Finite Group Databasebeta

← #14675249

Subgroups — #14675249

Order 2816.

2154 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×Dic11C212yesmaximal
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic
3C2×#10622261C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C211yesmaximal, characteristic
5#13066842C212yesmaximal, complemented
6#13066842C211yesmaximal, characteristic, complemented
7#13066840C211yesmaximal, characteristic, complemented
8#13066840C212yesmaximal, complemented
9#13066838C212yesmaximal
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2212yes—
24C4×C22⋊Dic11C418yescomplemented
25C2×C11⋊#95—24no—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C22⋊C4×Dic11C4116yescomplemented
38#10622261—24no—
39C25×C11C2311yescharacteristic
40C23×C4×C11—24no—
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—42no—
44C23×C4×C11C2×C414yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—24no—
50C23×Dic11—24no—
51C23×Dic11—24no—
52C23×Dic11—24no—
53C23×Dic11—42no—
54C23×Dic11—42no—
55C23×Dic11C2×C418yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4C2×C418yes—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11C2×C414yes—
68C2×C22⋊Dic11C2×C418yes—
69C2×C22⋊Dic11C2×C414yes—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11—42no—
77C2×C4×Dic11C2×C418yescomplemented
78C2×C4×Dic11C2×C414yescomplemented
79C2×C4×Dic11C2×C418yescomplemented
80C2×C4×Dic11C2×C414yescomplemented
81C11×#95—22no—
82C11×#95—22no—
83C11×#95—42no—
84C11⋊#95—22no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—42no—
89C11⋊#95—42no—
90C11⋊#95C2×C418yescomplemented
91C11⋊#95C2×C418yescomplemented
92C11⋊#95C2×C414yescomplemented
93C11⋊#95C2×C414yescomplemented
94C11⋊#95D414yes—
95#13809—111nomaximal, Sylow
96C24×C11—21no—
97C24×C11—22no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11—22no—
101C24×C11—21no—
102C24×C11C22×C412yes—
103C24×C11C22×C414yes—
104C24×C11#4112yes—
105C24×C11#4114yes—
106C24×C11#4112yes—
107C24×C11C2411yescharacteristic
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—28no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—28no—
128C22×C4×C11—44no—
129C22×C4×C11—48no—
130C22×C4×C11—48no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C414yes—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11#4112yes—
137C22×Dic11—216no—
138C22×Dic11—216no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—48no—
166C22×Dic11—48no—
167C22×Dic11—48no—
168C22×Dic11—48no—
169C22×Dic11—48no—
170C22×Dic11C22×C414yes—
171C22×Dic11C22×C412yes—
172C22×Dic11C22×C412yes—
173C22×Dic11C22×C414yes—
174C22×Dic11C22×C412yes—
175C22×Dic11C22×C414yes—
176C22×Dic11C22×C412yes—
177C22×Dic11C22×C414yes—
178C22×Dic11C2×D414yes—
179C22×Dic11#4114yes—
180C11×C22⋊C4—216no—
181C22⋊Dic11—28no—
182C22⋊Dic11C42116yes—
183C4×Dic11—216no—
184C4×Dic11—28no—
185C4×Dic11—44no—
186C4×Dic11—48no—
187C2×C4×C22⋊C4—111no—
188C2×C4×C22⋊C4—112no—
189C2×#376—111no—
190C22×#95—111no—
191#1434—112no—
192#1434—111no—
193#1434—112no—
194#1434—111no—
195C22⋊#95—112no—
196C22⋊#95D1111yescharacteristic
197C4×#95—111no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—22no—
216C23×C11C2×C4214yes—
217C23×C11#11718yes—
218C23×C11#11714yes—
219C23×C11#11714yes—
220C23×C11#11718yes—
221C23×C11C23×C411yescharacteristic
222C23×C11C23×C412yes—
223C23×C11C22×D411yescharacteristic
224C23×C11C2×#4112yes—
225C23×C11C2×#4111yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4112yes—
229C23×C11H(5,𝔽2)12yes—
230C23×C11H(5,𝔽2)11yescharacteristic
231C23×C112−1+411yescharacteristic
