Finite Group Databasebeta

← #14810289

Subgroups — #14810289

Order 2816.

1344 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622684C211yesmaximal, characteristic, complemented
2C2×#10622635C211yesmaximal, characteristic, complemented
3#13073782C211yesmaximal, characteristic, complemented
4#13069802C212yesmaximal, complemented
5#13069795C212yesmaximal, complemented
6#13069544C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068556C212yesmaximal, complemented
9#13068556C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#550C211yesmaximal, characteristic
12C22×C11×#41C2212yes—
13C11×#550—24no—
14C11×#550—24no—
15C2×C11×#127—21no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—22no—
18C2×C11×#121C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C2×#66899C2211yescharacteristic
24C2×#66899C2211yescharacteristic
25C2×#66899C2212yes—
26#10622835—21no—
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622825C2212yes—
32#10622825C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34C2×C22⋊(C11⋊C8)C2212yes—
35#10622684—24no—
36#10622635—24no—
37#10622595—21no—
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622558—22no—
41C4×C4⋊Dic11C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45C2×C11×#41—24no—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—42no—
50C2×C11×#41—42no—
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11D411yescharacteristic
57C22×D4×C11C2312yes—
58C23×C4×C11—22no—
59C23×C4×C11C2312yes—
60C11×#127—28no—
61C11×#127—22no—
62C11×#127D414yes—
63C11×#121—216no—
64C11×#121—24no—
65C11×#121—24no—
66C4×Q8×C11—22no—
67C4×Q8×C11D414yes—
68C4×D4×C11—28no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D412yes—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2312yes—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89#66923—22no—
90#66923—22no—
91#66899—22no—
92#66899—22no—
93#66899—24no—
94#66896—24no—
95#66896—24no—
96#66896—42no—
97#66896—42no—
98C11⋊#95—21no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C22⋊(C11⋊C8)—42no—
102C22⋊(C11⋊C8)—42no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107#25893—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11C2×D412yes—
110C11×#41—48no—
111C11×#41—48no—
112C11×#41—48no—
113C11×#41—48no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11C2×D412yes—
117C2×Q8×C11#4114yes—
118C2×D4×C11—28no—
119C2×D4×C11—28no—
120C2×D4×C11—22no—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—42no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—81no—
133C2×D4×C11—81no—
134C2×D4×C11—82no—
135C2×D4×C11—82no—
136C2×D4×C11C2×D414yes—
137C22×C4×C11—21no—
138C22×C4×C11—28no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—44no—
147C22×C4×C11—44no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—22no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—28no—
160C11×C22⋊C4—24no—
161C42×C11—24no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164C22⋊Dic11—44no—
165C22⋊Dic11—82no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172Dic11⋊C4—42no—
173Dic11⋊C4—42no—
174C4×Dic11—81no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×#550D1111yescharacteristic
183C2×#490—111no—
184C2×#479—111no—
185#2562—111no—
186#2034—112no—
187#2033—112no—
188#1982—111no—
189#1955—111no—
190#1788—112no—
191#1788—112no—
192#1763—111no—
193C23×C11—22no—
194C23×C11—24no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11C22×D411yescharacteristic
208Q8×C11—22no—
209Q8×C11—24no—
210Q8×C11#12414yes—
211D4×C11—24no—
212D4×C11—24no—
213D4×C11—44no—
214D4×C11—48no—
215D4×C11—416no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—84no—
219D4×C11—88no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—416no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11#12012yes—
237C2×C4×C11#12012yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4112yes—
241C2×C4×C11H(5,𝔽2)12yes—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C11⋊C8—41no—
251C11⋊C8—41no—
252C11⋊C8—42no—
253C22×#41C2×D1112yes—
254#550—24no—
255#550—24no—
256C2×#127—21no—
257C2×#127C2×D1111yescharacteristic
258C2×#125—111no—
259C2×#121—22no—
260C2×#121C2×D1112yes—
261C2×C4×Q8C2×D1111yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4C2×D1111yescharacteristic
264#490—224no—
265#479—224no—
266C2×#107—111no—
267C2×#106—111no—
268C2×C4⋊C8—111no—
269C2×#103—111no—
270C2×#103—111no—
271C2×#103—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—112no—
275C2×#102—112no—
276C2×C22⋊C8—112no—
277C2×C22⋊C8—112no—
278C2×#97—111no—
279#400—221no—
280#394—221no—
281#388—222no—
282#380—112no—
283#380—112no—
