Finite Group Databasebeta

← #14813837

Subgroups — #14813837

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622670C211yesmaximal, characteristic
2C2×C4×#4323C211yesmaximal, characteristic
3C4⋊C4×D44C211yesmaximal, characteristic, complemented
4#13070154C211yesmaximal, characteristic, complemented
5#13070112C211yesmaximal, characteristic, complemented
6#13070019C211yesmaximal, characteristic, complemented
7#13069852C211yesmaximal, characteristic, complemented
8#13069295C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068967C211yesmaximal, characteristic
11#13068953C211yesmaximal, characteristic, complemented
12#13068953C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068862C211yesmaximal, characteristic, complemented
15C11×#2447C211yesmaximal, characteristic, complemented
16C2×C11×#124C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×C4⋊C4×D11—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#397—21no—
25C11×#397—21no—
26C11×#391C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#385—21no—
31C11×#381—21no—
32C4×C11×C4⋊C4C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622670—24no—
40C4×#4323—24no—
41#10622600—21no—
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622281—21no—
52#10622281—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C11×#124—22no—
69C11×#124—41no—
70C4×D4×C11—22no—
71C4×D4×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×#4325—22no—
86C2×#4325—22no—
87C2×#4325—22no—
88C2×#4323—22no—
89C2×#4323—22no—
90C2×#4323D414yes—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C4⋊C4×D11—44no—
106C4×D44—22no—
107C4×D44—22no—
108C4×D44—22no—
109C4×D44—22no—
110C4×D44—41no—
111C4×D44—41no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119#66899—22no—
120#66899—22no—
121#66899—41no—
122#66896—22no—
123#66896—22no—
124#66896—22no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66873—22no—
128#66873—22no—
129#66871—22no—
130#66871—41no—
131C4⋊(C11⋊C8)—22no—
132C4×C11⋊C8—22no—
133#26164—111nomaximal, Sylow
134C24×C11—21no—
135C23×D11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11C2×D412yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—81no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44C2×D412yes—
168C2×D44#4112yes—
169C2×D44#4112yes—
170C2×C4×D11—24no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11—81no—
178C2×C4×D11—81no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—81no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—81no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197#4325—44no—
198#4323—28no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—42no—
208C4⋊Dic11—81no—
209C4⋊Dic11#4112yes—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8C2×D412yes—
224C2×#463—111no—
225C2×C4×D8—111no—
226#2447D1111yescharacteristic, complemented
227D4×C4⋊C4—111no—
228#2095—111no—
229#2087—111no—
230#2071—111no—
231#2042—111no—
232#1933—111no—
233#1916—111no—
234#1879—111no—
235#1877—111no—
236#1877—111no—
237#1862—111no—
238#1862—111no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C22×D411yescharacteristic
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254Q8×C11—41no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—41no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—41no—
261D4×C11—41no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—84no—
288C2×C4×C11#13512yes—
289C2×C4×C11AGL(1,ℤ/8)12yes—
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×C4×C112−1+411yescharacteristic
296C2×Dic11—22no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305D44—22no—
306D44—22no—
307D44—22no—
308D44#12314yes—
309C4×D11—48no—
310C4×D11—84no—
311C4×D11—84no—
312C11⋊C8—22no—
313C11⋊C8—41no—
314C11⋊C8—41no—
315C11⋊C8—41no—
316C22×SD16—111no—
317C22×D8—111no—
318C2×#124C2×D1111yescharacteristic
319C2×C4×D4—111no—
320C2×C4×D4—111no—
321C2×C4×D4—111no—
322C2×C4×D4C2×D1111yescharacteristic
323C22×C4⋊C4—221no—
324#463—224no—
325C4×D8—224no—
326C2×#107—111no—
327C2×#107—111no—
328C2×C4⋊C8—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×#102—111no—
337C2×C4×C8—111no—
338#397—21no—
339#397—21no—
340#391C2×D1111yescharacteristic
341#391C2×D1111yescharacteristic
342#390C2×D1111yescharacteristic
343#389—111no—
344#389—111no—
345#389C2×D1111yescharacteristic
346#385—21no—
347#385—221no—
348#385—221no—
349#384—111no—
350#381—21no—
351#380—221no—
352C4×C4⋊C4C2×D1111yescharacteristic
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#336—111no—
358#336—111no—
359#336—111no—
360#336—111no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11#52511yescharacteristic
369C22×C11D4211yescharacteristic
370C22×C11#54811yescharacteristic
371C22×C11C2×#13511yescharacteristic
372C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C11#57611yescharacteristic
374C22×C11#57811yescharacteristic
