Finite Group Databasebeta

← #14908836

Subgroups — #14908836

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079187C211yesmaximal, characteristic, complemented
2C2×D8×Dic11C211yesmaximal, characteristic, complemented
3#13070811C211yesmaximal, characteristic, complemented
4#13070797C211yesmaximal, characteristic, complemented
5#13070771C212yesmaximal, complemented
6#13070673C212yesmaximal, complemented
7#13070528C211yesmaximal, characteristic
8#13070489C212yesmaximal, complemented
9#13070481C212yesmaximal, complemented
10#13070416C211yesmaximal, characteristic, complemented
11C11×#2187C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×D4×Dic11—21no—
14#10623155—21no—
15C2×C11×SD32C2212yes—
16C11×#467C2211yescharacteristic
17C2×#66896—21no—
18#10622804C2211yescharacteristic, complemented
19Q16×Dic11C2211yescharacteristic, complemented
20D8×Dic11—21no—
21D8×Dic11—21no—
22D8×Dic11C2212yes—
23D8×Dic11C2212yes—
24C2×#66890C2212yes—
25#10622728C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622661—21no—
29#10622491C2211yescharacteristic, complemented
30#10622485C2211yescharacteristic, complemented
31#10622413—21no—
32#10622401—21no—
33C11×#357C2212yes—
34C11×C22⋊C16C2211yescharacteristic
35#10622202C2212yescomplemented
36#10622200C2212yes—
37C22⋊(C11⋊C16)C2211yescharacteristic
38#10622147C2212yescomplemented
39#10622142C2212yescomplemented
40#10622140C2212yescomplemented
41Dic11⋊C16C2212yescomplemented
42#10622128C2212yescomplemented
43C22×D4×C11—21no—
44C23×Dic11—41no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×D8—24no—
47C2×C11×D8—21no—
48C2×C11×D8C2312yes—
49C22×C8×C11C2311yescharacteristic
50C11×C22⋊Q8—21no—
51C2×C22⋊Dic11—41no—
52#67000—21no—
53Q8×Dic11—21no—
54C2×#4325—21no—
55D4×Dic11—22no—
56D4×Dic11—22no—
57D4×Dic11—41no—
58D4×Dic11—41no—
59#66983—21no—
60C2×C4⋊Dic11—21no—
61C2×C4×Dic11D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C2×D88C2311yescharacteristic
64#66951—41no—
65#66946—21no—
66#66945—41no—
67#66943—21no—
68#66939—41no—
69(C22⋊D11)⋊C4—41no—
70C11×SD32—24no—
71C2×C11×C16C2312yes—
72C11×#107C2311yescharacteristic
73C11×#103—21no—
74#66899—21no—
75#66896—22no—
76#66896—22no—
77#66890—24no—
78#66885—21no—
79#66882—21no—
80#66882C2311yescharacteristic
81#66882C2312yes—
82C8×Dic11D411yescharacteristic
83C8×Dic11D411yescharacteristic
84C8×Dic11C2311yescharacteristic
85C8×Dic11C2311yescharacteristic
86C2×C11⋊C16C2312yes—
87#66873—21no—
88#66872—21no—
89#33674—111nomaximal, Sylow
90C24×C11—41no—
91C2×Q8×C11—21no—
92C2×D4×C11—24no—
93C2×D4×C11—22no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—41no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—41no—
101C22×Dic11—84no—
102C22×Dic11D811yescharacteristic
103C22×Dic11D811yescharacteristic
104C2×D44—21no—
105C2×C4×D11—41no—
106C11×Q16—22no—
107C11×D8—24no—
108C11×D8—22no—
109C11×D8#4114yes—
110C2×C8×C11—22no—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2411yescharacteristic
113C11×C4⋊C4—21no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C22⋊Dic11—42no—
117C22⋊Dic11—42no—
118#4325—42no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128Dic11⋊C4—41no—
129C4×Dic11—41no—
130C4×Dic11D811yescharacteristic
131C4×Dic11D811yescharacteristic
132C4×Dic11C2×D411yescharacteristic
133C4×Dic11C2×D411yescharacteristic
134C2×C11⋊C8—41no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137D88—22no—
138C11×C16—22no—
139C11⋊C16—22no—
140#3168—111no—
141C2×C4×D8—111no—
142#2235—111no—
143#2232—111no—
144#2228—112no—
145#2210—112no—
146#2187D1111yescharacteristic, complemented
147#2184—111no—
148#2177—112no—
149#2175—112no—
150#2163—111no—
151C23×C11—44no—
152C23×C11—42no—
153C23×C11—82no—
154C23×C11—82no—
155C23×C11C2×D811yescharacteristic
156C22×D11—41no—
157Q8×C11—41no—
158Q8×C11—41no—
159D4×C11—24no—
160D4×C11—44no—
161D4×C11—42no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C22⋊D11—82no—
169C2×Dic11—22no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173C2×Dic11—84no—
174C2×Dic11—84no—
175C2×Dic11—82no—
176C2×Dic11C2×D811yescharacteristic
177C2×Dic11C2×D811yescharacteristic
178C2×Dic11C2×D811yescharacteristic
179C2×Dic11C2×D811yescharacteristic
180D44—41no—
181D44—41no—
182C4×D11—82no—
183C8×C11—21no—
184C8×C11C2×#4112yes—
185C11⋊C8—21no—
186C11⋊C8—21no—
187C22×D8C2×D1111yescharacteristic
188#529—221no—
189C2×C4×D4—221no—
190C2×SD32C2×D1112yes—
191C2×D16—112no—
192#499—111no—
193#495—111no—
194#488—221no—
195#467C2×D1111yescharacteristic
196#466—111no—
197#465—221no—
198C4×Q16—111no—
199C4×SD16—221no—
200C4×D8—112no—
201C4×D8—112no—
202C4×D8—111no—
