Finite Group Databasebeta

← #13127591

Subgroups — #13127591

Order 1664.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719290C211yesmaximal, characteristic, complemented
2#11719284C211yesmaximal, characteristic, complemented
3C13×#446C211yesmaximal, characteristic, complemented
4#11718508C211yesmaximal, characteristic, complemented
5#11718507C211yesmaximal, characteristic, complemented
6#11718505C211yesmaximal, characteristic, complemented
7#11718505C211yesmaximal, characteristic, complemented
8#11718504C211yesmaximal, characteristic
9#11718490C211yesmaximal, characteristic, complemented
10#11718375C211yesmaximal, characteristic, complemented
11#11718374C211yesmaximal, characteristic, complemented
12#11718372C211yesmaximal, characteristic, complemented
13#11718371C211yesmaximal, characteristic, complemented
14#11718358C211yesmaximal, characteristic, complemented
15C4×D104C211yesmaximal, characteristic, complemented
16C4×Q8×C13C2211yescharacteristic
17#88201—21no—
18#88200—21no—
19C2×D104C2211yescharacteristic
20C2×D104C2211yescharacteristic
21C2×#6095C2211yescharacteristic
22#88150—21no—
23#88150—21no—
24#88148—21no—
25#88148—21no—
26#88147—21no—
27C4⋊C4×D13—21no—
28#88129C2211yescharacteristic
29#88129C2211yescharacteristic
30#88128C2211yescharacteristic
31C4×D52C2211yescharacteristic
32C4×D52C2211yescharacteristic
33C4×D52C2211yescharacteristic
34C4×D52C2211yescharacteristic
35C4×D52C2211yescharacteristic
36#88124C2211yescharacteristic
37#88124C2211yescharacteristic
38#88123C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#97C2211yescharacteristic
44C13×#97C2211yescharacteristic
45C4×C8×C13C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88061C2211yescharacteristic
53#88058C2211yescharacteristic
54#88058C2211yescharacteristic
55#88057C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C2×Q8×C13D411yescharacteristic
60C2×D52—21no—
61C2×D52—21no—
62C2×D52C2311yescharacteristic
63C2×D52C2311yescharacteristic
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×Dic26—21no—
71C2×Dic26C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4D411yescharacteristic
77C13×C4⋊C4D411yescharacteristic
78C13×C4⋊C4D411yescharacteristic
79C42×C13C2311yescharacteristic
80C42×C13C2311yescharacteristic
81C42×C13C2311yescharacteristic
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102D104—22no—
103D104—22no—
104#6095—22no—
105#3370—131nomaximal, Sylow
106C22×D13—21no—
107C22×D13—21no—
108C22×D13—21no—
109Q8×C13—41no—
110C2×C4×C13C2×D411yescharacteristic
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2411yescharacteristic
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122D52—21no—
123D52—21no—
124D52—21no—
125D52—21no—
126D52—21no—
127D52—42no—
128D52—81no—
129D52#4112yes—
130C4×D13—42no—
131C4×D13—81no—
132C4×D13—81no—
133C4×D13—81no—
134C4×D13—81no—
135Dic26—21no—
136Dic26—21no—
137Dic26—81no—
138C8×C13—21no—
139C8×C13—21no—
140C8×C13—21no—
141C8×C13—21no—
142#559—131no—
143#554—131no—
144#490—131no—
145#489—131no—
146#488—131no—
147#479—131no—
148#478—131no—
149#474—131no—
150#463—131no—
151#463—131no—
152#459—131no—
153#446D1311yescharacteristic, complemented
154#442—131no—
155#440—131no—
156C4×D8—131no—
157C22×C13C22×D411yescharacteristic
158C2×D13—22no—
159C2×D13—41no—
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13C2×#4111yescharacteristic
174C4×C132−1+411yescharacteristic
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180C2×SD16—131no—
181C2×D8—131no—
