Finite Group Databasebeta

← #14909690

Subgroups — #14909690

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079197C211yesmaximal, characteristic, complemented
2C2×#10622764C211yesmaximal, characteristic
3#13070870C212yesmaximal, complemented
4#13070838C212yesmaximal, complemented
5#13070655C212yesmaximal, complemented
6#13070654C212yesmaximal, complemented
7#13070547C211yesmaximal, characteristic, complemented
8#13070545C211yesmaximal, characteristic, complemented
9#13070544C211yesmaximal, characteristic, complemented
10#13070412C211yesmaximal, characteristic, complemented
11C11×#2187C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×#66993—21no—
14C22×#4323—21no—
15C22×D88C2211yescharacteristic
16#10623153—21no—
17C2×C11×SD32C2212yescomplemented
18C11×#467C2211yescharacteristic
19Q16×Dic11C2211yescharacteristic, complemented
20#10622794C2211yescharacteristic, complemented
21C2×#66892C2212yescomplemented
22#10622764—21no—
23#10622764—21no—
24#10622764C2212yes—
25#10622764C2212yes—
26C2×#66891C2212yescomplemented
27#10622729C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622664—21no—
30C2×#66864C2212yescomplemented
31#10622487C2211yescharacteristic, complemented
32#10622486C2211yescharacteristic, complemented
33#10622405—21no—
34#10622403—21no—
35C11×#357C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37#10622200C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic
39#10622147C2212yescomplemented
40Dic11⋊C16C2212yescomplemented
41C16×Dic11C2212yescomplemented
42#10622129C2212yescomplemented
43C22×D4×C11—21no—
44C22×C22⋊D11—41no—
45C22×C22⋊D11—41no—
46C22×D44—21no—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×D8—21no—
49C2×C11×D8—42no—
50C2×C11×D8C2312yes—
51C22×C8×C11C2311yescharacteristic
52C11×C22⋊Q8—21no—
53Q8×Dic11—21no—
54#66997—21no—
55C2×#4326—21no—
56#66993—22no—
57#66993—22no—
58#66993—41no—
59#66993—41no—
60C2×#4323—22no—
61C2×#4323—22no—
62C2×#4323—44no—
63#66977—21no—
64C2×C4×Dic11D411yescharacteristic
65C22×C11⋊C8D411yescharacteristic
66C2×Dic44C2311yescharacteristic
67C2×D88—21no—
68C2×D88—42no—
69C2×D88C2312yes—
70#66942—41no—
71#66941—21no—
72#66940—21no—
73#66940—41no—
74#66931—41no—
75#66930—41no—
76C11×SD32—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#103—21no—
80#66899—21no—
81#66892—42no—
82#66891—42no—
83#66882C2311yescharacteristic
84#66880—21no—
85C8×Dic11D411yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C8×Dic11C2311yescharacteristic
89C2×C11⋊C16C2312yes—
90#66874—21no—
91#66871—21no—
92#66864—42no—
93#33774—111nomaximal, Sylow
94C24×C11—41no—
95C23×D11—41no—
96C2×Q8×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—42no—
103C2×C22⋊D11—42no—
104C2×C22⋊D11—42no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—84no—
107C2×C22⋊D11—84no—
108C22×Dic11D811yescharacteristic
109C22×Dic11D811yescharacteristic
110C2×D44—22no—
111C2×D44—42no—
112C2×D44—42no—
113C2×D44—41no—
114C2×Dic22—21no—
115C2×Dic22—41no—
116C11×Q16—22no—
117C11×D8—22no—
118C11×D8—22no—
119C11×D8—42no—
120C2×C8×C11—22no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—21no—
124C11×C4⋊C4—41no—
125C11×C22⋊C4—41no—
126C22⋊Dic11—41no—
127#4326—42no—
128#4323—44no—
129#4323—44no—
130C4⋊Dic11—21no—
131C4⋊Dic11—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134Dic11⋊C4—41no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C4×Dic11—41no—
