Finite Group Databasebeta

← #14675355

Subgroups — #14675355

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C212yesmaximal
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic11C211yesmaximal, characteristic
4#13066853C212yesmaximal
5#13066850C212yesmaximal, complemented
6#13066843C211yesmaximal, characteristic, complemented
7#13066843C211yesmaximal, characteristic, complemented
8#13066839C211yesmaximal, characteristic
9C4×C11⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic11C212yesmaximal, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2212yes—
23C4×C11×C22⋊C4C418yescomplemented
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C4×C22⋊Dic11—24no—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622564C4116yescomplemented
38C4×C4⋊Dic11—24no—
39C25×C11C2311yescharacteristic
40C23×C4×C11—22no—
41C23×C4×C11—24no—
42C23×C4×C11—22no—
43C23×C4×C11—42no—
44C23×C4×C11C2×C414yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4C2×C418yes—
58C2×C11×C22⋊C4C2×C414yes—
59C2×C11×C22⋊C4C2×C414yes—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11—42no—
63C2×C42×C11C2×C414yes—
64C2×C42×C11C2×C414yes—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11C2×C418yes—
70C2×C22⋊Dic11C2×C418yes—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11C2×C418yescomplemented
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—42no—
79C2×C4×Dic11—42no—
80C2×C4×Dic11—42no—
81C2×C4×Dic11—42no—
82C2×C4×Dic11C2×C418yescomplemented
83C11×#95C2×C414yes—
84C11×#95C2×C414yes—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—22no—
90C11⋊#95—24no—
91C11⋊#95—42no—
92C11⋊#95C2×C418yescomplemented
93C11⋊#95C2×C418yescomplemented
94C11⋊#95D414yes—
95#13822—111nomaximal, Sylow
96C24×C11—21no—
97C24×C11—22no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11—22no—
101C24×C11—21no—
102C24×C11—21no—
103C24×C11—22no—
104C24×C11—21no—
105C24×C11C22×C414yes—
106C24×C11C22×C412yes—
107C24×C11C2411yescharacteristic
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—28no—
128C22×C4×C11—28no—
129C22×C4×C11—44no—
130C22×C4×C11—48no—
131C22×C4×C11—48no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4112yes—
142C22×C4×C11#4114yes—
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11C22×C414yes—
168C22×Dic11C22×C414yes—
169C22×Dic11C22×C414yes—
170C22×Dic11C22×C414yes—
171C22×Dic11C2×D414yes—
172C22×Dic11#4114yes—
173C11×C22⋊C4—28no—
174C11×C22⋊C4C42116yescomplemented
175C42×C11—28no—
176C42×C11—44no—
177C22⋊Dic11—216no—
178C22⋊Dic11—48no—
179C4⋊Dic11—216no—
180C4×Dic11—48no—
181C4×Dic11—48no—
182C4×Dic11—48no—
183C2×#388—112no—
184C2×C4×C4⋊C4—111no—
185C2×C4×C22⋊C4—111no—
186C2×C4×C22⋊C4D1111yescharacteristic
187#1437—112no—
188#1436—112no—
189#1434—111no—
190#1434—111no—
191C22⋊#95—111no—
192C4×#95—111no—
193C4×#95—112no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—22no—
206C23×C11—42no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11C2×C4214yes—
217C23×C11C23×C412yes—
218C23×C11C23×C411yescharacteristic
219C23×C11C22×D411yescharacteristic
220C23×C11C2×#4112yes—
221C23×C11C2×#4111yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C23×C11C2×#4111yescharacteristic
224C23×C11C2×#4112yes—
225C23×C11H(5,𝔽2)12yes—
226C23×C11H(5,𝔽2)11yescharacteristic
227C23×C112−1+411yescharacteristic
