Finite Group Databasebeta

← #13127219

Subgroups — #13127219

Order 1664.

354 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#11719323C211yesmaximal, characteristic
2#11719218C211yesmaximal, characteristic, complemented
3C13×#480C211yesmaximal, characteristic, complemented
4#11718702C211yesmaximal, characteristic, complemented
5C2×#88048C211yesmaximal, characteristic, complemented
6#11718549C211yesmaximal, characteristic, complemented
7#11718541C211yesmaximal, characteristic, complemented
8#11718539C211yesmaximal, characteristic, complemented
9#11718538C211yesmaximal, characteristic, complemented
10#11718445C211yesmaximal, characteristic, complemented
11#11718439C211yesmaximal, characteristic, complemented
12#11718427C211yesmaximal, characteristic, complemented
13#11718419C211yesmaximal, characteristic, complemented
14#11718386C211yesmaximal, characteristic, complemented
15#11718383C211yesmaximal, characteristic, complemented
16C13×#121C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18#88193—21no—
19#88192C2211yescharacteristic
20D4×Dic13—21no—
21D4×Dic13C2211yescharacteristic
22C2×#6105C2211yescharacteristic
23#88183—21no—
24C4×C22⋊D13C2211yescharacteristic
25#88180—21no—
26C2×C4⋊Dic13C2211yescharacteristic
27#88178C2211yescharacteristic
28C22×#1055C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88152—21no—
31#88151C2211yescharacteristic
32#88146C2211yescharacteristic
33#88146C2211yescharacteristic
34#88144C2211yescharacteristic
35#88144C2211yescharacteristic
36#88143—21no—
37#88141C2211yescharacteristic
38#88140—21no—
39#88133—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88072C2211yescharacteristic
46#88060C2211yescharacteristic
47#88058C2211yescharacteristic
48#88058C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88048C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13D411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×C4×D13C2311yescharacteristic
68C2×Dic26C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C22⋊C4—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79C22⋊Dic13D411yescharacteristic
80#6105—22no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103D411yescharacteristic
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
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×#1055—22no—
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C8×D13—22no—
105#3337—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13C2×D411yescharacteristic
108C22×D13C2×D411yescharacteristic
109D4×C13—21no—
110D4×C13—21no—
111D4×C13—42no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—42no—
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—22no—
121C22⋊D13—81no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—81no—
127C2×Dic13—81no—
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C4×D13—21no—
132C4×D13—21no—
133Dic26—21no—
134Dic26—21no—
135C8×C13—21no—
136C8×C13—21no—
137#1055—21no—
138#1055#4112yes—
139#553—131no—
140#552—131no—
141#499—131no—
142#485—131no—
143#484—131no—
144#482—131no—
145#480D1311yescharacteristic, complemented
146#479—131no—
147#478—131no—
148#465—131no—
149#465—131no—
150C4×SD16—131no—
151C8×D4—131no—
152#427—131no—
153C2×#106—131no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13#13512yes—
160C22×C13C22×D411yescharacteristic
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—21no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13C2×#4111yescharacteristic
169C4×C132−1+411yescharacteristic
170Dic13—21no—
171Dic13—21no—
172Dic13—21no—
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×SD16—131no—
178C22×C8—131no—
179C22×C8—131no—
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—261no—
191#121C2×D1311yescharacteristic
192C4×Q8—131no—
193C4×D4—131no—
194C4×D4—131no—
195C4×D4—261no—
196#117—131no—
197#117—131no—
198#117—261no—
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#106—131no—
209#106—131no—
210C4⋊C8—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#102—131no—
215#102C2×D1311yescharacteristic
216#102C2×D1311yescharacteristic
217C22⋊C8—131no—
218C22⋊C8C2×D1311yescharacteristic
219C4×C8—131no—
220C2×C13—22no—
221C2×C13—81no—
222C2×C13#54711yescharacteristic
223C2×C13C2×#13511yescharacteristic
224C2×C13#57711yescharacteristic
225D13—41no—
226C2×Q8—131no—
227C2×D4—21no—
228C2×D4—131no—
229C2×D4—261no—
230C2×D4C22×D1311yescharacteristic
231C22×C4—21no—
232C22×C4—131no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4C22×D1311yescharacteristic
236SD16—262no—
237C2×C8—131no—
238C2×C8—131no—
239C2×C8—262no—
240C2×C8—262no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—131no—
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⋊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—131no—
269C42—261no—
270C42—261no—
271C42—261no—
272C13#333711yescharacteristic, complemented, Sylow
273C23—21no—
274C23—131no—
275C23D4×D1311yescharacteristic
276Q8—261no—
277Q8—261no—
278D4—21no—
279D4—21no—
280D4—42no—
281D4—262no—
282D4—1041no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—131no—
290C2×C4—131no—
291C2×C4—131no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4D4×D1311yescharacteristic
301C2×C4C23×D1311yescharacteristic
302C8—21no—
303C8—21no—
304C8—132no—
305C8—261no—
306C22—21no—
307C22—21no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—261no—
312C22—261no—
313C22—261no—
314C22#8816612yes—
315C22C2×D4×D1311yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—261no—
321C4—261no—
322C4—261no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4—521no—
327C4#41×D1311yescharacteristic
328C4#8825711yescharacteristic
329C2—22no—
330C2—81no—
331C2—521no—
332C2#1171936011yescharacteristic
333C2C2×#8816611yescharacteristic
334C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#480C2
socleC22×C13C22×D4
prime radical#11719323C2
hypercenter#480D13
hypocenterC13#3337
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #11719218C2semidirect
3. C13×#480C2semidirect
4. #11718702C2semidirect
5. C2×#88048C2semidirect
6. #11718549C2semidirect
7. #11718541C2semidirect
8. #11718539C2semidirect
9. #11718538C2semidirect
10. #11718445C2semidirect
11. #11718439C2semidirect
12. #11718427C2semidirect
13. #11718419C2semidirect
14. #11718386C2semidirect
15. #11718383C2semidirect
145. #480D13semidirect
272. C13#3337semidirect

Maximal subgroups

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

subgroupindex
#117193232
#117192182
C13×#4802
#117187022
C2×#880482
#117185492
#117185412
#117185392
#117185382
#117184452
#117184392
#117184272
#117184192
#117183862
#117183832
#333713