Finite Group Databasebeta

← #13127338

Subgroups — #13127338

Order 1664.

360 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#11719270C211yesmaximal, characteristic, complemented
2#11719268C211yesmaximal, characteristic, complemented
3C13×#435C211yesmaximal, characteristic, complemented
4#11718796C211yesmaximal, characteristic, complemented
5#11718782C211yesmaximal, characteristic, complemented
6#11718776C211yesmaximal, characteristic, complemented
7#11718767C211yesmaximal, characteristic, complemented
8#11718508C211yesmaximal, characteristic, complemented
9#11718507C211yesmaximal, characteristic, complemented
10#11718398C211yesmaximal, characteristic, complemented
11#11718398C211yesmaximal, characteristic, complemented
12#11718398C211yesmaximal, characteristic, complemented
13#11718397C211yesmaximal, characteristic, complemented
14#11718372C211yesmaximal, characteristic, complemented
15#11718363C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C22×C8×C13C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19#88193—21no—
20#88192—21no—
21#88184C2211yescharacteristic
22#88184C2211yescharacteristic
23#88184C2211yescharacteristic
24#88184C2211yescharacteristic
25#88180C2211yescharacteristic
26#88180C2211yescharacteristic
27#88180C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×D104C2211yescharacteristic
30#88152—21no—
31#88146—21no—
32#88139—21no—
33#88139—21no—
34#88137—21no—
35#88135—21no—
36C4×D52C2211yescharacteristic
37C4×D52C2211yescharacteristic
38#88124C2211yescharacteristic
39#88123C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42C13×C22⋊C8C2211yescharacteristic
43C13×#97C2211yescharacteristic
44#88061C2211yescharacteristic
45#88061C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88058C2211yescharacteristic
51#88058C2211yescharacteristic
52#88058C2211yescharacteristic
53#88058C2211yescharacteristic
54#88058C2211yescharacteristic
55#88057C2211yescharacteristic
56#88057C2211yescharacteristic
57#88057C2211yescharacteristic
58#88057C2211yescharacteristic
59C2×D4×C13D411yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67C2×D52C2311yescharacteristic
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×Dic26—21no—
72C13×M16—22no—
73C2×C8×C13—22no—
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4D411yescharacteristic
79C13×C22⋊C4D411yescharacteristic
80C13×C22⋊C4D411yescharacteristic
81C42×C13C2311yescharacteristic
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104D104—22no—
105#3347—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C23×C13C2×D411yescharacteristic
108C22×D13—21no—
109C22×D13—21no—
110D4×C13—41no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—42no—
121C22⋊D13—81no—
122C22⋊D13—81no—
123C22⋊D13—81no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—81no—
131D52—21no—
132D52—21no—
133D52—21no—
134D52—21no—
135C4×D13—42no—
136C4×D13—81no—
137Dic26—81no—
138C8×C13—21no—
139C8×C13—21no—
140C8×C13—21no—
141C8×C13#4112yes—
142#555—131no—
143#553—131no—
144#501—131no—
145#482—131no—
146#482—131no—
147#482—131no—
148#480—131no—
149#478—131no—
150#474—131no—
151#469—131no—
152#466—131no—
153#442—131no—
154#435D1311yescharacteristic, complemented
155#428—131no—
156#427—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13C22×D411yescharacteristic
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13C2×#4111yescharacteristic
175C4×C132−1+411yescharacteristic
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×D8—131no—
183C2×M16C2×D1311yescharacteristic
184C22×C8C2×D1311yescharacteristic
185C4⋊Q8—131no—
186#126—261no—
187#125—131no—
188#124—261no—
189#124—261no—
190#123—261no—
191#121—131no—
192#121—131no—
193#121—131no—
194#121—131no—
195#121—261no—
196#121—261no—
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—261no—
200C4×D4C2×D1311yescharacteristic
201#117—131no—
202#117—131no—
203#117—131no—
204#117—261no—
205C2×C4⋊C4—131no—
206#107—131no—
207#107—131no—
208#107—131no—
209#107—131no—
210#107—131no—
211#106—131no—
212#106—131no—
213#106—131no—
214#106—131no—
215C4⋊C8C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222C22⋊C8C2×D1311yescharacteristic
223C22⋊C8C2×D1311yescharacteristic
224#97C2×D1311yescharacteristic
225C2×C13—41no—
226C2×C13—41no—
227C2×C13#54711yescharacteristic
228C2×C13#57511yescharacteristic
229C2×C13#57611yescharacteristic
230D13—81no—
231D13—81no—
232C2×Q8—261no—
233C2×D4—131no—
234C2×D4—131no—
235C2×D4—261no—
236C2×D4—261no—
237C2×D4—261no—
238C2×D4—261no—
239C2×D4D5211yescharacteristic
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4C22×D1311yescharacteristic
244C22×C4C22×D1311yescharacteristic
245D8—262no—
246M16—22no—
247C2×C8—22no—
248C2×C8C22×D1311yescharacteristic
249C2×C8C22×D1311yescharacteristic
250C2×C8C22×D1311yescharacteristic
251C2×C8C22×D1311yescharacteristic
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4D5211yescharacteristic
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4D5211yescharacteristic
273C22⋊C4D5211yescharacteristic
274C42—261no—
275C42—261no—
276C42—261no—
277C42C22×D1311yescharacteristic
278C13#334711yescharacteristic, complemented, Sylow
279C23—261no—
280C23—261no—
281C23C2×D5211yescharacteristic
282C23C2×D5211yescharacteristic
283Q8—1041no—
284D4—41no—
285D4—261no—
286D4—261no—
287D4—261no—
288D4—261no—
289D4—522no—
290D4—1041no—
291D4—1041no—
292D4—1041no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—522no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4C2×D5211yescharacteristic
307C2×C4C2×D5211yescharacteristic
308C2×C4C2×D5211yescharacteristic
309C2×C4C2×D5211yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—21no—
312C8—21no—
313C8—21no—
314C8#612912yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—521no—
322C22—521no—
323C22—521no—
324C22—521no—
325C22—521no—
326C22—521no—
327C22C22×D5211yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—521no—
333C4—521no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4—521no—
338C4C2×#612911yescharacteristic
339C4#8825711yescharacteristic
340C2—41no—
341C2—41no—
342C2—1041no—
343C2—1041no—
344C2#1171926011yescharacteristic
345C2#1171945311yescharacteristic
346C2#1171945711yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
hypercenter#435D13
hypocenterC13#3347
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #11719270C2semidirect
2. #11719268C2semidirect
3. C13×#435C2semidirect
4. #11718796C2semidirect
5. #11718782C2semidirect
6. #11718776C2semidirect
7. #11718767C2semidirect
8. #11718508C2semidirect
9. #11718507C2semidirect
10. #11718398C2semidirect
11. #11718398C2semidirect
12. #11718398C2semidirect
13. #11718397C2semidirect
14. #11718372C2semidirect
15. #11718363C2semidirect
154. #435D13semidirect
278. C13#3347semidirect

Maximal subgroups

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

subgroupindex
#117192702
#117192682
C13×#4352
#117187962
#117187822
#117187762
#117187672
#117185082
#117185072
#117183982
#117183972
#117183722
#117183632
#334713