Finite Group Databasebeta

← #14908598

Subgroups — #14908598

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#466C211yesmaximal, characteristic
2D11×#427C211yesmaximal, characteristic, complemented
3#13070808C211yesmaximal, characteristic, complemented
4#13070807C211yesmaximal, characteristic, complemented
5#13070804C211yesmaximal, characteristic, complemented
6#13070803C211yesmaximal, characteristic, complemented
7#13070800C211yesmaximal, characteristic, complemented
8#13070798C211yesmaximal, characteristic, complemented
9#13070795C211yesmaximal, characteristic, complemented
10#13070403C211yesmaximal, characteristic, complemented
11#13070401C211yesmaximal, characteristic, complemented
12#13070330C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic, complemented
14#13070225C211yesmaximal, characteristic, complemented
15C11×#2234C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18D11×#121—21no—
19D11×#117—21no—
20C11×#466C2211yescharacteristic
21C11×#427C2211yescharacteristic, complemented
22#10622770C2211yescharacteristic
23#10622728C2211yescharacteristic
24#10622719C2211yescharacteristic, complemented
25#10622651—21no—
26#10622611—21no—
27C2×#66862C2211yescharacteristic
28C2×#66862C2211yescharacteristic
29#10622496C2211yescharacteristic
30#10622493C2211yescharacteristic
31#10622493C2211yescharacteristic
32D11×#107C2211yescharacteristic
33D11×#107C2211yescharacteristic, complemented
34D11×#107C2211yescharacteristic, complemented
35#10622473—21no—
36D11×#106—21no—
37#10622388—21no—
38D11×#102—21no—
39C11×#367C2211yescharacteristic, complemented
40C11×#366C2211yescharacteristic, complemented
41C11×#357C2211yescharacteristic, complemented
42C11×#357C2211yescharacteristic, complemented
43C11×C22⋊C16C2211yescharacteristic, complemented
44#10622200C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic, complemented
46C22⋊(C11⋊C16)C2211yescharacteristic, complemented
47#10622147C2211yescharacteristic, complemented
48#10622147C2211yescharacteristic, complemented
49(C2×D11)⋊C16C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic, complemented
51#10622143C2211yescharacteristic, complemented
52#10622142C2211yescharacteristic, complemented
53#10622129C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic, complemented
55#10622128C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×D4×D11—41no—
61C22×C4×D11D411yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#121—21no—
65C11×#117—21no—
66#66992—41no—
67#66991—21no—
68C2×#4323—21no—
69#66983—21no—
70#66979—21no—
71C22×C11⋊C8D411yescharacteristic
72D8×D11—22no—
73D8×D11—22no—
74C2×D88C2311yescharacteristic
75C2×C8×D11—22no—
76C2×C8×D11—22no—
77C2×C8×D11D411yescharacteristic
78C2×C8×D11D411yescharacteristic
79C2×C8×D11C2311yescharacteristic
80C2×C8×D11C2311yescharacteristic
81#66948—21no—
82#66945—21no—
83#66945—21no—
84C4⋊C4×D11—21no—
85C4⋊C4×D11—21no—
86C4⋊C4×D11—21no—
87#66937—41no—
88C22⋊C4×D11—41no—
89C22⋊C4×D11—41no—
90#66930—41no—
91#66925—41no—
92C42×D11—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#106—21no—
99C11×#102—21no—
100#66896—21no—
101#66885—21no—
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66873—21no—
109#66872—21no—
110#66872—21no—
111#66871—21no—
112#66871—21no—
113#66871—21no—
114#66862—22no—
115#66862—22no—
116#33648—111nomaximal, Sylow
117C23×D11—41no—
118C23×D11D811yescharacteristic
119C2×D4×C11—21no—
120C2×D4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C22×Dic11D811yescharacteristic
126D4×D11—42no—
127D4×D11—42no—
128D4×D11—84no—
129C2×D44—21no—
130C2×D44—41no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11D811yescharacteristic
137C2×C4×D11D811yescharacteristic
138C2×C4×D11C2×D411yescharacteristic
139C2×C4×D11C2×D411yescharacteristic
140C11×D8—21no—
141C11×D8—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11—41no—
