Finite Group Databasebeta

← #13120185

Subgroups — #13120185

Order 1664.

584 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4×C22⋊D13C211yesmaximal, characteristic
2C22×#6101C211yesmaximal, characteristic, complemented
3C13×#380C211yesmaximal, characteristic, complemented
4#11718655C212yesmaximal, complemented
5#11718644C212yesmaximal, complemented
6#11718619C211yesmaximal, characteristic
7#11718619C211yesmaximal, characteristic
8#11718611C211yesmaximal, characteristic, complemented
9#11718611C211yesmaximal, characteristic, complemented
10#11718329C212yesmaximal, complemented
11#11718314C212yesmaximal, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C23×Dic13C2211yescharacteristic
15C23×Dic13C2211yescharacteristic
16C22×C4×D13C2211yescharacteristic
17C2×C13×C4⋊C4C2212yes—
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C22⋊Dic13C2211yescharacteristic
21C4×C22⋊D13—24no—
22C2×#6103C2211yescharacteristic
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2212yes—
26C2×C4⋊Dic13C2212yes—
27C2×#6101—24no—
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C2×#6101C2211yescharacteristic
31C2×C4×Dic13C2211yescharacteristic
32C13×#95C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13—42no—
40C22×C4×C13D414yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C2×C22⋊D13Q814yes—
48C22×Dic13—22no—
49C22×Dic13—24no—
50C22×Dic13—22no—
51C22×Dic13—42no—
52C22×Dic13C2311yescharacteristic
53C22×Dic13C2312yes—
54C22×Dic13C2311yescharacteristic
55C22×Dic13C2311yescharacteristic
56C22×Dic13C2312yes—
57C2×C4×D13—22no—
58C2×C4×D13—42no—
59C13×C4⋊C4—42no—
60C13×C22⋊C4—22no—
61C13×C22⋊C4—22no—
62C22⋊Dic13—22no—
63#6103—22no—
64#6103—24no—
65#6103—42no—
66C4⋊Dic13—24no—
67C4⋊Dic13—42no—
68#6101—24no—
69#6101—24no—
70#6101—22no—
71C4×Dic13—22no—
72#2579—131nomaximal, Sylow
73C23×C13—22no—
74C23×C13—22no—
75C23×C13C2×D412yes—
76C23×C13C2×Q812yes—
77C23×C13#4112yes—
78C23×C13C2411yescharacteristic
79C22×D13—21no—
80C22×D13—22no—
81C22×D13—21no—
82C22×D13—22no—
83C22×D13C2×Q812yes—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—44no—
93C2×C4×C13C2×D412yes—
94C2×C4×C13C2×D412yes—
95C22⋊D13—28no—
96C2×Dic13—28no—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—44no—
109C2×Dic13C2×Q812yes—
110C2×Dic13#4114yes—
111C4×D13—44no—
112C2×C4×D4—131no—
113C22×C4⋊C4—131no—
114#398—132no—
115#396—132no—
116#387—132no—
117#386—131no—
118#386—131no—
119#385—131no—
120#385—131no—
121#385—132no—
122#380D1311yescharacteristic, complemented
123C22×C13—22no—
124C22×C13—22no—
125C22×C13—24no—
126C22×C13—24no—
127C22×C13C22⋊Q814yes—
128C22×C13C22×D411yescharacteristic
129C22×C13C22×Q811yescharacteristic
130C22×C13C2×#4111yescharacteristic
131C22×C13C2×#4112yes—
132C22×C13H(5,𝔽2)12yes—
133C2×D13—22no—
134C2×D13—24no—
135C2×D13—41no—
136C2×D13—41no—
137C2×D13—42no—
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—42no—
141C4×C13—42no—
142Dic13—22no—
143Dic13—24no—
144Dic13—41no—
145Dic13—41no—
146Dic13—42no—
147C22×D4—131no—
148C23×C4—131no—
