Finite Group Databasebeta

← #14816592

Subgroups — #14816592

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622374C211yesmaximal, characteristic, complemented
2C2×#10622494C211yesmaximal, characteristic, complemented
3#13072321C211yesmaximal, characteristic, complemented
4#13071659C211yesmaximal, characteristic
5#13070110C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13069942C211yesmaximal, characteristic, complemented
8#13069377C211yesmaximal, characteristic, complemented
9#13069195C211yesmaximal, characteristic, complemented
10#13069051C211yesmaximal, characteristic
11#13068930C211yesmaximal, characteristic
12#13068875C211yesmaximal, characteristic, complemented
13#13068812C211yesmaximal, characteristic, complemented
14#13068800C211yesmaximal, characteristic, complemented
15C11×#2093C211yesmaximal, characteristic, complemented
16C2×#66991C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66949—21no—
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622602—21no—
35#10622600C2211yescharacteristic
36#10622593—21no—
37#10622592—21no—
38#10622586C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622571—21no—
44#10622570—21no—
45#10622558—21no—
46C22⋊C4×Dic11—21no—
47C4×(C2×D11)⋊C4C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622541C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622494—24no—
52#10622374—24no—
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×Dic22—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66991—22no—
80#66991Q814yescomplemented
81D4×Dic11—22no—
82D4×Dic11—41no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×#4313—22no—
102C2×#4313—22no—
103C2×#4313—22no—
104#66949—44no—
105#66945—22no—
106#66945—41no—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—41no—
109#66941—22no—
110#66941—41no—
111C11×#107—22no—
112C11×#107—41no—
113C11×#102—22no—
114C11×#102—41no—
115#66896—22no—
116#66896—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124(C2×D11)⋊C8—22no—
125#66881D414yescomplemented
126Dic11⋊C8—22no—
127#66872—22no—
128#66872—22no—
129#66871—22no—
130C4⋊(C11⋊C8)—22no—
131#26359—111nomaximal, Sylow
132C24×C11—21no—
133C23×D11C2×D411yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C2×Q812yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—24no—
147C2×C22⋊D11—81no—
148C2×C22⋊D11—81no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—81no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×C4×D11C2×Q812yes—
167C2×C4×D11#4112yes—
168C2×Dic22—42no—
169C2×Dic22—42no—
170C2×Dic22—81no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D412yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—81no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—81no—
187C42×C11—21no—
188C42×C11—21no—
189C22⋊Dic11—24no—
190C22⋊Dic11—42no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2×D412yes—
201C4⋊Dic11C2×D412yes—
202C4⋊Dic11C2×Q812yes—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—81no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8#4112yes—
218#4313—28no—
219C2×#476—111no—
220C2×#428—111no—
221#2440—111no—
222#2363—111no—
223#2093D1111yescharacteristic, complemented
224#2087—111no—
225#2067—111no—
226#2057—111no—
227#1948—111no—
228#1919—111no—
229#1895—111no—
230#1874—111no—
231#1864—111no—
232#1854—111no—
233#1851—111no—
234C23×C11—22no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11C22×D411yescharacteristic
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11C22⋊Q812yes—
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—41no—
252D4×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×C11AGL(1,ℤ/8)12yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×Q811yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C22⋊D11—84no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
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—84no—
295C2×Dic11C22⋊Q812yes—
296C2×Dic11#13712yes—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—84no—
302Dic22—84no—
303C8×C11—22no—
304C8×C11—41no—
305C11⋊C8—22no—
306C11⋊C8—41no—
307C22×M16—111no—
308C2×C4⋊Q8—111no—
309C2×C22⋊Q8—221no—
310C2×#121—111no—
311C2×C4×D4—111no—
312C2×#117—111no—
313C22×C4⋊C4—111no—
314#476—224no—
315#428—224no—
316C2×#107—111no—
317C2×#107C2×D1111yescharacteristic
318C2×#107C2×D1111yescharacteristic
319C2×#106—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×C4⋊C8—111no—
323C2×C4⋊C8—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102C2×D1111yescharacteristic
327C2×#102C2×D1111yescharacteristic
328C2×C22⋊C8—111no—
329#398—221no—
330#395—221no—
331#390—221no—
332#390C2×D1111yescharacteristic
333#389—111no—
334#389—111no—
335#389—111no—
336#388—221no—
337#386—221no—
338#385—221no—
339#384C2×D1111yescharacteristic
340#380—111no—
341C4×C4⋊C4—111no—
342C4×C22⋊C4—111no—
343C4×C22⋊C4—221no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#336—111no—
351#336C2×D1111yescharacteristic
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11C2×C22⋊Q811yescharacteristic
360C22×C11D4211yescharacteristic
361C22×C11#54711yescharacteristic
