Finite Group Databasebeta

← #14908694

Subgroups — #14908694

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079190C211yesmaximal, characteristic, complemented
2C2×#10622485C211yesmaximal, characteristic, complemented
3#13070796C211yesmaximal, characteristic, complemented
4#13070752C212yesmaximal, complemented
5#13070650C212yesmaximal, complemented
6#13070530C211yesmaximal, characteristic, complemented
7#13070527C211yesmaximal, characteristic, complemented
8#13070462C212yesmaximal, complemented
9#13070460C212yesmaximal, complemented
10#13070412C211yesmaximal, characteristic, complemented
11C11×#2232C211yesmaximal, characteristic, complemented
12C22×D88C2211yescharacteristic
13#10623127—21no—
14C2×#66946—21no—
15C11×#466C2211yescharacteristic
16C2×C11×#107C2211yescharacteristic
17#10622764C2211yescharacteristic, complemented
18D8×Dic11C2211yescharacteristic, complemented
19C2×#66890C2212yes—
20#10622728C2211yescharacteristic
21C2×C8×Dic11C2211yescharacteristic
22#10622651—21no—
23C2×#66873—21no—
24C2×D176C2212yes—
25#10622487C2211yescharacteristic, complemented
26#10622485—21no—
27#10622485—21no—
28#10622485C2212yes—
29#10622485C2212yes—
30#10622485C2211yescharacteristic, complemented
31#10622373—21no—
32#10622369—21no—
33C11×#366C2212yescomplemented
34C11×#357C2212yescomplemented
35C11×C22⋊C16C2211yescharacteristic
36C22⋊(C11⋊C16)C2211yescharacteristic
37#10622147C2212yes—
38Dic11⋊C16C2212yescomplemented
39C16×Dic11C2212yescomplemented
40#10622129C2212yes—
41#10622129C2212yescomplemented
42#10622127C2212yescomplemented
43C2×#4341—41no—
44C22×D44—21no—
45C22×C4×D11—41no—
46C2×C11×D8C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×#121—21no—
49C2×C11×C4⋊C4—21no—
50#66993—21no—
51#66992—41no—
52D4×Dic11—21no—
53C2×#4323—21no—
54#66983—21no—
55C2×(C2×D11)⋊C4—41no—
56C2×C4×Dic11D411yescharacteristic
57C22×C11⋊C8D411yescharacteristic
58C2×D88—21no—
59C2×D88—24no—
60C2×D88C2311yescharacteristic
61C2×D88C2312yes—
62#66946—22no—
63#66946—22no—
64#66946—21no—
65#66946—41no—
66#66946—41no—
67#66941—21no—
68#66938—41no—
69(C22⋊D11)⋊C4—41no—
70C2×C11×C16C2312yes—
71C11×#107—21no—
72C11×#107C2312yes—
73C11×#107C2311yescharacteristic
74C11×#102—21no—
75#66896—21no—
76#66890—24no—
77#66885—21no—
78#66882C2311yescharacteristic
79C8×Dic11D411yescharacteristic
80C8×Dic11D411yescharacteristic
81C8×Dic11C2311yescharacteristic
82C8×Dic11C2311yescharacteristic
83C2×C11⋊C16C2312yes—
84#66873—22no—
85#66873—22no—
86#66873—21no—
87#66871—21no—
88D176—24no—
89#33660—111nomaximal, Sylow
90C23×D11—41no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C22×Dic11—41no—
99C22×Dic11D811yescharacteristic
100C22×Dic11D811yescharacteristic
101#4341—84no—
102C2×D44—24no—
103C2×D44—22no—
104C2×D44—21no—
105C2×D44—42no—
106C2×D44—41no—
107C2×C4×D11—41no—
108C2×C4×D11—42no—
109C2×C4×D11—42no—
110C2×C4×D11—84no—
111C2×Dic22—41no—
112C11×D8—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C22⋊Dic11—41no—
121#4323—42no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—42no—
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127Dic11⋊C4—41no—
128C4×Dic11D811yescharacteristic
