Finite Group Databasebeta

← #13127014

Subgroups — #13127014

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719432C211yesmaximal, characteristic, complemented
2#11719263C211yesmaximal, characteristic
3C13×#461C211yesmaximal, characteristic, complemented
4#11718835C211yesmaximal, characteristic, complemented
5#11718832C211yesmaximal, characteristic, complemented
6#11718831C211yesmaximal, characteristic, complemented
7#11718831C211yesmaximal, characteristic, complemented
8#11718743C211yesmaximal, characteristic, complemented
9#11718679C211yesmaximal, characteristic, complemented
10#11718497C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718476C211yesmaximal, characteristic, complemented
13#11718470C211yesmaximal, characteristic, complemented
14#11718463C211yesmaximal, characteristic, complemented
15D13×#103C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C13×C4⋊Q8C2211yescharacteristic
21C4×D4×C13C2211yescharacteristic
22#88200C2211yescharacteristic
23#88200C2211yescharacteristic
24#88192C2211yescharacteristic
25#88192C2211yescharacteristic
26C2×#6105C2211yescharacteristic
27#88183—21no—
28C4×C22⋊D13—21no—
29C2×#6094C2211yescharacteristic
30C2×C8×D13C2211yescharacteristic
31#88150—21no—
32#88150—21no—
33#88147—21no—
34#88146C2211yescharacteristic
35C4⋊C4×D13C2211yescharacteristic
36#88142—21no—
37#88138—21no—
38#88133—21no—
39C4×D52C2211yescharacteristic
40#88124C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88072C2211yescharacteristic
50#88060C2211yescharacteristic
51#88060C2211yescharacteristic
52#88058C2211yescharacteristic
53#88057C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88050C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65Q8×D13—22no—
66Q8×D13—22no—
67Q8×D13—41no—
68Q8×D13—41no—
69C2×D52D411yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×C4×D13C2311yescharacteristic
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26C2311yescharacteristic
78C13×SD16—41no—
79C13×SD16—41no—
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89#6105—22no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103D411yescharacteristic
94#6103D411yescharacteristic
95C4⋊Dic13D411yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6094—41no—
110C8×D13—41no—
111#3320—131nomaximal, Sylow
112C23×C13—21no—
113C22×D13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119D4×C13—21no—
120D4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—81no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C22⋊D13—42no—
129C22⋊D13—81no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136D52—22no—
137C4×D13—21no—
138C4×D13—21no—
139C4×D13—21no—
140C4×D13—21no—
141C4×D13—42no—
142C4×D13—42no—
143C4×D13—81no—
144Dic26—21no—
145Dic26—42no—
146Dic26—42no—
147Dic26#4112yes—
148C8×C13—21no—
149C8×C13—21no—
150#1055—21no—
151#1055—21no—
152#553—131no—
153D4×Q8—131no—
154#491—131no—
155#485—131no—
156#484—131no—
157#479—131no—
158#468—131no—
159#465—131no—
160#461D1311yescharacteristic, complemented
161#448—131no—
162#448—131no—
163#440—131no—
164#435—131no—
165#419—131no—
166C2×#103—131no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13C22×D411yescharacteristic
171C2×D13—21no—
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—21no—
175C2×D13—21no—
176C2×D13#13712yes—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13C2×#4111yescharacteristic
183C4×C13H(5,𝔽2)11yescharacteristic
184Dic13—22no—
185Dic13—21no—
186Dic13—21no—
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190C22×Q8—131no—
191C22×Q8—131no—
192C2×SD16—131no—
193C2×SD16C2×D1311yescharacteristic
194C2×SD16C2×D1311yescharacteristic
195C2×M16—131no—
196C22×C8—131no—
197C4⋊Q8—261no—
198C4⋊Q8C2×D1311yescharacteristic
199#126—261no—
200#125—131no—
201#123—261no—
202C22⋊Q8—131no—
203C22⋊Q8—131no—
204C22⋊Q8—261no—
205C22⋊Q8—261no—
206#121—131no—
207#121—131no—
208#121—261no—
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—261no—
212C4×D4—261no—
213C4×D4C2×D1311yescharacteristic
214#117—131no—
215C2×C4⋊C4—131no—
216#107—131no—
217#107—131no—
218#106—131no—
219C4⋊C8C2×D1311yescharacteristic
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103C2×D1311yescharacteristic
228#103C2×D1311yescharacteristic
229#102—131no—
230C22⋊C8—131no—
231C22⋊C8—131no—
232#97—131no—
233C2×C13—81no—
234C2×C13#54611yescharacteristic
235C2×C13C2×#13711yescharacteristic
236C2×C13#57711yescharacteristic
237D13—22no—
238D13—41no—
239C2×Q8—131no—
240C2×Q8—261no—
241C2×Q8—261no—
242C2×Q8—262no—
243C2×Q8—262no—
244C2×Q8—521no—
245C2×Q8—521no—
246C2×Q8C22×D1311yescharacteristic
247C2×Q8C22×D1311yescharacteristic
248C2×D4—131no—
249C2×D4—261no—
250C2×D4—261no—
251C2×D4C22×D1311yescharacteristic
252C22×C4—21no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258SD16—41no—
259SD16—41no—
260SD16—262no—
261M16—521no—
262C2×C8—131no—
263C2×C8—131no—
264C2×C8—521no—
265C2×C8C22×D1311yescharacteristic
266C2×C8C22×D1311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—131no—
270C4⋊C4—131no—
271C4⋊C4—131no—
272C4⋊C4—131no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4C22×D1311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—131no—
282C22⋊C4—131no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C42—261no—
289C42—261no—
290C42C22×D1311yescharacteristic
291C13#332011yescharacteristic, complemented, Sylow
292C23—21no—
293C23—131no—
294C23—131no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—132no—
300Q8—261no—
301Q8—522no—
302Q8—522no—
303D4—21no—
304D4—21no—
305D4—262no—
306D4—522no—
307D4—1041no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—522no—
323C2×C4—522no—
324C2×C4—1041no—
325C2×C4D4×D1311yescharacteristic
326C2×C4D4×D1311yescharacteristic
327C2×C4C23×D1311yescharacteristic
328C8—21no—
329C8—21no—
330C8—261no—
331C8—261no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—132no—
336C22—261no—
337C22—261no—
338C22—261no—
339C22—261no—
340C22—261no—
341C22C2×D4×D1311yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—261no—
348C4—261no—
349C4—262no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4#8825111yescharacteristic
354C4#41×D1311yescharacteristic
355C2—81no—
356C2—262no—
357C2—521no—
358C2#1171931711yescharacteristic
359C2#1171946711yescharacteristic
360C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radical#11719263C2
hypercenter#461D13
hypocenterC13#3320
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11719432C2semidirect
3. C13×#461C2semidirect
4. #11718835C2semidirect
5. #11718832C2semidirect
6. #11718831C2semidirect
7. #11718831C2semidirect
8. #11718743C2semidirect
9. #11718679C2semidirect
10. #11718497C2semidirect
11. #11718490C2semidirect
12. #11718476C2semidirect
13. #11718470C2semidirect
14. #11718463C2semidirect
15. D13×#103C2semidirect
160. #461D13semidirect
291. C13#3320semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117192632
C13×#4612
#117188352
#117188322
#117188312
#117187432
#117186792
#117184972
#117184902
#117184762
#117184702
#117184632
D13×#1032
#332013