Finite Group Databasebeta

← #13127320

Subgroups — #13127320

Order 1664.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719435C211yesmaximal, characteristic, complemented
2#11719400C211yesmaximal, characteristic
3C13×#501C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718724C211yesmaximal, characteristic, complemented
6#11718547C211yesmaximal, characteristic, complemented
7#11718545C211yesmaximal, characteristic, complemented
8#11718543C211yesmaximal, characteristic, complemented
9D13×#107C211yesmaximal, characteristic, complemented
10#11718528C211yesmaximal, characteristic, complemented
11#11718525C211yesmaximal, characteristic, complemented
12#11718524C211yesmaximal, characteristic, complemented
13#11718522C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15#11718367C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#125C2211yescharacteristic
18#88200—21no—
19#88200—21no—
20C2×#6095C2211yescharacteristic
21C2×#6094C2211yescharacteristic
22C2×C8×D13C2211yescharacteristic
23#88152—21no—
24#88151C2211yescharacteristic
25#88151C2211yescharacteristic
26#88149—21no—
27#88149C2211yescharacteristic
28#88149C2211yescharacteristic
29#88148—21no—
30#88147—21no—
31#88147—21no—
32#88146C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34C4⋊C4×D13C2211yescharacteristic
35C4⋊C4×D13C2211yescharacteristic
36#88144—21no—
37C4×D52C2211yescharacteristic
38C4×D52C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88061C2211yescharacteristic
46#88060C2211yescharacteristic
47#88060C2211yescharacteristic
48#88058C2211yescharacteristic
49#88056C2211yescharacteristic
50#88050C2211yescharacteristic
51#88050C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D52—21no—
61C2×D52—21no—
62C2×D52D411yescharacteristic
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13C2311yescharacteristic
69C2×C4×D13C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C42×C13C2311yescharacteristic
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103D411yescharacteristic
88#6103D411yescharacteristic
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13D411yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#6095—22no—
103#6094—22no—
104C8×D13—22no—
105#3346—131nomaximal, Sylow
106C22×D13—21no—
107C22×D13C2×D411yescharacteristic
108C22×D13C2×D411yescharacteristic
109Q8×C13—81no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2411yescharacteristic
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122D52—22no—
123D52—21no—
124D52—21no—
125D52—42no—
126D52—81no—
127C4×D13—21no—
128C4×D13—21no—
129C4×D13—21no—
130C4×D13—21no—
131C4×D13—81no—
132C4×D13—81no—
133C4×D13—81no—
134C4×D13—81no—
135Dic26—21no—
136Dic26—21no—
137C8×C13—21no—
138C8×C13#4112yes—
139#1055—21no—
140#1055—21no—
141#554—131no—
142#553—131no—
143#501D1311yescharacteristic, complemented
144#485—131no—
145#484—131no—
146#481—131no—
147#480—131no—
148#479—131no—
149#474—131no—
150#468—131no—
151#465—131no—
152#440—131no—
153#435—131no—
154#428—131no—
155C2×#107—131no—
156C22×C13C22×D411yescharacteristic
157C2×D13—21no—
158C2×D13—21no—
159C2×D13—21no—
160C2×D13—21no—
161C2×D13—21no—
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C2×D13#13712yes—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13C2×#4111yescharacteristic
173C4×C132−1+411yescharacteristic
174Dic13—21no—
175Dic13—21no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×SD16—131no—
180C2×M16—131no—
181C22×C8—131no—
182C4⋊Q8C2×D1311yescharacteristic
183#126—261no—
184#125—261no—
185#125C2×D1311yescharacteristic
186#123—261no—
187C22⋊Q8—131no—
188C22⋊Q8—131no—
189C22⋊Q8—261no—
190C22⋊Q8—261no—
191#121—131no—
192#121—131no—
193#121—261no—
194C4×Q8—131no—
195C4×D4—131no—
196C4×D4—131no—
197C4×D4—261no—
198C4×D4—261no—
199#117—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203#107—131no—
204#107—131no—
205#107—131no—
206#107—131no—
207#107C2×D1311yescharacteristic
208#107C2×D1311yescharacteristic
209#106—131no—
210#106C2×D1311yescharacteristic
211#106C2×D1311yescharacteristic
212C4⋊C8—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219C22⋊C8—131no—
220C22⋊C8—131no—
221#97C2×D1311yescharacteristic
222C2×C13#54711yescharacteristic
223C2×C13C2×#13711yescharacteristic
224C2×C13#57611yescharacteristic
225D13—22no—
226D13—41no—
227D13—81no—
228C2×Q8—21no—
229C2×Q8—131no—
230C2×D4—131no—
231C2×D4—131no—
232C2×D4—261no—
233C2×D4—261no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240SD16—262no—
241M16—262no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8—262no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4C22×D1311yescharacteristic
260C4⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C22⋊C4—131no—
264C22⋊C4—131no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C42—261no—
272C42—261no—
273C42C22×D1311yescharacteristic
274C13#334611yescharacteristic, complemented, Sylow
275C23—131no—
276C23—131no—
277C23—261no—
278Q8—81no—
279Q8—261no—
280Q8—261no—
281D4—262no—
282D4—261no—
283D4—261no—
284D4—522no—
285D4—1041no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—131no—
291C2×C4—131no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4—1041no—
302C2×C4—1041no—
303C2×C4D4×D1311yescharacteristic
304C2×C4D4×D1311yescharacteristic
305C2×C4C23×D1311yescharacteristic
306C8—21no—
307C8—261no—
308C8—261no—
309C8#613112yes—
310C22—132no—
311C22—261no—
312C22—261no—
313C22—261no—
314C22—261no—
315C22—261no—
316C22—521no—
317C22—521no—
318C22—521no—
319C22C2×D4×D1311yescharacteristic
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—261no—
327C4—261no—
328C4—521no—
329C4—521no—
330C4—521no—
331C4C2×#613111yescharacteristic
332C4#8825411yescharacteristic
333C2—262no—
334C2—521no—
335C2—1041no—
336C2#1171943111yescharacteristic
337C2#1171947911yescharacteristic
338C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radical#11719400C2
hypercenter#501D13
hypocenterC13#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
3. C13×#501C2semidirect
4. #11718748C2semidirect
5. #11718724C2semidirect
6. #11718547C2semidirect
7. #11718545C2semidirect
8. #11718543C2semidirect
9. D13×#107C2semidirect
10. #11718528C2semidirect
11. #11718525C2semidirect
12. #11718524C2semidirect
13. #11718522C2semidirect
14. #11718371C2semidirect
15. #11718367C2semidirect
143. #501D13semidirect
274. C13#3346semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117194002
C13×#5012
#117187482
#117187242
#117185472
#117185452
#117185432
D13×#1072
#117185282
#117185252
#117185242
#117185222
#117183712
#117183672
#334613