Finite Group Databasebeta

← #14908457

Subgroups — #14908457

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079149C211yesmaximal, characteristic, complemented
2#13077463C211yesmaximal, characteristic
3#13070775C211yesmaximal, characteristic, complemented
4#13070774C211yesmaximal, characteristic, complemented
5#13070773C211yesmaximal, characteristic, complemented
6#13070772C211yesmaximal, characteristic, complemented
7#13070762C211yesmaximal, characteristic, complemented
8#13070751C211yesmaximal, characteristic, complemented
9#13070750C211yesmaximal, characteristic, complemented
10#13070403C211yesmaximal, characteristic, complemented
11#13070399C211yesmaximal, characteristic, complemented
12#13070373C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic
14D11×#357C211yesmaximal, characteristic
15C11×#2226C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17#10623260—21no—
18#10623076—21no—
19C11×#500C2211yescharacteristic, complemented
20C4×C11×D8C2211yescharacteristic
21D8×Dic11C2211yescharacteristic
22#10622693—21no—
23#10622627—21no—
24C2×#66862C2211yescharacteristic
25C2×C16×D11C2211yescharacteristic
26#10622494—21no—
27#10622493C2211yescharacteristic
28#10622493C2211yescharacteristic
29D11×#107C2211yescharacteristic
30#10622491C2211yescharacteristic, complemented
31#10622489—21no—
32#10622487C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic
34#10622398—21no—
35#10622383—21no—
36C4×D88C2211yescharacteristic
37#10622302C2211yescharacteristic
38#10622296C2211yescharacteristic, complemented
39C11×#367C2211yescharacteristic, complemented
40C11×#367C2211yescharacteristic, complemented
41C11×C4⋊C16C2211yescharacteristic, complemented
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622143C2211yescharacteristic, complemented
49#10622142C2211yescharacteristic, complemented
50Dic11⋊C16C2211yescharacteristic, complemented
51Dic11⋊C16C2211yescharacteristic, complemented
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic, complemented
55#10622127C2211yescharacteristic, complemented
56#10622127C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58C4⋊(C11⋊C16)C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×C11×D8C2311yescharacteristic
61C11×C4⋊Q8—21no—
62C4×D4×C11—21no—
63#66999—41no—
64#66997—41no—
65D4×Dic11—21no—
66C2×#4323—21no—
67C4×C22⋊D11—41no—
68C2×(C2×D11)⋊C4—41no—
69D8×D11—22no—
70D8×D11Q814yescomplemented
71C2×D88C2311yescharacteristic
72C2×#4313D411yescharacteristic
73C2×C8×D11C2311yescharacteristic
74#66949—41no—
75#66946—21no—
76#66945—21no—
77#66945—21no—
78C4⋊C4×D11—21no—
79#66943—21no—
80#66942—41no—
81#66941—21no—
82(C22⋊D11)⋊C4—41no—
83C22⋊C4×D11—41no—
84C4×D44—21no—
85#66925D411yescharacteristic
86#66923—21no—
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C11×#107—21no—
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#102—21no—
94C4×C8×C11C2311yescharacteristic
95#66896—21no—
96#66885—21no—
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66881—21no—
101#66879D411yescharacteristic
102C8×Dic11C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104C2×C11⋊C16C2311yescharacteristic
105#66873—21no—
106#66872—21no—
107#66872—21no—
108#66872—21no—
109#66871—21no—
110#66871—21no—
111#66867D411yescharacteristic
112#66862—22no—
113C16×D11—22no—
114#33631—111nomaximal, Sylow
115C23×D11—41no—
116C2×Q8×C11—41no—
117C2×D4×C11—21no—
118C22×C4×C11—41no—
119C2×C22⋊D11—41no—
120C22×Dic11—41no—
121D4×D11—24no—
122D4×D11—42no—
123C2×D44—21no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×C4×D11C2×D411yescharacteristic
128C2×Dic22—41no—
129C11×D8—21no—
