Finite Group Databasebeta

← #13126751

Subgroups — #13126751

Order 1664.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719336C211yesmaximal, characteristic
2#11719238C211yesmaximal, characteristic, complemented
3C13×#485C211yesmaximal, characteristic, complemented
4#11718712C211yesmaximal, characteristic, complemented
5#11718663C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718548C211yesmaximal, characteristic, complemented
8#11718528C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718471C211yesmaximal, characteristic, complemented
11#11718465C211yesmaximal, characteristic, complemented
12#11718454C211yesmaximal, characteristic, complemented
13#11718453C211yesmaximal, characteristic, complemented
14#11718394C211yesmaximal, characteristic, complemented
15#11718386C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#117C2211yescharacteristic
20#88198C2211yescharacteristic
21C2×#6107C2211yescharacteristic
22C4×C22⋊D13C2211yescharacteristic
23#88178C2211yescharacteristic
24C22×#1055C2211yescharacteristic
25C2×Dic52C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27C2×C8×D13C2211yescharacteristic
28#88151C2211yescharacteristic
29#88151C2211yescharacteristic
30#88148—21no—
31#88147C2211yescharacteristic
32#88146C2211yescharacteristic
33C4⋊C4×D13—21no—
34#88142C2211yescharacteristic
35#88141C2211yescharacteristic
36#88139—21no—
37#88138—21no—
38#88137—21no—
39#88133—21no—
40#88130—21no—
41C4×Dic26—21no—
42C13×#107C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C13×C22⋊C8C2211yescharacteristic
47#88075C2211yescharacteristic
48#88061C2211yescharacteristic
49#88060C2211yescharacteristic
50#88056C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88049C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13—21no—
62C2×C22⋊D13D411yescharacteristic
63#6131—22no—
64#6131—41no—
65#6127—22no—
66#6127—41no—
67C2×D52—21no—
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13C2311yescharacteristic
73C2×Dic26—21no—
74C2×Dic26C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4—21no—
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C13×C22⋊C4—21no—
84C42×C13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13D411yescharacteristic
87#6107—41no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103D411yescharacteristic
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101D411yescharacteristic
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105C2×#1055—41no—
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108Dic52—41no—
109#6095—22no—
110C8×D13—41no—
111#3302—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C22×D13—21no—
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C22⋊D13—22no—
126C22⋊D13—42no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133D52—21no—
134D52—42no—
135D52#4112yes—
136C4×D13—21no—
137C4×D13—21no—
138C4×D13—42no—
139C4×D13—42no—
140C4×D13—42no—
141Dic26—21no—
142Dic26—21no—
143Dic26—21no—
144Dic26—21no—
145Dic26—42no—
146C8×C13—21no—
147C8×C13—21no—
148#1055—21no—
149#1055—21no—
150#556—131no—
151#547—131no—
152#487—131no—
153#485—131no—
154#485D1311yescharacteristic, complemented
155#474—131no—
156#467—131no—
157#467—131no—
158#462—131no—
159#452—131no—
160#452—131no—
161C4×SD16—131no—
162C8×D4—131no—
163#416—131no—
164#416—131no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13C22×D411yescharacteristic
169C2×D13—21no—
170C2×D13—22no—
171C2×D13—21no—
172C2×D13—21no—
173C2×D13—41no—
174C2×D13—41no—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13C2×#4111yescharacteristic
181C4×C13H(5,𝔽2)11yescharacteristic
182Dic13—21no—
183Dic13—21no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13#13512yes—
188C2×#41—131no—
189C2×#41—131no—
190C2×Q16—131no—
191C2×Q16—131no—
192C2×SD16—131no—
193C22×C8—131no—
194C22×C8—131no—
195C4⋊Q8—131no—
196C4⋊Q8—131no—
197#126—261no—
198#126—261no—
199#124—261no—
200#123—261no—
201#123—261no—
202C22⋊Q8—131no—
203C22⋊Q8—131no—
204C22⋊Q8—131no—
205C22⋊Q8C2×D1311yescharacteristic
206#121—261no—
207C4×Q8—131no—
208C4×Q8—261no—
209C4×D4—131no—
210C4×D4—131no—
211#117—131no—
212#117C2×D1311yescharacteristic
213C2×C4⋊C4—261no—
214#107—131no—
215#107C2×D1311yescharacteristic
216#106C2×D1311yescharacteristic
217C4⋊C8—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103C2×D1311yescharacteristic
224#103C2×D1311yescharacteristic
225#102—131no—
226#102—131no—
227#102—131no—
228C22⋊C8—131no—
229C22⋊C8C2×D1311yescharacteristic
230C4×C8—131no—
231C2×C13—41no—
232C2×C13#54611yescharacteristic
233C2×C13C2×#13511yescharacteristic
234C2×C13#57811yescharacteristic
235D13—41no—
236D13—42no—
237#41—262no—
238#41—262no—
239#41—521no—
240#41—521no—
241C2×Q8—131no—
242C2×Q8—131no—
243C2×Q8—261no—
244C2×Q8C22×D1311yescharacteristic
245C2×D4—131no—
246C2×D4—131no—
247C2×D4—261no—
248C2×D4—261no—
249C22×C4—131no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4C22×D1311yescharacteristic
254Q16—521no—
255Q16—521no—
256SD16—262no—
257C2×C8—131no—
258C2×C8—131no—
259C2×C8—521no—
260C2×C8—521no—
261C2×C8C22×D1311yescharacteristic
262C2×C8C22×D1311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4C22×D1311yescharacteristic
274C4⋊C4C22×D1311yescharacteristic
275C4⋊C4C22×D1311yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—131no—
279C22⋊C4—131no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C42—21no—
286C42—131no—
287C42—261no—
288C42—261no—
289C13#330211yescharacteristic, complemented, Sylow
290C23—131no—
291C23—261no—
292C23D4×D1311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—261no—
296Q8—261no—
297Q8—261no—
298Q8—261no—
299Q8—522no—
300D4—132no—
301D4—262no—
302D4—261no—
303D4—522no—
304D4—522no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4—522no—
322C2×C4D4×D1311yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C8—21no—
325C8—21no—
326C8—261no—
327C8—261no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—261no—
332C22—261no—
333C22—261no—
334C22—262no—
335C22—521no—
336C22—521no—
337C22C2×D4×D1311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—132no—
344C4—261no—
345C4—261no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4#41×D1311yescharacteristic
350C4#8825611yescharacteristic
351C2—41no—
352C2—521no—
353C2—522no—
354C2#1171935911yescharacteristic
355C2D13×#13511yescharacteristic
356C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
prime radical#11719336C2
hypercenter#485D13
hypocenterC13#3302
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #11719238C2semidirect
3. C13×#485C2semidirect
4. #11718712C2semidirect
5. #11718663C2semidirect
6. #11718551C2semidirect
7. #11718548C2semidirect
8. #11718528C2semidirect
9. #11718513C2semidirect
10. #11718471C2semidirect
11. #11718465C2semidirect
12. #11718454C2semidirect
13. #11718453C2semidirect
14. #11718394C2semidirect
15. #11718386C2semidirect
154. #485D13semidirect
289. C13#3302semidirect

Maximal subgroups

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

subgroupindex
#117193362
#117192382
C13×#4852
#117187122
#117186632
#117185512
#117185482
#117185282
#117185132
#117184712
#117184652
#117184542
#117184532
#117183942
#117183862
#330213