Finite Group Databasebeta

← #13125125

Subgroups — #13125125

Order 1664.

382 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#11719424C211yesmaximal, characteristic
2#11719277C211yesmaximal, characteristic, complemented
3C13×#460C211yesmaximal, characteristic, complemented
4#11718831C211yesmaximal, characteristic, complemented
5#11718831C211yesmaximal, characteristic, complemented
6#11718825C211yesmaximal, characteristic, complemented
7SD16×Dic13C211yesmaximal, characteristic, complemented
8#11718736C211yesmaximal, characteristic, complemented
9#11718683C211yesmaximal, characteristic, complemented
10#11718501C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718445C211yesmaximal, characteristic, complemented
13#11718440C211yesmaximal, characteristic, complemented
14#11718419C211yesmaximal, characteristic, complemented
15#11718418C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C13×#127C2211yescharacteristic
20C4×Q8×C13C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22#88193—21no—
23#88193—21no—
24#88192C2211yescharacteristic
25#88192C2211yescharacteristic
26#88189—21no—
27#88189—21no—
28D4×Dic13C2211yescharacteristic
29D4×Dic13C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31C2×#6105C2211yescharacteristic
32#88146—21no—
33#88146C2211yescharacteristic
34#88141—21no—
35#88141C2211yescharacteristic
36#88126—21no—
37#88126C2211yescharacteristic
38#88124C2211yescharacteristic
39C4×Dic26—21no—
40C4×Dic26C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88055C2211yescharacteristic
55C8×Dic13C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C2×D4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68Q8×D13—22no—
69Q8×D13—22no—
70C2×C4×D13—21no—
71C2×C4×D13C2311yescharacteristic
72C2×Dic26—21no—
73C2×Dic26C2311yescharacteristic
74C13×SD16—22no—
75C13×SD16—22no—
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4—21no—
79C13×C4⋊C4C2311yescharacteristic
80C42×C13—21no—
81C42×C13C2311yescharacteristic
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86#6105—22no—
87#6105—22no—
88#6103—21no—
89#6103D411yescharacteristic
90#6103D411yescharacteristic
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101D411yescharacteristic
100#6101D411yescharacteristic
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3126—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13—21no—
111C22×D13C2×D411yescharacteristic
112Q8×C13—21no—
113Q8×C13#4112yes—
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—21no—
118D4×C13—81no—
119D4×C13—81no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C22⋊D13—81no—
126C22⋊D13—81no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—81no—
132C2×Dic13—81no—
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C4×D13—24no—
137C4×D13—21no—
138C4×D13—21no—
139Dic26—24no—
140Dic26—21no—
141Dic26#4112yes—
142C8×C13—21no—
143C8×C13—21no—
144#1055—21no—
145#1055—21no—
146#540—131no—
147#519—131no—
148#482—131no—
149#482—131no—
150#479—131no—
151#479—131no—
152#460—131no—
153#460D1311yescharacteristic, complemented
154#448—131no—
155#448—131no—
156#440—131no—
157#440—131no—
158C4×SD16—131no—
159C4×SD16—131no—
160#433—131no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13C22×D411yescharacteristic
168C2×D13—21no—
169C2×D13—21no—
170C2×D13—21no—
171C4×C13—22no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13C2×#4111yescharacteristic
176C4×C13C2×#4111yescharacteristic
177Dic13—21no—
178Dic13—22no—
179Dic13—21no—
180Dic13—21no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184C22×Q8—131no—
185C2×SD16—131no—
186C2×SD16—131no—
187C2×SD16C2×D1311yescharacteristic
188C2×SD16C2×D1311yescharacteristic
189#127C2×D1311yescharacteristic
190#125—131no—
191#123—261no—
192#123—261no—
193#121—131no—
194#121—131no—
195#121—261no—
196#121—261no—
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8—131no—
200C4×Q8—261no—
201C4×Q8—261no—
202C4×Q8C2×D1311yescharacteristic
203C4×D4—131no—
204C4×D4—131no—
205#117—131no—
206#117—131no—
207#117—261no—
208#117—261no—
209#107—131no—
210#107—131no—
211#106—131no—
212#106—131no—
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—81no—
228C2×C13—81no—
229C2×C13#52511yescharacteristic
230C2×C13#57711yescharacteristic
231C2×C13#57711yescharacteristic
232D13—41no—
233C2×Q8—131no—
234C2×Q8—261no—
235C2×Q8—262no—
236C2×Q8—262no—
237C2×Q8C22×D1311yescharacteristic
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4C22×D1311yescharacteristic
243C2×D4C22×D1311yescharacteristic
244C22×C4—131no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248SD16—22no—
249SD16—22no—
250SD16—262no—
251SD16—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—131no—
261C4⋊C4—131no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4C22×D1311yescharacteristic
268C22⋊C4—131no—
269C22⋊C4—131no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C42—21no—
276C42—131no—
277C42—261no—
278C42—261no—
279C42—261no—
280C42—261no—
281C42C22×D1311yescharacteristic
282C13#312611yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—131no—
286Q8—21no—
287Q8—132no—
288Q8—264no—
289Q8—261no—
290Q8#612912yes—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4—81no—
297D4—1041no—
298D4—1041no—
299C2×C4—21no—
300C2×C4—21no—
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—261no—
311C2×C4—1041no—
312C2×C4—1041no—
313C2×C4D4×D1311yescharacteristic
314C2×C4D4×D1311yescharacteristic
315C2×C4C23×D1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—261no—
319C8—261no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—261no—
327C22—261no—
328C22—261no—
329C22C2×D4×D1311yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—261no—
335C4—261no—
336C4—261no—
337C4—262no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4C2×#612911yescharacteristic
342C4#41×D1311yescharacteristic
343C2—81no—
344C2—81no—
345C2—521no—
346C2#1171931111yescharacteristic
347C2#1171946711yescharacteristic
348C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#460C2
socleC22×C13C22×D4
prime radical#11719424C2
hypercenter#460D13
hypocenterC13#3126
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #11719277C2semidirect
3. C13×#460C2semidirect
4. #11718831C2semidirect
5. #11718831C2semidirect
6. #11718825C2semidirect
7. SD16×Dic13C2semidirect
8. #11718736C2semidirect
9. #11718683C2semidirect
10. #11718501C2semidirect
11. #11718490C2semidirect
12. #11718445C2semidirect
13. #11718440C2semidirect
14. #11718419C2semidirect
15. #11718418C2semidirect
153. #460D13semidirect
282. C13#3126semidirect

Maximal subgroups

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

subgroupindex
#117194242
#117192772
C13×#4602
#117188312
#117188252
SD16×Dic132
#117187362
#117186832
#117185012
#117184902
#117184452
#117184402
#117184192
#117184182
#312613