Finite Group Databasebeta

← #14816595

Subgroups — #14816595

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×#10622734C211yesmaximal, characteristic, complemented
3#13072319C211yesmaximal, characteristic, complemented
4#13071658C211yesmaximal, characteristic
5#13070142C211yesmaximal, characteristic, complemented
6#13070111C211yesmaximal, characteristic, complemented
7#13070002C211yesmaximal, characteristic, complemented
8#13069943C211yesmaximal, characteristic, complemented
9#13069378C211yesmaximal, characteristic, complemented
10#13069193C211yesmaximal, characteristic, complemented
11#13068934C211yesmaximal, characteristic
12#13068879C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068799C211yesmaximal, characteristic, complemented
15C11×#1895C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×#66931—21no—
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622834—21no—
27#10622834C2211yescharacteristic
28#10622833—21no—
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622734—24no—
34C2×#66882C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622598C2211yescharacteristic
42#10622589C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622586C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622564—21no—
48#10622559—21no—
49C22⋊C4×Dic11—21no—
50#10622374—24no—
51#10622270—21no—
52#10622269—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22—21no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#121—22no—
73C11×#121Q814yescomplemented
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85D4×Dic11—22no—
86D4×Dic11—41no—
87#66979—22no—
88#66979—41no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—41no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66941—22no—
109#66941—41no—
110#66931—44no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#95—21no—
114#66896—22no—
115#66896—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122C22⋊(C11⋊C8)—22no—
123#66882—22no—
124#66882—22no—
125#66881—22no—
126#66881D414yescomplemented
127Dic11⋊C8—22no—
128Dic11⋊C8—22no—
129#66872—22no—
130#66871—41no—
131#26359—111nomaximal, Sylow
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—81no—
141C2×D4×C11—81no—
142C2×D4×C11C2×Q812yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×Q812yes—
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—81no—
163C22×Dic11—81no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C2×Dic22—42no—
169C2×Dic22—42no—
170C2×Dic22—81no—
171C11×M16—28no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D412yes—
177C2×C8×C11#4112yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×Q812yes—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—42no—
186C22⋊Dic11—22no—
187C22⋊Dic11—22no—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C22⋊Dic11—42no—
191C22⋊Dic11—81no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11C2×D412yes—
202C4⋊Dic11C2×D412yes—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—81no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C4×Dic11—81no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×#476—111no—
220C2×#428—111no—
221#2440—111no—
222#2363—111no—
223#2093—111no—
224#2087—111no—
225#2067—111no—
226#2057—111no—
227#1948—111no—
228#1919—111no—
229#1895D1111yescharacteristic
230#1874—111no—
231#1864—111no—
232#1854—111no—
233#1851—111no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—22no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11C22⋊Q812yes—
248C23×C11C22×D411yescharacteristic
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—84no—
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×C11C22⋊Q812yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×Q811yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—84no—
299C2×Dic11—84no—
300C2×Dic11AGL(1,ℤ/8)12yes—
301C2×Dic11#13712yes—
302Dic22—84no—
303C8×C11—22no—
304C8×C11—22no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C22×M16C2×D1111yescharacteristic
308C2×C4⋊Q8—111no—
309C2×C22⋊Q8—221no—
310C2×#121C2×D1111yescharacteristic
311C2×C4×D4—111no—
312C2×#117—111no—
313C22×C4⋊C4—111no—
314#476—224no—
315#428—224no—
316C2×#107—111no—
317C2×#107—111no—
318C2×#107—111no—
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—111no—
332#390—221no—
333#389—111no—
334#389—111no—
335#389—111no—
336#388—221no—
337#386—221no—
338#385—221no—
339#384—111no—
340#380C2×D1111yescharacteristic
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#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350#336—111no—
351#336—111no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11C2×C22⋊Q811yescharacteristic
367C22×C11D4211yescharacteristic
368C22×C11#54711yescharacteristic
