Finite Group Databasebeta

← #13120693

Subgroups — #13120693

Order 1664.

628 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 131 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×#88190C211yesmaximal, characteristic, complemented
2C2×#88135C211yesmaximal, characteristic, complemented
3C13×#392C211yesmaximal, characteristic, complemented
4#11718884C211yesmaximal, characteristic, complemented
5#11718884C212yesmaximal, complemented
6#11718881C212yesmaximal, complemented
7#11718617C212yesmaximal, complemented
8#11718613C212yesmaximal, complemented
9#11718608C211yesmaximal, characteristic, complemented
10#11718334C211yesmaximal, characteristic, complemented
11#11718312C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×D4×C13C2212yes—
14C22×C22⋊D13C2211yescharacteristic
15C22×C22⋊D13C2212yes—
16C23×Dic13C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2212yes—
21C2×C22⋊Dic13C2212yes—
22C2×C22⋊Dic13C2212yes—
23C2×C22⋊Dic13C2212yes—
24C2×C22⋊Dic13C2212yes—
25#88190—24no—
26C2×#6103C2211yescharacteristic
27C2×#6103C2212yes—
28C2×#6101C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30#88135—24no—
31C13×#95C2211yescharacteristic
32#88071C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2312yes—
38C24×C13C2311yescharacteristic
39C23×D13C2311yescharacteristic
40C2×D4×C13—24no—
41C2×D4×C13—22no—
42C2×D4×C13—42no—
43C2×D4×C13—42no—
44C2×D4×C13—42no—
45C22×C4×C13C2312yes—
46C22×C4×C13C2311yescharacteristic
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—24no—
51C2×C22⋊D13—22no—
52C2×C22⋊D13—42no—
53C2×C22⋊D13—42no—
54C22×Dic13—22no—
55C22×Dic13—42no—
56C22×Dic13C2312yes—
57C22×Dic13C2311yescharacteristic
58C22×Dic13C2312yes—
59C22×Dic13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C2×C4×D13—22no—
62C2×C4×D13—42no—
63C2×Dic26—22no—
64C2×Dic26—42no—
65C13×C22⋊C4—22no—
66C13×C22⋊C4—42no—
67C22⋊Dic13—24no—
68C22⋊Dic13—24no—
69C22⋊Dic13—42no—
70C22⋊Dic13—42no—
71#6103—22no—
72#6103—42no—
73#6101—22no—
74C4×Dic13D414yescomplemented
75#2631—131nomaximal, Sylow
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—22no—
83C23×C13—22no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13—22no—
87C23×C13#4112yes—
88C23×C13C2411yescharacteristic
89C22×D13—21no—
90C22×D13—21no—
91C22×D13—22no—
92C22×D13—22no—
93C22×D13#4112yes—
94D4×C13—44no—
95D4×C13—48no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13C2×D412yes—
103C22⋊D13—28no—
104C22⋊D13—48no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—22no—
116C2×Dic13—44no—
117C2×Dic13C2×D412yes—
118C2×Dic13C2×D412yes—
119C4×D13—44no—
120Dic26—44no—
121C2×#124—131no—
122C2×C4×D4—131no—
123#397—132no—
124#393—131no—
125#393—131no—
126#392—131no—
127#392—132no—
128#392D1311yescharacteristic, complemented
129#386—132no—
130#386—132no—
131#383—131no—
132C22×C13—22no—
133C22×C13—24no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13—42no—
141C22×C13—42no—
142C22×C13—42no—
143C22×C13—42no—
144C22×C13C22×D411yescharacteristic
145C22×C13C2×#4111yescharacteristic
146C22×C13C2×#4111yescharacteristic
147C22×C13H(5,𝔽2)12yes—
148C22×C13H(5,𝔽2)12yes—
149C2×D13—22no—
150C2×D13—24no—
151C2×D13—41no—
152C2×D13—41no—
153C2×D13—42no—
154C4×C13—22no—
155C4×C13—41no—
156C4×C13—42no—
157Dic13—22no—
158Dic13—22no—
159Dic13—42no—
160Dic13—41no—
161Dic13—42no—
