Finite Group Databasebeta

← #13127350

Subgroups — #13127350

Order 1664.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719439C211yesmaximal, characteristic
2#11719399C211yesmaximal, characteristic, complemented
3C13×#501C211yesmaximal, characteristic, complemented
4#11718755C211yesmaximal, characteristic, complemented
5#11718727C211yesmaximal, characteristic, complemented
6#11718549C211yesmaximal, characteristic, complemented
7#11718547C211yesmaximal, characteristic, complemented
8#11718546C211yesmaximal, characteristic, complemented
9#11718541C211yesmaximal, 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#88201—21no—
19#88201—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#88146—21no—
31#88146—21no—
32#88146C2211yescharacteristic
33#88146C2211yescharacteristic
34#88146C2211yescharacteristic
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#88048C2211yescharacteristic
56#88048C2211yescharacteristic
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×D13C2311yescharacteristic
67C2×C4×D13C2311yescharacteristic
68C2×Dic26C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C42×C13C2311yescharacteristic
79#6103—21no—
80#6103—21no—
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—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#6095—22no—
103#6094—22no—
104C8×D13—22no—
105#3348—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—21no—
123D52—21no—
124D52—41no—
125D52—81no—
126D52—81no—
127C4×D13—21no—
128C4×D13—21no—
129C4×D13—21no—
130C4×D13—21no—
131C4×D13—42no—
132C4×D13—42no—
133Dic26—21no—
134Dic26—21no—
135C8×C13—21no—
136C8×C13#4112yes—
137#1055—21no—
138#1055—21no—
139#555—131no—
140#552—131no—
141#501D1311yescharacteristic, complemented
142#485—131no—
143#485—131no—
144#482—131no—
145#481—131no—
146#478—131no—
147#475—131no—
148#468—131no—
149#465—131no—
150#440—131no—
151#435—131no—
152#428—131no—
153#427—131no—
154C22×C13C22×D411yescharacteristic
155C2×D13—21no—
156C2×D13—21no—
157C2×D13—21no—
158C2×D13—21no—
159C2×D13—21no—
160C2×D13—21no—
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—41no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13C2×#4111yescharacteristic
171C4×C132−1+411yescharacteristic
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×SD16—131no—
178C2×M16—131no—
179C22×C8—131no—
180C4⋊Q8C2×D1311yescharacteristic
181#126—261no—
182#125—261no—
183#125C2×D1311yescharacteristic
184#124—261no—
185#124—261no—
186#123—261no—
187C22⋊Q8—131no—
188C22⋊Q8—131no—
189#121—131no—
190#121—131no—
191#121—261no—
192C4×Q8—131no—
193C4×D4—131no—
194C4×D4—131no—
195#117—131no—
196#117—131no—
197#117—131no—
198#117—261no—
199#117—261no—
200C2×C4⋊C4—131no—
201#107—131no—
202#107—131no—
203#107C2×D1311yescharacteristic
204#107C2×D1311yescharacteristic
205#106—131no—
206#106—131no—
207#106—131no—
208#106C2×D1311yescharacteristic
209#106C2×D1311yescharacteristic
210C4⋊C8—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#102—131no—
215#102—131no—
216#102—131no—
217C22⋊C8—131no—
218C22⋊C8—131no—
219#97C2×D1311yescharacteristic
220C2×C13#54711yescharacteristic
221C2×C13#57511yescharacteristic
222C2×C13#57711yescharacteristic
223D13—41no—
224D13—41no—
225D13—81no—
226C2×Q8—21no—
227C2×Q8—131no—
228C2×D4—131no—
229C2×D4—131no—
230C2×D4—261no—
231C2×D4—261no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—261no—
235C22×C4—261no—
236SD16—262no—
237M16—262no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—262no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4C22×D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—131no—
258C22⋊C4—131no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C42—261no—
268C42—261no—
269C42—261no—
270C42—261no—
271C42C22×D1311yescharacteristic
272C13#334811yescharacteristic, complemented, Sylow
273C23—131no—
274C23—131no—
275C23—261no—
276Q8—81no—
277Q8—261no—
278Q8—261no—
279D4—261no—
280D4—261no—
281D4—521no—
282D4—1041no—
283D4—1041no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—131no—
289C2×C4—131no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4D4×D1311yescharacteristic
300C2×C4D4×D1311yescharacteristic
301C2×C4C23×D1311yescharacteristic
302C8—21no—
303C8—261no—
304C8—261no—
305C8#613112yes—
306C22—261no—
307C22—261no—
308C22—261no—
309C22—261no—
310C22—261no—
311C22—261no—
312C22—521no—
313C22—521no—
314C22—521no—
315C22C2×D4×D1311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—261no—
323C4—261no—
324C4—521no—
325C4—521no—
326C4—521no—
327C4C2×#613111yescharacteristic
328C4#8825411yescharacteristic
329C2—521no—
330C2—521no—
331C2—1041no—
332C2#1171943111yescharacteristic
333C2#1171948011yescharacteristic
334C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radical#11719439C2
hypercenter#501D13
hypocenterC13#3348
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
2. #11719399C2semidirect
3. C13×#501C2semidirect
4. #11718755C2semidirect
5. #11718727C2semidirect
6. #11718549C2semidirect
7. #11718547C2semidirect
8. #11718546C2semidirect
9. #11718541C2semidirect
10. #11718528C2semidirect
11. #11718525C2semidirect
12. #11718524C2semidirect
13. #11718522C2semidirect
14. #11718371C2semidirect
15. #11718367C2semidirect
141. #501D13semidirect
272. C13#3348semidirect

Maximal subgroups

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

subgroupindex
#117194392
#117193992
C13×#5012
#117187552
#117187272
#117185492
#117185472
#117185462
#117185412
#117185282
#117185252
#117185242
#117185222
#117183712
#117183672
#334813