Finite Group Databasebeta

← #14813620

Subgroups — #14813620

Order 2816.

868 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
1C2×#10622475C211yesmaximal, characteristic, complemented
2C2×#10622474C211yesmaximal, characteristic, complemented
3#13072065C211yesmaximal, characteristic
4#13071548C211yesmaximal, characteristic
5#13070163C211yesmaximal, characteristic, complemented
6#13070097C211yesmaximal, characteristic, complemented
7#13070046C211yesmaximal, characteristic, complemented
8#13069822C211yesmaximal, characteristic, complemented
9#13069250C211yesmaximal, characteristic, complemented
10#13069048C211yesmaximal, characteristic, complemented
11#13068927C211yesmaximal, characteristic, complemented
12#13068912C211yesmaximal, characteristic
13#13068810C211yesmaximal, characteristic, complemented
14#13068810C211yesmaximal, characteristic, complemented
15C11×#1919C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C2×#66950C2211yescharacteristic
18C2×#66950C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33#10622607—21no—
34#10622600—21no—
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622553—21no—
44C4×(C2×D11)⋊C4—21no—
45#10622549C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622475—24no—
48#10622474—24no—
49#10622278—21no—
50#10622278—21no—
51#10622274—21no—
52#10622266—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D44D411yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313—22no—
98#66950—22no—
99#66950—22no—
100#66950—22no—
101#66950—41no—
102#66945—22no—
103#66945—41no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—41no—
107C4⋊C4×D11—41no—
108C4×D44—22no—
109C4×D44—22no—
110C11×#106D414yescomplemented
111C11×#95—21no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120(C2×D11)⋊C8—22no—
121(C2×D11)⋊C8—22no—
122(C2×D11)⋊C8—22no—
123#66882—22no—
124#66881—41no—
125#66880—22no—
126#66880—41no—
127#66874—22no—
128#66874—22no—
129#66872—22no—
130#66872—22no—
131#66871—22no—
132#26149—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—41no—
151C2×C4×D11—21no—
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—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×C4×D11#4112yes—
168C2×C4×D11#4112yes—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
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—81no—
188C11×C4⋊C4C2×D412yes—
189C11×C4⋊C4C2×D412yes—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—81no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—81no—
200(C2×D11)⋊C4—81no—
201C4⋊Dic11—22no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209C4⋊Dic11—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212C4×Dic11—42no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8#4112yes—
219#4313—28no—
220C2×#483—111no—
221C2×#428—111no—
222#2417—111no—
223#2352—111no—
224#2097—111no—
225#2085—111no—
226#2076—111no—
227#2036—111no—
228#1927—111no—
229#1919D1111yescharacteristic, complemented
230#1894—111no—
231#1873—111no—
232#1870—111no—
233#1853—111no—
234#1853—111no—
235C23×C11C22×D411yescharacteristic
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—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11#12312yes—
249C22×D11#13712yes—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
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×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11#12312yes—
292D44—44no—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—41no—
301C4×D11—84no—
302C4×D11—84no—
303Dic22—41no—
304Dic22—41no—
305Dic22—41no—
306Dic22—41no—
307C8×C11—22no—
308C8×C11—41no—
309C11⋊C8—22no—
310C11⋊C8—41no—
311C22×M16—111no—
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8—111no—
314C2×C4×D4—111no—
315C2×#117—111no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4—111no—
318#483—224no—
319#428—224no—
320C2×#107—111no—
321C2×#107—111no—
322C2×#106—111no—
323C2×#106—111no—
324C2×#106—111no—
325C2×#106C2×D1111yescharacteristic
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×C22⋊C8—111no—
331C2×C22⋊C8—111no—
332C2×C22⋊C8—111no—
333#398—221no—
334#396—221no—
335#391—111no—
336#389C2×D1111yescharacteristic
337#388—221no—
338#387—221no—
339#386—221no—
340#386—221no—
341#382—111no—
342#380—111no—
343#380—111no—
344#380—111no—
345#380—221no—
346C4×C4⋊C4C2×D1111yescharacteristic
347C4×C22⋊C4—221no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340C2×D1111yescharacteristic
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354#336—111no—
355#336C2×D1111yescharacteristic
356C22×C11C2×#12311yescharacteristic
357C22×C11D4211yescharacteristic
358C22×C11#54711yescharacteristic
359C22×C11C2×#13711yescharacteristic
360C22×C11#57511yescharacteristic
361C22×C11#57711yescharacteristic
362C22×C11#57711yescharacteristic
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—42no—
380C4×C11—42no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11#52511yescharacteristic
384C4×C11#53911yescharacteristic