284C4×C4⋊C4—111no—
285#340—112no—
286C22×C11—44no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—44no—
290C22×C11—42no—
291C22×C11—44no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#54612yes—
302C22×C11#57512yes—
303C22×C11#57611yescharacteristic
304C22×C11#57711yescharacteristic
305C4×C11—24no—
306C4×C11—22no—
307C4×C11—22no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11C2×#12411yescharacteristic
311C4×C11#53511yescharacteristic
312C4×C11#54612yes—
313Dic11—81no—
314Dic11—81no—
315Dic11—82no—
316C2×#41—24no—
317C2×#41—24no—
318C2×#41—24no—
319C2×#41—24no—
320C2×#41—42no—
321C2×#41—42no—
322C22×Q8C22×D1111yescharacteristic
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4C22⋊D1111yescharacteristic
328C22×D4C22×D1112yes—
329C23×C4—22no—
330C23×C4C22×D1112yes—
331C22×C8—112no—
332C22×C8—111no—
333C22×C8—111no—
334#127—28no—
335#127—22no—
336#127C22⋊D1114yes—
337#125—222no—
338#125—222no—
339#121—216no—
340#121—24no—
341#121—24no—
342C4×Q8—22no—
343C4×Q8C22⋊D1114yes—
344C4×D4—28no—
345C4×D4—22no—
346C4×D4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4C22⋊D1111yescharacteristic
354C2×C4⋊C4C22×D1111yescharacteristic
355C2×C22⋊C4—22no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4C22⋊D1112yes—
359C2×C42—21no—
360C2×C42—221no—
361C2×C42C22×D1111yescharacteristic
362#107—222no—
363#106—222no—
364C4⋊C8—222no—
365#103—224no—
366#103—222no—
367#103—222no—
368#102—224no—
369#102—224no—
370#102—442no—
371#102—442no—
372C22⋊C8—442no—
373C22⋊C8—442no—
374#97—222no—
375#95—221no—
376#95—222no—
377#95—222no—
378C2×C11—82no—
379C2×C11—84no—
380C2×C11#243511yescharacteristic
381C2×C11#300511yescharacteristic
382C2×C11#301211yescharacteristic
383C2×C11#330912yes—
384C2×C11#331712yes—
385C24—22no—
386C24C2×C22⋊D1112yes—
387#41—48no—
388#41—48no—
389#41—48no—
390#41—48no—
391C2×Q8—22no—
392C2×Q8—21no—
393C2×Q8#434114yes—
394C2×Q8C2×C22⋊D1112yes—
395C2×D4—28no—
396C2×D4—28no—
397C2×D4—22no—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—42no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4—82no—
412C2×D4—82no—
413C2×D4C2×C22⋊D1114yes—
414C22×C4—21no—
415C22×C4—28no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C23×D1111yescharacteristic
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—221no—
438C2×C8—221no—
439C4⋊C4—24no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—221no—
445C4⋊C4—221no—
446C4⋊C4—221no—
447C4⋊C4—221no—
448C4⋊C4—442no—
449C4⋊C4—442no—
450C4⋊C4C2×C22⋊D1112yes—
451C22⋊C4—28no—
452C22⋊C4—24no—
453C22⋊C4—444no—
454C22⋊C4—882no—
455C42—24no—
456C42—881no—
457C42C2×C22⋊D1112yes—
458C42C2×C22⋊D1112yes—
459C11#2589311yescharacteristic, complemented, Sylow
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—24no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23C22×C22⋊D1111yescharacteristic
475Q8—22no—
476Q8—24no—
477Q8#6698914yes—
478D4—24no—
479D4—24no—
480D4—44no—
481D4—48no—
482D4—416no—
483D4—42no—
484D4—42no—
485D4—84no—
486D4—88no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—416no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4#6700612yes—
512C2×C4#6700612yes—
513C2×C4C2×#434112yes—
514C2×C4#6703712yes—
515C2×C4C22×C22⋊D1111yescharacteristic
516C2×C4C22×C22⋊D1111yescharacteristic
517C8—441no—
518C8—441no—
519C8—442no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—44no—
524C22—44no—
525C22—42no—
526C22—42no—
527C22—44no—
528C22—42no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22#1062333712yes—
535C22#1062335312yes—
536C22#1062336611yescharacteristic
537C22#1062336711yescharacteristic
538C22C2×#6700611yescharacteristic
539C4—22no—
540C4—24no—
541C4—22no—
542C4—42no—
543C4—42no—
544C4—882no—
545C4—881no—
546C4—881no—
547C4C2×#6698911yescharacteristic
548C4#1062333611yescharacteristic
549C4#1062333712yes—
550C2—82no—
551C2—84no—
552C2#1307226311yescharacteristic
553C2#1307785811yescharacteristic
554C2#1307792011yescharacteristic
555C2#1308062212yes—
556C2#1308074212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11#25893
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622684C2semidirect
2. C2×#10622635C2semidirect
3. #13073782C2semidirect
4. #13069802C2semidirect
5. #13069795C2semidirect
6. #13069544C2semidirect
7. #13069415C2semidirect
8. #13068556C2semidirect
9. #13068556C2semidirect
10. #13068446C2semidirect
459. C11#25893semidirect

Maximal subgroups

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

subgroupindex
C2×#106226842
C2×#106226352
#130737822
#130698022
#130697952
#130695442
#130694152
#130685562
#130684462
C2×C11×#5502
#2589311