Finite Group Databasebeta

← #13125103

Subgroups — #13125103

Order 1664.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719438C211yesmaximal, characteristic, complemented
2#11719251C211yesmaximal, characteristic, complemented
3C13×#474C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718677C211yesmaximal, characteristic, complemented
6#11718550C211yesmaximal, characteristic, complemented
7#11718545C211yesmaximal, characteristic, complemented
8#11718543C211yesmaximal, characteristic, complemented
9#11718534C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718501C211yesmaximal, characteristic, complemented
12#11718444C211yesmaximal, characteristic, complemented
13#11718442C211yesmaximal, characteristic
14#11718418C211yesmaximal, characteristic, complemented
15#11718417C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C13×C4⋊Q8C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19#88201—21no—
20#88200—21no—
21D4×Dic13C2211yescharacteristic
22C2×#6105C2211yescharacteristic
23C2×#6104C2211yescharacteristic
24C4×C22⋊D13—21no—
25C2×#6101—21no—
26C2×Dic52C2211yescharacteristic
27C2×#6095C2211yescharacteristic
28#88152—21no—
29#88151C2211yescharacteristic
30#88149C2211yescharacteristic
31#88148—21no—
32#88147C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34#88141C2211yescharacteristic
35#88141C2211yescharacteristic
36#88135—21no—
37#88131—21no—
38#88129C2211yescharacteristic
39#88126C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#107C2211yescharacteristic
43C13×C4⋊C8C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88061C2211yescharacteristic
47#88060C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88055C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65#6129—22no—
66#6129—22no—
67C2×D52—21no—
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13C2311yescharacteristic
72C2×Dic26C2311yescharacteristic
73C2×Dic26C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4—21no—
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C42×C13C2311yescharacteristic
82C22⋊Dic13—21no—
83#6105—22no—
84#6104—22no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103D411yescharacteristic
91#6103D411yescharacteristic
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101D411yescharacteristic
99#6101D411yescharacteristic
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106Dic52—22no—
107#6095—22no—
108#3124—131nomaximal, Sylow
109C23×C13—21no—
110C22×D13—21no—
111C22×D13C2×D411yescharacteristic
112Q8×C13—81no—
113D4×C13—21no—
114D4×C13#4112yes—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—81no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C22⋊D13—24no—
123C2×Dic13—24no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—81no—
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131D52—21no—
132D52—21no—
133D52—81no—
134C4×D13—21no—
135C4×D13—21no—
136C4×D13—81no—
137C4×D13—81no—
138Dic26—21no—
139Dic26—21no—
140Dic26—21no—
141Dic26#4112yes—
142C8×C13—21no—
143C8×C13—21no—
144#1055—21no—
145#1055—21no—
146#542—131no—
147#520—131no—
148#484—131no—
149#480—131no—
150#477—131no—
151#474D1311yescharacteristic, complemented
152#464—131no—
153#463—131no—
154#452—131no—
155#449—131no—
156#440—131no—
157#440—131no—
158C4×Q16—131no—
159C4×D8—131no—
160#433—131no—
161C22×C13—22no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13C22×D411yescharacteristic
165C2×D13—21no—
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—41no—
169C2×D13—41no—
170C2×D13—41no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13C2×#4111yescharacteristic
177C4×C13C2×#4111yescharacteristic
178Dic13—22no—
179Dic13—21no—
180Dic13—21no—
181Dic13—21no—
182Dic13—41no—
183Dic13—41no—
184C2×#41—131no—
185C2×Q16—131no—
186C2×SD16—131no—
187C2×SD16—131no—
188C2×D8—131no—
189C4⋊Q8C2×D1311yescharacteristic
190#126—261no—
191#124—131no—
192#124—261no—
193#123—261no—
194C22⋊Q8—131no—
195C22⋊Q8—261no—
196#121—131no—
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8—131no—
200C4×D4—131no—
201C4×D4—131no—
202C4×D4—261no—
203C4×D4—261no—
204C4×D4C2×D1311yescharacteristic
205#117—131no—
206#117—261no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—261no—
209#107—131no—
210#107—131no—
211#107C2×D1311yescharacteristic
212#107C2×D1311yescharacteristic
213C4⋊C8—131no—
214C4⋊C8C2×D1311yescharacteristic
215#103—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#102—131no—
220#102—131no—
221#102C2×D1311yescharacteristic
222#102C2×D1311yescharacteristic
223C22⋊C8—131no—
224C22⋊C8—131no—
225#97—131no—
226C4×C8—131no—
227C2×C13—42no—
228C2×C13#52511yescharacteristic
229C2×C13#57611yescharacteristic
230C2×C13#57811yescharacteristic
231D13—41no—
232D13—81no—
233#41—262no—
234#41—262no—
235C2×Q8—21no—
236C2×Q8—131no—
237C2×Q8—131no—
238C2×D4—131no—
239C2×D4—261no—
240C2×D4—261no—
241C2×D4C22×D1311yescharacteristic
242C22×C4—21no—
243C22×C4—131no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248Q16—262no—
249SD16—262no—
250SD16—262no—
251D8—262no—
252C2×C8—131no—
253C2×C8—131no—
254C2×C8C22×D1311yescharacteristic
255C2×C8C22×D1311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4C22×D1311yescharacteristic
266C4⋊C4C22×D1311yescharacteristic
267C4⋊C4C22×D1311yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—131no—
270C22⋊C4—131no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C42—131no—
278C42—261no—
279C42—261no—
280C42—261no—
281C42C22×D1311yescharacteristic
282C13#312411yescharacteristic, complemented, Sylow
283C23—21no—
284C23—131no—
285C23—261no—
286Q8—81no—
287Q8—132no—
288Q8—261no—
289Q8—261no—
290Q8—261no—
291D4—21no—
292D4—264no—
293D4—261no—
294D4—261no—
295D4—1041no—
296D4#613112yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—264no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—1041no—
311C2×C4—1041no—
312C2×C4—1041no—
313C2×C4D4×D1311yescharacteristic
314C2×C4D4×D1311yescharacteristic
315C2×C4C23×D1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—261no—
319C8—261no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—261no—
324C22—261no—
325C22—261no—
326C22—521no—
327C22—521no—
328C22—521no—
329C22C2×D4×D1311yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—261no—
336C4—261no—
337C4—261no—
338C4—262no—
339C4—521no—
340C4—521no—
341C4C2×#613111yescharacteristic
342C4#41×D1311yescharacteristic
343C2—42no—
344C2—521no—
345C2—1041no—
346C2#1171933211yescharacteristic
347C2#1171946211yescharacteristic
348C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radical#11718442C2
hypercenter#474D13
hypocenterC13#3124
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719438C2semidirect
2. #11719251C2semidirect
3. C13×#474C2semidirect
4. #11718752C2semidirect
5. #11718677C2semidirect
6. #11718550C2semidirect
7. #11718545C2semidirect
8. #11718543C2semidirect
9. #11718534C2semidirect
10. #11718506C2semidirect
11. #11718501C2semidirect
12. #11718444C2semidirect
14. #11718418C2semidirect
15. #11718417C2semidirect
151. #474D13semidirect
282. C13#3124semidirect

Maximal subgroups

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

subgroupindex
#117194382
#117192512
C13×#4742
#117187522
#117186772
#117185502
#117185452
#117185432
#117185342
#117185062
#117185012
#117184442
#117184422
#117184182
#117184172
#312413