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—416no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11C2×C4214yes—
257C2×C4×C11C2×C4214yes—
258C2×C4×C11#11714yes—
259C2×C4×C11#11714yes—
260C2×C4×C11C4×D414yes—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11C4×D418yes—
289C24×C4C2×D1111yescharacteristic
290C22×C4⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4C2×D1111yescharacteristic
294C22×C22⋊C4C2×D1111yescharacteristic
295C22×C42—112no—
296C22×C42—112no—
297C22×C42—112no—
298C22×C42C2×D1111yescharacteristic
299C22×C42C2×D1111yescharacteristic
300#388—1116no—
301C4×C4⋊C4—224no—
302C4×C22⋊C4—224no—
303C4×C22⋊C4Dic1118yescomplemented
304C2×#95—112no—
305C2×#95—111no—
306C2×#95—112no—
307C2×#95—111no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—111no—
312C2×#95—111no—
313C2×#95—112no—
314C2×#95C2×D1111yescharacteristic
315C2×#95C2×D1111yescharacteristic
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11C22×C4211yescharacteristic
328C22×C11C2×#11711yescharacteristic
329C22×C11C2×#11711yescharacteristic
330C22×C11C2×C4×D411yescharacteristic
331C22×C11C2×C4×D412yes—
332C22×C11C4×#4112yes—
333C22×C11C4×#4112yes—
334C22×C11C4×#4112yes—
335C22×C11C4×#4111yescharacteristic
336C22×C11#51811yescharacteristic
337C22×C11#51812yes—
338C22×C11#52012yes—
339C22×C11#52011yescharacteristic
340C22×C11#54612yes—
341C22×C11#54611yescharacteristic
342C22×C11#54811yescharacteristic
343C22×C11#55112yes—
344C22×C11#55211yescharacteristic
345C22×C11#55312yes—
346C22×C11#55312yes—
347C22×C11#55311yescharacteristic
348C22×C11#55612yes—
349C22×C11#55912yes—
350C4×C11—24no—
351C4×C11—24no—
352C4×C11—24no—
353C4×C11—24no—
354C4×C11—24no—
355C4×C11—42no—
356Dic11—28no—
357Dic11—44no—
358Dic11—44no—
359Dic11—44no—
360C25C22×D1111yescharacteristic
361C23×C4—24no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—42no—
365C23×C4—112no—
366C23×C4—112no—
367C23×C4—112no—
368C23×C4—112no—
369C23×C4C2×Dic1114yes—
370C23×C4C22×D1111yescharacteristic
371C23×C4C22×D1111yescharacteristic
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×C4⋊C4—118no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C22⋊C4C4×D1118yes—
388C2×C22⋊C4C2×Dic1114yes—
389C2×C22⋊C4C2×Dic1114yes—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—42no—
393C2×C42—118no—
394C2×C42—224no—
395C2×C42—224no—
396C2×C42—224no—
397C2×C42—224no—
398C2×C42—442no—
399C2×C42—442no—
400C2×C42—442no—
401C2×C42—442no—
402C2×C42C2×Dic1114yes—
403C2×C42C2×Dic1114yes—
404#95—118no—
405#95—118no—
406#95—114no—
407#95—224no—
408#95—224no—
409#95—224no—
410#95—222no—
411#95—222no—
412#95—222no—
413#95—442no—
414#95C2×Dic1114yes—
415#95C2×Dic1114yes—
416C2×C11—44no—
417C2×C11C4×#11711yescharacteristic
418C2×C11C42×D411yescharacteristic
419C2×C11#227511yescharacteristic
420C2×C11#234211yescharacteristic
421C2×C11#234711yescharacteristic
422C2×C11#235211yescharacteristic
423C2×C11#235711yescharacteristic
424C2×C11#236412yes—
425C2×C11#236712yes—
426C2×C11#237312yes—
427C2×C11#237412yes—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24C2×C4×D1114yes—
438C24C22×Dic1112yes—
439C24C23×D1111yescharacteristic
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—44no—
462C22×C4—48no—
463C22×C4—48no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4C2×C4×D1114yes—
