Finite Group Databasebeta

← #14802181

Subgroups — #14802181

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×#10622583C211yesmaximal, characteristic, complemented
2C2×#10622747C211yesmaximal, characteristic
3#13073083C211yesmaximal, characteristic
4#13071643C211yesmaximal, characteristic, complemented
5#13070091C211yesmaximal, characteristic, complemented
6#13070028C211yesmaximal, characteristic, complemented
7#13070005C211yesmaximal, characteristic, complemented
8#13069935C211yesmaximal, characteristic, complemented
9#13069373C211yesmaximal, characteristic, complemented
10#13069234C211yesmaximal, characteristic, complemented
11#13068972C211yesmaximal, characteristic, complemented
12#13068938C211yesmaximal, characteristic
13#13068799C211yesmaximal, characteristic, complemented
14#13068620C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66982—21no—
21C2×#66982—21no—
22C2×#66977C2211yescharacteristic
23C22×#4314C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C4×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27#10622747—24no—
28C2×#66885C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622605—21no—
34#10622605—21no—
35#10622601C2211yescharacteristic
36#10622601C2211yescharacteristic
37#10622589C2211yescharacteristic
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622583—24no—
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622558—21no—
50#10622557—21no—
51#10622546—21no—
52C4×Dic11⋊C4—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#117—22no—
72C11×#117—41no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85#66983—22no—
86#66983—22no—
87#66982—44no—
88#66982—44no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96#66977—22no—
97#66977D414yes—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C2×#4314—22no—
112C2×#4314—22no—
113C2×#4314—41no—
114#66940—22no—
115#66940—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122C22⋊(C11⋊C8)—22no—
123#66885—22no—
124#66882—22no—
125#66880—22no—
126Dic11⋊C8—22no—
127Dic11⋊C8—41no—
128#66874—22no—
129#66874—22no—
130#66873—22no—
131#66873—41no—
132#66871—22no—
133#66871—22no—
134#25217—111nomaximal, Sylow
135C24×C11C2×D411yescharacteristic
136C23×D11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—42no—
153C2×C22⋊D11—42no—
154C2×C22⋊D11—42no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22C2×D412yes—
174C11×M16—44no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11#4112yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4#4112yes—
190C11×C22⋊C4—42no—
191C42×C11—42no—
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194C22⋊Dic11—24no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11C2×D412yes—
204Dic11⋊C4—24no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
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—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223#4314—44no—
224C2×#484—111no—
225C2×#468—111no—
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#1736D1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11#12112yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—84no—
273C2×C4×C11#12112yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C22⋊D11—84no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11AGL(1,ℤ/8)12yes—
301C2×Dic11AGL(1,ℤ/8)12yes—
302D44—41no—
303D44—41no—
304D44—41no—
305D44—41no—
306Dic22—22no—
307Dic22—22no—
308Dic22—41no—
309Dic22—41no—
310C8×C11—22no—
311C8×C11—41no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314C22×SD16—111no—
315C22×M16C2×D1111yescharacteristic
316C2×#123—221no—
317C2×#123—221no—
318C2×C22⋊Q8—111no—
319C2×#121—111no—
320C2×C4×Q8—111no—
321C2×#117C2×D1111yescharacteristic
322C22×C4⋊C4C2×D1111yescharacteristic
323#484—224no—
324#468—224no—
325C2×#107—111no—
326C2×#107—111no—
327C2×#107—111no—
328C2×C4⋊C8—111no—
329C2×C4⋊C8—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
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#340C2×D1111yescharacteristic
354#340C2×D1111yescharacteristic
355#340C2×D1111yescharacteristic
356#340C2×D1111yescharacteristic
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×C11C2×#12111yescharacteristic
367C22×C11#54611yescharacteristic
368C22×C11#54711yescharacteristic
369C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C11#57811yescharacteristic
372C22×C11#57811yescharacteristic
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C4×C11—22no—
