Finite Group Databasebeta

← #14909514

Subgroups — #14909514

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078193C211yesmaximal, characteristic, complemented
2D11×#466C211yesmaximal, characteristic, complemented
3#13070817C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic, complemented
5#13070804C211yesmaximal, characteristic, complemented
6#13070800C211yesmaximal, characteristic, complemented
7#13070715C211yesmaximal, characteristic, complemented
8#13070709C211yesmaximal, characteristic, complemented
9#13070701C211yesmaximal, characteristic, complemented
10#13070699C211yesmaximal, characteristic, complemented
11#13070543C211yesmaximal, characteristic, complemented
12#13070539C211yesmaximal, characteristic, complemented
13#13070526C211yesmaximal, characteristic, complemented
14D11×C22⋊C16C211yesmaximal, characteristic, complemented
15C11×#2186C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic, complemented
17#10623359—21no—
18C2×D8×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20D11×#121—21no—
21C2×C11×SD32C2211yescharacteristic, complemented
22C2×C11×D16C2211yescharacteristic, complemented
23C11×#466C2211yescharacteristic
24#10622846—21no—
25#10622801C2211yescharacteristic
26#10622801C2211yescharacteristic, complemented
27C2×#66892C2211yescharacteristic, complemented
28#10622784—21no—
29#10622784—21no—
30#10622770C2211yescharacteristic
31#10622770C2211yescharacteristic
32#10622770C2211yescharacteristic, complemented
33C2×#66890C2211yescharacteristic, complemented
34#10622728C2211yescharacteristic
35#10622719C2211yescharacteristic, complemented
36#10622651—21no—
37C2×C16×D11C2211yescharacteristic, complemented
38C2×C16×D11C2211yescharacteristic, complemented
39#10622496C2211yescharacteristic
40D11×#107C2211yescharacteristic
41#10622388—21no—
42D11×#102—21no—
43C11×#358C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic, complemented
45C11×C22⋊C16C2211yescharacteristic, complemented
46#10622202C2211yescharacteristic, complemented
47#10622200C2211yescharacteristic, complemented
48#10622200C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic, complemented
50C22⋊(C11⋊C16)C2211yescharacteristic, complemented
51#10622147C2211yescharacteristic, complemented
52#10622147C2211yescharacteristic, complemented
53(C2×D11)⋊C16C2211yescharacteristic
54(C2×D11)⋊C16C2211yescharacteristic
55#10622143C2211yescharacteristic, complemented
56#10622142C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C2×D4×D11—21no—
61C2×D4×D11—41no—
62C22×C4×D11D411yescharacteristic
63C11×#135—41no—
64C11×#135—41no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×SD16—21no—
67C2×C11×D8C2311yescharacteristic
68C2×C11×D8C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×#121—21no—
71#66999—21no—
72#66999—21no—
73#66992—41no—
74#66991—21no—
75#66991—21no—
76#66991—21no—
77#66990—41no—
78#66988—41no—
79C2×#4323—21no—
80#66983—21no—
81C4×C22⋊D11—41no—
82C4×C22⋊D11—41no—
83#66979—21no—
84C22×C11⋊C8D411yescharacteristic
85D8×D11—41no—
86D8×D11—41no—
87C2×D88C2311yescharacteristic
88C2×C8×D11—41no—
89C2×C8×D11—41no—
90C2×C8×D11D411yescharacteristic
91C2×C8×D11D411yescharacteristic
92C2×C8×D11C2311yescharacteristic
93C2×C8×D11C2311yescharacteristic
94#66948—21no—
95C4⋊C4×D11—21no—
96#66937—41no—
97C22⋊C4×D11—41no—
98C11×SD32—41no—
99C11×D16—41no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#102—21no—
104#66899—21no—
105#66899—21no—
106#66896—21no—
107#66896—21no—
108#66896—21no—
109#66892—41no—
110#66890—41no—
111#66885—21no—
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66882C2311yescharacteristic
115#66881—21no—
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118#66873—21no—
119#66871—21no—
120C16×D11—41no—
121C16×D11—41no—
122#33754—111nomaximal, Sylow
123C23×D11—41no—
124C23×D11D811yescharacteristic
125C11×#41—42no—
126C11×#41—42no—
127C2×Q8×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C2×C22⋊D11—41no—
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C22×Dic11D811yescharacteristic
140D4×D11—42no—
141D4×D11—42no—
142D4×D11—84no—
143C2×D44—21no—
144C2×D44—41no—
145C2×C4×D11—41no—
146C2×C4×D11—41no—
147C2×C4×D11—41no—
148C2×C4×D11D811yescharacteristic
149C2×C4×D11D811yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×C4×D11C2×D411yescharacteristic
152C11×Q16—21no—
153C11×Q16—21no—
154C11×SD16—42no—
155C11×D8—21no—
156C11×D8—21no—
157C11×D8—21no—
158C11×D8—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2411yescharacteristic
163C11×C4⋊C4—21no—
164C11×C22⋊C4—41no—
165C22⋊Dic11—41no—
166C22⋊Dic11—41no—
167C22⋊Dic11—41no—
168C22⋊Dic11—41no—
169#4323—42no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173(C2×D11)⋊C4—41no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179Dic11⋊C4—41no—
180C4×Dic11—41no—
181C2×C11⋊C8—41no—
182C2×C11⋊C8C2×D411yescharacteristic
183C2×C11⋊C8C2×D411yescharacteristic
184D88—21no—
185D88—21no—
186C8×D11—21no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—21no—
190C8×D11—41no—
191C8×D11—41no—
192C11×C16—21no—
193C11×C16—21no—
194C11⋊C16—21no—
195C11⋊C16—21no—
196#3050—111no—
197C2×#466—111no—
198#2236—111no—
199#2234—111no—
200#2234—111no—
201#2233—111no—
202#2217—111no—
203#2217—111no—
204#2215—111no—
205#2215—111no—
206#2187—111no—
207#2186—111no—
208#2186D1111yescharacteristic, complemented
209#2184—111no—
210C2×C22⋊C16—111no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11C2×D811yescharacteristic
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—82no—
219C22×D11—82no—
220C22×D11—82no—
221C22×D11C2×D811yescharacteristic
222C22×D11C2×D811yescharacteristic
223Q8×C11—41no—
224Q8×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—41no—
229D4×C11—82no—
