Finite Group Databasebeta

← #13127352

Subgroups — #13127352

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#11719237C211yesmaximal, characteristic
2#11719218C211yesmaximal, characteristic, complemented
3C13×#428C211yesmaximal, characteristic, complemented
4#11718795C211yesmaximal, characteristic, complemented
5#11718788C211yesmaximal, characteristic, complemented
6#11718657C211yesmaximal, characteristic, complemented
7#11718629C211yesmaximal, characteristic, complemented
8#11718552C211yesmaximal, characteristic, complemented
9#11718550C211yesmaximal, characteristic, complemented
10#11718549C211yesmaximal, characteristic, complemented
11#11718541C211yesmaximal, characteristic, complemented
12#11718527C211yesmaximal, characteristic, complemented
13#11718525C211yesmaximal, characteristic, complemented
14#11718517C211yesmaximal, characteristic, complemented
15#11718515C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C13×#117C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19#88184C2211yescharacteristic
20#88183—21no—
21C4×C22⋊D13C2211yescharacteristic
22#88180—21no—
23#88178C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25C2×C8×D13C2211yescharacteristic
26#88152—21no—
27#88151C2211yescharacteristic
28#88149C2211yescharacteristic
29#88147C2211yescharacteristic
30#88146C2211yescharacteristic
31#88146C2211yescharacteristic
32#88144C2211yescharacteristic
33#88143—21no—
34#88142C2211yescharacteristic
35#88141C2211yescharacteristic
36#88139—21no—
37#88138—21no—
38#88129—21no—
39#88126—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88061C2211yescharacteristic
46#88060C2211yescharacteristic
47#88058C2211yescharacteristic
48#88056C2211yescharacteristic
49#88055C2211yescharacteristic
50#88054C2211yescharacteristic
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×D13C2311yescharacteristic
67C2×Dic26—21no—
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#6103—21no—
87#6103D411yescharacteristic
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101D411yescharacteristic
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#6095—22no—
104C8×D13—22no—
105#3348—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—42no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2411yescharacteristic
118C22⋊D13—41no—
119C22⋊D13—81no—
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—
132Dic26—21no—
133Dic26—21no—
134Dic26—81no—
135C8×C13—21no—
136C8×C13#4112yes—
137#1055—21no—
138#1055—21no—
139#555—131no—
140#552—131no—
141#501—131no—
142#485—131no—
143#485—131no—
144#482—131no—
145#481—131no—
146#478—131no—
147#475—131no—
148#468—131no—
149#465—131no—
150#440—131no—
151#435—131no—
152#428D1311yescharacteristic, complemented
153#427—131no—
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×M16C2×D1311yescharacteristic
179C22×C8—131no—
180C4⋊Q8—131no—
181#126—261no—
182#125—131no—
183#125—261no—
184#124—261no—
185#124—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—
195#117—131no—
196#117—131no—
197#117—261no—
198#117—261no—
199#117C2×D1311yescharacteristic
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—
219#97—131no—
220C2×C13—41no—
221C2×C13#54711yescharacteristic
222C2×C13#57511yescharacteristic
223C2×C13#57711yescharacteristic
224D13—41no—
225D13—81no—
226C2×Q8—131no—
227C2×Q8—261no—
228C2×D4—131no—
229C2×D4—131no—
230C2×D4—261no—
231C2×D4—261no—
232C22×C4—21no—
233C22×C4—131no—
234C22×C4—261no—
235C22×C4C22×D1311yescharacteristic
236SD16—262no—
237M16—22no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—262no—
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⋊C4C22×D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—131no—
259C22⋊C4—131no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C42—21no—
268C42—131no—
269C42—261no—
270C42—261no—
271C42—261no—
272C13#334811yescharacteristic, complemented, Sylow
273C23—131no—
274C23—261no—
275C23D4×D1311yescharacteristic
276Q8—261no—
277Q8—261no—
278Q8—1041no—
279D4—261no—
280D4—261no—
281D4—521no—
282D4—1041no—
283D4—1041no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—522no—
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#1171947811yescharacteristic
334C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radical#11719237C2
hypercenter#428D13
hypocenterC13#3348
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
2. #11719218C2semidirect
3. C13×#428C2semidirect
4. #11718795C2semidirect
5. #11718788C2semidirect
6. #11718657C2semidirect
7. #11718629C2semidirect
8. #11718552C2semidirect
9. #11718550C2semidirect
10. #11718549C2semidirect
11. #11718541C2semidirect
12. #11718527C2semidirect
13. #11718525C2semidirect
14. #11718517C2semidirect
15. #11718515C2semidirect
152. #428D13semidirect
272. C13#3348semidirect

Maximal subgroups

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

subgroupindex
#117192372
#117192182
C13×#4282
#117187952
#117187882
#117186572
#117186292
#117185522
#117185502
#117185492
#117185412
#117185272
#117185252
#117185172
#117185152
#334813