Finite Group Databasebeta

← #13120523

Subgroups — #13120523

Order 1664.

576 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 145 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×C13×#117C211yesmaximal, characteristic, complemented
2C2×#88129C211yesmaximal, characteristic, complemented
3#11718874C212yesmaximal, complemented
4#11718652C211yesmaximal, characteristic, complemented
5#11718651C212yesmaximal, complemented
6#11718640C211yesmaximal, characteristic, complemented
7#11718621C211yesmaximal, characteristic
8#11718618C212yesmaximal, complemented
9#11718608C211yesmaximal, characteristic, complemented
10#11718601C212yesmaximal, complemented
11#11718593C211yesmaximal, characteristic, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C22×D52C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C13×#117—24no—
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C42×C13C2211yescharacteristic
22C2×C42×C13C2211yescharacteristic
23C2×C22⋊Dic13C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27C2×#6103C2212yes—
28C2×#6103C2212yes—
29C2×#6101C2212yes—
30C2×C4×Dic13C2212yes—
31#88129—24no—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2312yes—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C22×C4×C13C2311yescharacteristic
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—24no—
49C2×C22⋊D13—24no—
50C2×C22⋊D13—42no—
51C22×Dic13C2312yes—
52C22×Dic13C2312yes—
53C22×Dic13C2312yes—
54C2×D52—22no—
55C2×D52—42no—
56C2×Dic26—22no—
57C2×Dic26—42no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—22no—
60C13×C22⋊C4—22no—
61C13×C22⋊C4—22no—
62C42×C13—22no—
63C42×C13D414yescomplemented
64C22⋊Dic13—42no—
65#6103—24no—
66#6103—24no—
67#6103—24no—
68#6103—24no—
69#6103—42no—
70#6101—42no—
71C4×Dic13—24no—
72#2610—131nomaximal, Sylow
73C23×C13—21no—
74C23×C13—22no—
75C23×C13—21no—
76C23×C13—22no—
77C23×C13#4112yes—
78C23×C13C2411yescharacteristic
79C22×D13—22no—
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—22no—
86C2×C4×C13—28no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
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×C13C2×D412yes—
98C2×C4×C13C2×D412yes—
99C2×C4×C13C2×D412yes—
100C2×C4×C13#4112yes—
101C22⋊D13—48no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13#4114yes—
111D52—44no—
112Dic26—44no—
113C2×#124—131no—
114C2×#117D1311yescharacteristic, complemented
115#395—131no—
116#394—131no—
117#393—131no—
118#392—131no—
119#390—132no—
120#388—132no—
121#388—132no—
122#386—132no—
123#376—131no—
124C22×C13—22no—
125C22×C13—24no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13—42no—
129C22×C13C22×D411yescharacteristic
130C22×C13C2×#4111yescharacteristic
131C22×C13C2×#4111yescharacteristic
132C22×C13C2×#4112yes—
133C22×C13H(5,𝔽2)12yes—
134C2×D13—42no—
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—42no—
139C2×D13—42no—
140C2×D13—42no—
141C4×C13—22no—
142C4×C13—22no—
143C4×C13—22no—
144C4×C13—22no—
145C4×C13—41no—
146C4×C13—41no—
147Dic13—24no—
148Dic13—42no—
149Dic13—42no—
150C22×Q8—131no—
151C22×D4—132no—
152C22×D4—131no—
153C23×C4C2×D1311yescharacteristic
154#124—264no—
155#117—24no—
156C2×C4⋊C4—132no—
157C2×C4⋊C4C2×D1311yescharacteristic
158C2×C4⋊C4C2×D1311yescharacteristic
159C2×C22⋊C4—132no—
160C2×C22⋊C4—132no—
161C2×C22⋊C4—132no—
162C2×C22⋊C4—132no—
163C2×C22⋊C4—132no—
164C2×C22⋊C4—132no—
165C2×C22⋊C4C2×D1311yescharacteristic
166C2×C22⋊C4C2×D1311yescharacteristic
167C2×C42—132no—
168C2×C42C2×D1311yescharacteristic
169C2×C42C2×D1311yescharacteristic
170#95—132no—
171#95—131no—
172#95—131no—
173#95—132no—
174#95—132no—
175C2×C13—42no—
176C2×C13#52511yescharacteristic
177C2×C13#53211yescharacteristic
178C2×C13#53511yescharacteristic
179C2×C13#55112yes—
180C2×C13#55512yes—
181D13—82no—
182C24—132no—
183C24C22×D1311yescharacteristic
184C2×Q8—262no—
185C2×Q8—522no—
186C2×D4—264no—
187C2×D4—264no—
188C2×D4—262no—
189C2×D4—522no—
190C2×D4—522no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—132no—
195C22×C4—132no—
196C22×C4—132no—
197C22×C4C22×D1311yescharacteristic
198C22×C4C22×D1311yescharacteristic
199C22×C4C22×D1311yescharacteristic
200C22×C4C22×D1311yescharacteristic
201C22×C4C22×D1311yescharacteristic
202C22×C4C22×D1311yescharacteristic
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—522no—
206C22⋊C4—22no—
207C22⋊C4—22no—
208C22⋊C4—264no—
209C22⋊C4—264no—
210C22⋊C4—264no—
211C22⋊C4—264no—
212C22⋊C4—522no—
213C22⋊C4—522no—
214C42—22no—
215C42—264no—
216C42C22⋊D1314yescomplemented
217C13#261011yescharacteristic, complemented, Sylow
218C23—21no—
219C23—22no—
220C23—22no—
221C23—21no—
222C23—262no—
223C23—262no—
224C23—262no—
225C23—262no—
226C23—262no—
227C23—262no—
228C23—262no—
229C23#612712yes—
230C23C23×D1311yescharacteristic
231Q8—524no—
232D4—524no—
233D4—528no—
234C2×C4—28no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—134no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4#612712yes—
255C2×C4C2×C22⋊D1312yes—
256C2×C4C2×C22⋊D1312yes—
257C2×C4C2×C22⋊D1312yes—
258C22—24no—
259C22—22no—
260C22—42no—
261C22—41no—
262C22—41no—
263C22—522no—
264C22—522no—
265C22—522no—
266C22—522no—
267C22—522no—
268C22—522no—
269C22—522no—
270C22C2×#612711yescharacteristic
271C22C2×#612711yescharacteristic
272C22#41×D1312yes—
273C22#8825612yes—
274C22C22×C22⋊D1311yescharacteristic
275C4—22no—
276C4—22no—
277C4—22no—
278C4—22no—
279C4—41no—
280C4—41no—
281C4—264no—
282C4—522no—
283C4—522no—
284C2—42no—
285C2—1042no—
286C2#1171923212yes—
287C2#1171923712yes—
288C2#1171949611yescharacteristic
289C2#1171953511yescharacteristic
290C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#117C2
prime radical#11718621C2
hypercenterC2×#117D13
hypocenterC13#2610
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C13×#117C2semidirect
2. C2×#88129C2semidirect
3. #11718874C2semidirect
4. #11718652C2semidirect
5. #11718651C2semidirect
6. #11718640C2semidirect
8. #11718618C2semidirect
9. #11718608C2semidirect
10. #11718601C2semidirect
11. #11718593C2semidirect
63. C42×C13D4semidirect
114. C2×#117D13semidirect
216. C42C22⋊D13semidirect
217. C13#2610semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1172
C2×#881292
#117188742
#117186522
#117186512
#117186402
#117186212
#117186182
#117186082
#117186012
#117185932
#261013