Finite Group Databasebeta

← #13124822

Subgroups — #13124822

Order 1664.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719334C211yesmaximal, characteristic
2#11719228C211yesmaximal, characteristic, complemented
3C13×#485C211yesmaximal, characteristic, complemented
4#11718704C211yesmaximal, characteristic, complemented
5#11718664C211yesmaximal, characteristic, complemented
6#11718546C211yesmaximal, characteristic, complemented
7#11718542C211yesmaximal, characteristic, complemented
8#11718524C211yesmaximal, characteristic, complemented
9D13×#106C211yesmaximal, characteristic, complemented
10#11718476C211yesmaximal, characteristic, complemented
11#11718466C211yesmaximal, characteristic, complemented
12#11718465C211yesmaximal, characteristic, complemented
13#11718464C211yesmaximal, characteristic, complemented
14#11718396C211yesmaximal, characteristic, complemented
15#11718388C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#117C2211yescharacteristic
20#88200C2211yescharacteristic
21#88184C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6094C2211yescharacteristic
24C2×C8×D13C2211yescharacteristic
25#88150—21no—
26#88149—21no—
27#88149C2211yescharacteristic
28#88146C2211yescharacteristic
29#88146C2211yescharacteristic
30C4⋊C4×D13C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33#88138—21no—
34#88138—21no—
35#88135—21no—
36#88135—21no—
37C4×D52—21no—
38C4×Dic26—21no—
39C13×#107C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88060C2211yescharacteristic
50#88060C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13—21no—
62C2×C22⋊D13D411yescharacteristic
63C2×C22⋊D13D411yescharacteristic
64C22×Dic13—21no—
65#6131—22no—
66#6131—22no—
67#6127—22no—
68#6127—22no—
69C2×D52—21no—
70C2×D52—21no—
71C2×D52D411yescharacteristic
72C2×D52C2311yescharacteristic
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13C2311yescharacteristic
78C2×C4×D13C2311yescharacteristic
79C2×Dic26D411yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C22⋊C4—21no—
87C13×C22⋊C4—21no—
88C42×C13—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—22no—
107C8×D13—22no—
108#3099—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111C22×D13C2×D411yescharacteristic
112C22×D13C2×D411yescharacteristic
113Q8×C13—21no—
114Q8×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—22no—
124C22⋊D13—22no—
125C22⋊D13—81no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—81no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132D52—22no—
133D52—21no—
134D52—21no—
135D52—42no—
136D52—81no—
137C4×D13—21no—
138C4×D13—21no—
139C4×D13—42no—
140C4×D13—81no—
141C4×D13—81no—
142C4×D13—81no—
143C4×D13#4112yes—
144C4×D13#4112yes—
145Dic26—22no—
146C8×C13—21no—
147C8×C13—21no—
148#1055—21no—
149#1055—21no—
150#537—131no—
151#520—131no—
152#485—131no—
153#485D1311yescharacteristic, complemented
154#483—131no—
155#483—131no—
156#482—131no—
157#482—131no—
158#481—131no—
159#481—131no—
160#428—131no—
161C2×#106—131no—
162#417—131no—
163#416—131no—
164#408—131no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13C22×D411yescharacteristic
169C2×D13—21no—
170C2×D13—21no—
171C2×D13—21no—
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13#12312yes—
178C4×C13—21no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13C2×#4111yescharacteristic
184C4×C13C2×#4111yescharacteristic
185Dic13—21no—
186Dic13—41no—
187Dic13—41no—
188Dic13—41no—
189Dic13#12312yes—
190C2×#41—131no—
191C2×#41—131no—
192C2×M16—131no—
193C22×C8—131no—
194C22⋊Q8—131no—
195C22⋊Q8—261no—
196C22⋊Q8C2×D1311yescharacteristic
197#121—131no—
198#121—131no—
199#121—261no—
200#121—261no—
201#121—261no—
202C4×Q8—261no—
203C4×D4—261no—
204C4×D4—261no—
205C4×D4—261no—
206#117—131no—
207#117—131no—
208#117C2×D1311yescharacteristic
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213#107—131no—
214#107C2×D1311yescharacteristic
215#106—131no—
216#106—131no—
217#106—131no—
218#106—131no—
219#106—131no—
220#106C2×D1311yescharacteristic
221#103—131no—
222#103—131no—
223#103C2×D1311yescharacteristic
224#103C2×D1311yescharacteristic
225#102—131no—
226#102—131no—
227#102—131no—
228#102—131no—
229C22⋊C8—131no—
230C22⋊C8—131no—
231C22⋊C8—131no—
232C22⋊C8C2×D1311yescharacteristic
233C2×C13—41no—
234C2×C13C2×#12311yescharacteristic
235C2×C13#57711yescharacteristic
236C2×C13#57711yescharacteristic
237D13—22no—
238D13—41no—
239D13—81no—
240#41—262no—
241#41—262no—
242#41—262no—
243#41—262no—
244C2×Q8—131no—
245C2×Q8C22×D1311yescharacteristic
246C2×D4—131no—
247C2×D4—131no—
248C2×D4—131no—
249C2×D4—131no—
250C2×D4—261no—
251C2×D4—261no—
252C2×D4—261no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4C22×D1311yescharacteristic
261M16—262no—
262C2×C8—131no—
263C2×C8—131no—
264C2×C8—262no—
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⋊C4C22×D1311yescharacteristic
277C4⋊C4C22×D1311yescharacteristic
278C4⋊C4C22×D1311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C42—21no—
287C42—261no—
288C42—261no—
289C13#309911yescharacteristic, complemented, Sylow
290C23—131no—
291C23—131no—
292C23—261no—
293C23D4×D1311yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—262no—
297D4—262no—
298D4—262no—
299D4—262no—
300D4—261no—
301D4—261no—
302D4—522no—
303D4—1041no—
304D4—1041no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—131no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—131no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—522no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4—1041no—
324C2×C4—1041no—
325C2×C4D4×D1311yescharacteristic
326C2×C4C23×D1311yescharacteristic
327C8—21no—
328C8—21no—
329C8—261no—
330C8—261no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—132no—
335C22—261no—
336C22—261no—
337C22—261no—
338C22—261no—
339C22—261no—
340C22—521no—
341C22—521no—
342C22—521no—
343C22C2×D4×D1311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—132no—
350C4—261no—
351C4—521no—
352C4—521no—
353C4—521no—
354C4#41×D1311yescharacteristic
355C4#41×D1311yescharacteristic
356C2—41no—
357C2—262no—
358C2—521no—
359C2—1041no—
360C2D13×#12311yescharacteristic
361C2#1171947511yescharacteristic
362C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
prime radical#11719334C2
hypercenter#485D13
hypocenterC13#3099
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. #11719228C2semidirect
3. C13×#485C2semidirect
4. #11718704C2semidirect
5. #11718664C2semidirect
6. #11718546C2semidirect
7. #11718542C2semidirect
8. #11718524C2semidirect
9. D13×#106C2semidirect
10. #11718476C2semidirect
11. #11718466C2semidirect
12. #11718465C2semidirect
13. #11718464C2semidirect
14. #11718396C2semidirect
15. #11718388C2semidirect
153. #485D13semidirect
289. C13#3099semidirect

Maximal subgroups

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

subgroupindex
#117193342
#117192282
C13×#4852
#117187042
#117186642
#117185462
#117185422
#117185242
D13×#1062
#117184762
#117184662
#117184652
#117184642
#117183962
#117183882
#309913