Finite Group Databasebeta

← #14802187

Subgroups — #14802187

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C211yesmaximal, characteristic, complemented
2#13073088C211yesmaximal, characteristic
3#13071647C211yesmaximal, characteristic, complemented
4#13070090C211yesmaximal, characteristic, complemented
5#13070027C211yesmaximal, characteristic, complemented
6#13070000C211yesmaximal, characteristic, complemented
7#13069929C211yesmaximal, characteristic, complemented
8#13069371C211yesmaximal, characteristic, complemented
9#13069239C211yesmaximal, characteristic, complemented
10#13068973C211yesmaximal, characteristic, complemented
11#13068939C211yesmaximal, characteristic
12#13068799C211yesmaximal, characteristic, complemented
13#13068619C211yesmaximal, characteristic, complemented
14#13068336C211yesmaximal, characteristic, complemented
15C2×C11×#468C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66988—21no—
22C2×#66988—21no—
23C2×#66979C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C11×#468—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622834C2211yescharacteristic
33#10622834C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C4×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622657—24no—
41#10622598C2211yescharacteristic
42#10622594—21no—
43#10622589C2211yescharacteristic
44#10622589C2211yescharacteristic
45C4⋊C4×Dic11—21no—
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622564—21no—
50#10622564—21no—
51#10622562—21no—
52#10622562—21no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C2×C11×SD16—22no—
67C2×C11×SD16—22no—
68C2×C11×SD16—41no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8D414yes—
76C11×#121—22no—
77C11×#121—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90Q8×Dic11—22no—
91Q8×Dic11—41no—
92#66988—44no—
93#66988—44no—
94#66979—22no—
95#66979—41no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C11×#107—22no—
117C11×#103—22no—
118C11×#102—22no—
119#66899—22no—
120#66899—22no—
121#66896—22no—
122#66896—41no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95D411yescharacteristic
128C11⋊#95D411yescharacteristic
129C22⋊(C11⋊C8)—22no—
130Dic11⋊C8—22no—
131Dic11⋊C8—41no—
132#66871—22no—
133#66871—22no—
134#25217—111nomaximal, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C2×D412yes—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—42no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11—42no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C11×SD16—44no—
175C11×M16—44no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11#4112yes—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C2×D412yes—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—42no—
189C22⋊Dic11—22no—
190C22⋊Dic11—22no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195C22⋊Dic11—42no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11—42no—
205C4⋊Dic11—42no—
206C4⋊Dic11#4112yes—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217C4×Dic11—42no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×#484—111no—
225C2×#468D1111yescharacteristic
226#2501—111no—
227#2362—111no—
228#2083—111no—
229#2072—111no—
230#2067—111no—
231#2055—111no—
232#1947—111no—
233#1925—111no—
234#1880—111no—
235#1875—111no—
236#1851—111no—
237#1803—111no—
238#1736—111no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11#12112yes—
253C23×C11C22×D411yescharacteristic
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—84no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11#12112yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—84no—
308C2×Dic11AGL(1,ℤ/8)12yes—
309C2×Dic11AGL(1,ℤ/8)12yes—
310C8×C11—22no—
311C8×C11—41no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314C22×SD16C2×D1111yescharacteristic
315C22×M16C2×D1111yescharacteristic
316C2×#123—221no—
317C2×#123—221no—
318C2×C22⋊Q8C2×D1111yescharacteristic
319C2×#121C2×D1111yescharacteristic
320C2×C4×Q8—111no—
321C2×#117—111no—
322C22×C4⋊C4—111no—
323#484—224no—
324#468—24no—
325C2×#107—111no—
326C2×#107—111no—
327C2×#107C2×D1111yescharacteristic
328C2×C4⋊C8—111no—
329C2×C4⋊C8—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103C2×D1111yescharacteristic
333C2×#102—111no—
334C2×#102—111no—
335C2×#102C2×D1111yescharacteristic
336C2×C22⋊C8—111no—
337#399—221no—
338#399—221no—
339#391—111no—
340#390—111no—
341#390—111no—
342#389—111no—
343#388—221no—
344#388—221no—
345#387—221no—
346#384—111no—
347#384—111no—
348C4×C4⋊C4—111no—
349C4×C4⋊C4—221no—
350C4×C22⋊C4—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#336—111no—
358#336—111no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11C2×#12111yescharacteristic