230D4×C11—82no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—82no—
236C2×C4×C11C2×D811yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C22⋊D11—82no—
239C22⋊D11—82no—
240C22⋊D11—82no—
241C22⋊D11—82no—
242C22⋊D11—82no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11C2×D811yescharacteristic
248C2×Dic11C2×D811yescharacteristic
249D44—41no—
250D44—41no—
251D44—82no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—82no—
259C8×C11—21no—
260C8×C11H(5,𝔽2)11yescharacteristic
261C8×C11H(5,𝔽2)11yescharacteristic
262C11⋊C8—21no—
263C11⋊C8—21no—
264C2×#135C2×D1111yescharacteristic, complemented
265C22×D8—111no—
266C23×C8—111no—
267#525—221no—
268C2×#121—221no—
269C2×SD32—111no—
270C2×SD32C2×D1111yescharacteristic, complemented
271C2×D16—111no—
272C2×D16C2×D1111yescharacteristic, complemented
273C22×C16—111no—
274C22×C16—111no—
275#467—111no—
276#467—111no—
277#466—111no—
278#466—111no—
279#466—111no—
280#466—111no—
281#466—111no—
282#466—221no—
283#466—221no—
284#466C2×D1111yescharacteristic
285#465—221no—
286#465—221no—
287#427—111no—
288C2×#107—111no—
289#416—221no—
290C2×#102—221no—
291#367—111no—
292#367—111no—
293#366—111no—
294#366—111no—
295#358—111no—
296#358C2×D1111yescharacteristic, complemented
297#357—111no—
298#357—111no—
299#357—111no—
300#357—111no—
301#357—111no—
302#357C2×D1111yescharacteristic, complemented
303C22⋊C16—111no—
304C22⋊C16—111no—
305C22⋊C16—111no—
306C22⋊C16C2×D1111yescharacteristic, complemented
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11C22×D811yescharacteristic
317C2×D11—21no—
318C2×D11—21no—
319C2×D11—21no—
320C2×D11—21no—
321C2×D11—44no—
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—164no—
326C2×D11#50812yes—
327C2×D11#50912yes—
328C4×C11—21no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11#53411yescharacteristic
332C4×C11#57511yescharacteristic
333Dic11—21no—
334Dic11—21no—
335Dic11—81no—
336Dic11—81no—
337Dic11—81no—
338C2×#41—21no—
339C22×D4—221no—
340C22×D4—441no—
341C23×C4—111no—
342#135—41no—
343#135—41no—
344C2×Q16C22×D1111yescharacteristic
345C2×SD16—21no—
346C2×D8—111no—
347C2×D8—221no—
348C2×D8—441no—
349C2×D8—441no—
350C2×D8C22×D1111yescharacteristic
351C2×D8C22×D1111yescharacteristic
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—441no—
358C22×C8—441no—
359C22×C8C22×D1111yescharacteristic
360#123—441no—
361C22⋊Q8—221no—
362C22⋊Q8—221no—
363#121—21no—
364#121—221no—
365#121—221no—
366#121—221no—
367#121—221no—
368#121—221no—
369#121—441no—
370#121—441no—
371#120—441no—
372C4×D4—441no—
373C4×D4—441no—
374#117—221no—
375C2×C4⋊C4—221no—
376C2×C22⋊C4—441no—
377SD32—41no—
378SD32—441no—
379D16—41no—
380D16—441no—
381C2×C16—111no—
382C2×C16—111no—
383C2×C16—441no—
384C2×C16—441no—
385C2×C16C22×D1111yescharacteristic
386C2×C16C22×D1111yescharacteristic
387#107—111no—
388#107—111no—
389#107—111no—
390#107—221no—
391#107C22×D1111yescharacteristic
392#106—221no—
393#103—221no—
394#103—221no—
395#102—21no—
396#102—221no—
397#102—221no—
398#102—221no—
399#102—221no—
400#102—221no—
401C2×C11—41no—
402C2×C11—161no—
403C2×C11—161no—
404C2×C11#318611yescharacteristic
405C2×C11C2×#50811yescharacteristic
406C2×C11C2×#50911yescharacteristic
407D11—22no—
408D11—22no—
409D11—161no—
410C24—111no—
411C24—441no—
412#41—42no—
413#41—42no—
414C2×Q8—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—221no—
420C2×D4—441no—
421C2×D4—441no—
422C2×D4—442no—
423C2×D4—442no—
424C2×D4—441no—
425C2×D4—441no—
426C2×D4—441no—
427C2×D4—441no—
428C2×D4—884no—
429C22×C4—41no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—441no—
436C22×C4—441no—
437C22×C4—441no—
438C22×C4D4×D1111yescharacteristic
439Q16—21no—
440Q16—21no—
441SD16—42no—
442D8—21no—
443D8—21no—
444D8—21no—
445D8—21no—
446D8—221no—
447D8—221no—
448D8—442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—441no—
458C2×C8—441no—
459C2×C8—441no—
460C2×C8D4×D1111yescharacteristic
461C2×C8C23×D1111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—441no—
467C4⋊C4—441no—
468C4⋊C4—441no—
469C22⋊C4—41no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C22⋊C4—441no—
476C22⋊C4—441no—
477C22⋊C4—441no—
478C42—441no—
479C16—21no—
480C16—21no—
481C16—221no—
482C16—221no—
483C11#3375411yescharacteristic, complemented, Sylow
484C23—41no—
485C23—41no—
486C23—111no—
487C23—111no—
488C23—222no—
489C23—222no—
490C23—441no—
491C23—441no—
492C23—882no—
493C23—882no—
494C23—882no—
495C23D8×D1111yescharacteristic
496Q8—41no—
497Q8—41no—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—82no—
503D4—82no—
504D4—441no—
505D4—441no—
506D4—882no—
507D4—882no—
508D4—882no—
509D4—882no—
510D4—882no—
511D4—882no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—111no—
518C2×C4—111no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—882no—
530C2×C4D8×D1111yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C8—21no—
533C8—221no—
534C8—221no—
535C8#6703711yescharacteristic
536C8#6703711yescharacteristic
537C22—21no—
538C22—21no—
539C22—21no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—112no—
547C22—112no—
548C22—221no—
549C22—221no—
550C22—221no—
551C22—221no—
552C22—444no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22—1764no—
557C22C2×D8×D1111yescharacteristic
558C4—21no—
559C4—81no—
560C4—81no—
561C4—221no—
562C4—221no—
563C4—881no—
564C4—881no—
565C4—881no—
566C4#1062312011yescharacteristic
567C4#1062330411yescharacteristic
568C2—41no—
569C2—161no—
570C2—161no—
571C2—222no—
572C2—222no—
573C2—1761no—
574C2#1307936511yescharacteristic
575C2D11×#50811yescharacteristic
576C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2186C2
socleC22×C11C22×D8
hypercenter#2186D11
hypocenterC11#33754
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2186