375C2×D11—24no—
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—42no—
381C2×D11—42no—
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11C2×#12311yescharacteristic
392C4×C11#53911yescharacteristic
393C4×C11#54711yescharacteristic
394C4×C11#55311yescharacteristic
395Dic11—42no—
396Dic11—81no—
397Dic11—81no—
398C22×Q8C22×D1111yescharacteristic
399C22×D4—111no—
400C22×D4C22×D1111yescharacteristic
401C23×C4—21no—
402C23×C4—221no—
403C23×C4—221no—
404C23×C4—221no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×SD16—222no—
408C2×D8—114no—
409C2×D8—222no—
410C2×D8—222no—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8—111no—
415#124—22no—
416#124—41no—
417C4×D4—22no—
418C4×D4—41no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4—222no—
423C4×D4—441no—
424C4×D4—441no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—444no—
434C2×C4⋊C4C22⋊D1111yescharacteristic
435C2×C4⋊C4C22⋊D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1111yescharacteristic
448C2×C42C22×D1111yescharacteristic
449#107—222no—
450#107—441no—
451C4⋊C8—222no—
452#103—222no—
453#103—222no—
454#103—441no—
455#102—222no—
456#102—222no—
457#102—222no—
458#102—222no—
459#102—222no—
460C4×C8—222no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—221no—
467#95—221no—
468#95C22⋊D1111yescharacteristic
469#95C22⋊D1111yescharacteristic
470C2×C11—82no—
471C2×C11#244311yescharacteristic
472C2×C11#310511yescharacteristic
473C2×C11#312411yescharacteristic
474C2×C11#326411yescharacteristic
475C2×C11#328311yescharacteristic
476C2×C11#336111yescharacteristic
477C2×C11#336711yescharacteristic
478D11—44no—
479C24—21no—
480C24—221no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—112no—
493C2×D4—112no—
494C2×D4—112no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4D4×D1112yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—224no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—881no—
516C22×C4—881no—
517C22×C4C2×C22⋊D1111yescharacteristic
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C23×D1111yescharacteristic
524SD16—444no—
525D8—228no—
526C2×C8—112no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—81no—
545C4⋊C4—112no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—881no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—224no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C11#2616411yescharacteristic, complemented, Sylow
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—222no—
578C23—222no—
579C23—222no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23C22×C22⋊D1111yescharacteristic
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—114no—
594D4—222no—
595D4—222no—
596D4—222no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4—222no—
624C2×C4—448no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—884no—
634C2×C4—884no—
635C2×C4#6700212yes—
636C2×C4#6700312yes—
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4#6703711yescharacteristic
639C2×C4#41×D1111yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#6704311yescharacteristic
643C8—222no—
644C8—441no—
645C8—441no—
646C8—441no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—224no—
655C22—442no—
656C22—442no—
657C22—442no—
658C22—442no—
659C22—442no—
660C22—442no—
661C22D4×C22⋊D1111yescharacteristic
662C22C2×#6700211yescharacteristic
663C22C2×#6700311yescharacteristic
664C22#1062335911yescharacteristic
665C22#1062336211yescharacteristic
666C22#1062336611yescharacteristic
667C22#1062336911yescharacteristic
668C4—22no—
669C4—22no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—442no—
678C4—881no—
679C4—881no—
680C4D11×#12311yescharacteristic
681C4#1062318611yescharacteristic
682C4#1062319111yescharacteristic
683C4#1062319211yescharacteristic
684C2—82no—
685C2—444no—
686C2#1307234811yescharacteristic
687C2#1307865911yescharacteristic
688C2#1307887211yescharacteristic
689C2#1308009711yescharacteristic
690C2#1308033411yescharacteristic
691C2#1308127211yescharacteristic
692C2#1308133011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2447C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2447D11
hypocenterC11#26164
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2447

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×D44C2semidirect
4. #13070154C2semidirect
5. #13070112C2semidirect
6. #13070019C2semidirect
7. #13069852C2semidirect
8. #13069295C2semidirect
9. #13069175C2semidirect
11. #13068953C2semidirect
12. #13068953C2semidirect
13. #13068863C2semidirect
14. #13068862C2semidirect
15. C11×#2447C2semidirect
226. #2447D11semidirect
569. C11#26164semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×C4×#43232
C4⋊C4×D442
#130701542
#130701122
#130700192
#130698522
#130692952
#130691752
#130689672
#130689532
#130688632
#130688622
C11×#24472
#2616411