Finite Group Databasebeta

← #13127236

Subgroups — #13127236

Order 1664.

366 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719323C211yesmaximal, characteristic, complemented
2#11719219C211yesmaximal, characteristic, complemented
3C13×#481C211yesmaximal, characteristic, complemented
4#11718699C211yesmaximal, characteristic, complemented
5C2×#88047C211yesmaximal, characteristic, complemented
6#11718532C211yesmaximal, characteristic, complemented
7#11718527C211yesmaximal, characteristic, complemented
8#11718521C211yesmaximal, characteristic, complemented
9#11718519C211yesmaximal, characteristic, complemented
10#11718440C211yesmaximal, characteristic, complemented
11#11718436C211yesmaximal, characteristic, complemented
12#11718424C211yesmaximal, characteristic, complemented
13#11718417C211yesmaximal, characteristic, complemented
14#11718396C211yesmaximal, characteristic, complemented
15#11718386C211yesmaximal, characteristic, complemented
16C13×#121C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18#88193—21no—
19#88192C2211yescharacteristic
20D4×Dic13—21no—
21D4×Dic13C2211yescharacteristic
22C2×#6104C2211yescharacteristic
23#88184—21no—
24#88184C2211yescharacteristic
25C4×C22⋊D13—21no—
26C4×C22⋊D13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C22×#1055C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88152—21no—
31#88149C2211yescharacteristic
32#88148—21no—
33#88147C2211yescharacteristic
34#88146C2211yescharacteristic
35#88146C2211yescharacteristic
36#88144C2211yescharacteristic
37#88144C2211yescharacteristic
38#88140—21no—
39#88133—21no—
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88072C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88060C2211yescharacteristic
49#88057C2211yescharacteristic
50#88057C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88049C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13D411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68C2×D52—21no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13D411yescharacteristic
82#6104—22no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103D411yescharacteristic
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C2×#1055—22no—
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C8×D13—22no—
105#3339—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13C2×D411yescharacteristic
108C22×D13—21no—
109C22×D13C2×D411yescharacteristic
110D4×C13—21no—
111D4×C13—21no—
112D4×C13—42no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—81no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—22no—
122C22⋊D13—42no—
123C22⋊D13—81no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—81no—
128C2×Dic13—81no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132D52—21no—
133D52—21no—
134D52—81no—
135C4×D13—21no—
136C4×D13—21no—
137C4×D13—81no—
138C8×C13—21no—
139C8×C13—21no—
140#1055—21no—
141#1055#4112yes—
142#553—131no—
143#553—131no—
144#499—131no—
145#482—131no—
146#482—131no—
147#481—131no—
148#481D1311yescharacteristic, complemented
149#478—131no—
150#478—131no—
151#466—131no—
152#466—131no—
153C4×D8—131no—
154C8×D4—131no—
155#427—131no—
156C2×#107—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13#13512yes—
163C22×C13C22×D411yescharacteristic
164C2×D13—21no—
165C2×D13—21no—
166C2×D13—21no—
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13C2×#4111yescharacteristic
175C4×C132−1+411yescharacteristic
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×D8—131no—
183C22×C8—131no—
184C22×C8—131no—
185#126—261no—
186#126—261no—
187#125—131no—
188#125—131no—
189#123—261no—
190#123—261no—
191#121—131no—
192#121—131no—
193#121—131no—
194#121—261no—
195#121—261no—
196#121C2×D1311yescharacteristic
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—261no—
201C4×D4—261no—
202#117—131no—
203#117—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4C2×D1311yescharacteristic
206#107—131no—
207#107—131no—
208#107—131no—
209#107—131no—
210#107—131no—
211#106—131no—
212#106—131no—
213#106C2×D1311yescharacteristic
214#106C2×D1311yescharacteristic
215C4⋊C8—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#102C2×D1311yescharacteristic
221#102C2×D1311yescharacteristic
222C22⋊C8—131no—
223C22⋊C8C2×D1311yescharacteristic
224C4×C8—131no—
225C2×C13—22no—
226C2×C13—81no—
227C2×C13#54711yescharacteristic
228C2×C13C2×#13511yescharacteristic
229C2×C13#57611yescharacteristic
230D13—41no—
231D13—81no—
232C2×D4—21no—
233C2×D4—131no—
234C2×D4—131no—
235C2×D4—261no—
236C2×D4—261no—
237C2×D4—261no—
238C2×D4C22×D1311yescharacteristic
239C22×C4—21no—
240C22×C4—131no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4C22×D1311yescharacteristic
245D8—262no—
246C2×C8—131no—
247C2×C8—131no—
248C2×C8—262no—
249C2×C8—262no—
250C2×C8C22×D1311yescharacteristic
251C2×C8C22×D1311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4C22×D1311yescharacteristic
263C4⋊C4C22×D1311yescharacteristic
264C4⋊C4C22×D1311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—131no—
267C22⋊C4—131no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C42—131no—
276C42—261no—
277C42—261no—
278C13#333911yescharacteristic, complemented, Sylow
279C23—21no—
280C23—131no—
281C23—261no—
282C23D4×D1311yescharacteristic
283D4—21no—
284D4—21no—
285D4—42no—
286D4—262no—
287D4—261no—
288D4—261no—
289D4—522no—
290D4—1041no—
291D4—1041no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—131no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—1041no—
307C2×C4—1041no—
308C2×C4—1041no—
309C2×C4D4×D1311yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—21no—
312C8—21no—
313C8—132no—
314C8—261no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—261no—
321C22—261no—
322C22—261no—
323C22—521no—
324C22—521no—
325C22—521no—
326C22#8817012yes—
327C22C2×D4×D1311yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—261no—
333C4—261no—
334C4—261no—
335C4—521no—
336C4—521no—
337C4—521no—
338C4#41×D1311yescharacteristic
339C4#8825711yescharacteristic
340C2—22no—
341C2—81no—
342C2—521no—
343C2—1041no—
344C2#1171936011yescharacteristic
345C2C2×#8817011yescharacteristic
346C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#481C2
socleC22×C13C22×D4
hypercenter#481D13
hypocenterC13#3339
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #11719323C2semidirect
2. #11719219C2semidirect
3. C13×#481C2semidirect
4. #11718699C2semidirect
5. C2×#88047C2semidirect
6. #11718532C2semidirect
7. #11718527C2semidirect
8. #11718521C2semidirect
9. #11718519C2semidirect
10. #11718440C2semidirect
11. #11718436C2semidirect
12. #11718424C2semidirect
13. #11718417C2semidirect
14. #11718396C2semidirect
15. #11718386C2semidirect
148. #481D13semidirect
278. C13#3339semidirect

Maximal subgroups

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

subgroupindex
#117193232
#117192192
C13×#4812
#117186992
C2×#880472
#117185322
#117185272
#117185212
#117185192
#117184402
#117184362
#117184242
#117184172
#117183962
#117183862
#333913