Finite Group Databasebeta

← #13125947

Subgroups — #13125947

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#11719239C211yesmaximal, characteristic, complemented
2#11719231C211yesmaximal, characteristic, complemented
3C13×#433C211yesmaximal, characteristic, complemented
4#11718510C211yesmaximal, characteristic, complemented
5#11718506C211yesmaximal, characteristic, complemented
6#11718505C211yesmaximal, characteristic, complemented
7#11718502C211yesmaximal, characteristic, complemented
8#11718400C211yesmaximal, characteristic, complemented
9#11718399C211yesmaximal, characteristic, complemented
10#11718395C211yesmaximal, characteristic
11#11718394C211yesmaximal, characteristic, complemented
12#11718376C211yesmaximal, characteristic, complemented
13#11718375C211yesmaximal, characteristic, complemented
14#11718357C211yesmaximal, characteristic, complemented
15#11718342C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C13×#117C2211yescharacteristic
19#88184C2211yescharacteristic
20#88178C2211yescharacteristic
21C2×Dic52C2211yescharacteristic
22C2×Dic52C2211yescharacteristic
23C2×Dic52C2211yescharacteristic
24C2×D104C2211yescharacteristic
25C2×#6095C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27C2×#6095C2211yescharacteristic
28C2×#6095C2211yescharacteristic
29#88152—21no—
30#88151—21no—
31#88151—21no—
32#88150—21no—
33#88140—21no—
34#88140—21no—
35#88139—21no—
36#88137—21no—
37#88129C2211yescharacteristic
38#88129C2211yescharacteristic
39#88129C2211yescharacteristic
40C4×D52C2211yescharacteristic
41#88123C2211yescharacteristic
42#88123C2211yescharacteristic
43#88123C2211yescharacteristic
44C4×Dic26C2211yescharacteristic
45C13×C4⋊C8C2211yescharacteristic
46C13×C4⋊C8C2211yescharacteristic
47C13×C22⋊C8C2211yescharacteristic
48C13×C22⋊C8C2211yescharacteristic
49C13×#97C2211yescharacteristic
50C4×C8×C13C2211yescharacteristic
51#88061C2211yescharacteristic
52#88061C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C2×C22⋊D13—21no—
61C2×C22⋊D13—21no—
62C22×Dic13—21no—
63#6127—41no—
64#6127—41no—
65C2×D52C2311yescharacteristic
66C2×D52C2311yescharacteristic
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×Dic26—41no—
72C2×Dic26—41no—
73C2×Dic26C2311yescharacteristic
74C2×Dic26C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C2×Dic26C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4D411yescharacteristic
82C13×C4⋊C4D411yescharacteristic
83C13×C22⋊C4D411yescharacteristic
84C13×C22⋊C4D411yescharacteristic
85C42×C13C2311yescharacteristic
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13C2311yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106Dic52—41no—
107Dic52—41no—
108Dic52—41no—
109D104—41no—
110#6095—41no—
111#6095—41no—
112#6095—41no—
113#6095—41no—
114#3225—131nomaximal, Sylow
115C23×C13C2×D411yescharacteristic
116C22×D13—21no—
117C22×D13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C22⋊D13—42no—
127C22⋊D13—81no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—42no—
135D52—21no—
136D52—21no—
137D52—21no—
138D52—21no—
139C4×D13—42no—
140C4×D13—81no—
141Dic26—21no—
142Dic26—21no—
143Dic26—21no—
144Dic26—21no—
145Dic26—21no—
146Dic26—21no—
147Dic26—21no—
148Dic26—21no—
149Dic26—42no—
150Dic26—81no—
151C8×C13—21no—
152C8×C13—21no—
153C8×C13—21no—
154C8×C13—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#449—131no—
168#448—131no—
169#433D1311yescharacteristic, complemented
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13C22×D411yescharacteristic
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13—41no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13H(5,𝔽2)11yescharacteristic
