Finite Group Databasebeta

← #13124943

Subgroups — #13124943

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
1C4×#6131C211yesmaximal, characteristic, complemented
2#11719262C211yesmaximal, characteristic, complemented
3C13×#440C211yesmaximal, characteristic, complemented
4#11718833C211yesmaximal, characteristic
5#11718827C211yesmaximal, characteristic, complemented
6#11718691C211yesmaximal, characteristic, complemented
7#11718675C211yesmaximal, characteristic, complemented
8#11718552C211yesmaximal, characteristic, complemented
9#11718549C211yesmaximal, characteristic, complemented
10#11718471C211yesmaximal, characteristic, complemented
11#11718457C211yesmaximal, characteristic, complemented
12#11718448C211yesmaximal, characteristic, complemented
13#11718445C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15#11718366C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21C2×#6107C2211yescharacteristic
22#88192C2211yescharacteristic
23#88190C2211yescharacteristic
24C2×#6104C2211yescharacteristic
25C4×C22⋊D13—21no—
26#88180—21no—
27C2×#6095C2211yescharacteristic
28#88151C2211yescharacteristic
29#88147—21no—
30#88147C2211yescharacteristic
31#88146—21no—
32#88146C2211yescharacteristic
33#88144C2211yescharacteristic
34#88137—21no—
35#88133—21no—
36C4×D52—21no—
37C4×D52C2211yescharacteristic
38C42×D13—21no—
39C42×D13C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88061C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88058C2211yescharacteristic
51#88056C2211yescharacteristic
52#88054C2211yescharacteristic
53#88054C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63#6131—22no—
64#6131—22no—
65C2×D52—21no—
66C2×D52C2311yescharacteristic
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13D411yescharacteristic
71C2×C4×D13D411yescharacteristic
72C2×C4×D13C2311yescharacteristic
73C2×Dic26C2311yescharacteristic
74C13×SD16—22no—
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C13×C4⋊C4—21no—
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C42×C13—21no—
82C42×C13C2311yescharacteristic
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86#6107—22no—
87#6104—22no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13D411yescharacteristic
103C4×Dic13D411yescharacteristic
104C4×Dic13C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107#6095—22no—
108#3111—131nomaximal, Sylow
109C23×C13—21no—
110C22×D13—21no—
111C22×D13C2×D411yescharacteristic
112Q8×C13—21no—
113Q8×C13#4112yes—
114D4×C13—21no—
115D4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—42no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—42no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130D52—24no—
131D52—21no—
132D52#4112yes—
133C4×D13—24no—
134C4×D13—21no—
135C4×D13—21no—
136C4×D13—41no—
137C4×D13—41no—
138C4×D13—42no—
139C4×D13—42no—
140Dic26—21no—
141Dic26—21no—
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#452—131no—
155#449—131no—
156#442—131no—
157#441—131no—
158#440—131no—
159#440D1311yescharacteristic, complemented
160#432—131no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13C22×D411yescharacteristic
165C2×D13—21no—
166C2×D13—22no—
167C2×D13—21no—
168C2×D13—21no—
169C2×D13—41no—
170C2×D13—41no—
171C4×C13—22no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13C2×#4111yescharacteristic
177C4×C13C2×#4111yescharacteristic
178Dic13—21no—
179Dic13—21no—
180Dic13—21no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184C2×#41—131no—
185C2×Q16—131no—
186C2×SD16—131no—
187C2×SD16C2×D1311yescharacteristic
188C2×D8—131no—
189#126—261no—
190#125—131no—
191#124—131no—
192#123—261no—
193C22⋊Q8—131no—
194#121—131no—
195C4×Q8—131no—
196C4×Q8—131no—
197C4×Q8C2×D1311yescharacteristic
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—261no—
201C4×D4—261no—
202C4×D4—261no—
203C4×D4C2×D1311yescharacteristic
204#117—131no—
205#117—261no—
206#117—261no—
207C2×C42—131no—
208C2×C42—261no—
209#107—131no—
210#107C2×D1311yescharacteristic
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⋊C8—131no—
225#97—131no—
226#97C2×D1311yescharacteristic
227C2×C13—81no—
228C2×C13#52511yescharacteristic
229C2×C13#57511yescharacteristic
230C2×C13#57511yescharacteristic
231D13—41no—
232D13—42no—
233#41—262no—
234#41—262no—
235C2×Q8—131no—
236C2×Q8C22×D1311yescharacteristic
237C2×D4—131no—
238C2×D4—261no—
239C2×D4—261no—
240C2×D4C22×D1311yescharacteristic
241C22×C4—21no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248Q16—262no—
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—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4C22×D1311yescharacteristic
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—21no—
275C42—131no—
276C42—131no—
277C42—131no—
278C42—261no—
279C42—261no—
280C42—261no—
281C42C22×D1311yescharacteristic
282C13#311111yescharacteristic, complemented, Sylow
283C23—21no—
284C23—131no—
285C23—261no—
286Q8—21no—
287Q8—261no—
288Q8—261no—
289Q8#612712yes—
290D4—21no—
291D4—21no—
292D4—132no—
293D4—264no—
294D4—261no—
295D4—522no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—131no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—264no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—522no—
312C2×C4—522no—
313C2×C4D4×D1311yescharacteristic
314C2×C4D4×D1311yescharacteristic
315C2×C4C23×D1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—261no—
319C8—261no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—261no—
324C22—261no—
325C22—262no—
326C22—261no—
327C22—521no—
328C22—521no—
329C22C2×D4×D1311yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—261no—
336C4—261no—
337C4—261no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4C2×#612711yescharacteristic
342C4#41×D1311yescharacteristic
343C2—81no—
344C2—521no—
345C2—522no—
346C2#1171925211yescharacteristic
347C2#1171947811yescharacteristic
348C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#440C2
socleC22×C13C22×D4
prime radical#11718833C2
hypercenter#440D13
hypocenterC13#3111
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C4×#6131C2semidirect
2. #11719262C2semidirect
3. C13×#440C2semidirect
5. #11718827C2semidirect
6. #11718691C2semidirect
7. #11718675C2semidirect
8. #11718552C2semidirect
9. #11718549C2semidirect
10. #11718471C2semidirect
11. #11718457C2semidirect
12. #11718448C2semidirect
13. #11718445C2semidirect
14. #11718371C2semidirect
15. #11718366C2semidirect
159. #440D13semidirect
282. C13#3111semidirect

Maximal subgroups

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

subgroupindex
C4×#61312
#117192622
C13×#4402
#117188332
#117188272
#117186912
#117186752
#117185522
#117185492
#117184712
#117184572
#117184482
#117184452
#117183712
#117183662
#311113