Finite Group Databasebeta

← #14802112

Subgroups — #14802112

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622646C211yesmaximal, characteristic
2#13073102C211yesmaximal, characteristic, complemented
3#13071636C211yesmaximal, characteristic
4#13070101C211yesmaximal, characteristic, complemented
5#13070032C211yesmaximal, characteristic, complemented
6#13070007C211yesmaximal, characteristic, complemented
7#13069929C211yesmaximal, characteristic, complemented
8#13069385C211yesmaximal, characteristic, complemented
9#13069260C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068924C211yesmaximal, characteristic, complemented
12#13068794C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic, complemented
15C2×C11×#465C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×D4×Dic11—21no—
21C2×D4×Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C11×#465—24no—
25C2×C11×#106C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622834C2211yescharacteristic
33#10622833—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C4×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622646—24no—
41#10622599—21no—
42#10622599—21no—
43#10622598C2211yescharacteristic
44#10622590C2211yescharacteristic
45#10622590C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622564—21no—
50#10622563—21no—
51#10622556—21no—
52#10622556—21no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C23×Dic11—21no—
67C23×Dic11—21no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—41no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—41no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×#121—22no—
79C11×#121D414yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90D4×Dic11—22no—
91D4×Dic11—41no—
92D4×Dic11—44no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—41no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C11×#106—22no—
110C11×#103—22no—
111C11×#102—22no—
112#66899—22no—
113#66899—41no—
114#66896—22no—
115#66896—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128C22⋊(C11⋊C8)—22no—
129Dic11⋊C8—22no—
130Dic11⋊C8—41no—
131#66871—22no—
132#66871—22no—
133#25212—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11C2×D411yescharacteristic
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11C2×D412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—42no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—42no—
173C22×Dic11—81no—
174C22×Dic11—81no—
175C22×Dic11C2×D411yescharacteristic
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C11×SD16—44no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—44no—
186C2×C8×C11#4112yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4C2×D412yes—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—42no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—42no—
197C22⋊Dic11—42no—
198C22⋊Dic11—81no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C4⋊Dic11—42no—
208C4⋊Dic11—42no—
209C4⋊Dic11#4112yes—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×#480—111no—
222C2×#465D1111yescharacteristic
223#2503—111no—
224#2361—111no—
225#2085—111no—
226#2073—111no—
227#2068—111no—
228#2055—111no—
229#1949—111no—
230#1928—111no—
231#1877—111no—
232#1872—111no—
233#1850—111no—
234#1804—111no—
235C2×#340—111no—
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×C11#12112yes—
248C23×C11#13512yes—
249C23×C11AGL(1,ℤ/8)12yes—
250C23×C11C22×D411yescharacteristic
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—41no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—48no—
258D4×C11—41no—
259D4×C11—41no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11#12112yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C112−1+411yescharacteristic
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—84no—
307C2×Dic11—84no—
308C2×Dic11—84no—
309C8×C11—22no—
310C8×C11—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C22×SD16C2×D1111yescharacteristic
314C23×C8C2×D1111yescharacteristic
315C2×C22⋊Q8C2×D1111yescharacteristic
316C2×#121C2×D1111yescharacteristic
317C2×C4×D4—111no—
318C2×C4×D4—221no—
319C22×C4⋊C4—111no—
320C22×C4⋊C4—111no—
321#480—224no—
322#465—24no—
323C2×#107—111no—
324C2×#107—111no—
325C2×#106C2×D1111yescharacteristic
326C2×C4⋊C8—111no—
327C2×C4⋊C8—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#103C2×D1111yescharacteristic
331C2×#102—111no—
332C2×#102—111no—
333C2×#102C2×D1111yescharacteristic
334C2×C22⋊C8—111no—
335#400—221no—
336#400—221no—
337#391—111no—
338#391—111no—
339#390—111no—
340#389—111no—
341#388—221no—
342#386—221no—
343#385—221no—
344#382—111no—
345#382—111no—
346#381—221no—
347#381—221no—
348C4×C4⋊C4—111no—
349C4×C22⋊C4—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#336—111no—
357#336—111no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11#46314yes—
372C22×C11C2×#12111yescharacteristic
373C22×C11#54611yescharacteristic