186C4×C13H(5,𝔽2)11yescharacteristic
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193C2×#41—131no—
194C22×Q8—131no—
195C2×Q16—131no—
196C2×Q16—131no—
197C2×Q16—131no—
198C2×SD16—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×SD16—131no—
202C2×D8—131no—
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#121—131no—
219C4×Q8—131no—
220C4×D4—131no—
221#117C2×D1311yescharacteristic
222C4⋊C8C2×D1311yescharacteristic
223C4⋊C8C2×D1311yescharacteristic
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#103—131no—
229#103—131no—
230#102—131no—
231#102—131no—
232C22⋊C8C2×D1311yescharacteristic
233C22⋊C8C2×D1311yescharacteristic
234#97C2×D1311yescharacteristic
235C4×C8C2×D1311yescharacteristic
236C2×C13—41no—
237C2×C13#53511yescharacteristic
238C2×C13#57711yescharacteristic
239C2×C13#57811yescharacteristic
240D13—81no—
241D13—81no—
242#41—521no—
243#41—521no—
244C2×Q8—131no—
245C2×Q8—131no—
246C2×Q8—131no—
247C2×Q8—131no—
248C2×Q8—261no—
249C2×Q8—261no—
250C2×Q8—521no—
251C2×Q8—521no—
252C2×D4—131no—
253C2×D4—131no—
254C2×D4—261no—
255C2×D4—261no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4C22×D1311yescharacteristic
260Q16—521no—
261Q16—521no—
262Q16—521no—
263SD16—521no—
264SD16—521no—
265SD16—521no—
266SD16—521no—
267D8—521no—
268C2×C8C22×D1311yescharacteristic
269C2×C8C22×D1311yescharacteristic
270C2×C8C22×D1311yescharacteristic
271C2×C8C22×D1311yescharacteristic
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4D5211yescharacteristic
282C4⋊C4D5211yescharacteristic
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4D5211yescharacteristic
293C22⋊C4D5211yescharacteristic
294C42—261no—
295C42C22×D1311yescharacteristic
296C42C22×D1311yescharacteristic
297C13#322511yescharacteristic, complemented, Sylow
298C23—261no—
299C23—261no—
300C23C2×D5211yescharacteristic
301Q8—261no—
302Q8—261no—
303Q8—261no—
304Q8—261no—
305Q8—261no—
306Q8—261no—
307Q8—261no—
308Q8—261no—
309Q8—522no—
310Q8—1041no—
311D4—261no—
312D4—261no—
313D4—261no—
314D4—261no—
315D4—522no—
316D4—1041no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—1041no—
328C2×C4C2×D5211yescharacteristic
329C2×C4C2×D5211yescharacteristic
330C2×C4C2×D5211yescharacteristic
331C2×C4C2×D5211yescharacteristic
332C2×C4C2×D5211yescharacteristic
333C2×C4C23×D1311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—521no—
342C22—521no—
343C22—521no—
344C22—521no—
345C22—521no—
346C22—521no—
347C22C22×D5211yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—521no—
354C4—521no—
355C4—521no—
356C4—521no—
357C4—521no—
358C4—521no—
359C4#8825611yescharacteristic
360C4#8825611yescharacteristic
361C2—41no—
362C2—1041no—
363C2—1041no—
364C2#1171923011yescharacteristic
365C2#1171945611yescharacteristic
366C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#433C2
socleC22×C13C22×D4
prime radical#11718395C2
hypercenter#433D13
hypocenterC13#3225
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #11719239C2semidirect
2. #11719231C2semidirect
3. C13×#433C2semidirect
4. #11718510C2semidirect
5. #11718506C2semidirect
6. #11718505C2semidirect
7. #11718502C2semidirect
8. #11718400C2semidirect
9. #11718399C2semidirect
11. #11718394C2semidirect
12. #11718376C2semidirect
13. #11718375C2semidirect
14. #11718357C2semidirect
15. #11718342C2semidirect
169. #433D13semidirect
297. C13#3225semidirect

Maximal subgroups

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

subgroupindex
#117192392
#117192312
C13×#4332
#117185102
#117185062
#117185052
#117185022
#117184002
#117183992
#117183952
#117183942
#117183762
#117183752
#117183572
#117183422
#322513