Finite Group Databasebeta

← #14682173

Subgroups — #14682173

Order 2816.

2018 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×#10622833C212yesmaximal
2C2×#10622563C212yesmaximal, complemented
3#13066869C212yesmaximal, complemented
4#13066861C212yesmaximal, complemented
5#13066861C212yesmaximal, complemented
6#13066846C211yesmaximal, characteristic, complemented
7#13066843C211yesmaximal, characteristic, complemented
8#13066838C212yesmaximal, 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⋊Dic11C2212yes—
20C22×C4⋊Dic11C2212yes—
21C11×#390C418yescomplemented
22#10622833—28no—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33#10622563—28no—
34C25×C11C2312yes—
35C22×D4×C11—42no—
36C22×D4×C11—42no—
37C22×D4×C11C2×C414yes—
38C22×D4×C11D414yes—
39C22×D4×C11Q814yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—24no—
45C23×Dic11—24no—
46C23×Dic11—24no—
47C23×Dic11—42no—
48C23×Dic11—42no—
49C23×Dic11—42no—
50C23×Dic11—42no—
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—42no—
64C2×C42×C11C2×C414yescomplemented
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11—42no—
78C2×C4⋊Dic11—42no—
79C2×C4⋊Dic11—42no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—22no—
83C11⋊#95—24no—
84C11⋊#95—41no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—41no—
89C11⋊#95D414yescomplemented
90#14438—111nomaximal, Sylow
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
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×C11C22×C414yes—
104C24×C11C2×D414yes—
105C24×C11C2×Q814yes—
106C24×C11C2411yescharacteristic
107C2×D4×C11—44no—
108C2×D4×C11—44no—
109C2×D4×C11—48no—
110C2×D4×C11—48no—
111C2×D4×C11C4⋊C4116yescomplemented
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—21no—
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—21no—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C414yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×Q812yes—
133C22×C4×C11#4112yes—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
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—48no—
161C22×Dic11—48no—
162C22×Dic11—48no—
163C22×Dic11—48no—
164C22×Dic11—48no—
165C22×Dic11—48no—
166C22×Dic11—48no—
167C22×Dic11C2×D414yes—
168C22×Dic11#4114yes—
169C11×C4⋊C4—44no—
170C11×C22⋊C4—216no—
171C11×C22⋊C4—48no—
172C42×C11—44no—
173C22⋊Dic11—48no—
174C22⋊Dic11—48no—
175C22⋊Dic11—48no—
176C4⋊Dic11—48no—
177C4⋊Dic11—48no—
178C2×#390D1111yescharacteristic
179C2×#386—112no—
180C2×#385—112no—
181#1441—112no—
182#1439—112no—
183#1439—112no—
184C4⋊#95—111no—
185#1434—111no—
186C22⋊#95—112no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
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—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×C11C2×C4⋊C418yes—
222C23×C11C23×C411yescharacteristic
223C23×C11C22×D411yescharacteristic
224C23×C11C22×D411yescharacteristic
225C23×C11C22×Q811yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4112yes—
228C23×C11H(5,𝔽2)12yes—
229C23×C11H(5,𝔽2)12yes—
230C23×C11H(5,𝔽2)12yes—
231C23×C11H(5,𝔽2)11yescharacteristic
232C23×C112−1+411yescharacteristic
233D4×C11—416no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
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×C11C2×C4⋊C414yes—
255C2×C4×C11C4×D414yes—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—432no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
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—
285C23×D4C2×D1111yescharacteristic
286C24×C4—112no—
287C22×C4⋊C4—112no—
288C22×C4⋊C4—112no—
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4C2×D1112yes—
294C22×C22⋊C4C2×D1112yes—
295C22×C42C2×D1111yescharacteristic
296#390Dic1118yescomplemented
297#386—228no—
298#385—228no—
299C2×#95—111no—
300C2×#95—112no—
301C2×#95—111no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—111no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—111no—
308C2×#95—112no—
309C22×C11—28no—
310C22×C11—28no—
311C22×C11—28no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11C22×C4⋊C411yescharacteristic
325C22×C11C2×C4×D411yescharacteristic
326C22×C11C4×#4111yescharacteristic
327C22×C11#51811yescharacteristic
328C22×C11#51811yescharacteristic
329C22×C11#51811yescharacteristic
330C22×C11#52011yescharacteristic
331C22×C11#53412yes—
332C22×C11#53512yes—
333C22×C11#53812yes—
334C22×C11#54012yes—
335C22×C11#54212yes—
336C22×C11#54312yes—
337C22×C11D4211yescharacteristic
338C22×C11#54612yes—
339C22×C11#54612yes—
340C22×C11#54711yescharacteristic
341C22×C11D4×Q811yescharacteristic
342C22×C11#55312yes—
343C22×C11#55412yes—
344C22×C11#55411yescharacteristic
345C22×C11#56012yes—
346C22×C11#56212yes—
347C4×C11—24no—
348C4×C11—24no—
349C4×C11—44no—
350C4×C11—42no—
351Dic11—44no—
352Dic11—44no—
353Dic11—82no—
354Dic11—82no—
355C25C22×D1112yes—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4Dic2214yes—
