Finite Group Databasebeta

← #14816886

Subgroups — #14816886

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622676C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13070144C211yesmaximal, characteristic
5#13070092C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic
7#13069951C211yesmaximal, characteristic, complemented
8#13069346C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068974C211yesmaximal, characteristic
11#13068974C211yesmaximal, characteristic
12#13068877C211yesmaximal, characteristic
13#13068869C211yesmaximal, characteristic, complemented
14#13068869C211yesmaximal, characteristic, complemented
15C11×#2454C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×#4324C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#399—21no—
23C11×#396—21no—
24C11×#390C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#385—21no—
29C11×#380—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622676—24no—
35C4×#4324—24no—
36#10622589—21no—
37C4⋊C4×Dic11—21no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622260—21no—
52#10622260—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×Dic22C2311yescharacteristic
64C11×#125—22no—
65C11×#125—41no—
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×#4324—22no—
86C2×#4324—22no—
87C2×#4324Q814yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C4×Dic22—22no—
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C4×Dic22—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115#66896—22no—
116#66896—22no—
117#66896—41no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66874—22no—
121#66874—22no—
122#66874D414yes—
123#66872—22no—
124#66872—22no—
125#66871—22no—
126#66871—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129C4×C11⋊C8—22no—
130#26379—111nomaximal, Sylow
131C24×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11C2×Q812yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—81no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22C2×D412yes—
159C2×Dic22C2×Q812yes—
160C2×Dic22#4112yes—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4C2×D412yes—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—81no—
176C11×C22⋊C4—81no—
177C11×C22⋊C4—81no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184#4324—28no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—42no—
191C4⋊Dic11—81no—
192C4⋊Dic11#4112yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—81no—
197Dic11⋊C4—81no—
198C4×Dic11—24no—
199C4×Dic11—42no—
200C4×Dic11—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8C2×D412yes—
212C2×C11⋊C8C2×Q812yes—
213C2×#479—111no—
214C2×C4×SD16—111no—
215#2454D1111yescharacteristic
216Q8×C4⋊C4—111no—
217#2093—111no—
218#2084—111no—
219#2067—111no—
220#2059—111no—
221#1942—111no—
222#1916—111no—
223#1880—111no—
224#1880—111no—
225#1864—111no—
226#1863—111no—
227#1863—111no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—41no—
239D4×C11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
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—84no—
266C2×C4×C11#13512yes—
267C2×C4×C11#13712yes—
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
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286Dic22—22no—
287Dic22—22no—
288Dic22—22no—
289Dic22C22⋊Q814yes—
290C11⋊C8—22no—
291C11⋊C8—22no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C22×SD16—111no—
295C2×#125C2×D1111yescharacteristic
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8—111no—
299C2×C4×D4C2×D1111yescharacteristic
300#479—224no—
301C4×SD16—224no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#106—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×C4×C8—111no—
315#399—21no—
316#396—21no—
317#390C2×D1111yescharacteristic
318#390C2×D1111yescharacteristic
319#389—111no—
320#389—111no—
321#389—221no—
322#389—221no—
323#389C2×D1111yescharacteristic
324#389C2×D1111yescharacteristic
325#385—21no—
326#384—111no—
327#384—221no—
328#380—21no—
329C4×C4⋊C4—221no—
330C4×C4⋊C4C2×D1111yescharacteristic
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11#52511yescharacteristic
347C22×C11D4211yescharacteristic
348C22×C11D4×Q811yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11C2×#13711yescharacteristic
351C22×C11#57611yescharacteristic
352C22×C11#57711yescharacteristic
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11C2×C22⋊Q811yescharacteristic
363C4×C11#53911yescharacteristic
364C4×C11#54711yescharacteristic
365C4×C11#55411yescharacteristic
366Dic11—24no—
367Dic11—42no—
368Dic11—81no—
369Dic11—81no—
370C22×Q8—111no—
371C22×D4C22×D1111yescharacteristic
372C23×C4—21no—
373C2×SD16—114no—
374C2×SD16—222no—
375C2×SD16—222no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8—111no—
380#125—22no—
381#125—41no—
382C4×Q8—222no—
383C4×Q8—222no—
384C4×Q8—222no—
385C4×Q8—222no—
386C4×Q8—441no—
387C4×Q8—441no—
388C4×D4—22no—
389C4×D4—41no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22⋊D1111yescharacteristic
405C2×C4⋊C4C22⋊D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420#107—222no—
421#107—222no—
422#107—441no—
423#106—222no—
424#106—222no—
425C4⋊C8—222no—
426#103—114no—
427#103—222no—
428#103—222no—
429#102—222no—
430#102—222no—
431#102—441no—
432C4×C8—222no—
433#95—21no—
434#95—21no—
435#95—221no—
436#95—221no—
437#95C22⋊D1111yescharacteristic
438#95C22⋊D1111yescharacteristic
439C2×C11—82no—
440C2×C11#244911yescharacteristic
441C2×C11#310811yescharacteristic
442C2×C11#311911yescharacteristic
443C2×C11#326611yescharacteristic
444C2×C11#328711yescharacteristic
445C2×C11#338111yescharacteristic
446C2×C11#338511yescharacteristic
447C24—21no—
448C2×Q8—112no—
449C2×Q8—112no—
450C2×Q8—112no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4Q8×D1112yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—81no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477SD16—228no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—112no—
502C4⋊C4—224no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—442no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4—881no—
512C4⋊C4—881no—
513C4⋊C4—881no—
514C4⋊C4D4×D1112yes—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—81no—
518C22⋊C4—81no—
519C22⋊C4—81no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—224no—
527C42—442no—
528C42—442no—
529C11#2637911yescharacteristic, complemented, Sylow
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23C22×C22⋊D1111yescharacteristic
538Q8—114no—
539Q8—222no—
540Q8—222no—
541Q8—222no—
542D4—22no—
543D4—22no—
544D4—41no—
545D4—41no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—84no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4#6700312yes—
585C2×C4#6700412yes—
586C2×C4C2×D4×D1111yescharacteristic
587C2×C4#6703711yescharacteristic
588C2×C4C2×Q8×D1111yescharacteristic
589C2×C4#6704011yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C8—222no—
593C8—222no—
594C8—441no—
595C8—441no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22D4×C22⋊D1111yescharacteristic
604C22Q8×C22⋊D1111yescharacteristic
605C22C2×#6700311yescharacteristic
606C22C2×#6700411yescharacteristic
607C22#1062335911yescharacteristic
608C22#1062336611yescharacteristic
609C22#1062336711yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—81no—
619C4—224no—
620C4—442no—
621C4—881no—
622C4—881no—
623C4D11×C22⋊Q811yescharacteristic
624C4#1062316211yescharacteristic
625C4#1062316711yescharacteristic
626C4#1062316911yescharacteristic
627C2—82no—
628C2#1307242211yescharacteristic
629C2#1307869211yescharacteristic
630C2#1307880911yescharacteristic
631C2#1308012211yescharacteristic
632C2#1308037211yescharacteristic
633C2#1308149111yescharacteristic
634C2#1308152611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2454C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2454D11
hypocenterC11#26379
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2454

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
3. C4⋊C4×Dic22C2semidirect
5. #13070092C2semidirect
7. #13069951C2semidirect
8. #13069346C2semidirect
9. #13069175C2semidirect
13. #13068869C2semidirect
14. #13068869C2semidirect
529. C11#26379semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C2×C4×#43242
C4⋊C4×Dic222
#130701442
#130700922
#130700042
#130699512
#130693462
#130691752
#130689742
#130688772
#130688692
C11×#24542
#2637911