Finite Group Databasebeta

← #13125941

Subgroups — #13125941

Order 1664.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719530C211yesmaximal, characteristic, complemented
2#11719308C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic
4#11718900C211yesmaximal, characteristic, complemented
5#11718828C211yesmaximal, characteristic, complemented
6#11718823C211yesmaximal, characteristic, complemented
7#11718816C211yesmaximal, characteristic, complemented
8#11718814C211yesmaximal, characteristic, complemented
9#11718701C211yesmaximal, characteristic, complemented
10#11718454C211yesmaximal, characteristic, complemented
11#11718453C211yesmaximal, characteristic, complemented
12#11718428C211yesmaximal, characteristic, complemented
13#11718426C211yesmaximal, characteristic, complemented
14#11718400C211yesmaximal, characteristic, complemented
15#11718381C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C13×#121C2211yescharacteristic
21#88198C2211yescharacteristic
22#88198C2211yescharacteristic
23C2×#6107C2211yescharacteristic
24#88190—21no—
25#88190C2211yescharacteristic
26#88190C2211yescharacteristic
27#88190C2211yescharacteristic
28#88189—21no—
29#88189—21no—
30#88189—21no—
31D4×Dic13C2211yescharacteristic
32C2×#6105C2211yescharacteristic
33C2×#6105C2211yescharacteristic
34C2×#6105C2211yescharacteristic
35#88180C2211yescharacteristic
36#88178—21no—
37#88178—21no—
38#88178C2211yescharacteristic
39C2×Dic52C2211yescharacteristic
40C2×Dic52C2211yescharacteristic
41#88142C2211yescharacteristic
42#88141C2211yescharacteristic
43#88133—21no—
44#88132—21no—
45C13×#103C2211yescharacteristic
46C13×#102C2211yescharacteristic
47C13×C22⋊C8C2211yescharacteristic
48#88075C2211yescharacteristic
49#88072C2211yescharacteristic
50C22⋊#1055C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56C8×Dic13C2211yescharacteristic
57#88050C2211yescharacteristic
58#88050C2211yescharacteristic
59C13×#41—41no—
60C13×#41—41no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—41no—
73C2×Dic26—41no—
74C2×Dic26C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C2×Dic26C2311yescharacteristic
77C13×SD16—41no—
78C13×D8—41no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13D411yescharacteristic
92C22⋊Dic13D411yescharacteristic
93#6107—41no—
94#6105—41no—
95#6105—41no—
96#6105—41no—
97C4⋊Dic13D411yescharacteristic
98C4⋊Dic13D411yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101—21no—
107C4×Dic13—21no—
108C4×Dic13C2311yescharacteristic
109C4×Dic13C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112Dic52—41no—
113Dic52—41no—
114#3225—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C2×D411yescharacteristic
118Q8×C13—21no—
119Q8×C13—21no—
120D4×C13—21no—
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—42no—
125D4×C13—81no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—42no—
138C2×Dic13—81no—
139C2×Dic13C2×D411yescharacteristic
140C2×Dic13C2×D411yescharacteristic
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143Dic26—21no—
144Dic26—21no—
145Dic26—21no—
146Dic26—21no—
147Dic26—21no—
148Dic26—21no—
149Dic26—42no—
150Dic26—81no—
151C8×C13—21no—
152C8×C13—21no—
153#1055—21no—
154#1055—21no—
155#542—131no—
156#536—131no—
157#497—131no—
158#495—131no—
159#489—131no—
160#487—131no—
161#464—131no—
162#463—131no—
163#462—131no—
164#461—131no—
165#452—131no—
166#451—131no—
167#449D1311yescharacteristic
168#448—131no—
169#433—131no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13C22×D411yescharacteristic
180C4×C13—21no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13H(5,𝔽2)11yescharacteristic
184C4×C13H(5,𝔽2)11yescharacteristic