381C4×C11—42no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11#52911yescharacteristic
386C4×C11#53911yescharacteristic
387C4×C11#54611yescharacteristic
388C4×C11#54711yescharacteristic
389Dic11—22no—
390Dic11—22no—
391Dic11—41no—
392Dic11—41no—
393Dic11—42no—
394Dic11—42no—
395Dic11—81no—
396C22×Q8—111no—
397C22×D4—111no—
398C22×D4—221no—
399C23×C4—21no—
400C23×C4C22×D1111yescharacteristic
401C2×SD16—222no—
402C2×SD16—222no—
403C2×SD16—441no—
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—114no—
414C22⋊Q8—222no—
415#121—222no—
416#121—222no—
417C4×Q8—222no—
418C4×Q8—441no—
419#117—22no—
420#117—41no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C42—21no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—221no—
450C2×C42—221no—
451#107—222no—
452#107—222no—
453#107—222no—
454C4⋊C8—222no—
455C4⋊C8—441no—
456#103—222no—
457#103—222no—
458#103—222no—
459#102—222no—
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#242511yescharacteristic
471C2×C11#303811yescharacteristic
472C2×C11#304411yescharacteristic
473C2×C11#330811yescharacteristic
474C2×C11#333011yescharacteristic
475C2×C11#334311yescharacteristic
476C2×C11#335311yescharacteristic
477D11—161no—
478C24—221no—
479C24D4×D1111yescharacteristic
480C2×Q8—112no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—442no—
493C2×D4—442no—
494C2×D4—442no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4#433912yes—
514C22×C4D4×D1111yescharacteristic
515C22×C4D4×D1112yes—
516C22×C4C23×D1111yescharacteristic
517SD16—444no—
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#433912yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—112no—
540C4⋊C4—224no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4#433912yes—
551C22⋊C4—42no—
552C22⋊C4—222no—
553C22⋊C4—222no—
554C22⋊C4—224no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C42—42no—
561C42—221no—
562C42—221no—
563C42—221no—
564C42—221no—
565C42—442no—
566C42—442no—
567C11#2521711yescharacteristic, complemented, Sylow
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23—441no—
578C23—441no—
579C23—441no—
580C23—441no—
581C23#6693712yes—
582C23C2×D4×D1111yescharacteristic
583Q8—222no—
584Q8—222no—
585Q8—441no—
586Q8—441no—
587D4—441no—
588D4—441no—
589D4—441no—
590D4—441no—
591D4—884no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4—112no—
612C2×C4—112no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4#6693712yes—
633C2×C4C2×#433911yescharacteristic
634C2×C4C2×#433911yescharacteristic
635C2×C4C2×#433911yescharacteristic
636C2×C4C2×D4×D1111yescharacteristic
637C2×C4#6703711yescharacteristic
638C2×C4#6704011yescharacteristic
639C8—22no—
640C8—41no—
641C8—441no—
642C8—441no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22—881no—
654C22—881no—
655C22—881no—
656C22—881no—
657C22C2×#6693711yescharacteristic
658C22#1062302111yescharacteristic
659C22#1062303811yescharacteristic
660C22D11×AGL(1,ℤ/8)11yescharacteristic
661C22D11×AGL(1,ℤ/8)11yescharacteristic
662C22#1062331011yescharacteristic
663C22#1062331011yescharacteristic
664C4—22no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—222no—
670C4—222no—
671C4—442no—
672C4—442no—
673C4—441no—
674C4—441no—
675C4—881no—
676C4#1062301011yescharacteristic
677C4#1062302111yescharacteristic
678C4#1062303811yescharacteristic
679C4#1062304611yescharacteristic
680C2—42no—
681C2—1761no—
682C2#1307216711yescharacteristic
683C2#1307809511yescharacteristic
684C2#1307814511yescharacteristic
685C2#1308060811yescharacteristic
686C2#1308091711yescharacteristic
687C2#1308105711yescharacteristic
688C2#1308119611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1736D11
hypocenterC11#25217
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
1. C2×#10622583C2semidirect
4. #13071643C2semidirect
5. #13070091C2semidirect
6. #13070028C2semidirect
7. #13070005C2semidirect
8. #13069935C2semidirect
9. #13069373C2semidirect
10. #13069234C2semidirect
11. #13068972C2semidirect
13. #13068799C2semidirect
14. #13068620C2semidirect
15. C11×#1736C2semidirect
238. #1736D11semidirect
567. C11#25217semidirect

Maximal subgroups

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

subgroupindex
C2×#106225832
C2×#106227472
#130730832
#130716432
#130700912
#130700282
#130700052
#130699352
#130693732
#130692342
#130689722
#130689382
#130687992
#130686202
C11×#17362
#2521711