23—262no—
225C23—262no—
226C23—262no—
227C23—262no—
228C23—262no—
229C23—262no—
230C23C23×D1311yescharacteristic
231D4—268no—
232D4—528no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—132no—
245C2×C4—132no—
246C2×C4—268no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—528no—
256C2×C4D4×D1312yes—
257C2×C4#613112yes—
258C22—262no—
259C22—264no—
260C22—264no—
261C22—264no—
262C22—264no—
263C22—522no—
264C22—521no—
265C22—522no—
266C22—521no—
267C22—522no—
268C22—522no—
269C22—522no—
270C22C2×D4×D1311yescharacteristic
271C22C2×#613111yescharacteristic
272C22#41×D1311yescharacteristic
273C22#41×D1312yes—
274C22#8825612yes—
275C4—22no—
276C4—22no—
277C4—41no—
278C4—42no—
279C4—42no—
280C4—262no—
281C4—262no—
282C4—521no—
283C4—522no—
284C2—522no—
285C2—524no—
286C2#1171933211yescharacteristic
287C2#1171936111yescharacteristic
288C2#1171937911yescharacteristic
289C2#1171940012yes—
290C2#1171941012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#400C2
prime radical#11718332C2
hypercenter#400D13
hypocenterC13#2598
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#88147C2semidirect
2. C2×#88146C2semidirect
3. C13×#400C2semidirect
4. #11718653C2semidirect
5. #11718652C2semidirect
7. #11718330C2semidirect
8. #11718329C2semidirect
9. #11718326C2semidirect
10. #11718326C2semidirect
11. #11718312C2semidirect
71. C4×Dic13D4semidirect
115. #400D13semidirect
217. C13#2598semidirect

Maximal subgroups

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

subgroupindex
C2×#881472
C2×#881462
C13×#4002
#117186532
#117186522
#117183322
#117183302
#117183292
#117183262
#117183122
#259813