Finite Group Databasebeta

← #14675142

Subgroups — #14675142

Order 2816.

2194 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C212yesmaximal
2C2×C22⋊C4×Dic11C212yesmaximal, complemented
3#13066853C212yesmaximal, complemented
4#13066853C212yesmaximal, complemented
5#13066848C212yesmaximal, complemented
6#13066843C211yesmaximal, characteristic, complemented
7#13066838C212yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C42×C11C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C11×#390C418yescomplemented
23#10622833C4116yescomplemented
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C22⋊C4×Dic11—28no—
34C25×C11C2312yes—
35C22×D4×C11—41no—
36C22×D4×C11—41no—
37C22×D4×C11—42no—
38C22×D4×C11C2×C418yes—
39C22×D4×C11C2×C414yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—24no—
45C23×Dic11—24no—
46C23×Dic11—42no—
47C23×Dic11—42no—
48C23×Dic11—42no—
49C23×Dic11—42no—
50C23×Dic11C2×C418yescomplemented
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C2×C11×C4⋊C4—42no—
56C2×C11×C4⋊C4C2×C414yescomplemented
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—42no—
60C2×C11×C22⋊C4—42no—
61C2×C11×C22⋊C4C2×C418yescomplemented
62C2×C11×C22⋊C4C2×C418yescomplemented
63C2×C42×C11—41no—
64C2×C42×C11—41no—
65C2×C42×C11C2×C414yescomplemented
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11C2×C418yes—
73C2×C22⋊Dic11C2×C418yes—
74C2×C22⋊Dic11C2×C418yescomplemented
75C2×C4×Dic11—22no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—41no—
78C2×C4×Dic11—41no—
79C2×C4×Dic11—41no—
80C2×C4×Dic11—41no—
81C2×C4×Dic11—42no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11D414yescomplemented
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—42no—
88C11⋊#95—41no—
89C11⋊#95—42no—
90C11⋊#95—41no—
91C11⋊#95C2×C418yescomplemented
92C11⋊#95C2×C418yescomplemented
93#13791—111nomaximal, Sylow
94C24×C11—22no—
95C24×C11—22no—
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×C11C22×C414yes—
107C24×C11C22×C414yes—
108C24×C11C22×C414yes—
109C24×C11C2411yescharacteristic
110C2×D4×C11—44no—
111C2×D4×C11—44no—
112C2×D4×C11—48no—
113C2×D4×C11—48no—
114C2×D4×C11C42116yescomplemented
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11#4112yes—
139C22×Dic11—216no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
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—48no—
163C22×Dic11—48no—
164C22×Dic11—48no—
165C22×Dic11—48no—
166C22×Dic11—48no—
167C22×Dic11—48no—
168C22×Dic11C22×C414yes—
169C22×Dic11C22×C414yes—
170C22×Dic11C22×C414yes—
171C22×Dic11C22×C414yes—
172C22×Dic11C2×D414yes—
173C22×Dic11#4114yes—
174C11×C4⋊C4—44no—
175C11×C22⋊C4—216no—
176C11×C22⋊C4—48no—
177C42×C11—44no—
178C22⋊Dic11—216no—
179C22⋊Dic11—48no—
180C22⋊Dic11—48no—
181C4×Dic11—44no—
182C4×Dic11—44no—
183C4×Dic11—48no—
184C2×#390D1111yescharacteristic
185C2×#386—112no—
186C2×C4×C22⋊C4—112no—
187#1437—112no—
188#1437—112no—
189#1436—112no—
190#1434—111no—
191C22⋊#95—112no—
192C4×#95—111no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
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×C11C2×C4218yes—
228C23×C11C23×C412yes—
229C23×C11C23×C411yescharacteristic
230C23×C11C22×D411yescharacteristic
231C23×C11C2×#4111yescharacteristic
232C23×C11C2×#4112yes—
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C11H(5,𝔽2)12yes—
235C23×C11H(5,𝔽2)11yescharacteristic
236C23×C11H(5,𝔽2)12yes—
237C23×C11H(5,𝔽2)11yescharacteristic
238C23×C112−1+411yescharacteristic
239D4×C11—416no—
