Finite Group Databasebeta

← #13127590

Subgroups — #13127590

Order 1664.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719290C211yesmaximal, characteristic, complemented
2#11719244C211yesmaximal, characteristic, complemented
3C13×#440C211yesmaximal, characteristic, complemented
4#11718826C211yesmaximal, characteristic, complemented
5#11718826C211yesmaximal, characteristic, complemented
6#11718683C211yesmaximal, characteristic, complemented
7#11718676C211yesmaximal, characteristic
8#11718552C211yesmaximal, characteristic, complemented
9#11718551C211yesmaximal, characteristic, complemented
10#11718461C211yesmaximal, characteristic, complemented
11#11718456C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic, complemented
13#11718417C211yesmaximal, characteristic, complemented
14#11718374C211yesmaximal, characteristic, complemented
15#11718362C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19#88201C2211yescharacteristic
20#88201C2211yescharacteristic
21D4×Dic13C2211yescharacteristic
22D4×Dic13C2211yescharacteristic
23C2×#6104C2211yescharacteristic
24C2×#6104C2211yescharacteristic
25#88178—21no—
26C2×#6101—21no—
27#88148—21no—
28#88148—21no—
29#88147C2211yescharacteristic
30#88147C2211yescharacteristic
31#88144C2211yescharacteristic
32#88142C2211yescharacteristic
33#88132—21no—
34#88132—21no—
35#88129—21no—
36#88128C2211yescharacteristic
37C4×D52—21no—
38#88124C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#97C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88055C2211yescharacteristic
51#88054C2211yescharacteristic
52#88054C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×Dic13—21no—
63C22×Dic13—21no—
64C2×D52—21no—
65C2×D52—21no—
66C2×D52C2311yescharacteristic
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×Dic26—21no—
71C2×Dic26D411yescharacteristic
72C13×SD16—22no—
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C42×C13—21no—
80C42×C13C2311yescharacteristic
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83#6104—22no—
84#6104—22no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13D411yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101D411yescharacteristic
100#6101D411yescharacteristic
101C4×Dic13C2311yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3370—131nomaximal, Sylow
106C23×C13—21no—
107C22×D13—21no—
108C22×D13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111D4×C13—21no—
112D4×C13#4112yes—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—81no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—42no—
123C2×Dic13—81no—
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128D52—21no—
129D52—21no—
130D52—21no—
131D52—21no—
132D52—42no—
133D52—81no—
134C4×D13—81no—
135C4×D13—81no—
136Dic26—41no—
137Dic26—81no—
138C8×C13—21no—
139C8×C13—21no—
140#1055—21no—
141#1055—21no—
142#559—131no—
143#554—131no—
144#490—131no—
145#489—131no—
146#488—131no—
147#479—131no—
148#478—131no—
149#474—131no—
150#463—131no—
151#463—131no—
152#459—131no—
153#446—131no—
154#442—131no—
155#440D1311yescharacteristic, complemented
156C4×D8—131no—
157C22×C13—22no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13C22×D411yescharacteristic
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13C2×#4111yescharacteristic
173C4×C132−1+411yescharacteristic
174Dic13—21no—
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13—41no—
180C2×SD16C2×D1311yescharacteristic
181C2×D8—131no—
182C2×D8—131no—
183C4⋊Q8—131no—
184#127—131no—
185#125—131no—
186#125—131no—
187#124—131no—
188#124—131no—
189#124—261no—
190#123—261no—
191#123—261no—
192C22⋊Q8—261no—
193C22⋊Q8—261no—
194C22⋊Q8—261no—
195C4×Q8—131no—
196C4×Q8C2×D1311yescharacteristic
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—131no—
201C4×D4—261no—
202C4×D4C2×D1311yescharacteristic
203C2×C4⋊C4—261no—
204#107—131no—
205#107C2×D1311yescharacteristic
206#106—131no—
207C4⋊C8—131no—
208C4⋊C8—131no—
209C4⋊C8—131no—
210#103—131no—
211#103—131no—
212#103C2×D1311yescharacteristic
213#102—131no—
214#102—131no—
215#102—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219#102C2×D1311yescharacteristic
220#97—131no—
221#97C2×D1311yescharacteristic
222C4×C8—131no—
223C2×C13—42no—
224C2×C13#54811yescharacteristic
225C2×C13#57511yescharacteristic
226C2×C13#57611yescharacteristic
227D13—81no—
228D13—81no—
229C2×Q8—131no—
230C2×Q8—261no—
231C2×Q8C22×D1311yescharacteristic
232C2×D4—131no—
233C2×D4—131no—
234C2×D4—261no—
235C2×D4—261no—
236C2×D4C22×D1311yescharacteristic
237C22×C4—21no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242SD16—22no—
243D8—262no—
244D8—262no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8C22×D1311yescharacteristic
248C2×C8C22×D1311yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C42—21no—
272C42—131no—
273C42—131no—
274C42C22×D1311yescharacteristic
275C13#337011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—261no—
278C23—261no—
279Q8—21no—
280Q8—21no—
281Q8—521no—
282Q8—1041no—
283D4—21no—
284D4—261no—
285D4—261no—
286D4—261no—
287D4—261no—
288D4—522no—
289D4—1041no—
290D4#612712yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—522no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4—1041no—
305C2×C4D4×D1311yescharacteristic
306C2×C4D4×D1311yescharacteristic
307C2×C4C23×D1311yescharacteristic
308C8—21no—
309C8—21no—
310C8—261no—
311C8—261no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—521no—
316C22—521no—
317C22—521no—
318C22—521no—
319C22—521no—
320C22—521no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—261no—
328C4—261no—
329C4—261no—
330C4—261no—
331C4—521no—
332C4—521no—
333C4C2×#612711yescharacteristic
334C4#8825711yescharacteristic
335C2—42no—
336C2—1041no—
337C2—1041no—
338C2#1171925711yescharacteristic
339C2#1171947911yescharacteristic
340C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#440C2
socleC22×C13C22×D4
prime radical#11718676C2
hypercenter#440D13
hypocenterC13#3370
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #11719290C2semidirect
2. #11719244C2semidirect
3. C13×#440C2semidirect
4. #11718826C2semidirect
5. #11718826C2semidirect
6. #11718683C2semidirect
8. #11718552C2semidirect
9. #11718551C2semidirect
10. #11718461C2semidirect
11. #11718456C2semidirect
12. #11718446C2semidirect
13. #11718417C2semidirect
14. #11718374C2semidirect
15. #11718362C2semidirect
155. #440D13semidirect
275. C13#3370semidirect

Maximal subgroups

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

subgroupindex
#117192902
#117192442
C13×#4402
#117188262
#117186832
#117186762
#117185522
#117185512
#117184612
#117184562
#117184462
#117184172
#117183742
#117183622
#337013