Finite Group Databasebeta

← #14816908

Subgroups — #14816908

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622621C211yesmaximal, characteristic, complemented
2C2×D8×Dic11C211yesmaximal, characteristic
3#13072468C211yesmaximal, characteristic, complemented
4#13071521C211yesmaximal, characteristic, complemented
5#13070135C211yesmaximal, characteristic, complemented
6#13070103C211yesmaximal, characteristic, complemented
7#13069990C211yesmaximal, characteristic, complemented
8#13069945C211yesmaximal, characteristic, complemented
9#13069343C211yesmaximal, characteristic, complemented
10#13069176C211yesmaximal, characteristic, complemented
11#13068966C211yesmaximal, characteristic
12#13068875C211yesmaximal, characteristic, complemented
13#13068875C211yesmaximal, characteristic, complemented
14#13068865C211yesmaximal, characteristic, complemented
15C11×#1879C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66931—21no—
22C2×#66922C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#390C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31#10622823—21no—
32C2×C11⋊#95—21no—
33D8×Dic11—24no—
34C2×#66882C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622621—24no—
38#10622598C2211yescharacteristic
39#10622590C2211yescharacteristic
40#10622586C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622563—21no—
46#10622561—21no—
47#10622560—21no—
48#10622559—21no—
49#10622555—21no—
50C4×Dic11⋊C4C2211yescharacteristic
51#10622541C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C22×Dic22—21no—
68C2×C11×D8—22no—
69C2×C11×D8—22no—
70C2×C11×D8Q814yescomplemented
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×D4×C11—22no—
74C4×D4×C11—41no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86D4×Dic11—22no—
87D4×Dic11—22no—
88D4×Dic11—22no—
89D4×Dic11—22no—
90D4×Dic11—41no—
91D4×Dic11—41no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
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⋊C4D411yescharacteristic
102C2×Dic11⋊C4D411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66931—44no—
108#66922—22no—
109#66922—41no—
110C11×#102—22no—
111C11×#102—41no—
112#66896—22no—
113#66896—22no—
114#66896—22no—
115#66896D414yes—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66882—22no—
125#66882—41no—
126C8×Dic11—22no—
127#66872—22no—
128#66872—22no—
129#66872—22no—
130C4⋊(C11⋊C8)—22no—
131#26380—111nomaximal, Sylow
132C24×C11—21no—
133C24×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11C2×D412yes—
143C2×D4×C11C2×Q812yes—
144C2×D4×C11C2×Q812yes—
145C2×D4×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—24no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—81no—
164C22×Dic11—81no—
165C22×Dic11—81no—
166C22×Dic11—81no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C2×Dic22—42no—
172C2×Dic22—42no—
173C2×Dic22—81no—
174C11×D8—28no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×Q812yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C42×C11—21no—
189C42×C11—21no—
190C22⋊Dic11—24no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—81no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11—42no—
203C4⋊Dic11C2×D412yes—
204C4⋊Dic11#4112yes—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—42no—
208Dic11⋊C4—81no—
209Dic11⋊C4—81no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8C2×D412yes—
220C2×#476—111no—
221C2×C4×D8—111no—
222#2452—111no—
223#2349—111no—
224#2092—111no—
225#2085—111no—
226#2065—111no—
227#2057—111no—
228#1941—111no—
229#1916—111no—
230#1879—111no—
231#1879D1111yescharacteristic
232#1864—111no—
233#1864—111no—
234#1862—111no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11C22×D411yescharacteristic
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11C22⋊Q814yescomplemented
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
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—84no—
270C2×C4×C11#13512yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×Q811yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
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—41no—
299C2×Dic11—41no—
300C2×Dic11—84no—
301C2×Dic11—84no—
302C2×Dic11—84no—
303C2×Dic11AGL(1,ℤ/8)12yes—
304Dic22—84no—
305C8×C11—22no—
306C8×C11—41no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C22×D8C2×D1111yescharacteristic
310C2×C4⋊Q8—111no—
311C2×C22⋊Q8—221no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—111no—
315C2×C4×D4C2×D1111yescharacteristic
316#476—224no—
317C4×D8—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×C4⋊C8—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102C2×D1111yescharacteristic
329C2×#102C2×D1111yescharacteristic
330C2×C4×C8—111no—
331#396—221no—
332#393—221no—
333#390—111no—
334#390C2×D1111yescharacteristic
335#389—111no—
336#389—111no—
337#389—111no—
338#389—111no—
339#385—221no—
340#385—221no—
341#385—221no—
342#382—111no—
343#380—221no—
344C4×C4⋊C4—111no—
345C2×#95—221no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340C2×D1111yescharacteristic
350#336—111no—
351#336—111no—
352#336—111no—
353#336C2×D1111yescharacteristic
354C22×C11—24no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11#52511yescharacteristic
369C22×C11D4211yescharacteristic
370C22×C11D4×Q811yescharacteristic