129C4×Dic11D811yescharacteristic
130C4×Dic11C2×D411yescharacteristic
131C4×Dic11C2×D411yescharacteristic
132C2×C11⋊C8—41no—
133C2×C11⋊C8C2×D411yescharacteristic
134C2×C11⋊C8C2×D411yescharacteristic
135D88—24no—
136D88—22no—
137D88—22no—
138D88#4114yescomplemented
139C11×C16—22no—
140C11⋊C16—22no—
141#3169—111no—
142C2×C4×D8—111no—
143#2232—111no—
144#2232D1111yescharacteristic, complemented
145#2224—112no—
146#2206—112no—
147#2184—111no—
148#2184—111no—
149C4×D16—112no—
150C4×D16—112no—
151#2162—111no—
152C23×C11—41no—
153C23×C11C2×D811yescharacteristic
154C22×D11—44no—
155C22×D11—42no—
156C22×D11—41no—
157C22×D11—82no—
158C22×D11—82no—
159D4×C11—41no—
160D4×C11—41no—
161D4×C11—82no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C22⋊D11—82no—
170C22⋊D11—82no—
171C22⋊D11—82no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—82no—
175C2×Dic11D1614yescomplemented
176C2×Dic11C2×D811yescharacteristic
177C2×Dic11C2×D811yescharacteristic
178C2×Dic11C2×D811yescharacteristic
179C2×Dic11C2×D811yescharacteristic
180D44—24no—
181D44—44no—
182D44—41no—
183D44—42no—
184D44—41no—
185C4×D11—84no—
186C4×D11—84no—
187C4×D11—82no—
188Dic22—82no—
189C8×C11—21no—
190C8×C11C2×#4112yes—
191C11⋊C8—21no—
192C11⋊C8—21no—
193C22×D8—111no—
194#532—221no—
195C2×C4×D4—221no—
196C2×D16—112no—
197C2×D16—112no—
198#500—111no—
199#493—111no—
200#486—221no—
201#466—111no—
202#466—221no—
203#466C2×D1111yescharacteristic
204C4×D8—111no—
205C4×D8—112no—
206C4×D8—112no—
207C4×D8—111no—
208C4×D8—221no—
209C4×D8—221no—
210C4×D8—221no—
211C2×#107C2×D1111yescharacteristic
212C2×#102—221no—
213C2×C4×C8—111no—
214#366—112no—
215#366C2×D1112yescomplemented
216C4⋊C16—112no—
217#357—112no—
218#357—112no—
219#357—112no—
220#357C2×D1112yescomplemented
221C22⋊C16—111no—
222C22⋊C16C2×D1111yescharacteristic
223C4×C16—112no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11C2×D1612yes—
230C22×C11C22×D811yescharacteristic
231C2×D11—44no—
232C2×D11—88no—
233C2×D11—82no—
234C2×D11—82no—
235C2×D11—81no—
236C2×D11—81no—
237C2×D11—81no—
238C4×C11—21no—
239C4×C11—82no—
240C4×C11—81no—
241C4×C11#52511yescharacteristic
242C4×C11#57511yescharacteristic
243Dic11—21no—
244Dic11—21no—
245Dic11—81no—
246Dic11C2×D1612yes—
247Dic11C2×D1612yes—
248C2×#41—441no—
249C22×D4—221no—
250C23×C4—441no—
251C2×D8—112no—
252C2×D8—111no—
253C2×D8—224no—
254C2×D8—221no—
255C2×D8—221no—
256C2×D8C22×D1111yescharacteristic
257C22×C8—111no—
258C22×C8C22×D1111yescharacteristic
259C4⋊Q8—221no—
260#127—221no—
261#124—441no—
262#121—21no—
263#121—221no—
264#121—441no—
265C4×D4—222no—
266C4×D4—222no—
267C4×D4—221no—
268C4×D4—221no—
269C4×D4—441no—
270C4×D4—441no—
271C4×D4—441no—
272C2×C4⋊C4—21no—
273C2×C22⋊C4—441no—
274C2×C42—111no—
275D16—224no—
276D16—224no—
277C2×C16—112no—
278C2×C16C22×D1112yes—
279#107—21no—
280#107—111no—
281#107—221no—
282#107C22×D1111yescharacteristic
283#107C22×D1112yes—
284#102—21no—
285#102—222no—
286#102—222no—
287#102—221no—
288#102—221no—
289#102—221no—
290C4×C8—111no—
291C4×C8—111no—
292C4×C8—111no—
293C4×C8—111no—
294C2×C11—22no—
295C2×C11—161no—
296C2×C11#310011yescharacteristic
297C2×C11C22×D1611yescharacteristic