359C22×D4D4414yes—
360C22×D4C2×Dic1114yes—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4—112no—
365C23×C4—224no—
366C23×C4—224no—
367C23×C4—224no—
368C23×C4—442no—
369C23×C4—442no—
370C23×C4—442no—
371C23×C4—442no—
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×C4⋊C4—42no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—442no—
381C2×C4⋊C4—442no—
382C2×C4⋊C4—442no—
383C2×C4⋊C4C2×Dic1114yescomplemented
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—442no—
394C2×C22⋊C4—442no—
395C2×C22⋊C4—442no—
396C2×C22⋊C4—442no—
397C2×C22⋊C4C2×Dic1118yescomplemented
398C2×C22⋊C4C2×Dic1118yescomplemented
399C2×C42—42no—
400C2×C42C2×Dic1114yescomplemented
401#95—114no—
402#95—224no—
403#95—224no—
404#95—224no—
405#95—222no—
406#95—442no—
407#95—442no—
408#95—442no—
409#95—441no—
410#95—441no—
411C2×C11—48no—
412C2×C11#231511yescharacteristic
413C2×C11#232811yescharacteristic
414C2×C11#233711yescharacteristic
415C2×C11D4×C4⋊C411yescharacteristic
416C2×C11#234911yescharacteristic
417C2×C11#236411yescharacteristic
418C2×C11#237711yescharacteristic
419C2×C11#267812yes—
420C2×C11#269212yes—
421C2×C11#270112yes—
422C2×C11#278012yes—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24C2×Dic2214yes—
436C24C2×D4414yes—
437C24C22×Dic1114yes—
438C24C23×D1111yescharacteristic
439C2×D4—48no—
440C2×D4—48no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4C4⋊Dic11116yescomplemented
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—114no—
459C22×C4—114no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
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—448no—
487C22×C4—448no—
488C22×C4—448no—
489C22×C4—448no—
490C22×C4—448no—
491C22×C4—448no—
492C22×C4—448no—
493C22×C4C2×Dic2212yes—
494C22×C4C2×D4412yes—
495C22×C4D4×D1112yes—
496C22×C4#434112yes—
497C22×C4C22×Dic1112yes—
498C22×C4C22×Dic1114yes—
499C22×C4C22×Dic1112yes—
500C22×C4C22×Dic1112yes—
501C4⋊C4—44no—
502C4⋊C4—448no—
503C4⋊C4—448no—
504C22⋊C4—216no—
505C22⋊C4—48no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C22⋊C4—448no—
509C42—44no—
510C11#1443811yescharacteristic, complemented, Sylow
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23C2×C4⋊Dic1118yes—
546C23C22×Dic2211yescharacteristic
547C23C22×D4411yescharacteristic
548C23C2×D4×D1111yescharacteristic
549C23C2×#434111yescharacteristic
550C23#6703712yes—
551C23#6703712yes—
552C23#6703712yes—
553C23#41×D1112yes—
554C23#6704211yescharacteristic
555C23#6704311yescharacteristic
556C23C23×Dic1111yescharacteristic
557D4—416no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—4432no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
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×C4—442no—
607C2×C4C2×C4⋊Dic1114yes—
608C2×C4D4×Dic1114yes—
609C22—28no—
610C22—28no—
611C22—28no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—44no—
622C22—44no—
623C22—44no—
624C22#1062301412yes—
625C22#1062302412yes—
626C22D4×Dic2211yescharacteristic
627C22#1062307012yes—
628C22#1062307411yescharacteristic
629C22D4×D4411yescharacteristic
630C22#1062308512yes—
631C22#1062308611yescharacteristic
632C22#1062313212yes—
633C22#1062314112yes—
634C22#1062315112yes—
635C22#1062315212yes—
636C22#1062320012yes—
637C22#1062320912yes—
638C22#1062324612yes—
639C22#1062325012yes—
640C22C22×C4⋊Dic1111yescharacteristic
641C22C2×D4×Dic1111yescharacteristic
642C22#1062332911yescharacteristic
643C22#1062332911yescharacteristic
644C22#1062332911yescharacteristic
645C22#41×Dic1111yescharacteristic
646C22#1062335811yescharacteristic
647C4—24no—
648C4—24no—
649C4—42no—
650C4—44no—
651C4—444no—
652C4—444no—
653C4—882no—
654C4—882no—
655C2—48no—
656C2#1307123011yescharacteristic
657C2#1307134211yescharacteristic
658C2#1307143111yescharacteristic
659C2D4×C4⋊Dic1111yescharacteristic
660C2#1307152611yescharacteristic
661C2#1307166811yescharacteristic
662C2#1307177311yescharacteristic
663C2#1307493612yes—
664C2#1307510912yes—
665C2#1307522712yes—
666C2#1307626512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14438
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622563C2semidirect
3. #13066869C2semidirect
4. #13066861C2semidirect
5. #13066861C2semidirect
6. #13066846C2semidirect
7. #13066843C2semidirect
8. #13066838C2semidirect
21. C11×#390C4semidirect
56. C2×C11×C4⋊C4C2×C4semidirect
61. C2×C11×C22⋊C4C2×C4semidirect
62. C2×C11×C22⋊C4C2×C4semidirect
64. C2×C42×C11C2×C4semidirect
89. C11⋊#95D4semidirect
111. C2×D4×C11C4⋊C4semidirect
296. #390Dic11semidirect
383. C2×C4⋊C4C2×Dic11semidirect
397. C2×C22⋊C4C2×Dic11semidirect
398. C2×C22⋊C4C2×Dic11semidirect
400. C2×C42C2×Dic11semidirect
443. C2×D4C4⋊Dic11semidirect
510. C11#14438semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
C2×#106225632
#130668692
#130668612
#130668462
#130668432
#130668382
C2×C11×#3902
#1443811