371C22×C11C2×#13511yescharacteristic
372C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C11#57611yescharacteristic
374C22×C11#57711yescharacteristic
375C4×C11—22no—
376C4×C11—41no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11C2×C22⋊Q811yescharacteristic
380C4×C11#53911yescharacteristic
381C4×C11#54711yescharacteristic
382C4×C11#55411yescharacteristic
383Dic11—22no—
384Dic11—41no—
385Dic11—41no—
386Dic11—42no—
387Dic11—42no—
388Dic11—41no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—221no—
392C22×D4C22×D1111yescharacteristic
393C22×D4C22×D1111yescharacteristic
394C23×C4—21no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—221no—
398C2×D8—22no—
399C2×D8—22no—
400C2×D8Dic2214yescomplemented
401C22×C8—111no—
402C22×C8—111no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C4⋊Q8—222no—
406C4⋊Q8—441no—
407C22⋊Q8—444no—
408C4×D4—22no—
409C4×D4—41no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4—222no—
414C4×D4—441no—
415C4×D4—441no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42C22×D1111yescharacteristic
440#107—222no—
441#107—441no—
442#106—222no—
443#106—222no—
444#106—222no—
445C4⋊C8—222no—
446#102—22no—
447#102—41no—
448#102—114no—
449#102—222no—
450#102—222no—
451#102—222no—
452C4×C8—222no—
453#95—111no—
454#95—111no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—44no—
462C2×C11—82no—
463C2×C11#244911yescharacteristic
464C2×C11#310611yescharacteristic
465C2×C11#311811yescharacteristic
466C2×C11#326411yescharacteristic
467C2×C11#328211yescharacteristic
468C2×C11#338011yescharacteristic
469C2×C11#338411yescharacteristic
470C24—21no—
471C24—21no—
472C2×Q8—442no—
473C2×Q8—442no—
474C2×Q8—881no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4C2×Dic2212yes—
484C2×D4C2×Dic2212yes—
485C2×D4D4×D1112yes—
486C2×D4#434112yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—81no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—224no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—881no—
506C22×C4—881no—
507C22×C4—881no—
508C22×C4—881no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512D8—28no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—112no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8C2×Dic2212yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—112no—
530C4⋊C4—112no—
531C4⋊C4—222no—
532C4⋊C4—222no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4—442no—
542C4⋊C4—881no—
543C4⋊C4—881no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—224no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—442no—
551C22⋊C4—881no—
552C42—21no—
553C42—21no—
554C42—221no—
555C42—221no—
556C42—221no—
557C42—221no—
558C11#2638011yescharacteristic, complemented, Sylow
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C2×D4×D1111yescharacteristic
574Q8—884no—
575D4—22no—
576D4—22no—
577D4—22no—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582D4#6693114yescomplemented
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—84no—
595C2×C4—112no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—222no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—222no—
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—884no—
620C2×C4—884no—
621C2×C4—884no—
622C2×C4#6696512yes—
623C2×C4C22×Dic2211yescharacteristic
624C2×C4C2×D4×D1111yescharacteristic
625C2×C4C2×#434111yescharacteristic
626C2×C4#6703711yescharacteristic
627C2×C4#41×D1111yescharacteristic
628C2×C4#6704311yescharacteristic
629C8—22no—
630C8—41no—
631C8—222no—
632C8—441no—
633C22—24no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22D4×Dic2211yescharacteristic
648C22#1062312111yescharacteristic
649C22#1062313711yescharacteristic
650C22C2×#6696511yescharacteristic
651C22#1062330011yescharacteristic
652C22D11×AGL(1,ℤ/8)11yescharacteristic
653C22#1062330611yescharacteristic
654C4—22no—
655C4—41no—
656C4—81no—
657C4—81no—
658C4—222no—
659C4—441no—
660C4—441no—
661C4—442no—
662C4—442no—
663C4—441no—
664C4—881no—
665C4—881no—
666C4C2×#6693111yescharacteristic
667C4#1062307011yescharacteristic
668C4#1062313311yescharacteristic
669C4#1062318611yescharacteristic
670C2—44no—
671C2—82no—
672C2#1307242911yescharacteristic
673C2#1307867311yescharacteristic
674C2#1307879711yescharacteristic
675C2#1308009911yescharacteristic
676C2#1308032711yescharacteristic
677C2#1308148111yescharacteristic
678C2#1308151611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1879C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenter#1879D11
hypocenterC11#26380
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×#10622621C2semidirect
3. #13072468C2semidirect
4. #13071521C2semidirect
5. #13070135C2semidirect
6. #13070103C2semidirect
7. #13069990C2semidirect
8. #13069945C2semidirect
9. #13069343C2semidirect
10. #13069176C2semidirect
12. #13068875C2semidirect
13. #13068875C2semidirect
14. #13068865C2semidirect
70. C2×C11×D8Q8semidirect
257. D4×C11C22⋊Q8semidirect
400. C2×D8Dic22semidirect
558. C11#26380semidirect
582. D4#66931semidirect

Maximal subgroups

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

subgroupindex
C2×#106226212
C2×D8×Dic112
#130724682
#130715212
#130701352
#130701032
#130699902
#130699452
#130693432
#130691762
#130689662
#130688752
#130688652
C11×#18792
#2638011