Finite Group Databasebeta

← #13125091

Subgroups — #13125091

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#11719532C211yesmaximal, characteristic, complemented
2#11719308C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic
4#11718900C211yesmaximal, characteristic, complemented
5#11718827C211yesmaximal, characteristic, complemented
6#11718825C211yesmaximal, characteristic, complemented
7#11718814C211yesmaximal, characteristic, complemented
8D8×Dic13C211yesmaximal, characteristic, complemented
9#11718694C211yesmaximal, characteristic, complemented
10#11718455C211yesmaximal, characteristic, complemented
11#11718451C211yesmaximal, characteristic, complemented
12#11718420C211yesmaximal, characteristic, complemented
13#11718418C211yesmaximal, characteristic, complemented
14#11718383C211yesmaximal, characteristic, complemented
15#11718381C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C2×C13×D8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23#88190—21no—
24#88190C2211yescharacteristic
25#88189—21no—
26D4×Dic13—21no—
27D4×Dic13—21no—
28D4×Dic13C2211yescharacteristic
29D4×Dic13C2211yescharacteristic
30D4×Dic13C2211yescharacteristic
31C2×#6105C2211yescharacteristic
32#88180—21no—
33#88180C2211yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2211yescharacteristic
36#88178C2211yescharacteristic
37#88142C2211yescharacteristic
38#88141C2211yescharacteristic
39#88133—21no—
40#88132—21no—
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56C8×Dic13C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C13×#41—22no—
60C13×#41—22no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C2×Dic26—21no—
73C2×Dic26C2311yescharacteristic
74C13×SD16—22no—
75C13×D8—22no—
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13D411yescharacteristic
87C22⋊Dic13D411yescharacteristic
88#6107—22no—
89#6105—22no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13D411yescharacteristic
94C4⋊Dic13D411yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105C4×Dic13C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3124—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13—21no—
111C23×C13C2×D411yescharacteristic
112Q8×C13—21no—
113Q8×C13#4112yes—
114D4×C13—24no—
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—21no—
118D4×C13—81no—
119D4×C13#4112yes—
120C2×C4×C13—24no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—81no—
132C2×Dic13—81no—
133C2×Dic13—81no—
134C2×Dic13—81no—
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139Dic26—21no—
140Dic26—21no—
141Dic26—81no—
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#474—131no—
152#464—131no—
153#463—131no—
154#452—131no—
155#449D1311yescharacteristic
156#440—131no—
157#440—131no—
158C4×Q16—131no—
159C4×D8—131no—
160#433—131no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13C22×D411yescharacteristic
171C4×C13—21no—
172C4×C13—22no—
173C4×C13—41no—
174C4×C13C2×#4111yescharacteristic
175C4×C13C2×#4111yescharacteristic
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—21no—
180Dic13—41no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184C2×#41C2×D1311yescharacteristic
185C2×Q16—131no—
186C2×SD16—131no—
187C2×SD16C2×D1311yescharacteristic
188C2×D8C2×D1311yescharacteristic
189C4⋊Q8—131no—
190#126—261no—
191#124—131no—
192#124—261no—
193#123—261no—
194C22⋊Q8—131no—
195C22⋊Q8—261no—
196#121C2×D1311yescharacteristic
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8—131no—
200C4×D4—131no—
201C4×D4—131no—
202C4×D4—131no—
203C4×D4—261no—
204C4×D4—261no—
205#117—131no—
206#117—261no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—261no—
209#107—131no—
210#107—131no—
211#107—131no—
212#107—131no—
213C4⋊C8—131no—
214C4⋊C8—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#103C2×D1311yescharacteristic
219#102—131no—
220#102—131no—
221#102—131no—
222#102C2×D1311yescharacteristic
223C22⋊C8—131no—
224C22⋊C8C2×D1311yescharacteristic
225#97—131no—
226C4×C8—131no—
227C2×C13—41no—
228C2×C13—42no—
229C2×C13—81no—
230C2×C13#52511yescharacteristic
231C2×C13#57611yescharacteristic
232C2×C13#57811yescharacteristic
233#41—22no—
234#41—22no—
235C2×Q8—131no—
236C2×Q8—261no—
237C2×Q8C22×D1311yescharacteristic
238C2×D4—21no—
239C2×D4—21no—
240C2×D4C22×D1311yescharacteristic
241C2×D4C22×D1311yescharacteristic
242C22×C4—21no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4C22×D1311yescharacteristic
248Q16—262no—
249SD16—22no—
250SD16—262no—
251D8—22no—
252C2×C8—131no—
253C2×C8—131no—
254C2×C8C22×D1311yescharacteristic
255C2×C8C22×D1311yescharacteristic
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
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—131no—
279C42—261no—
280C42—261no—
281C42—261no—
282C13#312411yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23D4×D1311yescharacteristic
286Q8—21no—
287Q8—261no—
288Q8—261no—
289Q8—1041no—
290Q8#612912yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#612912yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—131no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—1041no—
311C2×C4—1041no—
312C2×C4—1041no—
313C2×C4—1041no—
314C2×C4D4×D1311yescharacteristic
315C2×C4C23×D1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—261no—
319C8—261no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D1311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—261no—
334C4—261no—
335C4—261no—
336C4—261no—
337C4—521no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4C2×#612911yescharacteristic
342C4C2×#612911yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#1171929111yescharacteristic
347C2#1171947611yescharacteristic
348C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3124
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11719532C2semidirect
2. #11719308C2semidirect
4. #11718900C2semidirect
5. #11718827C2semidirect
6. #11718825C2semidirect
7. #11718814C2semidirect
8. D8×Dic13C2semidirect
9. #11718694C2semidirect
10. #11718455C2semidirect
11. #11718451C2semidirect
12. #11718420C2semidirect
13. #11718418C2semidirect
14. #11718383C2semidirect
15. #11718381C2semidirect
282. C13#3124semidirect

Maximal subgroups

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

subgroupindex
#117195322
#117193082
C13×#4492
#117189002
#117188272
#117188252
#117188142
D8×Dic132
#117186942
#117184552
#117184512
#117184202
#117184182
#117183832
#117183812
#312413