152C22⋊Dic11—41no—
153C22⋊Dic11—41no—
154#4323—42no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C4×Dic11—41no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8C2×D411yescharacteristic
170C2×C11⋊C8C2×D411yescharacteristic
171D88—21no—
172D88—21no—
173C8×D11—22no—
174C8×D11—21no—
175C8×D11—21no—
176C8×D11—22no—
177C8×D11#4112yes—
178C8×D11#4112yes—
179C11×C16—21no—
180C11×C16—21no—
181C11⋊C16—21no—
182C11⋊C16—21no—
183C2×#466—111no—
184C2×#427—111no—
185#2234—111no—
186#2234—111no—
187#2234—111no—
188#2234D1111yescharacteristic, complemented
189#2233—111no—
190#2233—111no—
191#2232—111no—
192#2232—111no—
193#2159—111no—
194#2159—111no—
195#2140—111no—
196#2140—111no—
197#2112—111no—
198C23×C11—41no—
199C23×C11C2×D811yescharacteristic
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—82no—
205C22×D11—82no—
206C22×D11—82no—
207C22×D11C2×D811yescharacteristic
208C22×D11C2×D811yescharacteristic
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—82no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C22⋊D11—82no—
220C22⋊D11—82no—
221C22⋊D11—82no—
222C2×Dic11—22no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228D44—41no—
229D44—41no—
230D44—82no—
231C4×D11—22no—
232C4×D11—21no—
233C4×D11—21no—
234C4×D11—22no—
235C4×D11—82no—
236C4×D11—82no—
237C4×D11—82no—
238C4×D11#12312yes—
239C4×D11#13712yes—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11C2×#4111yescharacteristic
243C11⋊C8—21no—
244C11⋊C8#12312yes—
245C22×D8—111no—
246C23×C8—111no—
247C2×#121—221no—
248C2×#117—221no—
249C2×M32—111no—
250C2×M32—111no—
251#466—111no—
252#466—111no—
253#466—111no—
254#466—221no—
255#466—221no—
256#466C2×D1111yescharacteristic
257#427—111no—
258#427—111no—
259#427—111no—
260#427—221no—
261#427—221no—
262#427C2×D1111yescharacteristic, complemented
263C2×#107—111no—
264C2×#107—111no—
265C2×#107—111no—
266C2×#106—221no—
267C2×#102—221no—
268#367—111no—
269#367—111no—
270#367—111no—
271#367C2×D1111yescharacteristic, complemented
272#366—111no—
273#366—111no—
274#366—111no—
275#366C2×D1111yescharacteristic, complemented
276#357—111no—
277#357—111no—
278#357—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357C2×D1111yescharacteristic, complemented
283#357C2×D1111yescharacteristic, complemented
284C22⋊C16—111no—
285C22⋊C16—111no—
286C22⋊C16—111no—
287C22⋊C16C2×D1111yescharacteristic, complemented
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11C22×D811yescharacteristic
295C2×D11—21no—
296C2×D11—21no—
297C2×D11—21no—
298C2×D11—21no—
299C2×D11—44no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—164no—
304C2×D11#48012yes—
305C2×D11#50912yes—
306C4×C11—21no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11—81no—
310C4×C11C2×#12311yescharacteristic
311C4×C11C2×#13711yescharacteristic
312Dic11—21no—
313Dic11—81no—
314Dic11—81no—
315Dic11—81no—
316Dic11#48012yes—
317C22×D4—221no—
318C22×D4—441no—
319C23×C4—111no—
320C2×D8—111no—
321C2×D8—222no—
322C2×D8—222no—
323C2×D8—221no—
324C2×D8C22×D1111yescharacteristic
325C22×C8—111no—
326C22×C8—111no—
327C22×C8—111no—
328C22×C8—111no—
329C22×C8—111no—
330C22×C8—222no—
331C22×C8—222no—
332C22×C8C22×D1111yescharacteristic
333#121—21no—
334#121—221no—
335#121—221no—
336#121—221no—
337#121—441no—
338#121—441no—
339#117—21no—
340#117—221no—
341#117—221no—
342#117—221no—
343#117—441no—
344#117—441no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C22⋊C4—441no—
349C2×C22⋊C4—441no—
350C2×C42—441no—
351M32—222no—
352M32—222no—
353C2×C16—111no—
354C2×C16—111no—
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—111no—
358#107—111no—
359#107—111no—
360#107—221no—
361#107—221no—
362#107—221no—
363#107C22×D1111yescharacteristic
364#107C22×D1111yescharacteristic
365#107C22×D1111yescharacteristic
366#106—21no—
367#106—221no—
368#106—221no—
369#106—221no—
370#102—21no—
