Finite Group Databasebeta

← #13126710

Subgroups — #13126710

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719337C211yesmaximal, characteristic
2#11719216C211yesmaximal, characteristic
3C13×#484C211yesmaximal, characteristic, complemented
4#11718712C211yesmaximal, characteristic, complemented
5C2×#88050C211yesmaximal, characteristic, complemented
6#11718548C211yesmaximal, characteristic, complemented
7#11718545C211yesmaximal, characteristic, complemented
8#11718536C211yesmaximal, characteristic, complemented
9#11718534C211yesmaximal, characteristic, complemented
10#11718469C211yesmaximal, characteristic, complemented
11D13×#103C211yesmaximal, characteristic, complemented
12#11718454C211yesmaximal, characteristic, complemented
13#11718453C211yesmaximal, characteristic, complemented
14#11718400C211yesmaximal, characteristic, complemented
15#11718386C211yesmaximal, characteristic
16C2×Q8×D13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20#88198C2211yescharacteristic
21C2×#6107C2211yescharacteristic
22C4×C22⋊D13—21no—
23C4×C22⋊D13C2211yescharacteristic
24#88178—21no—
25#88178C2211yescharacteristic
26C22×#1055C2211yescharacteristic
27C2×Dic52C2211yescharacteristic
28C2×Dic52C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88151C2211yescharacteristic
31#88151C2211yescharacteristic
32#88150—21no—
33#88150—21no—
34C4⋊C4×D13C2211yescharacteristic
35#88143—21no—
36#88142—21no—
37#88142C2211yescharacteristic
38#88141C2211yescharacteristic
39#88141C2211yescharacteristic
40#88135—21no—
41#88132—21no—
42C13×#107C2211yescharacteristic
43C13×#107C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C13×C22⋊C8C2211yescharacteristic
47#88075C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88050C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13D411yescharacteristic
63C22×Dic13—21no—
64Q8×D13—22no—
65Q8×D13—41no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13C2311yescharacteristic
69C2×Dic26—22no—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—41no—
74C2×Dic26C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
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⋊Dic13D411yescharacteristic
87#6107—41no—
88#6103—21no—
89#6103—21no—
90#6103D411yescharacteristic
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
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—22no—
109Dic52—41no—
110C8×D13—41no—
111#3299—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C22×D13C2×D411yescharacteristic
114Q8×C13—21no—
115Q8×C13—21no—
116C2×C4×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—81no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C22⋊D13Q1614yescomplemented
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—42no—
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C4×D13—21no—
135C4×D13—21no—
136C4×D13—42no—
137C4×D13—81no—
138Dic26—21no—
139Dic26—21no—
140Dic26—21no—
141Dic26—21no—
142Dic26—21no—
143Dic26—42no—
144Dic26—42no—
145Dic26—81no—
146Dic26#4112yes—
147C8×C13—21no—
148C8×C13—21no—
149#1055—21no—
150#1055—21no—
151#554—131no—
152D4×Q8—131no—
153#487—131no—
154#484—131no—
155#484D1311yescharacteristic, complemented
156#477—131no—
157#467—131no—
158#467—131no—
159#462—131no—
160#451—131no—
161#451—131no—
162C4×Q16—131no—
163C8×D4—131no—
164C2×#103—131no—
165C2×#103—131no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13C2×Q1612yes—
169C22×C13C22×D411yescharacteristic
170C2×D13—21no—
171C2×D13—21no—
172C2×D13C2×Q1612yes—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13C2×#4111yescharacteristic
179C4×C13H(5,𝔽2)11yescharacteristic