149C23×C4—131no—
150C23×C4—131no—
151C23×C4C2×D1311yescharacteristic
152C4×D4—264no—
153C2×C4⋊C4—132no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—132no—
157C2×C4⋊C4—132no—
158C2×C4⋊C4—264no—
159C2×C4⋊C4C2×D1312yes—
160C2×C22⋊C4—131no—
161C2×C22⋊C4—131no—
162C2×C22⋊C4—132no—
163C2×C22⋊C4—132no—
164C2×C22⋊C4C2×D1311yescharacteristic
165C2×C22⋊C4C2×D1311yescharacteristic
166C2×C42—131no—
167#95—132no—
168#95—132no—
169#95—132no—
170#95—132no—
171#95C2×D1312yes—
172C2×C13—24no—
173C2×C13C2×C22⋊Q811yescharacteristic
174C2×C13#52511yescharacteristic
175C2×C13#53411yescharacteristic
176C2×C13#55312yes—
177C2×C13#55412yes—
178D13—42no—
179C24—131no—
180C24C22×D1311yescharacteristic
181C2×D4—134no—
182C2×D4—262no—
183C2×D4—262no—
184C22×C4—42no—
185C22×C4—131no—
186C22×C4—132no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4—132no—
190C22×C4—264no—
191C22×C4—262no—
192C22×C4—262no—
193C22×C4—262no—
194C22×C4—522no—
195C22×C4—522no—
196C22×C4D5214yes—
197C22×C4C22×D1312yes—
198C22×C4C22×D1312yes—
199C22×C4C22×D1311yescharacteristic
200C22×C4C22×D1311yescharacteristic
201C4⋊C4—42no—
202C4⋊C4—264no—
203C4⋊C4—264no—
204C4⋊C4—264no—
205C4⋊C4—262no—
206C4⋊C4—522no—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—264no—
210C22⋊C4—262no—
211C22⋊C4—262no—
212C22⋊C4—522no—
213C42—262no—
214C13#257911yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—132no—
218C23—261no—
219C23—261no—
220C23—262no—
221C23—262no—
222C23C2×D5212yes—
223C23#612912yes—
224C23Q8×D1312yes—
225C23C23×D1311yescharacteristic
226D4—268no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—44no—
236C2×C4—132no—
237C2×C4—134no—
238C2×C4—268no—
239C2×C4—261no—
240C2×C4—262no—
241C2×C4—261no—
242C2×C4—262no—
243C2×C4—261no—
244C2×C4—261no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—524no—
251C2×C4—524no—
252C2×C4C2×D5212yes—
253C2×C4C2×D5212yes—
254C22—22no—
255C22—22no—
256C22—24no—
257C22—24no—
258C22—262no—
259C22—264no—
260C22—521no—
261C22—521no—
262C22—522no—
263C22#8815114yes—
264C22C22×D5211yescharacteristic
265C22C2×#612911yescharacteristic
266C22#8825112yes—
267C22C2×Q8×D1311yescharacteristic
268C22#41×D1312yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—262no—
274C4—264no—
275C4—521no—
276C4—522no—
277C4—521no—
278C2—24no—
279C2—522no—
280C2#1171919811yescharacteristic
281C2C2×#8815111yescharacteristic
282C2#1171922911yescharacteristic
283C2#1171930612yes—
284C2#1171934112yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
prime radicalC22×C22⋊D13C22
hypercenter#380D13
hypocenterC13#2579
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C22×#6101C2semidirect
3. C13×#380C2semidirect
4. #11718655C2semidirect
5. #11718644C2semidirect
8. #11718611C2semidirect
9. #11718611C2semidirect
10. #11718329C2semidirect
11. #11718314C2semidirect
122. #380D13semidirect
214. C13#2579semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D132
C22×#61012
C13×#3802
#117186552
#117186442
#117186192
#117186112
#117183292
#117183142
#257913