130C11×D8C2×Q812yes—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11C2×D411yescharacteristic
139C22⋊Dic11—41no—
140#4323—24no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4D811yescharacteristic
146(C2×D11)⋊C4D811yescharacteristic
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4D811yescharacteristic
157Dic11⋊C4D811yescharacteristic
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163D88—21no—
164D88C2×Q812yes—
165#4313—22no—
166C8×D11C2×Q812yes—
167C8×D11#4112yes—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3164—111no—
173#2948—111no—
174#2228—111no—
175#2228—111no—
176#2228—111no—
177#2228—111no—
178#2226—111no—
179#2226D1111yescharacteristic, complemented
180#2224—111no—
181#2224—111no—
182#2159—111no—
183#2158—111no—
184#2151—111no—
185#2140—111no—
186C2×#357—111no—
187C23×C11—41no—
188C22×D11—41no—
189C22×D11—44no—
190C22×D11—161no—
191C22×D11—161no—
192C22×D11C2×D811yescharacteristic
193Q8×C11—161no—
194D4×C11—22no—
195D4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—161no—
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C22⋊D11—44no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—161no—
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211D44—22no—
212D44—41no—
213C4×D11—161no—
214C4×D11—161no—
215C4×D11—161no—
216C4×D11C22⋊Q812yes—
217C4×D11#13712yes—
218Dic22—161no—
219C8×C11—21no—
220C8×C11C22×Q811yescharacteristic
221C8×C11C2×#4111yescharacteristic
222C11⋊C8—21no—
223C11⋊C8C22⋊Q812yes—
224C22×D8—111no—
225#544—221no—
226#518—221no—
227C2×M32—111no—
228C22×C16—111no—
229#501—221no—
230#501—221no—
231#500—111no—
232#500C2×D1111yescharacteristic, complemented
233#499—111no—
234#499—111no—
235#442—221no—
236#442—221no—
237C4×D8—111no—
238C4×D8—111no—
239C4×D8—111no—
240C4×D8C2×D1111yescharacteristic
241#428—221no—
242#427—111no—
243#427—111no—
244C2×#107—111no—
245#418—221no—
246#405—111no—
247#367—111no—
248#367—111no—
249#367C2×D1111yescharacteristic, complemented
250#367C2×D1111yescharacteristic, complemented
251#366—111no—
252#366—111no—
253#366—111no—
254#366—111no—
255C4⋊C16—111no—
256C4⋊C16—111no—
257C4⋊C16—111no—
258C4⋊C16C2×D1111yescharacteristic, complemented
259#357—111no—
260#357—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264#357—111no—
265#357C2×D1111yescharacteristic
266#357C2×D1111yescharacteristic
267C22×C11—42no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11C22×D811yescharacteristic
271C2×D11—21no—
272C2×D11—21no—
273C2×D11—42no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—164no—
277C2×D11#47412yes—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11C2×C22⋊Q811yescharacteristic
284C4×C11C2×#13711yescharacteristic
285Dic11—21no—
286Dic11—21no—
287Dic11—81no—
288Dic11—81no—
289Dic11—81no—
290Dic11#47412yes—
291C22×D4—221no—
292C2×D8—114no—
293C2×D8—111no—
294C2×D8—222no—
295C2×D8—221no—
296C2×D8C22×D1111yescharacteristic
297C2×M16—111no—
298C22×C8—111no—
299C4⋊Q8—21no—
300C4⋊Q8—221no—
301C4⋊Q8—441no—
302#125—221no—
303#125—221no—
304#125—441no—
305C22⋊Q8—441no—
306C22⋊Q8—441no—
307C4×D4—21no—
308C4×D4—221no—
309C4×D4—221no—
310C4×D4—221no—
311C4×D4—441no—
312C4×D4—441no—
313#117—111no—
314#117—221no—
315#117—221no—
316C2×C4⋊C4—221no—
317C2×C22⋊C4—441no—
318C2×C22⋊C4—441no—
319M32—222no—
320C2×C16—111no—
321C2×C16—111no—
322C2×C16—222no—
323C2×C16C22×D1111yescharacteristic
324C2×C16C22×D1111yescharacteristic
325#107—21no—
326#107—111no—
327#107—111no—
328#107—111no—
329#107—221no—
330#107—221no—
331#107C22×D1111yescharacteristic
332#107C22×D1111yescharacteristic
333#107C22×D1111yescharacteristic
334#106—221no—
335#106—221no—
336#106—221no—
337#106—221no—
338#102—21no—
339#102—221no—
