Finite Group Databasebeta

← #14814197

Subgroups — #14814197

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622670C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3C4⋊C4×D44C211yesmaximal, characteristic, complemented
4#13070144C211yesmaximal, characteristic, complemented
5#13070112C211yesmaximal, characteristic, complemented
6#13070024C211yesmaximal, characteristic, complemented
7#13069852C211yesmaximal, characteristic, complemented
8#13069316C211yesmaximal, characteristic, complemented
9#13069182C211yesmaximal, characteristic, complemented
10#13068967C211yesmaximal, characteristic
11#13068967C211yesmaximal, characteristic
12#13068953C211yesmaximal, characteristic, complemented
13#13068870C211yesmaximal, characteristic, complemented
14#13068862C211yesmaximal, characteristic, complemented
15C11×#2448C211yesmaximal, characteristic, complemented
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×C4⋊C4×D11—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#399—21no—
25C11×#397—21no—
26C11×#391C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#388—21no—
31C11×#388—21no—
32C4×C11×C4⋊C4C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622670—24no—
40#10622639—24no—
41#10622600—21no—
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
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
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C11×#124—22no—
68C11×#124—41no—
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
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×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4325—22no—
88C2×#4325—22no—
89C2×#4325D414yes—
90C2×#4323—22no—
91C2×#4323—22no—
92C2×#4323—22no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C4⋊C4×D11—44no—
108C4×D44—22no—
109C4×D44—22no—
110C4×D44—22no—
111C4×D44—22no—
112C4×D44—41no—
113C4×D44—41no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119#66899—22no—
120#66899—22no—
121#66899—22no—
122#66896—22no—
123#66896—22no—
124#66896—41no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66873—22no—
128#66873—22no—
129#66871—22no—
130#66871—41no—
131C4⋊(C11⋊C8)—22no—
132#66867—22no—
133#26188—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×C11C2×D412yes—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44C2×D412yes—
165C2×D44#4112yes—
166C2×D44#4112yes—
167C2×C4×D11—24no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—81no—
175C2×C4×D11—81no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—81no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—81no—
189C11×C22⋊C4—81no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—42no—
197#4325—28no—
198#4323—44no—
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×#440—111no—
226#2448D1111yescharacteristic, complemented
227D4×C4⋊C4—111no—
228#2093—111no—
229#2087—111no—
230#2072—111no—
231#2042—111no—
232#1936—111no—
233#1917—111no—
234#1879—111no—
235#1879—111no—
236#1877—111no—
237#1863—111no—
238#1862—111no—
239C23×C11—41no—
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—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
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—22no—
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—21no—
279C2×C4×C11—21no—
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—41no—
288C2×C4×C11AGL(1,ℤ/8)12yes—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C112−1+411yescharacteristic
295C2×Dic11—22no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304D44—22no—
305D44—22no—
306D44—22no—
307D44#12314yes—
308C4×D11—48no—
309C4×D11—84no—
310C4×D11—84no—
311C11⋊C8—22no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314C11⋊C8—41no—
315C22×SD16—111no—
316C22×D8—111no—
317C2×#124C2×D1111yescharacteristic
318C2×C4×Q8C2×D1111yescharacteristic
319C2×C4×D4—111no—
320C2×C4×D4—111no—
321C2×C4×D4—111no—
322C22×C4⋊C4—221no—
323#463—224no—
324#440—224no—
325C2×#107—111no—
326C2×#107—111no—
327C2×C4⋊C8—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×#97—111no—
337#399—21no—
338#397—21no—
339#391C2×D1111yescharacteristic
340#390C2×D1111yescharacteristic
341#390C2×D1111yescharacteristic
342#389—111no—
343#389—111no—
344#389C2×D1111yescharacteristic
345#388—21no—
346#388—21no—
347#385—221no—
348#385—221no—
349#384—111no—
350#380—221no—
351C4×C4⋊C4C2×D1111yescharacteristic
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#336—111no—
357#336—111no—
358#336—111no—
359#336—111no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11#52511yescharacteristic
368C22×C11D4211yescharacteristic
369C22×C11#54811yescharacteristic
370C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C11#57511yescharacteristic
372C22×C11#57611yescharacteristic
373C22×C11#57811yescharacteristic
374C2×D11—24no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—42no—
381C4×C11—22no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11C2×#12311yescharacteristic
391C4×C11#53911yescharacteristic
392C4×C11#54711yescharacteristic
