Finite Group Databasebeta

← #13124946

Subgroups — #13124946

Order 1664.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic13C211yesmaximal, characteristic, complemented
2#11719329C211yesmaximal, characteristic, complemented
3C13×#452C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic
5#11718846C211yesmaximal, characteristic, complemented
6#11718845C211yesmaximal, characteristic, complemented
7#11718826C211yesmaximal, characteristic, complemented
8#11718825C211yesmaximal, characteristic, complemented
9#11718706C211yesmaximal, characteristic, complemented
10#11718478C211yesmaximal, characteristic, complemented
11#11718457C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic, complemented
13#11718424C211yesmaximal, characteristic, complemented
14#11718398C211yesmaximal, characteristic, complemented
15#11718380C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×Q16C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C13×C22⋊Q8C2211yescharacteristic
20#88201C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24C2×#6106C2211yescharacteristic
25D4×Dic13—21no—
26D4×Dic13—21no—
27D4×Dic13C2211yescharacteristic
28D4×Dic13C2211yescharacteristic
29C2×#6104C2211yescharacteristic
30#88184C2211yescharacteristic
31#88180—21no—
32#88180C2211yescharacteristic
33C2×C4×Dic13—21no—
34C2×C4×Dic13C2211yescharacteristic
35#88152—21no—
36#88147C2211yescharacteristic
37#88146—21no—
38#88144C2211yescharacteristic
39#88140—21no—
40#88135—21no—
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88058C2211yescharacteristic
52#88057C2211yescharacteristic
53#88055C2211yescharacteristic
54#88055C2211yescharacteristic
55#88054C2211yescharacteristic
56#88054C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C13×#41—22no—
60C13×#41—22no—
61C2×Q8×C13C2311yescharacteristic
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13D411yescharacteristic
71C22×Dic13D411yescharacteristic
72C2×D52C2311yescharacteristic
73C2×C4×D13—21no—
74C13×Q16—22no—
75C13×SD16—22no—
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4—21no—
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84#6106—22no—
85#6104—22no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13D411yescharacteristic
103C4×Dic13D411yescharacteristic
104C4×Dic13C2311yescharacteristic
105C4×Dic13C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3111—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111C22×D13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115Q8×C13#4112yes—
116D4×C13—24no—
117D4×C13—21no—
118D4×C13#4112yes—
119C2×C4×C13—24no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—42no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139D52—21no—
140D52—21no—
141C4×D13—42no—
142C8×C13—21no—
143C8×C13—21no—
144#1055—21no—
145#1055—21no—
146#529—131no—
147C4×#41—131no—
148#485—131no—
149#482—131no—
150#479—131no—
151#478—131no—
152#464—131no—
153#463—131no—
154#452D1311yescharacteristic, complemented
155#449—131no—
156#442—131no—
157#441—131no—
158#440—131no—
159#440—131no—
160#432—131no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13C22×D411yescharacteristic
168C2×D13—41no—
169C2×D13—41no—
170C2×D13—41no—
171C4×C13—21no—
172C4×C13—22no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13C2×#4111yescharacteristic
176C4×C13C2×#4111yescharacteristic
177Dic13—21no—
178Dic13—21no—
179Dic13—21no—
180Dic13—21no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184C2×#41C2×D1311yescharacteristic
185C2×Q16C2×D1311yescharacteristic
186C2×SD16—131no—
187C2×SD16C2×D1311yescharacteristic
188C2×D8—131no—
189#126—261no—
190#125—131no—
191#124—131no—
192#123—261no—
193C22⋊Q8C2×D1311yescharacteristic
194#121—131no—
195C4×Q8—131no—
196C4×Q8—131no—
197C4×Q8—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—131no—
201C4×D4—261no—
202C4×D4—261no—
203C4×D4—261no—
204#117—131no—
205#117—261no—
206#117—261no—
207C2×C42—131no—
208C2×C42—261no—
209#107—131no—
210#107—131no—
211#106—131no—
212#106—131no—
213C4⋊C8—131no—
214C4⋊C8—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#103C2×D1311yescharacteristic
219#102—131no—
220#102—131no—
221#102—131no—
222#102C2×D1311yescharacteristic
223C22⋊C8—131no—
224C22⋊C8C2×D1311yescharacteristic
225#97—131no—
226#97—131no—
227C2×C13—41no—
228C2×C13—42no—
229C2×C13#52511yescharacteristic
230C2×C13#57511yescharacteristic
231C2×C13#57511yescharacteristic
232D13—81no—
233#41—22no—
234#41—22no—
235C2×Q8C22×D1311yescharacteristic
236C2×Q8C22×D1311yescharacteristic
237C2×D4—21no—
238C2×D4—131no—
239C2×D4—261no—
240C2×D4C22×D1311yescharacteristic
241C22×C4—21no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4C22×D1311yescharacteristic
248Q16—22no—
249SD16—22no—
250SD16—262no—
251D8—262no—
252C2×C8—131no—
253C2×C8—131no—
254C2×C8C22×D1311yescharacteristic
255C2×C8C22×D1311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4C22×D1311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C42—131no—
275C42—131no—
276C42—131no—
277C42—131no—
278C42—261no—
279C42—261no—
280C42—261no—
281C42—261no—
282C13#311111yescharacteristic, complemented, Sylow
283C23—21no—
284C23—261no—
285C23D4×D1311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#612912yes—
290D4—24no—
291D4—21no—
292D4—261no—
293D4—261no—
294D4—522no—
295D4#612912yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—131no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—522no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—522no—
313C2×C4—522no—
314C2×C4D4×D1311yescharacteristic
315C2×C4C23×D1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—261no—
319C8—261no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—521no—
327C22—521no—
328C22—521no—
329C22C2×D4×D1311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—261no—
335C4—261no—
336C4—261no—
337C4—261no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4C2×#612911yescharacteristic
342C4C2×#612911yescharacteristic
343C2—41no—
344C2—42no—
345C2—1041no—
346C2#1171929111yescharacteristic
347C2#1171947311yescharacteristic
348C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#452C2
socleC22×C13C22×D4
prime radical#11718899C2
hypercenter#452D13
hypocenterC13#3111
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #41×Dic13C2semidirect
2. #11719329C2semidirect
3. C13×#452C2semidirect
5. #11718846C2semidirect
6. #11718845C2semidirect
7. #11718826C2semidirect
8. #11718825C2semidirect
9. #11718706C2semidirect
10. #11718478C2semidirect
11. #11718457C2semidirect
12. #11718446C2semidirect
13. #11718424C2semidirect
14. #11718398C2semidirect
15. #11718380C2semidirect
154. #452D13semidirect
282. C13#3111semidirect

Maximal subgroups

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

subgroupindex
#41×Dic132
#117193292
C13×#4522
#117188992
#117188462
#117188452
#117188262
#117188252
#117187062
#117184782
#117184572
#117184462
#117184242
#117183982
#117183802
#311113