Finite Group Databasebeta

← #14675574

Subgroups — #14675574

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic, complemented
2C2×#10622560C211yesmaximal, characteristic
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic
4C2×C22⋊C4×Dic11C212yesmaximal
5#13066886C211yesmaximal, characteristic, complemented
6#13066875C211yesmaximal, characteristic, complemented
7#13066871C212yesmaximal, complemented
8#13066859C212yesmaximal
9#95×Dic11C211yesmaximal, characteristic, complemented
10#95×Dic11C212yesmaximal, complemented
11C11×#1439C211yesmaximal, characteristic
12C24×Dic11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C2×#66940—28no—
25C2×#66940—24no—
26C2×C11×#95C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622560C418yescomplemented
38C22⋊C4×Dic11—28no—
39C22⋊C4×Dic11—24no—
40C25×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—24no—
46C23×Dic11—22no—
47C23×Dic11—24no—
48C23×Dic11—22no—
49C23×Dic11Q814yescomplemented
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2312yes—
55C23×Dic11C2311yescharacteristic
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—24no—
59C22×Dic22—24no—
60C22×Dic22C2×C414yescomplemented
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4C2×C414yes—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11C2×C418yes—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—24no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—24no—
86C2×C4×Dic11D414yes—
87C2×C4×Dic11D418yes—
88#66940—232no—
89C11×#95—24no—
90C11×#95—22no—
91C11⋊#95—24no—
92C11⋊#95—22no—
93C11⋊#95—24no—
94C11⋊#95—22no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95C2×C414yescomplemented
99C11⋊#95C2×C418yescomplemented
100C4×#393—111nomaximal, Sylow
101C24×C11—22no—
102C24×C11—21no—
103C24×C11—22no—
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—22no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11C22×C412yes—
110C24×C11C2×Q812yes—
111C24×C11#4112yes—
112C24×C11C2411yescharacteristic
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4114yes—
136C22×C4×C11#4112yes—
137C22×Dic11—28no—
138C22×Dic11—216no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—21no—
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—21no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—44no—
162C22×Dic11—44no—
163C22×Dic11—48no—
164C22×Dic11C22×C414yes—
165C22×Dic11C22×C414yes—
166C22×Dic11C2×D412yes—
167C22×Dic11C2×D414yes—
168C22×Dic11C2×D412yes—
169C22×Dic11C2×D414yes—
170C22×Dic11C2×Q812yes—
171C22×Dic11C2×Q812yes—
172C22×Dic11#4112yes—
173C22×Dic11#4114yes—
174C22×Dic11#4114yes—
175C22×Dic11#4112yes—
176C2×Dic22—28no—
177C2×Dic22—28no—
178C2×Dic22—216no—
179C2×Dic22—216no—
180C2×Dic22—28no—
181C11×C4⋊C4—28no—
182C11×C22⋊C4—216no—
183C11×C22⋊C4—28no—
184C22⋊Dic11—28no—
185C22⋊Dic11—216no—
186Dic11⋊C4—216no—
187C4×Dic11—28no—
188C4×Dic11—216no—
189C4×Dic11—48no—
190C4×Dic11—44no—
191C22×C4×Q8—111no—
192C2×#393—111no—
193C2×C4×C22⋊C4—112no—
194C2×C4×C22⋊C4—111no—
195#1446—111no—
196#1442—112no—
197#1442—111no—
198#1439—112no—
199#1439D1111yescharacteristic
200C4×#95—111no—
201C4×#95—112no—
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—22no—
211C23×C11—24no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—41no—
223C23×C11—42no—
224C23×C11C4×Q814yescomplemented
225C23×C11C23×C411yescharacteristic
226C23×C11C22×D411yescharacteristic
227C23×C11C22×D412yes—
228C23×C11C22×Q811yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11C2×#4112yes—
232C23×C11C2×#4112yes—
233C23×C11C2×#4112yes—
234C23×C11C2×#4111yescharacteristic
235C23×C11C2×#4111yescharacteristic