298C2×C11#341411yescharacteristic
299D11—84no—
300D11—161no—
301C24—441no—
302#41—884no—
303C2×Q8—441no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—224no—
307C2×D4—222no—
308C2×D4—221no—
309C2×D4—442no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C22×C4—41no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—884no—
322C22×C4D4×D1111yescharacteristic
323D8—22no—
324D8—114no—
325D8—224no—
326D8—222no—
327D8—222no—
328D8—442no—
329C2×C8—22no—
330C2×C8—111no—
331C2×C8—111no—
332C2×C8—441no—
333C2×C8D4×D1111yescharacteristic
334C2×C8C23×D1111yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—221no—
339C4⋊C4—441no—
340C22⋊C4—41no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C42—111no—
347C42—111no—
348C42—111no—
349C42—111no—
350C16—22no—
351C16—222no—
352C11#3366011yescharacteristic, complemented, Sylow
353C23—41no—
354C23—444no—
355C23—442no—
356C23—441no—
357C23—882no—
358C23—882no—
359C23D8×D1111yescharacteristic
360Q8—882no—
361D4—41no—
362D4—41no—
363D4—82no—
364D4—224no—
365D4—444no—
366D4—442no—
367D4—441no—
368D4—441no—
369D4—882no—
370D4—882no—
371D4—882no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—82no—
377C2×C4—111no—
378C2×C4—111no—
379C2×C4—114no—
380C2×C4—111no—
381C2×C4—111no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—884no—
385C2×C4—884no—
386C2×C4—882no—
387C2×C4—882no—
388C2×C4D8×D1111yescharacteristic
389C2×C4C2×D4×D1111yescharacteristic
390C8—21no—
391C8—221no—
392C8—221no—
393C8#41×D1112yes—
394C22—21no—
395C22—21no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—444no—
400C22—888no—
401C22—882no—
402C22—882no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22D11×D1612yes—
407C22C2×D8×D1111yescharacteristic
408C4—21no—
409C4—82no—
410C4—81no—
411C4—112no—
412C4—112no—
413C4—221no—
414C4—221no—
415C4—881no—
416C4#1062318711yescharacteristic
417C4#1062330811yescharacteristic
418C2—22no—
419C2—161no—
420C2—884no—
421C2—1761no—
422C2#1307861311yescharacteristic
423C2C2×D11×D1611yescharacteristic
424C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2232C2
socleC22×C11C22×D8
hypercenter#2232D11
hypocenterC11#33660
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
1. #13079190C2semidirect
2. C2×#10622485C2semidirect
3. #13070796C2semidirect
4. #13070752C2semidirect
5. #13070650C2semidirect
6. #13070530C2semidirect
7. #13070527C2semidirect
8. #13070462C2semidirect
9. #13070460C2semidirect
10. #13070412C2semidirect
11. C11×#2232C2semidirect
17. #10622764C22semidirect
18. D8×Dic11C22semidirect
25. #10622487C22semidirect
30. #10622485C22semidirect
33. C11×#366C22semidirect
34. C11×#357C22semidirect
38. Dic11⋊C16C22semidirect
39. C16×Dic11C22semidirect
41. #10622129C22semidirect
42. #10622127C22semidirect
138. D88#41semidirect
144. #2232D11semidirect
175. C2×Dic11D16semidirect
215. #366C2×D11semidirect
220. #357C2×D11semidirect
352. C11#33660semidirect

Maximal subgroups

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

subgroupindex
#130791902
C2×#106224852
#130707962
#130707522
#130706502
#130705302
#130705272
#130704622
#130704602
#130704122
C11×#22322
#3366011