Finite Group Databasebeta

← #14814383

Subgroups — #14814383

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072070C211yesmaximal, characteristic
2#13071516C211yesmaximal, characteristic
3#13070173C211yesmaximal, characteristic, complemented
4#13070055C211yesmaximal, characteristic, complemented
5#13069811C211yesmaximal, characteristic, complemented
6#13069247C211yesmaximal, characteristic, complemented
7#13069202C211yesmaximal, characteristic, complemented
8#13069036C211yesmaximal, characteristic, complemented
9#13068920C211yesmaximal, characteristic, complemented
10#13068920C211yesmaximal, characteristic, complemented
11#13068907C211yesmaximal, characteristic
12#13068810C211yesmaximal, characteristic, complemented
13#13068701C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#2072C211yesmaximal, characteristic, complemented
16C2×#66999C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66946—21no—
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#384C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34#10622602—21no—
35#10622602—21no—
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622586—21no—
40C2×#66872C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622289—21no—
44#10622280—21no—
45#10622278—21no—
46#10622270—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#336C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44D411yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74#66999—22no—
75#66999—22no—
76#66999—22no—
77#66999—41no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×C8×D11—22no—
100C2×C8×D11—41no—
101C2×C8×D11—41no—
102#66946—44no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—41no—
107C4⋊C4×D11—41no—
108C4⋊C4×D11—41no—
109C4×D44—22no—
110C4×D44—22no—
111C11×#103—41no—
112C11×#103—41no—
113C11×#95—21no—
114C11×#95—21no—
115#66899—22no—
116#66899—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122(C2×D11)⋊C8—22no—
123(C2×D11)⋊C8—41no—
124(C2×D11)⋊C8—41no—
125#66881—22no—
126#66872—41no—
127#26200—111nomaximal, Sylow
128C23×D11C2×D411yescharacteristic
129C23×D11C2×D411yescharacteristic
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×D44—22no—
150C2×D44—22no—
151C2×D44SD1614yes—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—81no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×C4×D11#4112yes—
172C2×C4×D11#4112yes—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—81no—
187C42×C11—21no—
188C42×C11—21no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—22no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11#4112yes—
204C4⋊Dic11#4112yes—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211C4×Dic11—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—
218C8×D11—44no—
219#2417—111no—
220D4×C4⋊C4—111no—
221#2099—111no—
222#2077—111no—
223#2072D1111yescharacteristic, complemented
224#2035—111no—
225#1927—111no—
226#1920—111no—
227#1892—111no—
228#1872—111no—
229#1872—111no—
230#1869—111no—
231#1853—111no—
232#1823—111no—
233C2×#340—111no—
234C23×C11C22×D411yescharacteristic
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11#12312yes—
246C22×D11C2×SD1612yes—
247C22×D11C2×SD1612yes—
248C22×D11#13712yes—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
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×C11C2×SD1612yes—
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11#12312yes—
295D44—28no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—41no—
301C4×D11—41no—
302C4×D11—41no—
303C4×D11—41no—
304C4×D11—84no—
305C4×D11—84no—
306C4×D11—84no—
307C8×C11—41no—
308C8×C11—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C23×C8—111no—
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8—111no—
314C2×C4×D4—111no—
315C2×C4×D4—221no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4—111no—
318C22×C4⋊C4—111no—
319C2×#106—111no—
320C2×#106—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103C2×D1111yescharacteristic
324C2×#103C2×D1111yescharacteristic
325C2×C22⋊C8—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
328#398—221no—
329#396—221no—
330#391C2×D1111yescharacteristic
331#389—111no—
332#389—221no—
333#386—221no—
334#385—221no—
335#385—221no—
336#384C2×D1111yescharacteristic
337#380—111no—
338#380—111no—
339#380—111no—
340#380—221no—
341C4×C4⋊C4—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340C2×D1111yescharacteristic
351#340C2×D1111yescharacteristic
352#336—111no—
353#336C2×D1111yescharacteristic
354C22×C11C2×#12311yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11C22×SD1611yescharacteristic
358C22×C11C2×#13711yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57811yescharacteristic
