Finite Group Databasebeta

← #13127594

Subgroups — #13127594

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#11719264C211yesmaximal, characteristic, complemented
2#11719248C211yesmaximal, characteristic, complemented
3C13×#442C211yesmaximal, characteristic, complemented
4#11718814C211yesmaximal, characteristic, complemented
5#11718811C211yesmaximal, characteristic
6#11718677C211yesmaximal, characteristic, complemented
7#11718668C211yesmaximal, characteristic, complemented
8#11718532C211yesmaximal, characteristic, complemented
9#11718518C211yesmaximal, characteristic, complemented
10#11718429C211yesmaximal, characteristic, complemented
11#11718425C211yesmaximal, characteristic, complemented
12#11718418C211yesmaximal, characteristic, complemented
13#11718417C211yesmaximal, characteristic, complemented
14#11718375C211yesmaximal, characteristic, complemented
15#11718362C211yesmaximal, characteristic, complemented
16C2×C13×D8C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19#88194C2211yescharacteristic
20#88190C2211yescharacteristic
21D4×Dic13C2211yescharacteristic
22D4×Dic13C2211yescharacteristic
23C2×#6105C2211yescharacteristic
24C2×#6104C2211yescharacteristic
25#88183—21no—
26C4×C22⋊D13—21no—
27C2×C4⋊Dic13—21no—
28#88178—21no—
29#88147C2211yescharacteristic
30#88144C2211yescharacteristic
31#88144C2211yescharacteristic
32#88141C2211yescharacteristic
33#88139—21no—
34#88137—21no—
35#88132—21no—
36#88132—21no—
37#88129C2211yescharacteristic
38#88123C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×#102C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#97C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88056C2211yescharacteristic
49#88056C2211yescharacteristic
50#88055C2211yescharacteristic
51#88054C2211yescharacteristic
52#88054C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×D4×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×Dic26—21no—
70C2×Dic26D411yescharacteristic
71C2×Dic26C2311yescharacteristic
72C13×D8—22no—
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C42×C13C2311yescharacteristic
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84#6105—22no—
85#6104—22no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13D411yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101D411yescharacteristic
99#6101D411yescharacteristic
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3370—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C22×D13—21no—
109D4×C13—21no—
110D4×C13—21no—
111D4×C13—21no—
112D4×C13#4112yes—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13—81no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—42no—
121C22⋊D13—81no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—81no—
126C2×Dic13—81no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131D52—21no—
132D52—21no—
133C4×D13—81no—
134Dic26—21no—
135Dic26—21no—
136Dic26—41no—
137Dic26—81no—
138C8×C13—21no—
139C8×C13—21no—
140#1055—21no—
141#1055—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#446—131no—
154#442D1311yescharacteristic, complemented
155#440—131no—
156C4×D8—131no—
157C22×C13—22no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#4111yescharacteristic
172C4×C132−1+411yescharacteristic
173Dic13—21no—
174Dic13—21no—
175Dic13—21no—
176Dic13—21no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180C2×SD16—131no—
181C2×D8—131no—
182C2×D8C2×D1311yescharacteristic
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×Q8—131no—
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—261no—
201C4×D4C2×D1311yescharacteristic
202C4×D4C2×D1311yescharacteristic
203C2×C4⋊C4—261no—
204#107—131no—
205#107—131no—
206#106C2×D1311yescharacteristic
207C4⋊C8—131no—
208C4⋊C8—131no—
209C4⋊C8—131no—
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#102C2×D1311yescharacteristic
219#102C2×D1311yescharacteristic
220#97—131no—
221#97C2×D1311yescharacteristic
222C4×C8—131no—
223C2×C13—42no—
224C2×C13—81no—
225C2×C13#54811yescharacteristic
226C2×C13#57511yescharacteristic
227C2×C13#57611yescharacteristic
228D13—81no—
229C2×Q8—131no—
230C2×Q8—131no—
231C2×Q8—261no—
232C2×D4—131no—
233C2×D4—261no—
234C2×D4—261no—
235C2×D4C22×D1311yescharacteristic
236C2×D4C22×D1311yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242SD16—262no—
243D8—22no—
244D8—262no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8C22×D1311yescharacteristic
248C2×C8C22×D1311yescharacteristic
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C42—131no—
272C42—131no—
273C42—261no—
274C42C22×D1311yescharacteristic
275C13#337011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—261no—
279Q8—261no—
280Q8—261no—
281Q8—521no—
282Q8—1041no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—261no—
287D4—261no—
288D4—522no—
289D4—1041no—
290D4#612712yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4—1041no—
305C2×C4D4×D1311yescharacteristic
306C2×C4D4×D1311yescharacteristic
307C2×C4C23×D1311yescharacteristic
308C8—21no—
309C8—21no—
310C8—261no—
311C8—261no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—521no—
319C22—521no—
320C22—521no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—261no—
327C4—261no—
328C4—261no—
329C4—261no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4C2×#612711yescharacteristic
334C4#8825711yescharacteristic
335C2—42no—
336C2—81no—
337C2—1041no—
338C2#1171925711yescharacteristic
339C2#1171947811yescharacteristic
340C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#442C2
socleC22×C13C22×D4
prime radical#11718811C2
hypercenter#442D13
hypocenterC13#3370
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11719264C2semidirect
2. #11719248C2semidirect
3. C13×#442C2semidirect
4. #11718814C2semidirect
6. #11718677C2semidirect
7. #11718668C2semidirect
8. #11718532C2semidirect
9. #11718518C2semidirect
10. #11718429C2semidirect
11. #11718425C2semidirect
12. #11718418C2semidirect
13. #11718417C2semidirect
14. #11718375C2semidirect
15. #11718362C2semidirect
154. #442D13semidirect
275. C13#3370semidirect

Maximal subgroups

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

subgroupindex
#117192642
#117192482
C13×#4422
#117188142
#117188112
#117186772
#117186682
#117185322
#117185182
#117184292
#117184252
#117184182
#117184172
#117183752
#117183622
#337013