Finite Group Databasebeta

← #13119692

Subgroups — #13119692

Order 1664.

406 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#376C211yesmaximal, characteristic, complemented
2#11718601C211yesmaximal, characteristic
3#11718601C211yesmaximal, characteristic
4#11718601C211yesmaximal, characteristic
5#11718594C211yesmaximal, characteristic, complemented
6C4×#6101C211yesmaximal, characteristic, complemented
7#11718590C211yesmaximal, characteristic, complemented
8#11718336C211yesmaximal, characteristic
9#11718334C211yesmaximal, characteristic
10#11718331C211yesmaximal, characteristic
11#11718330C211yesmaximal, characteristic
12#11718319C211yesmaximal, characteristic, complemented
13#11718318C211yesmaximal, characteristic, complemented
14#11718312C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×Dic26C2211yescharacteristic
17C2×C42×C13C2211yescharacteristic
18C2×C42×C13C2211yescharacteristic
19C2×C42×C13C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×C4×Dic13C2211yescharacteristic
34C2×C4×Dic13C2211yescharacteristic
35C13×#95C2211yescharacteristic
36C13×#95C2211yescharacteristic
37C13×#95C2211yescharacteristic
38C13×#95C2211yescharacteristic
39#88071C2211yescharacteristic
40#88071C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C23×D13C2311yescharacteristic
52C22×C4×C13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C2×Dic26—22no—
67C2×Dic26—22no—
68C2×Dic26—41no—
69C42×C13—22no—
70C42×C13—22no—
71C42×C13—22no—
72#6103—22no—
73#6103—22no—
74#6103—22no—
75#6103—22no—
76#6103—22no—
77#6103—41no—
78#6103—41no—
79C4⋊Dic13—41no—
80#6101—22no—
81#6101—22no—
82#6101—22no—
83#6101—41no—
84#6101—41no—
85C4×Dic13—22no—
86C4×Dic13—22no—
87#2532—131nomaximal, Sylow
88C23×C13C2411yescharacteristic
89C22×D13—21no—
90C22×D13—21no—
91C22×D13—21no—
92C22×D13—21no—
93C22×D13—21no—
94C22×D13—21no—
95C22×D13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13#4112yes—
115C2×C4×C13#4112yes—
116C2×C4×C13#4112yes—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13#4112yes—
137C2×Dic13#4112yes—
138Dic26—44no—
139#400—131no—
140#398—131no—
141#397—131no—
142#393—131no—
143#391—131no—
144#391—131no—
145#388—131no—
146#388—131no—
147#388—131no—
148#388—131no—
149#388—131no—
150#387—131no—
151#383—131no—
152C4×C4⋊C4—131no—
153#376D1311yescharacteristic, complemented
154C22×C13C2×#4111yescharacteristic
155C22×C13C2×#4111yescharacteristic
156C22×C13C2×#4111yescharacteristic
157C22×C13C2×#4111yescharacteristic
158C22×C13C2×#4111yescharacteristic
159C22×C13H(5,𝔽2)11yescharacteristic
160C22×C132−1+411yescharacteristic
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—41no—
168C4×C13—22no—
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175Dic13—22no—
176Dic13—22no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C22×Q8—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C22⋊C4—131no—
190C2×C22⋊C4—131no—
191C2×C22⋊C4—131no—
192C2×C22⋊C4—131no—
193C2×C22⋊C4—131no—
194C2×C22⋊C4—131no—
195C2×C22⋊C4—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42C2×D1311yescharacteristic
199C2×C42C2×D1311yescharacteristic
200C2×C42C2×D1311yescharacteristic
201#95—131no—
202#95—131no—
203#95—131no—
204#95—131no—
205#95—131no—
206#95—131no—
207#95—131no—
208#95—131no—
209#95—131no—
210#95—131no—
211#95—131no—
212#95—131no—
213#95C2×D1311yescharacteristic
214#95C2×D1311yescharacteristic
215#95C2×D1311yescharacteristic
216#95C2×D1311yescharacteristic
217C2×C13#52911yescharacteristic
218C2×C13#52911yescharacteristic
219C2×C13#54211yescharacteristic
220C2×C13#55111yescharacteristic
221C2×C13#55211yescharacteristic
222C2×C13#55511yescharacteristic
223C2×C13#55611yescharacteristic
224D13—81no—
225C24—131no—
226C2×Q8—262no—
227C2×Q8—262no—
228C2×Q8—521no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4C22×D1311yescharacteristic
237C22×C4C22×D1311yescharacteristic
238C22×C4C22×D1311yescharacteristic
239C22×C4C22×D1311yescharacteristic
240C22×C4C22×D1311yescharacteristic
241C22×C4C22×D1311yescharacteristic
242C22×C4C22×D1311yescharacteristic
243C4⋊C4—262no—
244C4⋊C4—262no—
245C4⋊C4—262no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C4⋊C4—521no—
249C22⋊C4—262no—
250C22⋊C4—262no—
251C22⋊C4—262no—
252C22⋊C4—262no—
253C22⋊C4—262no—
254C22⋊C4—521no—
255C22⋊C4—521no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—262no—
260C42—262no—
261C13#253211yescharacteristic, complemented, Sylow
262C23—261no—
263C23—261no—
264C23—261no—
265C23—261no—
266C23—261no—
267C23—261no—
268C23—261no—
269C23C23×D1311yescharacteristic
270Q8—524no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—132no—
290C2×C4—132no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4#612712yes—
311C2×C4#612712yes—
312C2×C4#612712yes—
313C22—521no—
314C22—521no—
315C22—521no—
316C22—521no—
317C22—521no—
318C22—521no—
319C22—521no—
320C22C2×#612711yescharacteristic
321C22C2×#612711yescharacteristic
322C22C2×#612711yescharacteristic
323C22#41×D1311yescharacteristic
324C22#41×D1311yescharacteristic
325C22#8825611yescharacteristic
326C22#8825711yescharacteristic
327C4—22no—
328C4—22no—
329C4—22no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—262no—
335C4—262no—
336C4—521no—
337C4—521no—
338C4—521no—
339C4—521no—
340C4—521no—
341C2—1041no—
342C2#1171918411yescharacteristic
343C2#1171923211yescharacteristic
344C2#1171923311yescharacteristic
345C2#1171923611yescharacteristic
346C2#1171923711yescharacteristic
347C2#1171923811yescharacteristic
348C2#1171923911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#376C2
prime radicalC23×D13C23
hypercenter#376D13
hypocenterC13#2532
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
1. C13×#376C2semidirect
5. #11718594C2semidirect
6. C4×#6101C2semidirect
7. #11718590C2semidirect
12. #11718319C2semidirect
13. #11718318C2semidirect
14. #11718312C2semidirect
15. #11718307C2semidirect
153. #376D13semidirect
261. C13#2532semidirect

Maximal subgroups

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

subgroupindex
C13×#3762
#117186012
#117185942
C4×#61012
#117185902
#117183362
#117183342
#117183312
#117183302
#117183192
#117183182
#117183122
#117183072
#253213