Finite Group Databasebeta

← #13127390

Subgroups — #13127390

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
1C13×#553C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic, complemented
3#11718725C211yesmaximal, characteristic, complemented
4#11718724C211yesmaximal, characteristic, complemented
5#11718703C211yesmaximal, characteristic, complemented
6#11718703C211yesmaximal, characteristic, complemented
7#11718696C211yesmaximal, characteristic, complemented
8#11718695C211yesmaximal, characteristic, complemented
9C4×#6105C211yesmaximal, characteristic, complemented
10#11718673C211yesmaximal, characteristic, complemented
11#11718670C211yesmaximal, characteristic, complemented
12#11718657C211yesmaximal, characteristic, complemented
13#11718656C211yesmaximal, characteristic, complemented
14#11718632C211yesmaximal, characteristic, complemented
15#11718625C211yesmaximal, characteristic, complemented
16C13×#126—21no—
17C13×#125C2211yescharacteristic
18C13×#123—21no—
19C13×#121—21no—
20C13×#121C2211yescharacteristic
21C13×#121C2211yescharacteristic
22C4×D4×C13—21no—
23C4×D4×C13C2211yescharacteristic
24C4×D4×C13C2211yescharacteristic
25C13×#117C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27#88189—21no—
28C2×#6105C2211yescharacteristic
29#88180C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31#88178C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C2×#6099C2211yescharacteristic
35#88143—21no—
36#88133—21no—
37#88131—21no—
38#88124C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40#88072C2211yescharacteristic
41#88072C2211yescharacteristic
42#88072C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88050C2211yescharacteristic
46#88050C2211yescharacteristic
47#88050C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13D411yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×Dic13—21no—
68C2×Dic26C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4D411yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4D411yescharacteristic
81C13×C22⋊C4D411yescharacteristic
82C42×C13—21no—
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87#6105—22no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99#6099—22no—
100#6099—22no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3351—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13C2×D411yescharacteristic
108C23×C13C2×D411yescharacteristic
109D4×C13—21no—
110D4×C13—21no—
111D4×C13—41no—
112D4×C13—42no—
113D4×C13—81no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—81no—
122C2×C4×C13—81no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—42no—
133Dic26—21no—
134Dic26—21no—
135#1055—21no—
136#1055—21no—
137#1055—21no—
138#1055#4112yes—
139#553D1311yescharacteristic
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#428—131no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#4111yescharacteristic
172C4×C132−1+411yescharacteristic
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×SD16—131no—
178C2×M16—131no—
179C2×M16—131no—
180#126—21no—
181#126—261no—
182#125—131no—
183#125—261no—
184#125C2×D1311yescharacteristic
185#123—21no—
186#123—261no—
187C22⋊Q8—131no—
188C22⋊Q8—131no—
189#121—21no—
190#121C2×D1311yescharacteristic
191#121C2×D1311yescharacteristic
192C4×Q8—131no—
193C4×D4—21no—
194C4×D4C2×D1311yescharacteristic
195C4×D4C2×D1311yescharacteristic
196#117—131no—
197#117—261no—
198#117C2×D1311yescharacteristic
199C2×C4⋊C4—131no—
200C2×C4⋊C4C2×D1311yescharacteristic
201#107—131no—
202#107—131no—
203#107—131no—
204#107—131no—
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#102—131no—
216#102—131no—
217C22⋊C8—131no—
218C22⋊C8—131no—
219C4×C8—131no—
220C2×C13—41no—
221C2×C13—41no—
222C2×C13—81no—
223C2×C13#54711yescharacteristic
224C2×C13#57511yescharacteristic
225C2×C13#57711yescharacteristic
226C2×Q8—131no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4C22⋊D1311yescharacteristic
230C2×D4C22×D1311yescharacteristic
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—261no—
234C22×C4C22×D1311yescharacteristic
235C22×C4C22×D1311yescharacteristic
236SD16—262no—
237M16—262no—
238M16—262no—
239C2×C8—131no—
240C2×C8—131no—
241C2×C8—131no—
242C2×C8—131no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—131no—
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—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4C22⋊D1311yescharacteristic
267C22⋊C4C22⋊D1311yescharacteristic
268C42—21no—
269C42—261no—
270C42—261no—
271C42C22×D1311yescharacteristic
272C13#335111yescharacteristic, complemented, Sylow
273C23—21no—
274C23C2×C22⋊D1311yescharacteristic
275C23C2×C22⋊D1311yescharacteristic
276Q8—261no—
277Q8—261no—
278D4—21no—
279D4—21no—
280D4—41no—
281D4—42no—
282D4—81no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—522no—
297C2×C4C2×C22⋊D1311yescharacteristic
298C2×C4C2×C22⋊D1311yescharacteristic
299C2×C4C2×C22⋊D1311yescharacteristic
300C2×C4C2×C22⋊D1311yescharacteristic
301C2×C4C23×D1311yescharacteristic
302C8—132no—
303C8—261no—
304C8—261no—
305C8—261no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C22×C22⋊D1311yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4—521no—
327C4#41×D1311yescharacteristic
328C4#8825711yescharacteristic
329C2—41no—
330C2—41no—
331C2—81no—
332C2#1171952711yescharacteristic
333C2#1171952911yescharacteristic
334C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#553C2
socleC22×C13C22×D4
hypercenter#553D13
hypocenterC13#3351
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
2. #11719246C2semidirect
3. #11718725C2semidirect
4. #11718724C2semidirect
5. #11718703C2semidirect
6. #11718703C2semidirect
7. #11718696C2semidirect
8. #11718695C2semidirect
9. C4×#6105C2semidirect
10. #11718673C2semidirect
11. #11718670C2semidirect
12. #11718657C2semidirect
13. #11718656C2semidirect
14. #11718632C2semidirect
15. #11718625C2semidirect
272. C13#3351semidirect

Maximal subgroups

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

subgroupindex
C13×#5532
#117192462
#117187252
#117187242
#117187032
#117186962
#117186952
C4×#61052
#117186732
#117186702
#117186572
#117186562
#117186322
#117186252
#335113