369C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C11C2×#13711yescharacteristic
371C22×C11#57611yescharacteristic
372C22×C11#57711yescharacteristic
373C4×C11—22no—
374C4×C11—42no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11#52511yescharacteristic
378C4×C11#53911yescharacteristic
379C4×C11D4×Q811yescharacteristic
380C4×C11#55411yescharacteristic
381Dic11—22no—
382Dic11—22no—
383Dic11—41no—
384Dic11—42no—
385Dic11—41no—
386Dic11—42no—
387Dic11—81no—
388Dic11—81no—
389C22×Q8—221no—
390C22×D4—21no—
391C22×D4C22×D1111yescharacteristic
392C23×C4—221no—
393C23×C4—221no—
394C23×C4C22×D1111yescharacteristic
395C2×M16—22no—
396C2×M16—22no—
397C2×M16—22no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C4⋊Q8—222no—
403C4⋊Q8—441no—
404C22⋊Q8—444no—
405#121—22no—
406#121Dic2214yescomplemented
407C4×D4—222no—
408C4×D4—441no—
409#117—222no—
410#117—441no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
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—111no—
437C2×C42—221no—
438C2×C42—221no—
439#107—222no—
440#107—222no—
441#107—441no—
442#106—114no—
443#106—222no—
444#106—222no—
445C4⋊C8—222no—
446C4⋊C8—222no—
447#102—22no—
448#102—22no—
449#102—222no—
450#102—441no—
451C22⋊C8—222no—
452#95—21no—
453#95—111no—
454#95—111no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11—42no—
460C2×C11—82no—
461C2×C11#244911yescharacteristic
462C2×C11#307911yescharacteristic
463C2×C11#308111yescharacteristic
464C2×C11#326611yescharacteristic
465C2×C11#327411yescharacteristic
466C2×C11#334511yescharacteristic
467C2×C11#335711yescharacteristic
468C24—21no—
469C24D4×D1111yescharacteristic
470C2×Q8—442no—
471C2×Q8—442no—
472C2×Q8—881no—
473C2×D4—24no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—81no—
480C2×D4—81no—
481C2×D4C2×Dic2212yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—881no—
502C22×C4—881no—
503C22×C4C2×Dic2212yes—
504C22×C4D4×D1111yescharacteristic
505C22×C4#434112yes—
506C22×C4C23×D1111yescharacteristic
507M16—28no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8D4×D1112yes—
519C2×C8#434112yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—112no—
526C4⋊C4—112no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4—881no—
539C4⋊C4—881no—
540C4⋊C4C2×Dic2212yes—
541C22⋊C4—24no—
542C22⋊C4—42no—
543C22⋊C4—222no—
544C22⋊C4—222no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—881no—
549C42—221no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—442no—
554C42—881no—
555C11#2635911yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23#6693112yes—
570C23C2×D4×D1111yescharacteristic
571Q8—884no—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576D4—84no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—221no—
606C2×C4—441no—
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#6693112yes—
619C2×C4C22×Dic2211yescharacteristic
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4C2×#434111yescharacteristic
622C2×C4C2×#434111yescharacteristic
623C2×C4#6704211yescharacteristic
624C2×C4#6704311yescharacteristic
625C8—22no—
626C8—22no—
627C8—441no—
628C8—441no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C2×#6693111yescharacteristic
644C22#1062314011yescharacteristic
645C22#1062314211yescharacteristic
646C22D11×AGL(1,ℤ/8)11yescharacteristic
647C22#1062330511yescharacteristic
648C22#1062330611yescharacteristic
649C22D11×#13711yescharacteristic
650C4—22no—
651C4—42no—
652C4—81no—
653C4—81no—
654C4—222no—
655C4—222no—
656C4—442no—
657C4—441no—
658C4—441no—
659C4—442no—
660C4—881no—
661C4—881no—
662C4D4×Dic2211yescharacteristic
663C4#1062307411yescharacteristic
664C4#1062311711yescharacteristic
665C4#1062319611yescharacteristic
666C2—42no—
667C2—82no—
668C2#1307243111yescharacteristic
669C2#1307842711yescharacteristic
670C2#1307844911yescharacteristic
671C2#1308013311yescharacteristic
672C2#1308023311yescharacteristic
673C2#1308108111yescharacteristic
674C2#1308123711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#1895D11
hypocenterC11#26359
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
1. C2×#10622374C2semidirect
2. C2×#10622734C2semidirect
3. #13072319C2semidirect
5. #13070142C2semidirect
6. #13070111C2semidirect
7. #13070002C2semidirect
8. #13069943C2semidirect
9. #13069378C2semidirect
10. #13069193C2semidirect
12. #13068879C2semidirect
13. #13068813C2semidirect
14. #13068799C2semidirect
73. C11×#121Q8semidirect
126. #66881D4semidirect
406. #121Dic22semidirect
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×#106227342
#130723192
#130716582
#130701422
#130701112
#130700022
#130699432
#130693782
#130691932
#130689342
#130688792
#130688132
#130687992
C11×#18952
#2635911