374C22×C11#54611yescharacteristic
375C22×C11#54711yescharacteristic
376C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C11#57811yescharacteristic
379C22×C11#57811yescharacteristic
380C4×C11—22no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—81no—
384C4×C11#52911yescharacteristic
385C4×C11#53911yescharacteristic
386C4×C11#54611yescharacteristic
387C4×C11#54711yescharacteristic
388Dic11—22no—
389Dic11—22no—
390Dic11—41no—
391Dic11—42no—
392Dic11—41no—
393Dic11—81no—
394Dic11—81no—
395Dic11—81no—
396C22×Q8C22×D1111yescharacteristic
397C22×D4—21no—
398C22×D4C22×D1111yescharacteristic
399C23×C4—221no—
400C23×C4C22×D1111yescharacteristic
401C2×SD16—22no—
402C2×SD16—22no—
403C2×SD16—41no—
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—41no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411#123—444no—
412#123—444no—
413C22⋊Q8—22no—
414C22⋊Q8C22⋊D1114yes—
415#121—22no—
416#121—22no—
417C4×Q8—222no—
418C4×Q8—441no—
419#117—222no—
420#117—441no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—111no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—221no—
449C2×C42—221no—
450C2×C42—221no—
451#107—22no—
452#107—222no—
453#107—222no—
454C4⋊C8—222no—
455C4⋊C8—441no—
456#103—22no—
457#103—222no—
458#103—222no—
459#102—22no—
460#102—222no—
461#102—441no—
462C22⋊C8—222no—
463#95—111no—
464#95—111no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469C2×C11—42no—
470C2×C11—161no—
471C2×C11#242511yescharacteristic
472C2×C11#303811yescharacteristic
473C2×C11#304411yescharacteristic
474C2×C11#330811yescharacteristic
475C2×C11#333011yescharacteristic
476C2×C11#334311yescharacteristic
477C2×C11#335311yescharacteristic
478C24—21no—
479C24D4×D1111yescharacteristic
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8C2×C22⋊D1112yes—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4D4×D1111yescharacteristic
514C22×C4#434112yes—
515C22×C4C2×C22⋊D1112yes—
516C22×C4C23×D1111yescharacteristic
517SD16—44no—
518M16—44no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8#434112yes—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—112no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4C2×C22⋊D1112yes—
551C22⋊C4—24no—
552C22⋊C4—42no—
553C22⋊C4—222no—
554C22⋊C4—222no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C42—221no—
561C42—221no—
562C42—221no—
563C42—221no—
564C42—442no—
565C42—442no—
566C42—442no—
567C11#2521711yescharacteristic, complemented, Sylow
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23#6699212yes—
582C23C2×D4×D1111yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—41no—
586Q8—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—84no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—112no—
608C2×C4—112no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—884no—
632C2×C4#6699212yes—
633C2×C4C2×#434111yescharacteristic
634C2×C4C2×#434111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4#41×D1111yescharacteristic
637C2×C4#6704311yescharacteristic
638C2×C4C22×C22⋊D1111yescharacteristic
639C8—22no—
640C8—41no—
641C8—441no—
642C8—441no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22#1062314111yescharacteristic
658C22#1062314211yescharacteristic
659C22D11×AGL(1,ℤ/8)11yescharacteristic
660C22D11×AGL(1,ℤ/8)11yescharacteristic
661C22#1062331011yescharacteristic
662C22#1062331011yescharacteristic
663C22C2×#6699211yescharacteristic
664C4—22no—
665C4—42no—
666C4—42no—
667C4—81no—
668C4—222no—
669C4—222no—
670C4—441no—
671C4—442no—
672C4—441no—
673C4—881no—
674C4—881no—
675C4—881no—
676C4#1062313111yescharacteristic
677C4#1062313311yescharacteristic
678C4#1062333711yescharacteristic
679C4#1062335511yescharacteristic
680C2—42no—
681C2—161no—
682C2#1307217311yescharacteristic
683C2#1307809411yescharacteristic
684C2#1307814811yescharacteristic
685C2#1308060211yescharacteristic
686C2#1308091611yescharacteristic
687C2#1308105111yescharacteristic
688C2#1308119511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#468D11
hypocenterC11#25217
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10622657C2semidirect
3. #13071647C2semidirect
4. #13070090C2semidirect
5. #13070027C2semidirect
6. #13070000C2semidirect
7. #13069929C2semidirect
8. #13069371C2semidirect
9. #13069239C2semidirect
10. #13068973C2semidirect
12. #13068799C2semidirect
13. #13068619C2semidirect
14. #13068336C2semidirect
567. C11#25217semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
#130730882
#130716472
#130700902
#130700272
#130700002
#130699292
#130693712
#130692392
#130689732
#130689392
#130687992
#130686192
#130683362
C2×C11×#4682
#2521711