Complements

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

NH ≅ G/Ntype
1. #13078193C2semidirect
2. D11×#466C2semidirect
3. #13070817C2semidirect
4. #13070808C2semidirect
5. #13070804C2semidirect
6. #13070800C2semidirect
7. #13070715C2semidirect
8. #13070709C2semidirect
9. #13070701C2semidirect
10. #13070699C2semidirect
11. #13070543C2semidirect
12. #13070539C2semidirect
13. #13070526C2semidirect
14. D11×C22⋊C16C2semidirect
15. C11×#2186C2semidirect
16. C2×C11×#135C22semidirect
21. C2×C11×SD32C22semidirect
22. C2×C11×D16C22semidirect
26. #10622801C22semidirect
27. C2×#66892C22semidirect
32. #10622770C22semidirect
33. C2×#66890C22semidirect
35. #10622719C22semidirect
37. C2×C16×D11C22semidirect
38. C2×C16×D11C22semidirect
43. C11×#358C22semidirect
44. C11×#357C22semidirect
45. C11×C22⋊C16C22semidirect
46. #10622202C22semidirect
47. #10622200C22semidirect
48. #10622200C22semidirect
49. #10622200C22semidirect
50. C22⋊(C11⋊C16)C22semidirect
51. #10622147C22semidirect
52. #10622147C22semidirect
55. #10622143C22semidirect
56. #10622142C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
208. #2186D11semidirect
264. C2×#135C2×D11semidirect
270. C2×SD32C2×D11semidirect
272. C2×D16C2×D11semidirect
296. #358C2×D11semidirect
302. #357C2×D11semidirect
306. C22⋊C16C2×D11semidirect
483. C11#33754semidirect

Maximal subgroups

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

subgroupindex
#130781932
D11×#4662
#130708172
#130708082
#130708042
#130708002
#130707152
#130707092
#130707012
#130706992
#130705432
#130705392
#130705262
D11×C22⋊C162
C11×#21862
#3375411