Finite Group Databasebeta

← #14680815

Subgroups — #14680815

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622835C211yesmaximal, characteristic
2C2×#10622546C211yesmaximal, characteristic, complemented
3#13066875C211yesmaximal, characteristic, complemented
4#13066866C211yesmaximal, characteristic, complemented
5#13066863C212yesmaximal, complemented
6#13066859C212yesmaximal, complemented
7#13066857C211yesmaximal, characteristic
8#13066853C212yesmaximal, complemented
9#13066853C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#390C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C11×#390—24no—
25#10622835C418yescomplemented
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622546—24no—
38C25×C11C2312yes—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—42no—
42C22×D4×C11—42no—
43C22×D4×C11C2×C414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2312yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—42no—
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—42no—
61C2×C11×C22⋊C4—42no—
62C2×C42×C11—42no—
63C2×C42×C11D414yes—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11C2×C418yes—
75C2×C22⋊Dic11C2×C418yes—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—42no—
80C2×Dic11⋊C4C2×C414yes—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11—42no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—24no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93C11⋊#95—42no—
94C11⋊#95C2×C414yes—
95#14325—111nomaximal, Sylow
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C22×C414yes—
111C24×C11C2411yescharacteristic
112C2×D4×C11—28no—
113C2×D4×C11—48no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—48no—
117C22×C4×C11—21no—
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—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4114yes—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—21no—
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—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11C22×C414yes—
172C22×Dic11C22×C412yes—
173C22×Dic11C22×C412yes—
174C22×Dic11#4114yes—
175C11×C4⋊C4—44no—
176C11×C22⋊C4—48no—
177C11×C22⋊C4—48no—
178C42×C11—44no—
179C22⋊Dic11—48no—
180C22⋊Dic11—48no—
181C22⋊Dic11—48no—
182C22⋊Dic11—48no—
183Dic11⋊C4—28no—
184Dic11⋊C4—44no—
185C4×Dic11—48no—
186C2×#394—111no—
187C2×#390D1111yescharacteristic
188C2×#387—111no—
189#1442—111no—
190#1441—111no—
191#1440—112no—
192#1439—112no—
193#1438—111no—
194#1437—112no—
195#1437—112no—
196C4×#95—111no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11C23×C411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C2×#4111yescharacteristic
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11H(5,𝔽2)12yes—
238C23×C11H(5,𝔽2)12yes—
239C23×C11H(5,𝔽2)11yescharacteristic
240C23×C11H(5,𝔽2)11yescharacteristic
241C23×C11H(5,𝔽2)11yescharacteristic
242C23×C112−1+411yescharacteristic
243D4×C11—416no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11C4×D414yes—
265C2×C4×C11#12414yes—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—41no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302C23×D4C2×D1111yescharacteristic
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4C2×D1111yescharacteristic
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4C2×D1112yes—
311C22×C22⋊C4C2×D1112yes—
312C22×C42—112no—
313C22×C42C2×D1111yescharacteristic
314#394—118no—
315#390—24no—
316#387—224no—
317C2×#95—111no—
318C2×#95—111no—
319C2×#95—112no—
320C2×#95—111no—
321C2×#95—111no—
322C2×#95—111no—
323C2×#95—111no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—112no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—82no—
336C22×C11—82no—
337C22×C11—82no—
338C22×C11—82no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11—82no—
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C4×#4112yes—
345C22×C11#51812yes—
346C22×C11#51811yescharacteristic
347C22×C11#52011yescharacteristic
348C22×C11C2×#12411yescharacteristic
349C22×C11#52912yes—
350C22×C11#53211yescharacteristic
351C22×C11#53411yescharacteristic
352C22×C11#53511yescharacteristic
353C22×C11#53511yescharacteristic
354C22×C11#53711yescharacteristic
355C22×C11#53812yes—
356C22×C11#53812yes—
357C22×C11#53812yes—
358C22×C11#53812yes—
359C22×C11#53912yes—
360C22×C11#54012yes—
361C22×C11#54012yes—
362C22×C11#54011yescharacteristic
363C22×C11#54012yes—
364C22×C11#54211yescharacteristic
365C22×C11#54212yes—
366C4×C11—24no—
367C4×C11—24no—
368C4×C11—42no—
369C4×C11—82no—
370Dic11—42no—
371Dic11—42no—