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—416no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11C4×D414yes—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—432no—
281C2×Dic11—41no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—41no—
289C2×Dic11—42no—
290C2×Dic11—41no—
291C2×Dic11C2×C4214yes—
292C2×Dic11C2×C4214yes—
293C2×Dic11C4×D418yes—
294C24×C4—112no—
295C24×C4C2×D1111yescharacteristic
296C22×C22⋊C4—111no—
297C22×C22⋊C4—111no—
298C22×C22⋊C4C2×D1112yes—
299C22×C42—112no—
300C22×C42—111no—
301C22×C42—112no—
302C22×C42—111no—
303C4×C22⋊C4—118no—
304C4×C22⋊C4—1116no—
305#376—224no—
306C2×#95—111no—
307C2×#95—111no—
308C2×#95—111no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95—111no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—224no—
318C2×#95C2×D1111yescharacteristic
319C2×#95C2×D1111yescharacteristic
320C2×#95C2×D1112yes—
321C22×C11—24no—
322C22×C11—28no—
323C22×C11—28no—
324C22×C11—24no—
325C22×C11—28no—
326C22×C11—24no—
327C22×C11—28no—
328C22×C11—24no—
329C22×C11—24no—
330C22×C11—24no—
331C22×C11#37618yescomplemented
332C22×C11C22×C4211yescharacteristic
333C22×C11C2×#11711yescharacteristic
334C22×C11C2×#11712yes—
335C22×C11C2×#11712yes—
336C22×C11C2×#11711yescharacteristic
337C22×C11C2×C4×D411yescharacteristic
338C22×C11C2×C4×D412yes—
339C22×C11C4×#4111yescharacteristic
340C22×C11C4×#4112yes—
341C22×C11#51811yescharacteristic
342C22×C11#51812yes—
343C22×C11#52011yescharacteristic
344C22×C11#52012yes—
345C22×C11#54612yes—
346C22×C11#54611yescharacteristic
347C22×C11#54811yescharacteristic
348C22×C11#55112yes—
349C22×C11#55112yes—
350C22×C11#55112yes—
351C22×C11#55211yescharacteristic
352C22×C11#55212yes—
353C22×C11#55312yes—
354C22×C11#55311yescharacteristic
355C4×C11—24no—
356C4×C11—42no—
357C4×C11—44no—
358C4×C11—44no—
359Dic11—28no—
360Dic11—24no—
361Dic11—24no—
362Dic11—44no—
363Dic11—42no—
364Dic11—42no—
365C25C22×D1111yescharacteristic
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—112no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—112no—
376C23×C4—118no—
377C23×C4—224no—
378C23×C4—224no—
379C23×C4—224no—
380C23×C4—224no—
381C23×C4—442no—
382C23×C4—442no—
383C23×C4C4×D1114yes—
384C23×C4C22×D1112yes—
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4C4×D1118yes—
396C2×C42—118no—
397C2×C42—114no—
398C2×C42—118no—
399C2×C42—114no—
400C2×C42—224no—
401C2×C42—224no—
402C2×C42—222no—
403C2×C42—222no—
404C2×C42—442no—
405C2×C42—442no—
406C2×C42—442no—
407#95—22no—
408#95—22no—
409#95—42no—
410#95—118no—
411#95—118no—
412#95—114no—
413#95—114no—
414#95—114no—
415#95—224no—
416#95—224no—
417#95—224no—
418#95—222no—
419#95—442no—
420#95—442no—
421C2×C11—28no—
422C2×C11C2×#37611yescharacteristic
423C2×C11C42×D411yescharacteristic
424C2×C11#227511yescharacteristic
425C2×C11#234212yes—
426C2×C11#234211yescharacteristic
427C2×C11#234312yes—
428C2×C11#234311yescharacteristic
429C2×C11#235212yes—
430C2×C11#235211yescharacteristic
431C2×C11#235312yes—
432C2×C11#235311yescharacteristic
433C24—21no—
434C24—21no—
435C24—22no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24C2×C4×D1112yes—
440C24C2×C4×D1114yes—
441C24#434112yes—
442C24#434114yes—
443C24#434312yes—
444C24C23×D1111yescharacteristic
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—28no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—28no—
465C22×C4—44no—
466C22×C4—48no—
467C22×C4—48no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—2216no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—221no—
487C22×C4—222no—
488C22×C4—221no—