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11C4×D414yes—
260C2×Dic11—24no—
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—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—42no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—42no—
281C2×Dic11—41no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—416no—
289C2×Dic11C4×D418yes—
290C2×Dic11#12014yes—
291C2×Dic11C22⋊Q814yes—
292C2×Dic11C22⋊Q818yes—
293C2×Dic11#12414yes—
294C2×Dic11#12418yes—
295Dic22—232no—
296C23×Q8—111no—
297C24×C4—111no—
298C2×C4×Q8—224no—
299C2×C4×Q8—228no—
300C22×C4⋊C4—112no—
301C22×C4⋊C4C2×D1111yescharacteristic
302C22×C22⋊C4—112no—
303C22×C22⋊C4—111no—
304C22×C22⋊C4C2×D1112yes—
305C22×C22⋊C4C2×D1111yescharacteristic
306C22×C42—112no—
307C22×C42—111no—
308C22×C42—111no—
309C22×C42—112no—
310#393—118no—
311C4×C22⋊C4—228no—
312C4×C22⋊C4—224no—
313C2×#95—112no—
314C2×#95—111no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95—111no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95—111no—
322C2×#95C2×D1112yes—
323C2×#95C2×D1111yescharacteristic
324C22×C11—24no—
325C22×C11—28no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—44no—
330C22×C11—42no—
331C22×C11—44no—
332C22×C11—42no—
333C22×C11—44no—
334C22×C11—42no—
335C22×C11C2×C4×D411yescharacteristic
336C22×C11C2×C4×D412yes—
337C22×C11C2×C4×Q811yescharacteristic
338C22×C11C4×#4111yescharacteristic
339C22×C11C4×#4112yes—
340C22×C11C2×#12011yescharacteristic
341C22×C11C2×C22⋊Q811yescharacteristic
342C22×C11C2×C22⋊Q812yes—
343C22×C11#52512yes—
344C22×C11#52511yescharacteristic
345C22×C11#52512yes—
346C22×C11#52511yescharacteristic
347C22×C11C2×#12411yescharacteristic
348C22×C11C2×#12412yes—
349C22×C11#52912yes—
350C22×C11#52912yes—
351C22×C11#52911yescharacteristic
352C22×C11#52912yes—
353C22×C11#52912yes—
354C22×C11#53211yescharacteristic
355C22×C11#53212yes—
356C22×C11#53312yes—
357C22×C11#53311yescharacteristic
358C4×C11—24no—
359C4×C11—44no—
360C4×C11—44no—
361C4×C11—42no—
362Dic11—28no—
363Dic11—42no—
364Dic11—42no—
365Dic11—42no—
366Dic11—44no—
367Dic11#39318yescomplemented
368C25C22×D1111yescharacteristic
369C22×Q8—114no—
370C22×Q8—224no—
371C22×Q8—224no—
372C22×Q8—222no—
373C22×Q8—222no—
374C23×C4—111no—
375C23×C4—112no—
376C23×C4—114no—
377C23×C4—111no—
378C23×C4—112no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—222no—
382C23×C4—224no—
383C23×C4—224no—
384C23×C4—222no—
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1112yes—
387C23×C4C22×D1112yes—
388C23×C4C22×D1111yescharacteristic
389C4×Q8—2232no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—224no—
394C2×C4⋊C4—224no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—222no—
406C2×C22⋊C4C4×D1114yes—
407C2×C42—118no—
408C2×C42—114no—
409C2×C42—224no—
410C2×C42—224no—
411C2×C42—224no—
412C2×C42—222no—
413C2×C42—224no—
414C2×C42—224no—
415C2×C42—224no—
416C2×C42—224no—
417#95—24no—
418#95—22no—
419#95—118no—
420#95—114no—
421#95—224no—
422#95—224no—
423#95—224no—
424#95—222no—
425#95—224no—
426#95—222no—
427#95—224no—
428C2×C11—44no—
429C2×C11C4×#12011yescharacteristic
430C2×C11C4×C22⋊Q811yescharacteristic
431C2×C11C4×C22⋊Q812yes—
432C2×C11C4×#12412yes—
433C2×C11C4×#12411yescharacteristic
434C2×C11C2×#39311yescharacteristic
435C2×C11#238811yescharacteristic
436C2×C11#239611yescharacteristic
437C2×C11#239612yes—
438C2×C11#239811yescharacteristic
439C2×C11#239812yes—
440C24—21no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—22no—
446C24—21no—
447C24—22no—
448C24C2×C4×D1112yes—
449C24#434112yes—
450C24Q8×D1112yes—
451C24C23×D1111yescharacteristic
452C2×Q8—2216no—
453C2×Q8—228no—
454C2×Q8—2216no—
455C2×Q8—228no—