203C4×D8—221no—
204C4×D8—221no—
205C2×#107—111no—
206C2×#102—221no—
207C2×C4×C8—111no—
208#367—112no—
209#366—112no—
210C4⋊C16—112no—
211#358—112no—
212#357—112no—
213#357—112no—
214#357C2×D1112yes—
215C22⋊C16—111no—
216C22⋊C16C2×D1111yescharacteristic
217#346—112no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11—88no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11#50912yes—
225C22×C11C22×D811yescharacteristic
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C4×C11—21no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11#52511yescharacteristic
233C4×C11#57511yescharacteristic
234Dic11—21no—
235Dic11—21no—
236Dic11—21no—
237Dic11—21no—
238Dic11—82no—
239Dic11—81no—
240C22×D4—21no—
241C23×C4—441no—
242C2×Q16C22×D1111yescharacteristic
243C2×SD16—221no—
244C2×D8—24no—
245C2×D8—21no—
246C2×D8—111no—
247C2×D8C22×D1112yes—
248C22×C8—111no—
249C22×C8C22×D1111yescharacteristic
250#126—441no—
251#125—221no—
252#124—221no—
253#123—441no—
254C22⋊Q8—21no—
255#121—221no—
256C4×Q8—221no—
257C4×D4—221no—
258C4×D4—222no—
259C4×D4—222no—
260C4×D4—441no—
261C4×D4—441no—
262C4×D4—441no—
263#117—441no—
264C2×C4⋊C4—221no—
265C2×C22⋊C4—441no—
266C2×C42—111no—
267SD32—24no—
268D16—224no—
269C2×C16—112no—
270C2×C16C22×D1112yes—
271#107—111no—
272#107—112no—
273#107—221no—
274#107C22×D1111yescharacteristic
275#106—221no—
276#103—21no—
277#103—221no—
278#102—221no—
279#102—222no—
280#102—222no—
281#102—221no—
282C4×C8—111no—
283C4×C8—111no—
284C4×C8—111no—
285C4×C8—111no—
286C2×C11—22no—
287C2×C11—84no—
288C2×C11#310011yescharacteristic
289C2×C11C2×#50911yescharacteristic
290C2×C11#341411yescharacteristic
291D11—161no—
292C24—41no—
293C2×Q8—21no—
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—221no—
299C2×D4—441no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—441no—
303C22×C4—442no—
304C22×C4—442no—
305C22×C4—441no—
306C22×C4—884no—
307C22×C4D4×D1111yescharacteristic
308Q16—22no—
309SD16—442no—
310D8—24no—
311D8—22no—
312D8—222no—
313D8#434114yes—
314C2×C8—22no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8—441no—
318C2×C8D4×D1111yescharacteristic
319C2×C8C23×D1111yescharacteristic
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—222no—
323C4⋊C4—221no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C22⋊C4—41no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C22⋊C4—441no—
332C22⋊C4—442no—
333C22⋊C4—442no—
334C22⋊C4—441no—
335C42—111no—
336C42—111no—
337C42—111no—
338C42—111no—
339C42—441no—
340C16—22no—
341C16—222no—
342C11#3367411yescharacteristic, complemented, Sylow
343C23—44no—
344C23—42no—
345C23—82no—
346C23—82no—
347C23—441no—
348C23D8×D1111yescharacteristic
349Q8—41no—
350Q8—41no—
351D4—24no—
352D4—44no—
353D4—42no—
354D4—441no—
355D4—441no—
356D4—882no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—111no—
362C2×C4—111no—
363C2×C4—111no—
364C2×C4—111no—
365C2×C4—222no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—442no—
369C2×C4—882no—
370C2×C4—884no—
371C2×C4—884no—
372C2×C4—882no—
373C2×C4D8×D1111yescharacteristic
374C2×C4C2×D4×D1111yescharacteristic
375C8—21no—
376C8—221no—
377C8—221no—
378C8C2×#434112yes—
379C22—21no—
380C22—21no—
381C22—44no—
382C22—88no—
383C22—82no—
384C22—82no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22#1062252712yes—
389C22C2×D8×D1111yescharacteristic
390C4—21no—
391C4—81no—
392C4—81no—
393C4—221no—
394C4—221no—
395C4—221no—
396C4—221no—
397C4—882no—
398C4—881no—
399C4#1062311711yescharacteristic
400C4#1062330411yescharacteristic
401C2—22no—
402C2—84no—
403C2—1761no—
404C2#1307861111yescharacteristic
405C2C2×#1062252711yescharacteristic
406C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
prime radical#13070528C2
hypercenter#2187D11
hypocenterC11#33674
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #13079187C2semidirect
2. C2×D8×Dic11C2semidirect
3. #13070811C2semidirect
4. #13070797C2semidirect
5. #13070771C2semidirect
6. #13070673C2semidirect
8. #13070489C2semidirect
9. #13070481C2semidirect
10. #13070416C2semidirect
11. C11×#2187C2semidirect
18. #10622804C22semidirect
19. Q16×Dic11C22semidirect
29. #10622491C22semidirect
30. #10622485C22semidirect
35. #10622202C22semidirect
38. #10622147C22semidirect
39. #10622142C22semidirect
40. #10622140C22semidirect
41. Dic11⋊C16C22semidirect
42. #10622128C22semidirect
146. #2187D11semidirect
342. C11#33674semidirect

Maximal subgroups

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

subgroupindex
#130791872
C2×D8×Dic112
#130708112
#130707972
#130707712
#130706732
#130705282
#130704892
#130704812
#130704162
C11×#21872
#3367411