362C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C11C2×#13711yescharacteristic
364C22×C11#57611yescharacteristic
365C22×C11#57711yescharacteristic
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C4×C11—22no—
374C4×C11—41no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11#52511yescharacteristic
379C4×C11#53911yescharacteristic
380C4×C11D4×Q811yescharacteristic
381C4×C11#55411yescharacteristic
382Dic11—22no—
383Dic11—22no—
384Dic11—42no—
385Dic11—42no—
386Dic11—41no—
387Dic11—42no—
388Dic11—81no—
389C22×Q8—221no—
390C22×D4—221no—
391C22×D4C22×D1111yescharacteristic
392C23×C4—111no—
393C23×C4—221no—
394C23×C4—221no—
395C2×M16—222no—
396C2×M16—222no—
397C2×M16—222no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C4⋊Q8—222no—
403C4⋊Q8—441no—
404C22⋊Q8—444no—
405#121—114no—
406#121—222no—
407C4×D4—222no—
408C4×D4—441no—
409#117—222no—
410#117—441no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—441no—
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—111no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C42—111no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42C22×D1111yescharacteristic
439#107—22no—
440#107—41no—
441#107—222no—
442#106—114no—
443#106—222no—
444#106—222no—
445C4⋊C8—222no—
446C4⋊C8—222no—
447#102—22no—
448#102—41no—
449#102—222no—
450#102—222no—
451C22⋊C8—222no—
452#95—111no—
453#95—111no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11—82no—
460C2×C11#244911yescharacteristic
461C2×C11#307911yescharacteristic
462C2×C11#308111yescharacteristic
463C2×C11#326611yescharacteristic
464C2×C11#327411yescharacteristic
465C2×C11#334511yescharacteristic
466C2×C11#335711yescharacteristic
467D11—42no—
468C24—21no—
469C24—111no—
470C2×Q8—442no—
471C2×Q8—442no—
472C2×Q8—881no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—224no—
479C2×D4—881no—
480C2×D4—881no—
481C2×D4Q8×D1112yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—111no—
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—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—881no—
503C22×C4—881no—
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4C23×D1111yescharacteristic
507M16—228no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—112no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8D4×D1112yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—81no—
528C4⋊C4—112no—
529C4⋊C4—112no—
530C4⋊C4—112no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—881no—
541C22⋊C4—42no—
542C22⋊C4—81no—
543C22⋊C4—222no—
544C22⋊C4—224no—
545C22⋊C4—222no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C42—21no—
550C42—21no—
551C42—221no—
552C42—221no—
553C42—442no—
554C42—881no—
555C11#2635911yescharacteristic, complemented, Sylow
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—112no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23C2×D4×D1111yescharacteristic
571Q8—884no—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576D4—884no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—884no—
617C2×C4—884no—
618C2×C4#6696412yes—
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4#6703711yescharacteristic
621C2×C4C2×Q8×D1111yescharacteristic
622C2×C4#41×D1111yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#6704311yescharacteristic
625C8—22no—
626C8—41no—
627C8—222no—
628C8—441no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—222no—
637C22—222no—
638C22—222no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22D11×C22⋊Q811yescharacteristic
644C22#1062318611yescharacteristic
645C22#1062324811yescharacteristic
646C22C2×#6696411yescharacteristic
647C22#1062328811yescharacteristic
648C22D11×#13711yescharacteristic
649C22#1062330911yescharacteristic
650C4—22no—
651C4—41no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—222no—
656C4—222no—
657C4—442no—
658C4—442no—
659C4—441no—
660C4—442no—
661C4—881no—
662C4#1062316311yescharacteristic
663C4#1062316711yescharacteristic
664C4#1062318711yescharacteristic
665C4#1062319111yescharacteristic
666C2—82no—
667C2—442no—
668C2#1307242811yescharacteristic
669C2#1307842411yescharacteristic
670C2#1307844011yescharacteristic
671C2#1308012511yescharacteristic
672C2#1308023511yescharacteristic
673C2#1308109011yescharacteristic
674C2#1308123511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2093C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2093D11
hypocenterC11#26359
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
1. C2×#10622374C2semidirect
2. C2×#10622494C2semidirect
3. #13072321C2semidirect
5. #13070110C2semidirect
6. #13070004C2semidirect
7. #13069942C2semidirect
8. #13069377C2semidirect
9. #13069195C2semidirect
12. #13068875C2semidirect
13. #13068812C2semidirect
14. #13068800C2semidirect
15. C11×#2093C2semidirect
80. #66991Q8semidirect
125. #66881D4semidirect
223. #2093D11semidirect
555. C11#26359semidirect

Maximal subgroups

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

subgroupindex
C2×#106223742
C2×#106224942
#130723212
#130716592
#130701102
#130700042
#130699422
#130693772
#130691952
#130690512
#130689302
#130688752
#130688122
#130688002
C11×#20932
#2635911