385C4×C11#54811yescharacteristic
386C4×C11#55311yescharacteristic
387Dic11—22no—
388Dic11—41no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8—111no—
394C22×D4—111no—
395C23×C4—111no—
396C23×C4—111no—
397C23×C4—221no—
398C23×C4—221no—
399C2×M16—222no—
400C2×M16—222no—
401C2×M16—222no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406C22⋊Q8—222no—
407C22⋊Q8—222no—
408C22⋊Q8—222no—
409C22⋊Q8—441no—
410C4×D4—222no—
411C4×D4—222no—
412#117—222no—
413#117—441no—
414C2×C4⋊C4—21no—
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—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—441no—
426C2×C4⋊C4—441no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—111no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C42—21no—
440C2×C42—221no—
441C2×C42C22×D1111yescharacteristic
442#107—222no—
443#107—222no—
444#106—222no—
445#106—222no—
446#106—441no—
447#106D4414yescomplemented
448#103—222no—
449#103—222no—
450#103—222no—
451#103—441no—
452C22⋊C8—222no—
453C22⋊C8—222no—
454C22⋊C8—222no—
455#95—21no—
456#95—21no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464C2×C11#244311yescharacteristic
465C2×C11#309511yescharacteristic
466C2×C11#309911yescharacteristic
467C2×C11#326611yescharacteristic
468C2×C11#327511yescharacteristic
469C2×C11#334411yescharacteristic
470C2×C11#335111yescharacteristic
471D11—42no—
472D11—42no—
473C24—111no—
474C24—111no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×D4—222no—
482C2×D4—222no—
483C2×D4—441no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—111no—
489C22×C4—112no—
490C22×C4—112no—
491C22×C4—111no—
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—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—881no—
511C22×C4—881no—
512C22×C4D4×D1111yescharacteristic
513C22×C4D4×D1111yescharacteristic
514C22×C4C23×D1111yescharacteristic
515M16—228no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—112no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8C2×D4412yes—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—81no—
535C4⋊C4—222no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4C2×D4412yes—
547C4⋊C4C2×D4412yes—
548C22⋊C4—222no—
549C22⋊C4—222no—
550C22⋊C4—442no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—881no—
555C22⋊C4—881no—
556C42—21no—
557C42—21no—
558C42—81no—
559C42—442no—
560C11#2614911yescharacteristic, complemented, Sylow
561C23—112no—
562C23—112no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23C2×D4×D1111yescharacteristic
576Q8—441no—
577Q8—441no—
578Q8—441no—
579Q8—441no—
580D4—444no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
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—41no—
598C2×C4—41no—
599C2×C4—112no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—221no—
607C2×C4—221no—
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—441no—
624C2×C4—441no—
625C2×C4—884no—
626C2×C4—884no—
627C2×C4C22×D4411yescharacteristic
628C2×C4#6704011yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#6704211yescharacteristic
633C8—22no—
634C8—41no—
635C8—222no—
636C8—441no—
637C22—222no—
638C22—222no—
639C22—222no—
640C22—222no—
641C22—222no—
642C22—222no—
643C22—441no—
644C22—441no—
645C22—441no—
646C22—441no—
647C22—441no—
648C22—441no—
649C22—441no—
650C22—441no—
651C22D4×D4411yescharacteristic
652C22#1062316211yescharacteristic
653C22D11×#12311yescharacteristic
654C22#1062329311yescharacteristic
655C22#1062329911yescharacteristic
656C22#1062330611yescharacteristic
657C22D11×#13711yescharacteristic
658C4—41no—
659C4—42no—
660C4—41no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—222no—
665C4—441no—
666C4—881no—
667C4—881no—
668C4—881no—
669C4—881no—
670C4#1062305511yescharacteristic
671C4#1062310711yescharacteristic
672C4#1062322311yescharacteristic
673C4#1062324011yescharacteristic
674C2—442no—
675C2—442no—
676C2#1307235611yescharacteristic
677C2#1307856311yescharacteristic
678C2#1307860611yescharacteristic
679C2#1308012811yescharacteristic
680C2#1308024911yescharacteristic
681C2#1308106811yescharacteristic
682C2#1308118311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1919C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1919D11
hypocenterC11#26149
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
1. C2×#10622475C2semidirect
2. C2×#10622474C2semidirect
5. #13070163C2semidirect
6. #13070097C2semidirect
7. #13070046C2semidirect
8. #13069822C2semidirect
9. #13069250C2semidirect
10. #13069048C2semidirect
11. #13068927C2semidirect
13. #13068810C2semidirect
14. #13068810C2semidirect
15. C11×#1919C2semidirect
110. C11×#106D4semidirect
229. #1919D11semidirect
447. #106D44semidirect
560. C11#26149semidirect

Maximal subgroups

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

subgroupindex
C2×#106224752
C2×#106224742
#130720652
#130715482
#130701632
#130700972
#130700462
#130698222
#130692502
#130690482
#130689272
#130689122
#130688102
C11×#19192
#2614911