180Dic13—22no—
181Dic13—21no—
182Dic13—21no—
183Dic13—41no—
184Dic13—41no—
185Dic13—41no—
186Dic13C2×Q1612yes—
187C22×Q8—131no—
188C22×Q8—131no—
189C2×Q16—131no—
190C2×Q16—131no—
191C2×Q16—131no—
192C22×C8—131no—
193C22×C8—131no—
194C4⋊Q8—131no—
195C4⋊Q8—131no—
196C4⋊Q8—261no—
197#125—261no—
198C22⋊Q8—131no—
199C22⋊Q8—131no—
200C22⋊Q8—131no—
201C22⋊Q8—261no—
202C22⋊Q8—261no—
203C22⋊Q8—261no—
204C22⋊Q8—261no—
205C22⋊Q8C2×D1311yescharacteristic
206C4×Q8—131no—
207C4×Q8—131no—
208C4×D4—131no—
209C4×D4—261no—
210C4×D4—261no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4C2×D1311yescharacteristic
213#107—131no—
214#107C2×D1311yescharacteristic
215#107C2×D1311yescharacteristic
216C4⋊C8—131no—
217#103—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103C2×D1311yescharacteristic
226#103C2×D1311yescharacteristic
227C22⋊C8—131no—
228C22⋊C8C2×D1311yescharacteristic
229C4×C8—131no—
230C2×C13—22no—
231C2×C13#54611yescharacteristic
232C2×C13C22×Q1611yescharacteristic
233C2×C13#57711yescharacteristic
234D13—22no—
235C2×Q8—131no—
236C2×Q8—131no—
237C2×Q8—131no—
238C2×Q8—261no—
239C2×Q8—261no—
240C2×Q8—262no—
241C2×Q8—261no—
242C2×Q8—262no—
243C2×Q8—521no—
244C2×Q8—521no—
245C2×Q8C22×D1311yescharacteristic
246C2×D4—131no—
247C22×C4—21no—
248C22×C4—131no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4C22×D1311yescharacteristic
253Q16—262no—
254Q16—521no—
255Q16—521no—
256C2×C8—131no—
257C2×C8—131no—
258C2×C8—521no—
259C2×C8—521no—
260C2×C8C22×D1311yescharacteristic
261C2×C8C22×D1311yescharacteristic
262C4⋊C4—21no—
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⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4C22×D1311yescharacteristic
276C4⋊C4C22×D1311yescharacteristic
277C4⋊C4C22×D1311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—131no—
280C22⋊C4—131no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C42—131no—
285C42—261no—
286C42—261no—
287C13#329911yescharacteristic, complemented, Sylow
288C23—131no—
289C23D4×D1311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—132no—
293Q8—261no—
294Q8—261no—
295Q8—261no—
296Q8—261no—
297Q8—261no—
298Q8—522no—
299Q8—522no—
300Q8—1041no—
301D4—134no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4—1041no—
321C2×C4D4×D1311yescharacteristic
322C2×C4C23×D1311yescharacteristic
323C8—21no—
324C8—21no—
325C8—261no—
326C8—261no—
327C22—21no—
328C22—21no—
329C22—132no—
330C22—261no—
331C22—261no—
332C22Q16×D1312yes—
333C22C2×D4×D1311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—132no—
340C4—261no—
341C4—261no—
342C4—262no—
343C4—521no—
344C4—521no—
345C4—521no—
346C4#41×D1311yescharacteristic
347C4#8825611yescharacteristic
348C2—22no—
349C2—262no—
350C2#1171935911yescharacteristic
351C2C2×Q16×D1311yescharacteristic
352C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#484C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenter#484D13
hypocenterC13#3299
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. #11718712C2semidirect
5. C2×#88050C2semidirect
6. #11718548C2semidirect
7. #11718545C2semidirect
8. #11718536C2semidirect
9. #11718534C2semidirect
10. #11718469C2semidirect
11. D13×#103C2semidirect
12. #11718454C2semidirect
13. #11718453C2semidirect
14. #11718400C2semidirect
125. C22⋊D13Q16semidirect
155. #484D13semidirect
287. C13#3299semidirect

Maximal subgroups

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

subgroupindex
#117193372
#117192162
C13×#4842
#117187122
C2×#880502
#117185482
#117185452
#117185362
#117185342
#117184692
D13×#1032
#117184542
#117184532
#117184002
#117183862
#329913