372Dic11—44no—
373Dic11—44no—
374Dic11—81no—
375Dic11—81no—
376C25C22×D1112yes—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4C4×D1114yes—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—112no—
385C23×C4—112no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4C22×D1112yes—
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—442no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—118no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4—224no—
409C2×C22⋊C4—442no—
410C2×C22⋊C4—442no—
411C2×C22⋊C4—442no—
412C2×C22⋊C4—442no—
413C2×C22⋊C4—442no—
414C2×C22⋊C4—442no—
415C2×C22⋊C4—442no—
416C2×C22⋊C4—442no—
417C2×C42—42no—
418C2×C42—224no—
419C2×C42—442no—
420C2×C42—442no—
421C2×C42C22⋊D1114yes—
422#95—114no—
423#95—224no—
424#95—222no—
425#95—222no—
426#95—222no—
427#95—222no—
428#95—222no—
429#95—442no—
430#95—442no—
431#95—442no—
432#95—442no—
433C2×C11—84no—
434C2×C11C4×#12411yescharacteristic
435C2×C11#232111yescharacteristic
436C2×C11#232411yescharacteristic
437C2×C11#233312yes—
438C2×C11#233512yes—
439C2×C11#263911yescharacteristic
440C2×C11#264111yescharacteristic
441C2×C11#264812yes—
442C2×C11#265112yes—
443C2×C11#266111yescharacteristic
444C2×C11#266211yescharacteristic
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C2×C4×D1114yes—
460C24C23×D1111yescharacteristic
461C2×D4—28no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—44no—
465C2×D4—44no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—114no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—222no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—222no—
510C22×C4—221no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4C2×C4×D1112yes—
519C22×C4#433912yes—
520C22×C4#434114yes—
521C22×C4C2×C22⋊D1112yes—
522C22×C4C2×C22⋊D1112yes—
523C22×C4C2×C22⋊D1112yes—
524C4⋊C4—44no—
525C4⋊C4—228no—
526C4⋊C4—444no—
527C22⋊C4—48no—
528C22⋊C4—48no—
529C22⋊C4—448no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C42—44no—
534C42—448no—
535C11#1432511yescharacteristic, complemented, Sylow
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23C22×C4×D1111yescharacteristic
572C23C2×#433911yescharacteristic
573C23C2×#434112yes—
574C23#6703712yes—
575C23#6703711yescharacteristic
576C23#6703711yescharacteristic
577C23#6703712yes—
578C23#41×D1112yes—
579C23#6704211yescharacteristic
580C23#6704311yescharacteristic
581C23C22×C22⋊D1111yescharacteristic
582D4—416no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—224no—
610C2×C4—222no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—442no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4C4×C22⋊D1114yes—
640C2×C4#6698914yes—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22—44no—
648C22—82no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—82no—
653C22—82no—
654C22—82no—
655C22—82no—
656C22#1062301712yes—
657C22#1062302512yes—
658C22C4×#434112yes—
659C22#1062307611yescharacteristic
660C22#1062307711yescharacteristic
661C22#1062308812yes—
662C22#1062309211yescharacteristic
663C22#1062309311yescharacteristic
664C22#1062313312yes—
665C22#1062314412yes—
666C22#1062314612yes—
667C22#1062314812yes—
668C22#1062320012yes—
669C22#1062320912yes—
670C22#1062325012yes—
671C22#1062325012yes—
672C22C2×C4×C22⋊D1111yescharacteristic
673C22C2×#6698911yescharacteristic
674C22#1062333511yescharacteristic
675C22#1062333611yescharacteristic
676C22#1062333611yescharacteristic
677C22#1062336311yescharacteristic
678C22#1062336411yescharacteristic
679C4—24no—
680C4—24no—
681C4—42no—
682C4—82no—
683C4—444no—
684C4—442no—
685C4—444no—
686C4—442no—
687C4—881no—
688C4—881no—
689C2—84no—
690C2C4×#6698911yescharacteristic
691C2#1307127411yescharacteristic
692C2#1307130311yescharacteristic
693C2#1307137512yes—
694C2#1307140312yes—
695C2#1307454911yescharacteristic
696C2#1307456111yescharacteristic
697C2#1307460812yes—
698C2#1307465312yes—
699C2#1307474511yescharacteristic
700C2#1307475511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14325
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622546C2semidirect
3. #13066875C2semidirect
4. #13066866C2semidirect
5. #13066863C2semidirect
6. #13066859C2semidirect
8. #13066853C2semidirect
9. #13066853C2semidirect
10. C4×C11⋊#95C2semidirect
25. #10622835C4semidirect
535. C11#14325semidirect

Maximal subgroups

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

subgroupindex
C2×#106228352
C2×#106225462
#130668752
#130668662
#130668632
#130668592
#130668572
#130668532
C4×C11⋊#952
C2×C11×#3902
#1432511