182C2×D8—131no—
183C4⋊Q8—131no—
184#127—131no—
185#125—131no—
186#125—131no—
187#124—131no—
188#124—131no—
189#124—261no—
190#123—261no—
191#123—261no—
192C22⋊Q8—261no—
193C22⋊Q8—261no—
194C22⋊Q8—261no—
195C4×Q8—131no—
196C4×Q8C2×D1311yescharacteristic
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—131no—
201C4×D4—131no—
202C4×D4—261no—
203C2×C4⋊C4—261no—
204#107—131no—
205#107—131no—
206#106—131no—
207C4⋊C8C2×D1311yescharacteristic
208C4⋊C8C2×D1311yescharacteristic
209C4⋊C8C2×D1311yescharacteristic
210#103—131no—
211#103—131no—
212#103—131no—
213#102—131no—
214#102—131no—
215#102—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#97C2×D1311yescharacteristic
221#97C2×D1311yescharacteristic
222C4×C8C2×D1311yescharacteristic
223C2×C13#54811yescharacteristic
224C2×C13#57511yescharacteristic
225C2×C13#57611yescharacteristic
226D13—42no—
227D13—81no—
228D13—81no—
229C2×Q8—131no—
230C2×Q8—261no—
231C2×Q8D5211yescharacteristic
232C2×D4—131no—
233C2×D4—131no—
234C2×D4—131no—
235C2×D4—261no—
236C2×D4—261no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242SD16—262no—
243D8—262no—
244D8—262no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C2×C8C22×D1311yescharacteristic
248C2×C8C22×D1311yescharacteristic
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4D5211yescharacteristic
260C4⋊C4D5211yescharacteristic
261C4⋊C4D5211yescharacteristic
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C42—261no—
272C42C22×D1311yescharacteristic
273C42C22×D1311yescharacteristic
274C42C22×D1311yescharacteristic
275C13#337011yescharacteristic, complemented, Sylow
276C23—261no—
277C23—261no—
278C23—261no—
279Q8—41no—
280Q8—261no—
281Q8—261no—
282Q8—1041no—
283D4—132no—
284D4—261no—
285D4—261no—
286D4—261no—
287D4—261no—
288D4—261no—
289D4—522no—
290D4—1041no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—522no—
297C2×C4—1041no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4C2×D5211yescharacteristic
302C2×C4C2×D5211yescharacteristic
303C2×C4C2×D5211yescharacteristic
304C2×C4C2×D5211yescharacteristic
305C2×C4C2×D5211yescharacteristic
306C2×C4C2×D5211yescharacteristic
307C2×C4C23×D1311yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C22—262no—
313C22—521no—
314C22—521no—
315C22—521no—
316C22—521no—
317C22—521no—
318C22—521no—
319C22—521no—
320C22—521no—
321C22C22×D5211yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—521no—
329C4—521no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4#8825411yescharacteristic
334C4#41×D1311yescharacteristic
335C2—522no—
336C2—1041no—
337C2—1041no—
338C2#1171928111yescharacteristic
339C2#1171945311yescharacteristic
340C2#1171945711yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#446C2
socleC22×C13C22×D4
prime radical#11718504C2
hypercenter#446D13
hypocenterC13#3370
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #11719290C2semidirect
2. #11719284C2semidirect
3. C13×#446C2semidirect
4. #11718508C2semidirect
5. #11718507C2semidirect
6. #11718505C2semidirect
7. #11718505C2semidirect
9. #11718490C2semidirect
10. #11718375C2semidirect
11. #11718374C2semidirect
12. #11718372C2semidirect
13. #11718371C2semidirect
14. #11718358C2semidirect
15. C4×D104C2semidirect
153. #446D13semidirect
275. C13#3370semidirect

Maximal subgroups

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

subgroupindex
#117192902
#117192842
C13×#4462
#117185082
#117185072
#117185052
#117185042
#117184902
#117183752
#117183742
#117183722
#117183712
#117183582
C4×D1042
#337013