489C22×C4—2216no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—221no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—448no—
507C22×C4—448no—
508C22×C4—448no—
509C22×C4—448no—
510C22×C4—448no—
511C22×C4C2×C4×D1112yes—
512C22×C4C2×C4×D1114yes—
513C22×C4C2×C4×D1114yes—
514C22×C4C2×C4×D1112yes—
515C22×C4D4×D1112yes—
516C22×C4#434112yes—
517C22⋊C4—216no—
518C22⋊C4—1116no—
519C22⋊C4—228no—
520C42—2216no—
521C42—228no—
522C42—444no—
523C42—448no—
524C11#1380911yescharacteristic, complemented, Sylow
525C23—22no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—22no—
536C23—24no—
537C23—22no—
538C23—22no—
539C23—24no—
540C23—22no—
541C23—24no—
542C23—24no—
543C23C42×D1114yes—
544C23#6693018yes—
545C23#6693014yes—
546C23#6694514yes—
547C23#6694518yes—
548C23C22×C4×D1111yescharacteristic
549C23C22×C4×D1112yes—
550C23C2×D4×D1111yescharacteristic
551C23C2×#434112yes—
552C23C2×#434111yescharacteristic
553C23C2×#434111yescharacteristic
554C23#6703712yes—
555C23C2×#434311yescharacteristic
556C23#41×D1112yes—
557C23#6704211yescharacteristic
558C23#6704311yescharacteristic
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—416no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—114no—
584C2×C4—114no—
585C2×C4—118no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—4432no—
610C2×C4—442no—
611C2×C4—441no—
612C2×C4—442no—
613C2×C4—441no—
614C2×C4—442no—
615C2×C4—441no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—441no—
619C2×C4—442no—
620C2×C4(C22⋊D11)⋊C414yes—
621C22—28no—
622C22—24no—
623C22—24no—
624C22—28no—
625C22—24no—
626C22—24no—
627C22—28no—
628C22—24no—
629C22—28no—
630C22—24no—
631C22#1062226118yescomplemented
632C22C2×C42×D1111yescharacteristic
633C22C2×#6693011yescharacteristic
634C22C2×#6693012yes—
635C22C2×(C22⋊D11)⋊C411yescharacteristic
636C22#1062301711yescharacteristic
637C22C2×#6694512yes—
638C22C2×#6694511yescharacteristic
639C22#1062305311yescharacteristic
640C22#1062305411yescharacteristic
641C22C4×#434112yes—
642C22C4×D4×D1112yes—
643C22#1062307612yes—
644C22#1062307712yes—
645C22#1062311812yes—
646C22#1062312212yes—
647C22#1062312911yescharacteristic
648C22#1062313212yes—
649C22#1062314911yescharacteristic
650C22#1062316111yescharacteristic
651C22#1062316812yes—
652C22#1062317311yescharacteristic
653C22#1062318112yes—
654C22#1062318912yes—
655C4—24no—
656C4—42no—
657C4—44no—
658C4—44no—
659C4—228no—
660C4—224no—
661C4—224no—
662C4—444no—
663C4—442no—
664C4—442no—
665C2—28no—
666C2C2×#1062226111yescharacteristic
667C2C4×(C22⋊D11)⋊C411yescharacteristic
668C2#1307097511yescharacteristic
669C2#1307146312yes—
670C2#1307146711yescharacteristic
671C2#1307147412yes—
672C2#1307147811yescharacteristic
673C2#1307154312yes—
674C2#1307154711yescharacteristic
675C2#1307155412yes—
676C2#1307155811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#13809
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622261C2semidirect
5. #13066842C2semidirect
6. #13066842C2semidirect
7. #13066840C2semidirect
8. #13066840C2semidirect
10. #95×Dic11C2semidirect
24. C4×C22⋊Dic11C4semidirect
37. C22⋊C4×Dic11C4semidirect
77. C2×C4×Dic11C2×C4semidirect
78. C2×C4×Dic11C2×C4semidirect
79. C2×C4×Dic11C2×C4semidirect
80. C2×C4×Dic11C2×C4semidirect
90. C11⋊#95C2×C4semidirect
91. C11⋊#95C2×C4semidirect
92. C11⋊#95C2×C4semidirect
93. C11⋊#95C2×C4semidirect
331. C22×C11#376semidirect
524. C11#13809semidirect
631. C22#10622261semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×Dic112
C2×C4×C22⋊Dic112
C2×#106222612
C22×C11⋊#952
#130668422
#130668402
#130668382
#95×Dic112
C11×C22⋊#952
#1380911