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—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
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×C11C2×C4214yes—
263C2×C4×C11C4×D414yes—
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—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—432no—
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×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11C4×D418yes—
293C23×D4C2×D1111yescharacteristic
294C24×C4—112no—
295C22×C4⋊C4C2×D1111yescharacteristic
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4C2×D1112yes—
300C22×C22⋊C4C2×D1112yes—
301C22×C42—111no—
302C22×C42—111no—
303C22×C42—112no—
304C22×C42C2×D1111yescharacteristic
305#390Dic1118yescomplemented
306#386—1116no—
307C4×C22⋊C4—228no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95—111no—
314C2×#95—112no—
315C2×#95—111no—
316C2×#95—112no—
317C22×C11—28no—
318C22×C11—28no—
319C22×C11—28no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11C22×C4211yescharacteristic
333C22×C11C2×C4×D411yescharacteristic
334C22×C11C2×C4×D412yes—
335C22×C11C4×#4112yes—
336C22×C11C4×#4111yescharacteristic
337C22×C11#51812yes—
338C22×C11#51812yes—
339C22×C11#51811yescharacteristic
340C22×C11#51811yescharacteristic
341C22×C11#51811yescharacteristic
342C22×C11#51812yes—
343C22×C11#52012yes—
344C22×C11#52011yescharacteristic
345C22×C11#53411yescharacteristic
346C22×C11#53512yes—
347C22×C11#53711yescharacteristic
348C22×C11#53812yes—
349C22×C11#53811yescharacteristic
350C22×C11#53812yes—
351C22×C11#53911yescharacteristic
352C22×C11#54012yes—
353C22×C11#54012yes—
354C22×C11#54212yes—
355C4×C11—24no—
356C4×C11—24no—
357C4×C11—44no—
358C4×C11—42no—
359Dic11—28no—
360Dic11—44no—
361Dic11—44no—
362Dic11—44no—
363C25C22×D1112yes—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4—42no—
367C22×D4C4×D1118yes—
368C22×D4C2×Dic1114yes—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4—112no—
372C23×C4—112no—
373C23×C4—118no—
374C23×C4—224no—
375C23×C4—224no—
376C23×C4—442no—
377C23×C4—442no—
378C23×C4—442no—
379C23×C4—442no—
380C23×C4C22×D1112yes—
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C2×C4⋊C4—42no—
385C2×C4⋊C4C2×Dic1114yescomplemented
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—442no—
396C2×C22⋊C4—442no—
397C2×C22⋊C4—442no—
398C2×C22⋊C4—442no—
399C2×C22⋊C4C2×Dic1118yescomplemented
400C2×C22⋊C4C2×Dic1118yescomplemented
401C2×C42—41no—
402C2×C42—41no—
403C2×C42—114no—
404C2×C42—224no—
405C2×C42—222no—
406C2×C42—441no—
407C2×C42—441no—
408C2×C42—441no—
409C2×C42—441no—
410C2×C42—442no—
411C2×C42—442no—
412C2×C42C2×Dic1114yescomplemented
413#95—118no—
414#95—118no—
415#95—224no—
416#95—224no—
417#95—224no—
418#95—441no—
419#95—441no—
420#95—442no—
421#95—442no—
422C2×C11—48no—
423C2×C11C42×D411yescharacteristic
424C2×C11#227311yescharacteristic
425C2×C11#227511yescharacteristic
426C2×C11#232112yes—
427C2×C11#232412yes—
428C2×C11#232511yescharacteristic
429C2×C11#232811yescharacteristic
430C2×C11#233312yes—
431C2×C11#233311yescharacteristic
432C2×C11#233512yes—
433C2×C11#233711yescharacteristic
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24C2×C4×D1114yes—
447C24C2×C4×D1114yes—
448C24C22×Dic1114yes—
449C24C23×D1111yescharacteristic
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4C4×Dic11116yescomplemented
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—2216no—
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×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—448no—