456C2×Q8—228no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—112no—
478C22×C4—114no—
479C22×C4—112no—
480C22×C4—114no—
481C22×C4—114no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—112no—
487C22×C4—228no—
488C22×C4—2216no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—221no—
509C22×C4—222no—
510C22×C4—221no—
511C22×C4—444no—
512C22×C4—444no—
513C22×C4—448no—
514C22×C4C2×C4×D1112yes—
515C22×C4C2×C4×D1112yes—
516C22×C4D4×D1114yes—
517C22×C4D4×D1112yes—
518C22×C4#434114yes—
519C22×C4#434112yes—
520C4⋊C4—28no—
521C4⋊C4—2216no—
522C22⋊C4—216no—
523C22⋊C4—28no—
524C22⋊C4—2216no—
525C22⋊C4—228no—
526C42—228no—
527C42—2216no—
528C42—448no—
529C42—444no—
530C11C4×#39311yescharacteristic, complemented, Sylow
531C23—22no—
532C23—22no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—24no—
540C23—22no—
541C23—24no—
542C23—24no—
543C23—42no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—41no—
551C23—41no—
552C23—42no—
553C23#6694014yescomplemented
554C23C22×C4×D1111yescharacteristic
555C23C2×D4×D1111yescharacteristic
556C23C2×D4×D1112yes—
557C23C2×#434112yes—
558C23C2×#434111yescharacteristic
559C23C2×#434111yescharacteristic
560C23C2×Q8×D1111yescharacteristic
561C23#41×D1111yescharacteristic
562C23#41×D1112yes—
563C23#41×D1112yes—
564C23#41×D1111yescharacteristic
565Q8—2232no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—114no—
590C2×C4—114no—
591C2×C4—118no—
592C2×C4—114no—
593C2×C4—118no—
594C2×C4—118no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—4416no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—441no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—442no—
622C2×C4—441no—
623C2×C4—442no—
624C2×C4(C22⋊D11)⋊C414yes—
625C22—24no—
626C22—28no—
627C22—42no—
628C22—42no—
629C22—44no—
630C22—42no—
631C22—44no—
632C22—44no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22C2×(C22⋊D11)⋊C411yescharacteristic
637C22C2×#6694011yescharacteristic
638C22#1062305311yescharacteristic
639C22C4×#434112yes—
640C22C4×D4×D1112yes—
641C22#1062311712yes—
642C22D11×#12011yescharacteristic
643C22#1062312712yes—
644C22#1062313112yes—
645C22#1062313111yescharacteristic
646C22#1062313712yes—
647C22#1062313711yescharacteristic
648C22#1062315312yes—
649C22#1062315311yescharacteristic
650C22D11×C22⋊Q811yescharacteristic
651C22D11×C22⋊Q812yes—
652C22#1062318012yes—
653C22#1062318012yes—
654C22#1062318711yescharacteristic
655C22D11×#12411yescharacteristic
656C22D11×#12412yes—
657C22#1062323712yes—
658C22#1062324711yescharacteristic
659C4—24no—
660C4—44no—
661C4—42no—
662C4—44no—
663C4—118no—
664C4—228no—
665C4—442no—
666C4—444no—
667C4—442no—
668C4—442no—
669C2—44no—
670C2#1307112111yescharacteristic
671C2#1307114411yescharacteristic
672C2#1307114812yes—
673C2#1307115712yes—
674C2#1307116311yescharacteristic
675C2D11×#39311yescharacteristic
676C2#1307182811yescharacteristic
677C2#1307188511yescharacteristic
678C2#1307189112yes—
679C2#1307190111yescharacteristic
680C2#1307190412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11C4×#393
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#66940C2semidirect
5. #13066886C2semidirect
6. #13066875C2semidirect
7. #13066871C2semidirect
9. #95×Dic11C2semidirect
10. #95×Dic11C2semidirect
37. #10622560C4semidirect
49. C23×Dic11Q8semidirect
60. C22×Dic22C2×C4semidirect
98. C11⋊#95C2×C4semidirect
99. C11⋊#95C2×C4semidirect
224. C23×C11C4×Q8semidirect
367. Dic11#393semidirect
530. C11C4×#393semidirect
553. C23#66940semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106225602
C2×C22⋊C4×Dic112
#130668862
#130668752
#130668712
#130668592
#95×Dic112
C11×#14392
C4×#39311