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11#48314yes—
375C4×C11—22no—
376C4×C11—41no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11#52911yescharacteristic
382C4×C11#53811yescharacteristic
383C4×C11#55311yescharacteristic
384C4×C11#55311yescharacteristic
385Dic11—22no—
386Dic11—41no—
387Dic11—42no—
388Dic11—42no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8C22×D1111yescharacteristic
392C22×D4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—221no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—222no—
401C22×C8—441no—
402C22×C8—441no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C22⋊Q8—222no—
406C22⋊Q8—222no—
407C22⋊Q8—222no—
408C22⋊Q8—441no—
409C4×D4—222no—
410C4×D4—222no—
411C4×D4—444no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—441no—
429C2×C4⋊C4—441no—
430C2×C4⋊C4—441no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#106—222no—
444#106—441no—
445#103—41no—
446#103—41no—
447#103—222no—
448#103—441no—
449C22⋊C8—222no—
450C22⋊C8—441no—
451C22⋊C8—441no—
452#95—21no—
453#95—21no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11#244411yescharacteristic
460C2×C11C2×#48311yescharacteristic
461C2×C11#309811yescharacteristic
462C2×C11#329511yescharacteristic
463C2×C11#329811yescharacteristic
464C2×C11#331211yescharacteristic
465C2×C11#331411yescharacteristic
466D11—24no—
467D11—42no—
468C24—111no—
469C24—111no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×D4—114no—
477C2×D4—222no—
478C2×D4—222no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—111no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—111no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—881no—
508C22×C4—881no—
509C22×C4—881no—
510C22×C4D4×D1111yescharacteristic
511C22×C4D4×D1111yescharacteristic
512C22×C4C23×D1111yescharacteristic
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—444no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4—112no—
535C4⋊C4—112no—
536C4⋊C4—222no—
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—881no—
549C22⋊C4—222no—
550C22⋊C4—222no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—881no—
556C42—21no—
557C42—21no—
558C42—442no—
559C11#2620011yescharacteristic, complemented, Sylow
560C23—112no—
561C23—112no—
562C23—112no—
563C23—112no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23C2×D4×D1111yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—228no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—112no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—222no—
608C2×C4—221no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—884no—
624C2×C4—884no—
625C2×C4—884no—
626C2×C4SD16×D1112yes—
627C2×C4#6703711yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#6704211yescharacteristic
633C8—41no—
634C8—41no—
635C8—441no—
636C8—441no—
637C22—114no—
638C22—222no—
639C22—222no—
640C22—222no—
641C22—222no—
642C22—222no—
643C22—222no—
644C22—222no—
645C22—222no—
646C22—222no—
647C22—441no—
648C22—441no—
649C22—441no—
650C22—441no—
651C22#1062314311yescharacteristic
652C22D11×#12311yescharacteristic
653C22#1062320711yescharacteristic
654C22C2×SD16×D1111yescharacteristic
655C22#1062329711yescharacteristic
656C22#1062330511yescharacteristic
657C22D11×#13711yescharacteristic
658C4—22no—
659C4—41no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—222no—
665C4—442no—
666C4—442no—
667C4—441no—
668C4—881no—
669C4—881no—
670C4#1062318811yescharacteristic
671C4#1062319211yescharacteristic
672C4#1062323711yescharacteristic
673C4#1062324011yescharacteristic
674C2—224no—
675C2—442no—
676C2#1307236911yescharacteristic
677C2D11×#48311yescharacteristic
678C2#1307859511yescharacteristic
679C2#1308044311yescharacteristic
680C2#1308048011yescharacteristic
681C2#1308067411yescharacteristic
682C2#1308069611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2072C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#2072D11
hypocenterC11#26200
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
3. #13070173C2semidirect
4. #13070055C2semidirect
5. #13069811C2semidirect
6. #13069247C2semidirect
7. #13069202C2semidirect
8. #13069036C2semidirect
9. #13068920C2semidirect
10. #13068920C2semidirect
12. #13068810C2semidirect
13. #13068701C2semidirect
14. D11×#340C2semidirect
15. C11×#2072C2semidirect
223. #2072D11semidirect
559. C11#26200semidirect

Maximal subgroups

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

subgroupindex
#130720702
#130715162
#130701732
#130700552
#130698112
#130692472
#130692022
#130690362
#130689202
#130689072
#130688102
#130687012
D11×#3402
C11×#20722
#2620011