371#102—221no—
372#102—221no—
373#102—221no—
374C2×C11—41no—
375C2×C11—161no—
376C2×C11C2×#48011yescharacteristic
377C2×C11C2×#50911yescharacteristic
378C2×C11#341411yescharacteristic
379D11—22no—
380D11—22no—
381D11—161no—
382C24—111no—
383C24—441no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—221no—
387C2×D4—441no—
388C2×D4—442no—
389C2×D4—442no—
390C2×D4—441no—
391C2×D4—441no—
392C2×D4—441no—
393C2×D4—884no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4D4×D1111yescharacteristic
405D8—21no—
406D8—21no—
407D8—221no—
408D8—221no—
409D8—442no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—111no—
413C2×C8—112no—
414C2×C8—112no—
415C2×C8—111no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—221no—
420C2×C8—221no—
421C2×C8D4×D1111yescharacteristic
422C2×C8C23×D1111yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C42—41no—
441C42—441no—
442C42—441no—
443C42—441no—
444C16—21no—
445C16—21no—
446C16—221no—
447C16—221no—
448C11#3364811yescharacteristic, complemented, Sylow
449C23—41no—
450C23—111no—
451C23—111no—
452C23—222no—
453C23—222no—
454C23—441no—
455C23—441no—
456C23—882no—
457C23—882no—
458C23—882no—
459C23D8×D1111yescharacteristic
460D4—41no—
461D4—41no—
462D4—82no—
463D4—441no—
464D4—441no—
465D4—882no—
466D4—882no—
467D4—882no—
468D4—882no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—111no—
475C2×C4—112no—
476C2×C4—112no—
477C2×C4—111no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—882no—
487C2×C4—882no—
488C2×C4—882no—
489C2×C4D8×D1111yescharacteristic
490C2×C4C2×D4×D1111yescharacteristic
491C8—21no—
492C8—112no—
493C8—221no—
494C8#41×D1111yescharacteristic
495C8#41×D1111yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—112no—
503C22—112no—
504C22—221no—
505C22—221no—
506C22—221no—
507C22—221no—
508C22—444no—
509C22—881no—
510C22—881no—
511C22—881no—
512C22—1764no—
513C22C2×D8×D1111yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—112no—
519C4—221no—
520C4—881no—
521C4—881no—
522C4—881no—
523C4D11×#12311yescharacteristic
524C4D11×#13711yescharacteristic
525C2—41no—
526C2—161no—
527C2—222no—
528C2—222no—
529C2—1761no—
530C2D11×#48011yescharacteristic
531C2D11×#50911yescharacteristic
532C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2234C2
socleC22×C11C22×D8
prime radicalD11×#466C2
hypercenter#2234D11
hypocenterC11#33648
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
2. D11×#427C2semidirect
3. #13070808C2semidirect
4. #13070807C2semidirect
5. #13070804C2semidirect
6. #13070803C2semidirect
7. #13070800C2semidirect
8. #13070798C2semidirect
9. #13070795C2semidirect
10. #13070403C2semidirect
11. #13070401C2semidirect
12. #13070330C2semidirect
13. #13070330C2semidirect
14. #13070225C2semidirect
15. C11×#2234C2semidirect
21. C11×#427C22semidirect
24. #10622719C22semidirect
33. D11×#107C22semidirect
34. D11×#107C22semidirect
39. C11×#367C22semidirect
40. C11×#366C22semidirect
41. C11×#357C22semidirect
42. C11×#357C22semidirect
43. C11×C22⋊C16C22semidirect
44. #10622200C22semidirect
45. #10622200C22semidirect
46. C22⋊(C11⋊C16)C22semidirect
47. #10622147C22semidirect
48. #10622147C22semidirect
49. (C2×D11)⋊C16C22semidirect
50. (C2×D11)⋊C16C22semidirect
51. #10622143C22semidirect
52. #10622142C22semidirect
53. #10622129C22semidirect
54. #10622129C22semidirect
55. #10622128C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
188. #2234D11semidirect
262. #427C2×D11semidirect
271. #367C2×D11semidirect
275. #366C2×D11semidirect
282. #357C2×D11semidirect
283. #357C2×D11semidirect
287. C22⋊C16C2×D11semidirect
448. C11#33648semidirect

Maximal subgroups

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

subgroupindex
D11×#4662
D11×#4272
#130708082
#130708072
#130708042
#130708032
#130708002
#130707982
#130707952
#130704032
#130704012
#130703302
#130702252
C11×#22342
#3364811