185Dic13—21no—
186Dic13—21no—
187Dic13—21no—
188Dic13—21no—
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193C2×#41C2×D1311yescharacteristic
194C22×Q8—131no—
195C2×Q16—131no—
196C2×Q16—131no—
197C2×Q16—131no—
198C2×SD16—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×SD16C2×D1311yescharacteristic
202C2×D8C2×D1311yescharacteristic
203C4⋊Q8—131no—
204C4⋊Q8—131no—
205C4⋊Q8—131no—
206#126—261no—
207#124—131no—
208#124—131no—
209#124—131no—
210#124—261no—
211#123—261no—
212#123—261no—
213#123—261no—
214C22⋊Q8—131no—
215C22⋊Q8—261no—
216C22⋊Q8—261no—
217C22⋊Q8—261no—
218#121C2×D1311yescharacteristic
219C4×Q8—131no—
220C4×D4—131no—
221#117—131no—
222C4⋊C8—131no—
223C4⋊C8—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#103—131no—
229#103C2×D1311yescharacteristic
230#102—131no—
231#102C2×D1311yescharacteristic
232C22⋊C8—131no—
233C22⋊C8C2×D1311yescharacteristic
234#97—131no—
235C4×C8—131no—
236C2×C13—41no—
237C2×C13—81no—
238C2×C13—81no—
239C2×C13#53511yescharacteristic
240C2×C13#57711yescharacteristic
241C2×C13#57811yescharacteristic
242#41—41no—
243#41—41no—
244C2×Q8—131no—
245C2×Q8—131no—
246C2×Q8—131no—
247C2×Q8—261no—
248C2×Q8—261no—
249C2×Q8—521no—
250C2×Q8—521no—
251C2×Q8C22×D1311yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4C22×D1311yescharacteristic
255C2×D4C22×D1311yescharacteristic
256C22×C4—21no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4C22×D1311yescharacteristic
260Q16—521no—
261Q16—521no—
262Q16—521no—
263SD16—41no—
264SD16—521no—
265SD16—521no—
266SD16—521no—
267D8—41no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8C22×D1311yescharacteristic
271C2×C8C22×D1311yescharacteristic
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4C22×D1311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—131no—
285C22⋊C4—131no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C42—131no—
295C42—131no—
296C42—261no—
297C13#322511yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23D4×D1311yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—261no—
304Q8—261no—
305Q8—261no—
306Q8—261no—
307Q8—261no—
308Q8—261no—
309Q8—522no—
310Q8—1041no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—81no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—131no—
323C2×C4—131no—
324C2×C4—131no—
325C2×C4—131no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—522no—
331C2×C4—1041no—
332C2×C4D4×D1311yescharacteristic
333C2×C4C23×D1311yescharacteristic
334C8—21no—
335C8—21no—
336C8—261no—
337C8—261no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22C2×D4×D1311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—261no—
352C4—261no—
353C4—261no—
354C4—261no—
355C4—521no—
356C4—521no—
357C4—521no—
358C4—521no—
359C4#8825111yescharacteristic
360C4#8825111yescharacteristic
361C2—41no—
362C2—81no—
363C2—81no—
364C2#1171929711yescharacteristic
365C2#1171947611yescharacteristic
366C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3225
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11719530C2semidirect
2. #11719308C2semidirect
4. #11718900C2semidirect
5. #11718828C2semidirect
6. #11718823C2semidirect
7. #11718816C2semidirect
8. #11718814C2semidirect
9. #11718701C2semidirect
10. #11718454C2semidirect
11. #11718453C2semidirect
12. #11718428C2semidirect
13. #11718426C2semidirect
14. #11718400C2semidirect
15. #11718381C2semidirect
297. C13#3225semidirect

Maximal subgroups

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

subgroupindex
#117195302
#117193082
C13×#4492
#117189002
#117188282
#117188232
#117188162
#117188142
#117187012
#117184542
#117184532
#117184282
#117184262
#117184002
#117183812
#322513