Finite Group Databasebeta

← #13124653

Subgroups — #13124653

Order 1664.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#125C211yesmaximal, characteristic, complemented
2C4×#6129C211yesmaximal, characteristic
3C13×#478C211yesmaximal, characteristic, complemented
4#11718724C211yesmaximal, characteristic, complemented
5#11718670C211yesmaximal, characteristic, complemented
6#11718542C211yesmaximal, characteristic, complemented
7#11718538C211yesmaximal, characteristic, complemented
8#11718522C211yesmaximal, characteristic, complemented
9#11718518C211yesmaximal, characteristic, complemented
10#11718498C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718432C211yesmaximal, characteristic
13#11718432C211yesmaximal, characteristic
14#11718427C211yesmaximal, characteristic, complemented
15#11718424C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C13×#125C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19D4×Dic13C2211yescharacteristic
20C4×C22⋊D13—21no—
21C2×C4×Dic13—21no—
22C2×#6094C2211yescharacteristic
23C2×#6094C2211yescharacteristic
24#88146C2211yescharacteristic
25C4⋊C4×D13—21no—
26C4⋊C4×D13—21no—
27C4⋊C4×D13C2211yescharacteristic
28C4⋊C4×D13C2211yescharacteristic
29#88144C2211yescharacteristic
30#88144C2211yescharacteristic
31#88143—21no—
32#88143—21no—
33#88141C2211yescharacteristic
34#88135—21no—
35#88131—21no—
36C42×D13C2211yescharacteristic
37#88124C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C13×#107C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88058C2211yescharacteristic
47#88057C2211yescharacteristic
48#88056C2211yescharacteristic
49#88056C2211yescharacteristic
50#88054C2211yescharacteristic
51#88054C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×D4×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C2×C22⋊D13—21no—
62C22×Dic13—21no—
63C22×Dic13—21no—
64#6129—22no—
65#6129Q814yes—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13D411yescharacteristic
69C2×C4×D13D411yescharacteristic
70C2×C4×D13C2311yescharacteristic
71C2×Dic26C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C42×C13C2311yescharacteristic
81C22⋊Dic13—21no—
82#6103—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13C2311yescharacteristic
86C4⋊Dic13C2311yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13D411yescharacteristic
100C4×Dic13D411yescharacteristic
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105#6094—22no—
106#3080—131nomaximal, Sylow
107C23×C13—21no—
108C22×D13C2×D411yescharacteristic
109D4×C13—21no—
110D4×C13C2×Q812yes—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2411yescharacteristic
118C22⋊D13—24no—
119C2×Dic13—21no—
120C2×Dic13—24no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—42no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C4×D13—41no—
129C4×D13—41no—
130C4×D13—42no—
131C4×D13—42no—
132C4×D13C2×Q812yes—
133C4×D13#4112yes—
134Dic26—21no—
135Dic26C2×Q812yes—
136C8×C13—21no—
137C8×C13—21no—
138#1055—21no—
139#1055—21no—
140C2×#125—131no—
141C4×#41—131no—
142#479—131no—
143#479—131no—
144#479—131no—
145#479—131no—
146#478—131no—
147#478—131no—
148#478—131no—
149#478D1311yescharacteristic, complemented
150#428—131no—
151#428—131no—
152#423—131no—
153#417—131no—
154#417—131no—
155C22×C13—22no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13C22×D411yescharacteristic
159C2×D13—21no—
160C2×D13—21no—
161C2×D13C22⋊Q812yes—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13C22×Q811yescharacteristic
168C4×C13C2×#4111yescharacteristic
169Dic13—22no—
170Dic13—21no—
171Dic13—21no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175Dic13C22⋊Q812yes—
176C2×#41—131no—
177C2×M16—131no—
178C2×M16—131no—
179#125—131no—
180#125—131no—
181#125—131no—
182#125—261no—
183#125—261no—
184#125C2×D1311yescharacteristic
185C4×Q8—131no—
186C4×Q8—131no—
187C4×D4—131no—
188C4×D4—261no—
189C4×D4—261no—
190C4×D4C2×D1311yescharacteristic
191#117—131no—
192#117—261no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C42—131no—
198C2×C42—261no—
199#107—131no—
200#107—131no—
201#107—131no—
202#107C2×D1311yescharacteristic
203#106—131no—
204#106—131no—
205#106—131no—
206#106C2×D1311yescharacteristic
207C4⋊C8—131no—
208C4⋊C8—131no—
209C4⋊C8—131no—
210C4⋊C8C2×D1311yescharacteristic
211#103—131no—
212#103—131no—
213#103—131no—
214#103—131no—
215#102—131no—
216#102—131no—
217#102C2×D1311yescharacteristic
218#102C2×D1311yescharacteristic
219C2×C13—42no—
220C2×C13C2×C22⋊Q811yescharacteristic
221C2×C13#57511yescharacteristic
222C2×C13#57511yescharacteristic
223D13—22no—
224#41—134no—
225#41—262no—
226C2×Q8—131no—
227C2×D4—261no—
228C2×D4C22×D1311yescharacteristic
229C22×C4—21no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237M16—262no—
238M16—262no—
239C2×C8—131no—
240C2×C8—131no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C4⋊C4C22×D1311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—131no—
265C42—131no—
266C42—131no—
267C42—261no—
268C42—261no—
269C42—261no—
270C42C22×D1311yescharacteristic
271C13#308011yescharacteristic, complemented, Sylow
272C23—21no—
273C23—131no—
274Q8—132no—
275Q8—261no—
276D4—21no—
277D4—264no—
278D4Q8×D1312yes—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—131no—
284C2×C4—132no—
285C2×C4—132no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—264no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4D4×D1311yescharacteristic
299C2×C4D4×D1311yescharacteristic
300C2×C4C23×D1311yescharacteristic
301C8—21no—
302C8—21no—
303C8—261no—
304C8—261no—
305C22—22no—
306C22—41no—
307C22—41no—
308C22—132no—
309C22—261no—
310C22—261no—
311C22C2×D4×D1311yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—132no—
318C4—261no—
319C4—261no—
320C4—262no—
321C4—521no—
322C4—521no—
323C4—521no—
324C4C2×Q8×D1311yescharacteristic
325C4#41×D1311yescharacteristic
326C2—42no—
327C2—262no—
328C2D13×C22⋊Q811yescharacteristic
329C2#1171947311yescharacteristic
330C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#478C2
socleC22×C13C22×D4
prime radicalC2×#6129C22
hypercenter#478D13
hypocenterC13#3080
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. D13×#125C2semidirect
3. C13×#478C2semidirect
4. #11718724C2semidirect
5. #11718670C2semidirect
6. #11718542C2semidirect
7. #11718538C2semidirect
8. #11718522C2semidirect
9. #11718518C2semidirect
10. #11718498C2semidirect
11. #11718490C2semidirect
14. #11718427C2semidirect
15. #11718424C2semidirect
149. #478D13semidirect
271. C13#3080semidirect

Maximal subgroups

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

subgroupindex
D13×#1252
C4×#61292
C13×#4782
#117187242
#117186702
#117185422
#117185382
#117185222
#117185182
#117184982
#117184902
#117184322
#117184272
#117184242
#308013