340#102—221no—
341#102—221no—
342#97—111no—
343#97—111no—
344C4×C8—111no—
345C4×C8C22×D1111yescharacteristic
346C2×C11—82no—
347C2×C11C2×#47411yescharacteristic
348C2×C11#341511yescharacteristic
349C2×C11#341611yescharacteristic
350D11—22no—
351D11—82no—
352C24—441no—
353C2×Q8—41no—
354C2×Q8—441no—
355C2×D4—21no—
356C2×D4—224no—
357C2×D4—221no—
358C2×D4—442no—
359C2×D4—441no—
360C22×C4—41no—
361C22×C4—111no—
362C22×C4—441no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4—441no—
366D8—21no—
367D8—112no—
368D8—224no—
369D8—221no—
370D8Q8×D1112yes—
371M16—222no—
372C2×C8—111no—
373C2×C8—112no—
374C2×C8—112no—
375C2×C8—111no—
376C2×C8D4×D1111yescharacteristic
377C2×C8C23×D1111yescharacteristic
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—111no—
383C4⋊C4—111no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C22⋊C4—41no—
394C22⋊C4—111no—
395C22⋊C4—111no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C42—111no—
402C42—441no—
403C42—441no—
404C42D4×D1111yescharacteristic
405C16—21no—
406C16—21no—
407C16—221no—
408C16—221no—
409C11#3363111yescharacteristic, complemented, Sylow
410C23—41no—
411C23—111no—
412C23—444no—
413C23—441no—
414C23—1761no—
415C23—1761no—
416Q8—161no—
417Q8—1761no—
418D4—22no—
419D4—41no—
420D4—222no—
421D4—444no—
422D4—441no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—111no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—111no—
430C2×C4—111no—
431C2×C4—161no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—1761no—
436C2×C4—1761no—
437C2×C4—1761no—
438C2×C4—1761no—
439C2×C4D8×D1111yescharacteristic
440C2×C4D8×D1111yescharacteristic
441C2×C4C2×D4×D1111yescharacteristic
442C8—21no—
443C8—112no—
444C8—221no—
445C8C2×Q8×D1111yescharacteristic
446C8#41×D1111yescharacteristic
447C22—42no—
448C22—81no—
449C22—81no—
450C22—112no—
451C22—221no—
452C22—221no—
453C22—442no—
454C22—881no—
455C22—881no—
456C22—1764no—
457C22C2×D8×D1111yescharacteristic
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—112no—
464C4—221no—
465C4—221no—
466C4—881no—
467C4—881no—
468C4—881no—
469C4D11×C22⋊Q811yescharacteristic
470C4D11×#13711yescharacteristic
471C2—82no—
472C2—222no—
473C2—882no—
474C2D11×#47411yescharacteristic
475C2#1308175611yescharacteristic
476C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2226C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenter#2226D11
hypocenterC11#33631
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #13079149C2semidirect
3. #13070775C2semidirect
4. #13070774C2semidirect
5. #13070773C2semidirect
6. #13070772C2semidirect
7. #13070762C2semidirect
8. #13070751C2semidirect
9. #13070750C2semidirect
10. #13070403C2semidirect
11. #13070399C2semidirect
12. #13070373C2semidirect
15. C11×#2226C2semidirect
19. C11×#500C22semidirect
30. #10622491C22semidirect
32. #10622487C22semidirect
38. #10622296C22semidirect
39. C11×#367C22semidirect
40. C11×#367C22semidirect
41. C11×C4⋊C16C22semidirect
48. #10622143C22semidirect
49. #10622142C22semidirect
50. Dic11⋊C16C22semidirect
51. Dic11⋊C16C22semidirect
54. #10622128C22semidirect
55. #10622127C22semidirect
56. #10622127C22semidirect
57. #10622127C22semidirect
58. C4⋊(C11⋊C16)C22semidirect
70. D8×D11Q8semidirect
179. #2226D11semidirect
232. #500C2×D11semidirect
249. #367C2×D11semidirect
250. #367C2×D11semidirect
258. C4⋊C16C2×D11semidirect
409. C11#33631semidirect

Maximal subgroups

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

subgroupindex
#130791492
#130774632
#130707752
#130707742
#130707732
#130707722
#130707622
#130707512
#130707502
#130704032
#130703992
#130703732
#130703302
D11×#3572
C11×#22262
#3363111