Finite Group Databasebeta

← #13124804

Subgroups — #13124804

Order 1664.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719333C211yesmaximal, characteristic
2#11719209C211yesmaximal, characteristic
3C13×#484C211yesmaximal, characteristic, complemented
4#11718706C211yesmaximal, characteristic, complemented
5#11718632C211yesmaximal, characteristic, complemented
6#11718549C211yesmaximal, characteristic, complemented
7#11718545C211yesmaximal, characteristic, complemented
8#11718542C211yesmaximal, characteristic, complemented
9#11718541C211yesmaximal, characteristic, complemented
10#11718475C211yesmaximal, characteristic, complemented
11#11718466C211yesmaximal, characteristic, complemented
12#11718463C211yesmaximal, characteristic, complemented
13D13×#103C211yesmaximal, characteristic, complemented
14#11718388C211yesmaximal, characteristic
15#11718384C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20#88200C2211yescharacteristic
21C4×C22⋊D13—21no—
22C4×C22⋊D13—21no—
23#88180C2211yescharacteristic
24#88178C2211yescharacteristic
25C2×#6094C2211yescharacteristic
26C2×C8×D13C2211yescharacteristic
27#88151C2211yescharacteristic
28#88148—21no—
29#88147—21no—
30#88146C2211yescharacteristic
31#88146C2211yescharacteristic
32#88146C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34C4⋊C4×D13C2211yescharacteristic
35#88142—21no—
36#88141—21no—
37#88139—21no—
38#88137—21no—
39C13×#107C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
47#88060C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88057C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13D411yescharacteristic
63C2×C22⋊D13D411yescharacteristic
64Q8×D13—22no—
65Q8×D13—22no—
66#6127—22no—
67#6127—22no—
68C2×D52D411yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13C2311yescharacteristic
73C2×C4×D13C2311yescharacteristic
74C2×Dic26—21no—
75C2×Dic26D411yescharacteristic
76C2×Dic26C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—22no—
107C8×D13—22no—
108#3097—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13C2×D411yescharacteristic
111C22×D13C2×D411yescharacteristic
112Q8×C13—21no—
113Q8×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—81no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—22no—
124C22⋊D13—22no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131D52—22no—
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—42no—
135C4×D13—81no—
136C4×D13—81no—
137C4×D13#4112yes—
138C4×D13#4112yes—
139Dic26—22no—
140Dic26—21no—
141Dic26—21no—
142Dic26—42no—
143C8×C13—21no—
144C8×C13—21no—
145#1055—21no—
146#1055—21no—
147#536—131no—
148#520—131no—
149#485—131no—
150#485—131no—
151#485—131no—
152#485—131no—
153#484—131no—
154#484D1311yescharacteristic, complemented
155#483—131no—
156#483—131no—
157#428—131no—
158#427—131no—
159#419—131no—
160C2×#103—131no—
161#408—131no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13C22×D411yescharacteristic
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—21no—
169C2×D13—21no—
170C2×D13—21no—
171C2×D13#12312yes—
172C4×C13—21no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13C2×#4111yescharacteristic
178C4×C13C2×#4111yescharacteristic
179Dic13—21no—
180Dic13—41no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184Dic13#12312yes—
185C2×#41—131no—
186C22×Q8—131no—
187C2×M16—131no—
188C22×C8—131no—
189C4⋊Q8—261no—
190#124—261no—
191#123—261no—
192#123—261no—
193C22⋊Q8—131no—
194C22⋊Q8—131no—
195C22⋊Q8—131no—
196C22⋊Q8C2×D1311yescharacteristic
197C4×Q8—261no—
198C4×D4—261no—
199C4×D4—261no—
200C4×D4—261no—
201#117—131no—
202#117—131no—
203#117—131no—
204#117—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4C2×D1311yescharacteristic
208#107—131no—
209#107—131no—
210#107C2×D1311yescharacteristic
211#107C2×D1311yescharacteristic
212#106—131no—
213#106—131no—
214#106—131no—
215#106—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103C2×D1311yescharacteristic
223#103C2×D1311yescharacteristic
224C22⋊C8—131no—
225C22⋊C8—131no—
226C22⋊C8—131no—
227C22⋊C8C2×D1311yescharacteristic
228C2×C13—41no—
229C2×C13C2×#12311yescharacteristic
230C2×C13#57711yescharacteristic
231C2×C13#57811yescharacteristic
232D13—22no—
233D13—41no—
234#41—262no—
235#41—262no—
236C2×Q8—131no—
237C2×Q8—131no—
238C2×Q8—261no—
239C2×Q8—262no—
240C2×Q8—262no—
241C2×Q8C22×D1311yescharacteristic
242C2×D4—131no—
243C2×D4—131no—
244C2×D4—131no—
245C22×C4—21no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4C22×D1311yescharacteristic
252M16—262no—
253C2×C8—131no—
254C2×C8—131no—
255C2×C8—262no—
256C2×C8C22×D1311yescharacteristic
257C2×C8C22×D1311yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—131no—
261C4⋊C4—131no—
262C4⋊C4—131no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4C22×D1311yescharacteristic
269C4⋊C4C22×D1311yescharacteristic
270C4⋊C4C22×D1311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C42—261no—
280C42—261no—
281C42—261no—
282C42—261no—
283C13#309711yescharacteristic, complemented, Sylow
284C23—131no—
285C23—131no—
286C23D4×D1311yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—262no—
290Q8—261no—
291Q8—261no—
292Q8—522no—
293D4—262no—
294D4—262no—
295D4—262no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—131no—
304C2×C4—132no—
305C2×C4—132no—
306C2×C4—131no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—522no—
314C2×C4—1041no—
315C2×C4—1041no—
316C2×C4D4×D1311yescharacteristic
317C2×C4C23×D1311yescharacteristic
318C8—21no—
319C8—21no—
320C8—261no—
321C8—261no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—132no—
326C22—261no—
327C22—261no—
328C22—261no—
329C22—261no—
330C22—261no—
331C22C2×D4×D1311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—132no—
338C4—261no—
339C4—521no—
340C4—521no—
341C4—521no—
342C4—521no—
343C4#41×D1311yescharacteristic
344C4#41×D1311yescharacteristic
345C2—41no—
346C2—262no—
347C2—521no—
348C2D13×#12311yescharacteristic
349C2#1171947111yescharacteristic
350C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#484C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#484D13
hypocenterC13#3097
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. C13×#484C2semidirect
4. #11718706C2semidirect
5. #11718632C2semidirect
6. #11718549C2semidirect
7. #11718545C2semidirect
8. #11718542C2semidirect
9. #11718541C2semidirect
10. #11718475C2semidirect
11. #11718466C2semidirect
12. #11718463C2semidirect
13. D13×#103C2semidirect
15. #11718384C2semidirect
154. #484D13semidirect
283. C13#3097semidirect

Maximal subgroups

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

subgroupindex
#117193332
#117192092
C13×#4842
#117187062
#117186322
#117185492
#117185452
#117185422
#117185412
#117184752
#117184662
#117184632
D13×#1032
#117183882
#117183842
#309713