493C22×C4C2×C4×D1114yes—
494C22×C4#433912yes—
495C22×C4#433914yes—
496C22×C4#433912yes—
497C22×C4D4×D1112yes—
498C22×C4#434112yes—
499C22×C4C22×Dic1112yes—
500C22×C4C22×Dic1112yes—
501C22×C4C22×Dic1112yes—
502C22×C4C22×Dic1112yes—
503C22×C4C22×Dic1112yes—
504C22×C4C22×Dic1112yes—
505C4⋊C4—2216no—
506C22⋊C4—28no—
507C22⋊C4—2216no—
508C22⋊C4—448no—
509C22⋊C4C4×Dic11116yescomplemented
510C42—28no—
511C42—44no—
512C42—448no—
513C42—448no—
514C42—448no—
515C11#1382211yescharacteristic, complemented, Sylow
516C23—24no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—24no—
521C23—22no—
522C23—22no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—22no—
527C23—22no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23C2×C4×Dic1114yes—
539C23C22×C4×D1112yes—
540C23C2×#433912yes—
541C23C2×#433911yescharacteristic
542C23C2×#433911yescharacteristic
543C23C2×D4×D1111yescharacteristic
544C23C2×#434111yescharacteristic
545C23#6703712yes—
546C23#41×D1112yes—
547C23#6704211yescharacteristic
548C23#6704311yescharacteristic
549C23C23×Dic1111yescharacteristic
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—416no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—118no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4C2×C4×Dic1114yes—
607C2×C4C2×C4×Dic1114yes—
608C2×C4#6697914yes—
609C2×C4#6697914yes—
610C2×C4D4×Dic1114yes—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22C4×#433912yes—
623C22C4×#433912yes—
624C22#1062302112yes—
625C22#1062302612yes—
626C22#1062306112yes—
627C22#1062306412yes—
628C22C4×#434112yes—
629C22#1062307211yescharacteristic
630C22C4×D4×D1112yes—
631C22#1062307612yes—
632C22#1062307712yes—
633C22#1062308111yescharacteristic
634C22#1062308311yescharacteristic
635C22#1062308912yes—
636C22#1062309012yes—
637C22#1062309611yescharacteristic
638C22C22×C4×Dic1111yescharacteristic
639C22C2×#6697911yescharacteristic
640C22C2×#6697911yescharacteristic
641C22C2×D4×Dic1111yescharacteristic
642C22#1062332911yescharacteristic
643C22#41×Dic1111yescharacteristic
644C22#1062335811yescharacteristic
645C4—24no—
646C4—24no—
647C4—24no—
648C4—24no—
649C4—24no—
650C4—42no—
651C4—228no—
652C4—444no—
653C4—444no—
654C4—444no—
655C2—44no—
656C2C4×#6697911yescharacteristic
657C2C4×D4×Dic1111yescharacteristic
658C2#1307097711yescharacteristic
659C2#1307146511yescharacteristic
660C2#1307150911yescharacteristic
661C2#1307154511yescharacteristic
662C2#1307158911yescharacteristic
663C2#1307166712yes—
664C2#1307168812yes—
665C2#1307173812yes—
666C2#1307175012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13822
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic11C2semidirect
5. #13066850C2semidirect
6. #13066843C2semidirect
7. #13066843C2semidirect
9. C4×C11⋊#95C2semidirect
10. #95×Dic11C2semidirect
23. C4×C11×C22⋊C4C4semidirect
37. #10622564C4semidirect
73. C2×C4⋊Dic11C2×C4semidirect
82. C2×C4×Dic11C2×C4semidirect
92. C11⋊#95C2×C4semidirect
93. C11⋊#95C2×C4semidirect
174. C11×C22⋊C4C42semidirect
303. C4×C22⋊C4Dic11semidirect
509. C22⋊C4C4×Dic11semidirect
515. C11#13822semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×C4×C4⋊Dic112
C2×C4×C22⋊Dic112
#130668532
#130668502
#130668432
#130668392
C4×C11⋊#952
#95×Dic112
C2×C4×C11×C22⋊C42
#1382211