502C22×C4—448no—
503C22×C4—448no—
504C22×C4—448no—
505C22×C4—448no—
506C22×C4—448no—
507C22×C4C2×C4×D1114yes—
508C22×C4D4×D1112yes—
509C22×C4#434112yes—
510C22×C4C22×Dic1112yes—
511C22×C4C22×Dic1114yes—
512C22×C4C22×Dic1112yes—
513C22×C4C22×Dic1112yes—
514C4⋊C4—44no—
515C22⋊C4—216no—
516C22⋊C4—48no—
517C22⋊C4—2216no—
518C22⋊C4—448no—
519C22⋊C4—448no—
520C42—44no—
521C42—444no—
522C42—444no—
523C42—448no—
524C11#1379111yescharacteristic, complemented, Sylow
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
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—
559C23C2×C4×Dic1118yes—
560C23C22×C4×D1112yes—
561C23C2×D4×D1111yescharacteristic
562C23C2×#434111yescharacteristic
563C23#6703712yes—
564C23#6703712yes—
565C23#6703711yescharacteristic
566C23#6703711yescharacteristic
567C23#41×D1112yes—
568C23#6704211yescharacteristic
569C23#6704311yescharacteristic
570C23C23×Dic1111yescharacteristic
571D4—416no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
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—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—4432no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4C2×C4×Dic1114yes—
624C2×C4D4×Dic1114yes—
625C22—28no—
626C22—28no—
627C22—28no—
628C22—44no—
629C22—44no—
630C22—44no—
631C22—44no—
632C22—44no—
633C22—44no—
634C22—44no—
635C22—44no—
636C22—44no—
637C22—44no—
638C22—44no—
639C22—44no—
640C22#1062301712yes—
641C22#1062301712yes—
642C22C4×#434112yes—
643C22C4×D4×D1112yes—
644C22#1062307612yes—
645C22#1062307712yes—
646C22#1062312811yescharacteristic
647C22#1062313311yescharacteristic
648C22#1062313611yescharacteristic
649C22#1062314412yes—
650C22#1062314612yes—
651C22#1062314811yescharacteristic
652C22#1062320012yes—
653C22#1062320912yes—
654C22#1062324612yes—
655C22#1062325012yes—
656C22C22×C4×Dic1111yescharacteristic
657C22C2×D4×Dic1111yescharacteristic
658C22#1062332911yescharacteristic
659C22#1062332911yescharacteristic
660C22#1062332911yescharacteristic
661C22#41×Dic1111yescharacteristic
662C22#1062335811yescharacteristic
663C4—24no—
664C4—24no—
665C4—42no—
666C4—44no—
667C4—228no—
668C4—444no—
669C4—444no—
670C4—444no—
671C2—48no—
672C2C4×D4×Dic1111yescharacteristic
673C2#1307096911yescharacteristic
674C2#1307097711yescharacteristic
675C2#1307127512yes—
676C2#1307130212yes—
677C2#1307132111yescharacteristic
678C2#1307134211yescharacteristic
679C2#1307137512yes—
680C2#1307138311yescharacteristic
681C2#1307140312yes—
682C2#1307143111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#13791
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×Dic11C2semidirect
3. #13066853C2semidirect
4. #13066853C2semidirect
5. #13066848C2semidirect
6. #13066843C2semidirect
7. #13066838C2semidirect
8. C4×C11⋊#95C2semidirect
22. C11×#390C4semidirect
23. #10622833C4semidirect
50. C23×Dic11C2×C4semidirect
56. C2×C11×C4⋊C4C2×C4semidirect
61. C2×C11×C22⋊C4C2×C4semidirect
62. C2×C11×C22⋊C4C2×C4semidirect
65. C2×C42×C11C2×C4semidirect
74. C2×C22⋊Dic11C2×C4semidirect
83. C2×C4×Dic11D4semidirect
91. C11⋊#95C2×C4semidirect
92. C11⋊#95C2×C4semidirect
114. C2×D4×C11C42semidirect
305. #390Dic11semidirect
385. C2×C4⋊C4C2×Dic11semidirect
399. C2×C22⋊C4C2×Dic11semidirect
400. C2×C22⋊C4C2×Dic11semidirect
412. C2×C42C2×Dic11semidirect
454. C2×D4C4×Dic11semidirect
524. C11#13791semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
C2×C22⋊C4×Dic112
#130668532
#130668482
#130668432
#130668382
C4×C11⋊#952
C2×C11×#3902
#1379111