374C22×C11#54711yescharacteristic
375C22×C11C2×#13511yescharacteristic
376C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C11#57711yescharacteristic
378C22×C11#57811yescharacteristic
379C4×C11—22no—
380C4×C11—42no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11#52911yescharacteristic
384C4×C11#53911yescharacteristic
385C4×C11#54611yescharacteristic
386C4×C11#54711yescharacteristic
387Dic11—41no—
388Dic11—41no—
389Dic11—41no—
390Dic11—41no—
391Dic11—42no—
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8C22×D1111yescharacteristic
396C22×D4—21no—
397C22×D4C22×D1111yescharacteristic
398C23×C4—221no—
399C23×C4—221no—
400C23×C4—221no—
401C23×C4C22×D1111yescharacteristic
402C2×SD16—22no—
403C2×SD16—22no—
404C2×SD16—41no—
405C22×C8—22no—
406C22×C8—22no—
407C22×C8—41no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414#121—22no—
415#121C22⋊D1114yes—
416C4×D4—222no—
417C4×D4—441no—
418C4×D4—444no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—441no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—221no—
443#107—222no—
444#107—222no—
445#106—22no—
446C4⋊C8—222no—
447C4⋊C8—441no—
448#103—22no—
449#103—222no—
450#103—441no—
451#102—22no—
452#102—222no—
453#102—222no—
454C22⋊C8—222no—
455#95—111no—
456#95—111no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467C2×C11—24no—
468C2×C11—82no—
469C2×C11#242511yescharacteristic
470C2×C11C2×#46311yescharacteristic
471C2×C11#304611yescharacteristic
472C2×C11#330011yescharacteristic
473C2×C11#331011yescharacteristic
474C2×C11#333711yescharacteristic
475C2×C11#334311yescharacteristic
476C24—21no—
477C24D4×D1111yescharacteristic
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×D4—24no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4C2×C22⋊D1112yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—881no—
516C22×C4—881no—
517C22×C4D4×D1111yescharacteristic
518C22×C4#434112yes—
519C22×C4C2×C22⋊D1112yes—
520C22×C4C23×D1111yescharacteristic
521SD16—44no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—44no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8#434112yes—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—112no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4C2×C22⋊D1112yes—
551C22⋊C4—24no—
552C22⋊C4—42no—
553C22⋊C4—222no—
554C22⋊C4—222no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—881no—
558C42—221no—
559C42—221no—
560C42—221no—
561C42—221no—
562C42—442no—
563C11#2521211yescharacteristic, complemented, Sylow
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23#6696712yes—
576C23#6696912yes—
577C23#6699212yes—
578C23C2×D4×D1111yescharacteristic
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583D4—22no—
584D4—22no—
585D4—48no—
586D4—41no—
587D4—41no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—222no—
614C2×C4—221no—
615C2×C4—221no—
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—441no—
626C2×C4—441no—
627C2×C4—884no—
628C2×C4—884no—
629C2×C4—884no—
630C2×C4#6699212yes—
631C2×C4C2×#434111yescharacteristic
632C2×C4C2×#434111yescharacteristic
633C2×C4#6703711yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C2×C4#6704311yescharacteristic
636C2×C4C22×C22⋊D1111yescharacteristic
637C8—22no—
638C8—41no—
639C8—441no—
640C8—441no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22#1062277814yes—
655C22#1062314111yescharacteristic
656C22#1062314211yescharacteristic
657C22C2×#6696711yescharacteristic
658C22C2×#6696911yescharacteristic
659C22#1062330111yescharacteristic
660C22#1062330211yescharacteristic
661C22C2×#6699211yescharacteristic
662C4—22no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—441no—
667C4—442no—
668C4—441no—
669C4—441no—
670C4—441no—
671C4—881no—
672C4—881no—
673C4—881no—
674C4#1062313111yescharacteristic
675C4#1062313311yescharacteristic
676C4#1062333711yescharacteristic
677C4#1062335511yescharacteristic
678C2—24no—
679C2—82no—
680C2#1307217311yescharacteristic
681C2C2×#1062277811yescharacteristic
682C2#1307816411yescharacteristic
683C2#1308050911yescharacteristic
684C2#1308064311yescharacteristic
685C2#1308100111yescharacteristic
686C2#1308106211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#465D11
hypocenterC11#25212
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. #13073102C2semidirect
4. #13070101C2semidirect
5. #13070032C2semidirect
6. #13070007C2semidirect
7. #13069929C2semidirect
8. #13069385C2semidirect
9. #13069260C2semidirect
10. #13068952C2semidirect
11. #13068924C2semidirect
12. #13068794C2semidirect
13. #13068624C2semidirect
14. C2×#10622189C2semidirect
563. C11#25212semidirect

Maximal subgroups

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

subgroupindex
C2×#106226462
#130731022
#130716362
#130701012
#130700322
#130700072
#130699292
#130693852
#130692602
#130689522
#130689242
#130687942
#130686242
C2×#106221892
C2×C11×#4652
#2521211