393C4×C11#55311yescharacteristic
394Dic11—42no—
395Dic11—81no—
396Dic11—81no—
397C22×Q8C22×D1111yescharacteristic
398C22×D4—111no—
399C22×D4C22×D1111yescharacteristic
400C23×C4—221no—
401C23×C4—221no—
402C23×C4—221no—
403C2×SD16—114no—
404C2×SD16—222no—
405C2×SD16—222no—
406C2×D8—222no—
407C2×D8—222no—
408C2×D8—222no—
409C22×C8—111no—
410C22×C8—111no—
411C22×C8—111no—
412C22×C8—111no—
413#124—22no—
414#124—41no—
415C4×Q8—22no—
416C4×Q8—41no—
417C4×D4—222no—
418C4×D4—222no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—441no—
422C4×D4—441no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—444no—
433C2×C4⋊C4C22⋊D1111yescharacteristic
434C2×C4⋊C4C22⋊D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
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×C42—21no—
447C2×C42C22×D1111yescharacteristic
448C2×C42C22×D1111yescharacteristic
449C2×C42C22×D1111yescharacteristic
450#107—222no—
451#107—441no—
452C4⋊C8—222no—
453#103—222no—
454#103—222no—
455#103—222no—
456#102—222no—
457#102—222no—
458#102—222no—
459#102—222no—
460#102—441no—
461#97—222no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—221no—
466#95—221no—
467#95C22⋊D1111yescharacteristic
468#95C22⋊D1111yescharacteristic
469C2×C11—161no—
470C2×C11#244311yescharacteristic
471C2×C11#311411yescharacteristic
472C2×C11#312411yescharacteristic
473C2×C11#326911yescharacteristic
474C2×C11#327411yescharacteristic
475C2×C11#336711yescharacteristic
476C2×C11#337011yescharacteristic
477D11—44no—
478C24—21no—
479C24—221no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8D4×D1112yes—
486C2×D4—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—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—224no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—881no—
512C22×C4—881no—
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C2×C22⋊D1111yescharacteristic
517C22×C4C2×C22⋊D1111yescharacteristic
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520SD16—228no—
521D8—444no—
522C2×C8—112no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—41no—
540C4⋊C4—42no—
541C4⋊C4—81no—
542C4⋊C4—112no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4—442no—
551C4⋊C4—881no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C22⋊C4—224no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—42no—
568C11#2618811yescharacteristic, complemented, Sylow
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—222no—
577C23—222no—
578C23—222no—
579C23—441no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23C22×C22⋊D1111yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—41no—
587Q8—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—114no—
593D4—222no—
594D4—222no—
595D4—222no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
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—21no—
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—222no—
623C2×C4—448no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—884no—
633C2×C4—884no—
634C2×C4#6700212yes—
635C2×C4C2×D4×D1111yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4#41×D1111yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#41×D1111yescharacteristic
640C2×C4#6704311yescharacteristic
641C8—222no—
642C8—441no—
643C8—441no—
644C8—441no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—224no—
653C22—442no—
654C22—442no—
655C22—442no—
656C22—442no—
657C22—442no—
658C22—442no—
659C22D4×C22⋊D1111yescharacteristic
660C22C2×#6700211yescharacteristic
661C22#1062335311yescharacteristic
662C22#1062335911yescharacteristic
663C22#1062336211yescharacteristic
664C22#1062336611yescharacteristic
665C22#1062336911yescharacteristic
666C4—22no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—42no—
673C4—81no—
674C4—81no—
675C4—442no—
676C4—881no—
677C4—881no—
678C4D11×#12311yescharacteristic
679C4#1062318611yescharacteristic
680C4#1062319111yescharacteristic
681C4#1062319211yescharacteristic
682C2—161no—
683C2—444no—
684C2#1307234811yescharacteristic
685C2#1307875011yescharacteristic
686C2#1307887211yescharacteristic
687C2#1308017211yescharacteristic
688C2#1308023611yescharacteristic
689C2#1308133011yescharacteristic
690C2#1308136311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2448C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2448D11
hypocenterC11#26188
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2448

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
3. C4⋊C4×D44C2semidirect
4. #13070144C2semidirect
5. #13070112C2semidirect
6. #13070024C2semidirect
7. #13069852C2semidirect
8. #13069316C2semidirect
9. #13069182C2semidirect
12. #13068953C2semidirect
13. #13068870C2semidirect
14. #13068862C2semidirect
15. C11×#2448C2semidirect
226. #2448D11semidirect
568. C11#26188semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×#106226392
C4⋊C4×D442
#130701442
#130701122
#130700242
#130698522
#130693162
#130691822
#130689672
#130689532
#130688702
#130688622
C11×#24482
#2618811