Finite Group Databasebeta

← #13127397

Subgroups — #13127397

Order 1664.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719234C211yesmaximal, characteristic, complemented
2#11719219C211yesmaximal, characteristic
3C13×#428C211yesmaximal, characteristic, complemented
4#11718795C211yesmaximal, characteristic, complemented
5#11718789C211yesmaximal, characteristic, complemented
6#11718664C211yesmaximal, characteristic, complemented
7#11718632C211yesmaximal, characteristic, complemented
8#11718552C211yesmaximal, characteristic, complemented
9#11718549C211yesmaximal, characteristic, complemented
10#11718547C211yesmaximal, characteristic, complemented
11#11718539C211yesmaximal, characteristic, complemented
12#11718524C211yesmaximal, characteristic, complemented
13#11718522C211yesmaximal, characteristic, complemented
14#11718518C211yesmaximal, characteristic, complemented
15#11718513C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C13×#117C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19#88184—21no—
20#88184C2211yescharacteristic
21C4×C22⋊D13—21no—
22C4×C22⋊D13C2211yescharacteristic
23#88178C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25C2×#6094C2211yescharacteristic
26#88152—21no—
27#88151C2211yescharacteristic
28#88149C2211yescharacteristic
29#88148—21no—
30#88147C2211yescharacteristic
31#88146C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33#88144C2211yescharacteristic
34#88144C2211yescharacteristic
35#88141C2211yescharacteristic
36#88137—21no—
37#88133—21no—
38#88126—21no—
39#88124—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88061C2211yescharacteristic
46#88060C2211yescharacteristic
47#88058C2211yescharacteristic
48#88056C2211yescharacteristic
49#88054C2211yescharacteristic
50C8×Dic13C2211yescharacteristic
51#88050C2211yescharacteristic
52#88050C2211yescharacteristic
53#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13—21no—
62C2×C22⋊D13D411yescharacteristic
63C2×D52—21no—
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13C2311yescharacteristic
68C2×Dic26C2311yescharacteristic
69C13×M16—22no—
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C42×C13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13D411yescharacteristic
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103D411yescharacteristic
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#6095—22no—
104#6094—22no—
105#3351—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C22×D13—21no—
108C22×D13C2×D411yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—81no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2411yescharacteristic
118C22⋊D13—41no—
119C22⋊D13—42no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126D52—21no—
127D52—21no—
128D52—81no—
129C4×D13—21no—
130C4×D13—21no—
131C4×D13—42no—
132C4×D13—81no—
133Dic26—21no—
134Dic26—21no—
135C8×C13—21no—
136C8×C13#4112yes—
137#1055—21no—
138#1055—21no—
139#553—131no—
140#552—131no—
141#499—131no—
142#485—131no—
143#483—131no—
144#482—131no—
145#481—131no—
146#479—131no—
147#478—131no—
148#468—131no—
149#468—131no—
150C4×SD16—131no—
151#436—131no—
152#428—131no—
153#428D1311yescharacteristic, complemented
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13C22×D411yescharacteristic
158C2×D13—21no—
159C2×D13—21no—
160C2×D13—21no—
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—41no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13C2×#4111yescharacteristic
170C4×C132−1+411yescharacteristic
171Dic13—21no—
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×SD16—131no—
178C2×M16—131no—
179C2×M16C2×D1311yescharacteristic
180#126—261no—
181#126—261no—
182#125—131no—
183#125—131no—
184#125—261no—
185#123—261no—
186#123—261no—
187C22⋊Q8—131no—
188C22⋊Q8—131no—
189#121—131no—
190#121—131no—
191#121—261no—
192C4×Q8—131no—
193C4×D4—131no—
194C4×D4—131no—
195C4×D4—261no—
196#117—131no—
197#117—261no—
198#117C2×D1311yescharacteristic
199C2×C4⋊C4—131no—
200C2×C4⋊C4C2×D1311yescharacteristic
201#107—131no—
202#107—131no—
203#107C2×D1311yescharacteristic
204#107C2×D1311yescharacteristic
205#106—131no—
206#106—131no—
207#106—131no—
208#106C2×D1311yescharacteristic
209#106C2×D1311yescharacteristic
210C4⋊C8—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#102—131no—
215#102—131no—
216#102—131no—
217C22⋊C8—131no—
218C22⋊C8—131no—
219C4×C8—131no—
220C2×C13—41no—
221C2×C13#54711yescharacteristic
222C2×C13#57511yescharacteristic
223C2×C13#57711yescharacteristic
224D13—41no—
225D13—81no—
226C2×Q8—131no—
227C2×D4—131no—
228C2×D4—131no—
229C2×D4—261no—
230C2×D4—261no—
231C22×C4—21no—
232C22×C4—131no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4C22×D1311yescharacteristic
236SD16—262no—
237M16—22no—
238M16—262no—
239C2×C8—131no—
240C2×C8—131no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C4⋊C4C22×D1311yescharacteristic
258C4⋊C4C22×D1311yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—131no—
261C22⋊C4—131no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C42—21no—
269C42—131no—
270C42—261no—
271C42—261no—
272C13#335111yescharacteristic, complemented, Sylow
273C23—131no—
274C23—261no—
275C23D4×D1311yescharacteristic
276Q8—261no—
277Q8—261no—
278D4—261no—
279D4—261no—
280D4—521no—
281D4—522no—
282D4—1041no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—131no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—522no—
299C2×C4—1041no—
300C2×C4D4×D1311yescharacteristic
301C2×C4C23×D1311yescharacteristic
302C8—21no—
303C8—261no—
304C8—261no—
305C8#612712yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—261no—
310C22—261no—
311C22—261no—
312C22—521no—
313C22—521no—
314C22—521no—
315C22C2×D4×D1311yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—261no—
322C4—261no—
323C4—261no—
324C4—521no—
325C4—521no—
326C4—521no—
327C4C2×#612711yescharacteristic
328C4#8825411yescharacteristic
329C2—41no—
330C2—521no—
331C2—1041no—
332C2#1171921211yescharacteristic
333C2#1171948011yescharacteristic
334C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radical#11719219C2
hypercenter#428D13
hypocenterC13#3351
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #11719234C2semidirect
3. C13×#428C2semidirect
4. #11718795C2semidirect
5. #11718789C2semidirect
6. #11718664C2semidirect
7. #11718632C2semidirect
8. #11718552C2semidirect
9. #11718549C2semidirect
10. #11718547C2semidirect
11. #11718539C2semidirect
12. #11718524C2semidirect
13. #11718522C2semidirect
14. #11718518C2semidirect
15. #11718513C2semidirect
153. #428D13semidirect
272. C13#3351semidirect

Maximal subgroups

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

subgroupindex
#117192342
#117192192
C13×#4282
#117187952
#117187892
#117186642
#117186322
#117185522
#117185492
#117185472
#117185392
#117185242
#117185222
#117185182
#117185132
#335113