Finite Group Databasebeta

← #13126303

Subgroups — #13126303

Order 1664.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719387C211yesmaximal, characteristic, complemented
2#11719266C211yesmaximal, characteristic, complemented
3C13×#463C211yesmaximal, characteristic, complemented
4#11718832C211yesmaximal, characteristic, complemented
5#11718827C211yesmaximal, characteristic, complemented
6#11718820C211yesmaximal, characteristic
7#11718814C211yesmaximal, characteristic, complemented
8#11718715C211yesmaximal, characteristic, complemented
9#11718669C211yesmaximal, characteristic, complemented
10#11718512C211yesmaximal, characteristic, complemented
11#11718500C211yesmaximal, characteristic, complemented
12#11718477C211yesmaximal, characteristic, complemented
13#11718452C211yesmaximal, characteristic, complemented
14#11718439C211yesmaximal, characteristic, complemented
15#11718422C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×D8C2211yescharacteristic
18C13×#124C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88200C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23#88192C2211yescharacteristic
24#88192C2211yescharacteristic
25#88190C2211yescharacteristic
26D4×Dic13C2211yescharacteristic
27C2×#6105C2211yescharacteristic
28#88183—21no—
29#88178—21no—
30C2×#6094C2211yescharacteristic
31C2×C8×D13C2211yescharacteristic
32#88151C2211yescharacteristic
33#88142C2211yescharacteristic
34#88140—21no—
35#88139—21no—
36#88139—21no—
37#88133—21no—
38#88133—21no—
39#88132—21no—
40#88126C2211yescharacteristic
41#88123C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43C13×C4⋊C8C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88057C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66C2×C4×D13C2311yescharacteristic
67C2×Dic26—21no—
68C2×Dic26—21no—
69C2×Dic26C2311yescharacteristic
70C13×SD16—41no—
71C13×D8—41no—
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C22⋊C4—21no—
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C42×C13C2311yescharacteristic
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84#6107—41no—
85#6105—41no—
86#6103—21no—
87#6103—21no—
88#6103D411yescharacteristic
89#6103D411yescharacteristic
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101D411yescharacteristic
100#6101D411yescharacteristic
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—41no—
107C8×D13—41no—
108#3263—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13—21no—
111C22×D13C2×D411yescharacteristic
112Q8×C13—21no—
113Q8×C13—21no—
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—81no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2411yescharacteristic
124C22⋊D13—81no—
125C22⋊D13—81no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—81no—
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C4×D13—21no—
135C4×D13—21no—
136Dic26—21no—
137Dic26—21no—
138Dic26—81no—
139Dic26—81no—
140C8×C13—21no—
141C8×C13—21no—
142#1055—21no—
143#1055—21no—
144#542—131no—
145#542—131no—
146#476—131no—
147#476—131no—
148#475—131no—
149#475—131no—
150#470—131no—
151#469—131no—
152#465—131no—
153#465—131no—
154#464—131no—
155#464—131no—
156#463—131no—
157#463D1311yescharacteristic, complemented
158#424—131no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13C22×D411yescharacteristic
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13H(5,𝔽2)11yescharacteristic
174C4×C132−1+411yescharacteristic
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×Q16—131no—
183C2×SD16—131no—
184C2×SD16C2×D1311yescharacteristic
185C2×D8C2×D1311yescharacteristic
186C2×M16—131no—
187C22×C8—131no—
188C4⋊Q8—131no—
189C4⋊Q8—131no—
190#126—261no—
191#126—261no—
192#124—131no—
193#124—261no—
194#124—261no—
195#124C2×D1311yescharacteristic
196#123—261no—
197#123—261no—
198C22⋊Q8—131no—
199C22⋊Q8—131no—
200C22⋊Q8—261no—
201C22⋊Q8—261no—
202#121—131no—
203#121—131no—
204C4×Q8—131no—
205C4×Q8—131no—
206C4×D4—131no—
207C4×D4C2×D1311yescharacteristic
208#117—131no—
209#106—131no—
210#106—131no—
211#106—131no—
212#106—131no—
213C4⋊C8—131no—
214C4⋊C8—131no—
215C4⋊C8—131no—
216C4⋊C8C2×D1311yescharacteristic
217#103—131no—
218#103—131no—
219#103—131no—
220#103C2×D1311yescharacteristic
221#102—131no—
222#102—131no—
223#102—131no—
224#102C2×D1311yescharacteristic
225C2×C13—81no—
226C2×C13—81no—
227C2×C13#53711yescharacteristic
228C2×C13#57711yescharacteristic
229C2×C13#57711yescharacteristic
230D13—41no—
231C2×Q8—131no—
232C2×Q8—261no—
233C2×Q8—261no—
234C2×Q8C22×D1311yescharacteristic
235C2×D4—261no—
236C2×D4—261no—
237C2×D4C22×D1311yescharacteristic
238C2×D4C22×D1311yescharacteristic
239C22×C4—21no—
240C22×C4—131no—
241C22×C4—261no—
242Q16—521no—
243SD16—41no—
244SD16—521no—
245D8—41no—
246M16—521no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—521no—
250C2×C8C22×D1311yescharacteristic
251C2×C8C22×D1311yescharacteristic
252C4⋊C4—131no—
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⋊C4—261no—
263C4⋊C4C22×D1311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—131no—
268C22⋊C4—131no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C42—131no—
277C42—261no—
278C42—261no—
279C42C22×D1311yescharacteristic
280C13#326311yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—131no—
284Q8—21no—
285Q8—21no—
286Q8—261no—
287Q8—261no—
288Q8—1041no—
289Q8—1041no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—1041no—
295D4—1041no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—81no—
299C2×C4—131no—
300C2×C4—131no—
301C2×C4—131no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—1041no—
309C2×C4D4×D1311yescharacteristic
310C2×C4D4×D1311yescharacteristic
311C2×C4C23×D1311yescharacteristic
312C8—21no—
313C8—21no—
314C8—261no—
315C8—261no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—261no—
323C22—261no—
324C22—261no—
325C22C2×D4×D1311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—261no—
331C4—261no—
332C4—261no—
333C4—521no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4#8825111yescharacteristic
338C4#8825711yescharacteristic
339C2—81no—
340C2—81no—
341C2—521no—
342C2#1171931311yescharacteristic
343C2#1171947511yescharacteristic
344C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#463C2
socleC22×C13C22×D4
prime radical#11718820C2
hypercenter#463D13
hypocenterC13#3263
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #11719387C2semidirect
2. #11719266C2semidirect
3. C13×#463C2semidirect
4. #11718832C2semidirect
5. #11718827C2semidirect
7. #11718814C2semidirect
8. #11718715C2semidirect
9. #11718669C2semidirect
10. #11718512C2semidirect
11. #11718500C2semidirect
12. #11718477C2semidirect
13. #11718452C2semidirect
14. #11718439C2semidirect
15. #11718422C2semidirect
157. #463D13semidirect
280. C13#3263semidirect

Maximal subgroups

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

subgroupindex
#117193872
#117192662
C13×#4632
#117188322
#117188272
#117188202
#117188142
#117187152
#117186692
#117185122
#117185002
#117184772
#117184522
#117184392
#117184222
#326313