162C22×Q8—131no—
163C22×D4—131no—
164C22×D4—132no—
165C22×D4C2×D1311yescharacteristic
166C22×D4C2×D1312yes—
167C23×C4—131no—
168C23×C4—131no—
169#124—264no—
170C4×D4—264no—
171C2×C4⋊C4—131no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4—131no—
175C2×C22⋊C4—132no—
176C2×C22⋊C4—132no—
177C2×C22⋊C4—132no—
178C2×C22⋊C4C2×D1311yescharacteristic
179C2×C22⋊C4C2×D1312yes—
180C2×C42—131no—
181#95—132no—
182#95—131no—
183#95—132no—
184#95—132no—
185#95—132no—
186#95C2×D1311yescharacteristic
187C2×C13—42no—
188C2×C13—82no—
189C2×C13#52511yescharacteristic
190C2×C13#53511yescharacteristic
191C2×C13#53511yescharacteristic
192C2×C13#53812yes—
193C2×C13#53812yes—
194D13—42no—
195C24—131no—
196C24C22×D1312yes—
197C24C22×D1311yescharacteristic
198C2×Q8—262no—
199C2×Q8—522no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—262no—
206C2×D4—262no—
207C2×D4—262no—
208C2×D4—264no—
209C2×D4—522no—
210C2×D4—522no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—132no—
214C22×C4—132no—
215C22×C4—131no—
216C22×C4—262no—
217C22×C4—262no—
218C22×C4—522no—
219C22×C4—522no—
220C22×C4C22×D1312yes—
221C22×C4C22×D1311yescharacteristic
222C22×C4C22×D1311yescharacteristic
223C4⋊C4—262no—
224C22⋊C4—22no—
225C22⋊C4—42no—
226C22⋊C4—264no—
227C22⋊C4—264no—
228C22⋊C4—262no—
229C22⋊C4—522no—
230C22⋊C4—522no—
231C22⋊C4—522no—
232C42—134no—
233C13#263111yescharacteristic, complemented, Sylow
234C23—21no—
235C23—22no—
236C23—22no—
237C23—21no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—132no—
246C23—261no—
247C23—261no—
248C23—262no—
249C23—262no—
250C23#612912yes—
251C23C23×D1311yescharacteristic
252Q8—524no—
253D4—44no—
254D4—48no—
255D4—268no—
256D4—528no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—132no—
264C2×C4—132no—
265C2×C4—261no—
266C2×C4—262no—
267C2×C4—261no—
268C2×C4—262no—
269C2×C4—261no—
270C2×C4—262no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—262no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—524no—
277C2×C4—524no—
278C2×C4D4×D1312yes—
279C22—24no—
280C22—22no—
281C22—41no—
282C22—42no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—262no—
292C22—264no—
293C22—521no—
294C22—522no—
295C22—521no—
296C22C2×D4×D1311yescharacteristic
297C22C2×#612911yescharacteristic
298C22#8825112yes—
299C22#8825112yes—
300C22#41×D1311yescharacteristic
301C4—22no—
302C4—42no—
303C4—41no—
304C4—262no—
305C4—262no—
306C4—522no—
307C4—522no—
308C4—521no—
309C2—42no—
310C2—82no—
311C2—522no—
312C2#1171929711yescharacteristic
313C2#1171929812yes—
314C2#1171931111yescharacteristic
315C2#1171931812yes—
316C2#1171942011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#392C2
hypercenter#392D13
hypocenterC13#2631
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#88190C2semidirect
2. C2×#88135C2semidirect
3. C13×#392C2semidirect
4. #11718884C2semidirect
5. #11718884C2semidirect
6. #11718881C2semidirect
7. #11718617C2semidirect
8. #11718613C2semidirect
9. #11718608C2semidirect
10. #11718334C2semidirect
11. #11718312C2semidirect
74. C4×Dic13D4semidirect
128. #392D13semidirect
233. C13#2631semidirect

Maximal subgroups

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

subgroupindex
C2×#881902
C2×#881352
C13×#3922
#117188842
#117188812
#117186172
#117186132
#117186082
#117183342
#117183122
#263113