138C4×Dic11—41no—
139C4×Dic11D811yescharacteristic
140C4×Dic11D811yescharacteristic
141C4×Dic11C2×D411yescharacteristic
142C4×Dic11C2×D411yescharacteristic
143C2×C11⋊C8—22no—
144C2×C11⋊C8C2×D411yescharacteristic
145C2×C11⋊C8C2×D411yescharacteristic
146Dic44—22no—
147D88—22no—
148D88—22no—
149D88—42no—
150C11×C16—22no—
151C11⋊C16—22no—
152#3170—111no—
153C2×#493—111no—
154#2248—112no—
155#2240—112no—
156#2207—112no—
157#2207—112no—
158#2187—111no—
159#2187—111no—
160#2187—111no—
161#2187D1111yescharacteristic, complemented
162#2162—111no—
163C23×C11—42no—
164C23×C11—82no—
165C23×C11—82no—
166C23×C11—82no—
167C23×C11C2×D811yescharacteristic
168C22×D11—42no—
169C22×D11—82no—
170C22×D11—82no—
171C22×D11—82no—
172Q8×C11—41no—
173Q8×C11—41no—
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—82no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C22⋊D11—84no—
184C22⋊D11—84no—
185C22⋊D11—84no—
186C22⋊D11—84no—
187C2×Dic11—22no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11SD3214yescomplemented
191C2×Dic11C2×D811yescharacteristic
192C2×Dic11C2×D811yescharacteristic
193C2×Dic11C2×D811yescharacteristic
194C2×Dic11C2×D811yescharacteristic
195D44—42no—
196D44—42no—
197D44—82no—
198Dic22—41no—
199Dic22—41no—
200Dic22—82no—
201C8×C11—21no—
202C8×C11H(5,𝔽2)12yes—
203C11⋊C8—21no—
204C11⋊C8AGL(1,ℤ/8)12yes—
205C22×D8—111no—
206C22×D8—221no—
207C22×D8C2×D1111yescharacteristic
208#533—221no—
209C2×#127—221no—
210C2×SD32—112no—
211C2×SD32—112no—
212C2×SD32—112no—
213C2×SD32C2×D1112yescomplemented
214#500—111no—
215#494—111no—
216#493—112no—
217#493—112no—
218#493—221no—
219#493—221no—
220#487—221no—
221#467—111no—
222#467—221no—
223#467C2×D1111yescharacteristic
224C4×Q16—111no—
225C4×Q16—111no—
226C4×Q16—221no—
227C2×C4×C8—111no—
228C4⋊C16—112no—
229#357—112no—
230#357—112no—
231#357—112no—
232#357C2×D1112yescomplemented
233C22⋊C16—111no—
234C22⋊C16C2×D1111yescharacteristic
235C4×C16—112no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11—164no—
242C22×C11C2×SD3212yes—
243C22×C11C22×D811yescharacteristic
244C2×D11—82no—
245C2×D11—82no—
246C2×D11—82no—
247C2×D11—164no—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11#53511yescharacteristic
252C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
253Dic11—21no—
254Dic11—81no—
255Dic11—81no—
256Dic11C2×SD3212yes—
257Dic11C2×SD3212yes—
258Dic11#50912yes—
259C22×D4—21no—
260C22×D4—221no—
261C22×D4—441no—
262C22×D4—441no—
263C2×Q16—111no—
264C2×Q16—221no—
265C2×Q16C22×D1111yescharacteristic
266C2×D8—21no—
267C2×D8—42no—
268C2×D8—112no—
269C2×D8—222no—
270C2×D8—222no—
271C2×D8—221no—
272C2×D8—442no—
273C2×D8—444no—
274C2×D8C22×D1112yes—
275C22×C8—111no—
276C22×C8C22×D1111yescharacteristic
277C4⋊Q8—221no—
278C4⋊Q8—221no—
279#127—222no—
280#127—222no—
281#127—441no—
282#127—441no—
283#125—441no—
284C22⋊Q8—21no—
285C22⋊Q8—221no—
286C22⋊Q8—441no—
287C4×Q8—221no—
288C4×Q8—221no—
289C4×Q8—441no—
290#117—441no—
291C2×C42—111no—
292SD32—42no—
293SD32—442no—
294SD32—442no—
295SD32—442no—
296C2×C16—112no—
297C2×C16C22×D1112yes—
298#107—111no—
299#107—221no—
300#107C22×D1111yescharacteristic
301#103—21no—
302#103—221no—
303#103—221no—
304#103—221no—
305C4×C8—111no—
306C4×C8—111no—
307C4×C8—111no—
308C4×C8—111no—
309C2×C11—22no—
310C2×C11—162no—
311C2×C11#320511yescharacteristic
312C2×C11C22×SD3211yescharacteristic
