Finite Group Databasebeta

← #13127013

Subgroups — #13127013

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#11719337C211yesmaximal, characteristic, complemented
2#11719323C211yesmaximal, characteristic
3C13×#465C211yesmaximal, characteristic, complemented
4#11718831C211yesmaximal, characteristic, complemented
5#11718823C211yesmaximal, characteristic, complemented
6#11718772C211yesmaximal, characteristic, complemented
7C2×#88056C211yesmaximal, characteristic, complemented
8#11718705C211yesmaximal, characteristic, complemented
9#11718701C211yesmaximal, characteristic, complemented
10#11718528C211yesmaximal, characteristic, complemented
11#11718518C211yesmaximal, characteristic, complemented
12#11718463C211yesmaximal, characteristic, complemented
13#11718458C211yesmaximal, characteristic, complemented
14#11718441C211yesmaximal, characteristic, complemented
15#11718418C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C22×C8×C13C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21C13×#121C2211yescharacteristic
22#88198C2211yescharacteristic
23#88193—21no—
24#88192C2211yescharacteristic
25D4×Dic13—21no—
26D4×Dic13C2211yescharacteristic
27C2×#6105C2211yescharacteristic
28C2×#6105C2211yescharacteristic
29C4×C22⋊D13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×#6094C2211yescharacteristic
32#88151C2211yescharacteristic
33#88150—21no—
34#88146C2211yescharacteristic
35#88144C2211yescharacteristic
36#88142—21no—
37#88141C2211yescharacteristic
38#88140—21no—
39#88135—21no—
40#88133—21no—
41#88132—21no—
42C13×#106C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#102C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13D411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68Q8×D13—22no—
69Q8×D13—41no—
70C2×C4×D13—21no—
71C2×C4×D13C2311yescharacteristic
72C2×Dic26—22no—
73C2×Dic26—21no—
74C2×Dic26—21no—
75C2×Dic26—41no—
76C2×Dic26C2311yescharacteristic
77C2×Dic26C2311yescharacteristic
78C13×SD16—41no—
79C2×C8×C13—41no—
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C13×C22⋊C4—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13D411yescharacteristic
90#6105—22no—
91#6105—41no—
92#6103—21no—
93#6103—21no—
94#6103D411yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101D411yescharacteristic
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6094—41no—
111#3320—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117D4×C13—21no—
118D4×C13—21no—
119D4×C13—42no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—22no—
128C22⋊D13—81no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—42no—
134C2×Dic13—81no—
135C2×Dic13—81no—
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C4×D13—21no—
140C4×D13—21no—
141C4×D13—42no—
142Dic26—21no—
143Dic26—21no—
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#465D1311yescharacteristic, complemented
160#461—131no—
161#448—131no—
162#448—131no—
163#440—131no—
164#435—131no—
165#419—131no—
166C2×#103—131no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13#13712yes—
173C22×C13C22×D411yescharacteristic
174C2×D13—21no—
175C2×D13—21no—
176C2×D13—21no—
177C4×C13—21no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13C2×#4111yescharacteristic
182C4×C13H(5,𝔽2)11yescharacteristic
183Dic13—22no—
184Dic13—21no—
185Dic13—21no—
186Dic13—21no—
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190C22×Q8—131no—
191C22×Q8—131no—
192C2×SD16—131no—
193C2×SD16—131no—
194C2×SD16C2×D1311yescharacteristic
195C2×M16—131no—
196C22×C8C2×D1311yescharacteristic
197C4⋊Q8—131no—
198C4⋊Q8—261no—
199#126—261no—
200#125—131no—
201#123—261no—
202C22⋊Q8—131no—
203C22⋊Q8—261no—
204C22⋊Q8—261no—
205C22⋊Q8C2×D1311yescharacteristic
206#121—131no—
207#121—261no—
208#121C2×D1311yescharacteristic
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—131no—
212C4×D4—261no—
213C4×D4—261no—
214#117—131no—
215C2×C4⋊C4—131no—
216#107—131no—
217#107—131no—
218#106C2×D1311yescharacteristic
219C4⋊C8—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#103C2×D1311yescharacteristic
229#102C2×D1311yescharacteristic
230C22⋊C8—131no—
231C22⋊C8—131no—
232#97—131no—
233C2×C13—22no—
234C2×C13—81no—
235C2×C13#54611yescharacteristic
236C2×C13C2×#13711yescharacteristic
237C2×C13#57711yescharacteristic
238D13—41no—
239C2×Q8—131no—
240C2×Q8—131no—
241C2×Q8—261no—
242C2×Q8—262no—
243C2×Q8—261no—
244C2×Q8—262no—
245C2×Q8—521no—
246C2×Q8—521no—
247C2×Q8C22×D1311yescharacteristic
248C2×D4—21no—
249C2×D4—131no—
250C2×D4—261no—
251C2×D4C22×D1311yescharacteristic
252C22×C4—131no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4C22×D1311yescharacteristic
258SD16—41no—
259SD16—262no—
260SD16—521no—
261M16—521no—
262C2×C8—41no—
263C2×C8—131no—
264C2×C8—131no—
265C2×C8C22×D1311yescharacteristic
266C2×C8C22×D1311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—131no—
269C4⋊C4—131no—
270C4⋊C4—131no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4C22×D1311yescharacteristic
279C4⋊C4C22×D1311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—131no—
283C22⋊C4—131no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C42—131no—
289C42—261no—
290C42—261no—
291C13#332011yescharacteristic, complemented, Sylow
292C23—21no—
293C23—131no—
294C23D4×D1311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—132no—
298Q8—261no—
299Q8—261no—
300Q8—261no—
301Q8—522no—
302Q8—522no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—262no—
307D4—1041no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—131no—
314C2×C4—131no—
315C2×C4—131no—
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×C4—1041no—
326C2×C4D4×D1311yescharacteristic
327C2×C4C23×D1311yescharacteristic
328C8—21no—
329C8—21no—
330C8—261no—
331C8—261no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—261no—
338C22—261no—
339C22—261no—
340C22#8816912yes—
341C22C2×D4×D1311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—261no—
347C4—261no—
348C4—261no—
349C4—262no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4#8825111yescharacteristic
354C4#41×D1311yescharacteristic
355C2—22no—
356C2—81no—
357C2—521no—
358C2#1171931511yescharacteristic
359C2C2×#8816911yescharacteristic
360C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
prime radical#11719323C2
hypercenter#465D13
hypocenterC13#3320
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11719337C2semidirect
3. C13×#465C2semidirect
4. #11718831C2semidirect
5. #11718823C2semidirect
6. #11718772C2semidirect
7. C2×#88056C2semidirect
8. #11718705C2semidirect
9. #11718701C2semidirect
10. #11718528C2semidirect
11. #11718518C2semidirect
12. #11718463C2semidirect
13. #11718458C2semidirect
14. #11718441C2semidirect
15. #11718418C2semidirect
159. #465D13semidirect
291. C13#3320semidirect

Maximal subgroups

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

subgroupindex
#117193372
#117193232
C13×#4652
#117188312
#117188232
#117187722
C2×#880562
#117187052
#117187012
#117185282
#117185182
#117184632
#117184582
#117184412
#117184182
#332013