313C2×C11C2×#50911yescharacteristic
314D11—162no—
315C24—41no—
316C24—441no—
317C2×Q8—21no—
318C2×Q8—221no—
319C2×Q8—441no—
320C2×D4—22no—
321C2×D4—42no—
322C2×D4—42no—
323C2×D4—41no—
324C2×D4—222no—
325C2×D4—442no—
326C2×D4—442no—
327C2×D4—442no—
328C2×D4—442no—
329C2×D4—442no—
330C2×D4—442no—
331C2×D4—441no—
332C2×D4—884no—
333C2×D4—884no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4D4×D1111yescharacteristic
337Q16—22no—
338Q16—222no—
339Q16—442no—
340D8—22no—
341D8—22no—
342D8—42no—
343D8—222no—
344D8—222no—
345D8—442no—
346D8—444no—
347D8—444no—
348C2×C8—22no—
349C2×C8—111no—
350C2×C8—111no—
351C2×C8—222no—
352C2×C8D4×D1111yescharacteristic
353C2×C8C23×D1111yescharacteristic
354C4⋊C4—21no—
355C4⋊C4—41no—
356C4⋊C4—221no—
357C4⋊C4—441no—
358C4⋊C4—441no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C22⋊C4—41no—
364C22⋊C4—441no—
365C42—111no—
366C42—111no—
367C42—111no—
368C42—111no—
369C42—441no—
370C42—441no—
371C16—22no—
372C16—222no—
373C11#3377411yescharacteristic, complemented, Sylow
374C23—42no—
375C23—82no—
376C23—82no—
377C23—82no—
378C23—442no—
379C23—882no—
380C23—882no—
381C23—882no—
382C23D8×D1111yescharacteristic
383Q8—41no—
384Q8—41no—
385Q8—441no—
386Q8—441no—
387Q8—882no—
388D4—42no—
389D4—42no—
390D4—82no—
391D4—442no—
392D4—442no—
393D4—882no—
394D4—884no—
395D4—884no—
396D4—884no—
397D4—884no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—111no—
403C2×C4—111no—
404C2×C4—111no—
405C2×C4—114no—
406C2×C4—111no—
407C2×C4—222no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4D8×D1111yescharacteristic
411C2×C4C2×D4×D1111yescharacteristic
412C8—21no—
413C8—112no—
414C8—221no—
415C8#6703712yes—
416C22—21no—
417C22—21no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—164no—
422C22—882no—
423C22—882no—
424C22—882no—
425C22—1764no—
426C22D11×SD3212yes—
427C22C2×D8×D1111yescharacteristic
428C4—21no—
429C4—81no—
430C4—81no—
431C4—112no—
432C4—112no—
433C4—112no—
434C4—221no—
435C4—881no—
436C4—881no—
437C4#1062312311yescharacteristic
438C4D11×AGL(1,ℤ/8)11yescharacteristic
439C2—22no—
440C2—162no—
441C2—1762no—
442C2#1307953211yescharacteristic
443C2C2×D11×SD3211yescharacteristic
444C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
prime radicalC2×#10622764C2
hypercenter#2187D11
hypocenterC11#33774
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. #13079197C2semidirect
3. #13070870C2semidirect
4. #13070838C2semidirect
5. #13070655C2semidirect
6. #13070654C2semidirect
7. #13070547C2semidirect
8. #13070545C2semidirect
9. #13070544C2semidirect
10. #13070412C2semidirect
11. C11×#2187C2semidirect
17. C2×C11×SD32C22semidirect
19. Q16×Dic11C22semidirect
20. #10622794C22semidirect
21. C2×#66892C22semidirect
26. C2×#66891C22semidirect
30. C2×#66864C22semidirect
31. #10622487C22semidirect
32. #10622486C22semidirect
35. C11×#357C22semidirect
37. #10622200C22semidirect
39. #10622147C22semidirect
40. Dic11⋊C16C22semidirect
41. C16×Dic11C22semidirect
42. #10622129C22semidirect
161. #2187D11semidirect
190. C2×Dic11SD32semidirect
213. C2×SD32C2×D11semidirect
232. #357C2×D11semidirect
373. C11#33774semidirect

Maximal subgroups

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

subgroupindex
#130791972
C2×#106227642
#130708702
#130708382
#130706552
#130706542
#130705472
#130705452
#130705442
#130704122
C11×#21872
#3377411