Finite Group Databasebeta

← #14685162

Subgroups — #14685162

Order 2816.

3654 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D11)⋊C4C211yesmaximal, characteristic
2C2×#10622844C212yesmaximal, complemented
3C2×#10622568C212yesmaximal
4#13066858C214yesmaximal, complemented
5#13066858C212yesmaximal, complemented
6#13066839C211yesmaximal, characteristic, complemented
7#13066838C212yesmaximal, complemented
8C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
9C25×D11C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic, complemented
11C24×C4×C11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C2×C11×C22⋊Q8—24no—
14C2×C11×C22⋊Q8—28no—
15C22×C11×C4⋊C4C2211yescharacteristic, complemented
16C22×C11×C4⋊C4C2212yescomplemented
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4—24no—
20C22×(C2×D11)⋊C4—28no—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2214yes—
23C22×(C2×D11)⋊C4C2214yes—
24C22×(C2×D11)⋊C4C2212yes—
25#10622844—28no—
26C2×C11⋊#95C2214yescomplemented
27C2×C11⋊#95C2212yescomplemented
28C2×C11⋊#95C2214yescomplemented
29C2×C11⋊#95C2212yescomplemented
30#10622568—28no—
31C25×C11C2311yescharacteristic
32C24×D11—22no—
33C24×D11—22no—
34C24×D11—24no—
35C24×D11—24no—
36C24×D11—24no—
37C24×D11—24no—
38C24×D11—42no—
39C24×D11—42no—
40C24×D11Q814yescomplemented
41C24×D11C2312yes—
42C22×Q8×C11—24no—
43C22×Q8×C11—22no—
44C22×Q8×C11—24no—
45C22×Q8×C11—42no—
46C23×C4×C11—24no—
47C23×C4×C11—24no—
48C23×C4×C11—42no—
49C23×C4×C11D414yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—22no—
55C23×Dic11—24no—
56C23×Dic11—24no—
57C23×Dic11—42no—
58C23×Dic11C2314yes—
59C23×Dic11C2312yes—
60C11×C22⋊Q8—232no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4D418yes—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×(C2×D11)⋊C4—232no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—44no—
83C2×(C2×D11)⋊C4—44no—
84C2×(C2×D11)⋊C4D418yes—
85C11⋊#95—24no—
86C11⋊#95—28no—
87C11⋊#95—44no—
88C11⋊#95—42no—
89#14717—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11C2×D414yes—
95C24×C11C2×D412yes—
96C24×C11C2×Q812yes—
97C24×C11#4112yes—
98C24×C11#4114yes—
99C24×C11C2411yescharacteristic
100C23×D11—28no—
101C23×D11—216no—
102C23×D11—28no—
103C23×D11—28no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—24no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—216no—
113C23×D11—216no—
114C23×D11—48no—
115C23×D11—416no—
116C23×D11—416no—
117C23×D11—416no—
118C23×D11—416no—
119C23×D11—44no—
120C23×D11—44no—
121C23×D11—48no—
122C23×D11—44no—
123C23×D11—48no—
124C23×D11—44no—
125C23×D11C2×D414yes—
126C23×D11C2×Q814yes—
127C23×D11#4114yes—
128C2×Q8×C11—28no—
129C2×Q8×C11—416no—
130C2×Q8×C11—44no—
131C2×Q8×C11—44no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—28no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—28no—
147C22×C4×C11—44no—
148C22×C4×C11—416no—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D412yes—
154C22×Dic11—28no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—416no—
167C22×Dic11—44no—
168C22×Dic11—44no—
169C22×Dic11C2×D414yes—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—216no—
172C11×C22⋊C4—216no—
173C22⋊Dic11—48no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—416no—
177(C2×D11)⋊C4—416no—
178C22×C22⋊Q8D1111yescharacteristic, complemented
179C23×C22⋊C4—111no—
180C2×#393—112no—
181C2×#379—112no—
182#1439—112no—
183#1439—114no—
184C22⋊#95—111no—
185C22⋊#95—112no—
186C23×C11—22no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—28no—
197C23×C11—28no—
198C23×C11#12014yes—
199C23×C11C22⋊Q814yes—
200C23×C11C22⋊Q818yes—
201C23×C11#12418yes—
202C23×C11#12414yes—
203C23×C11C22×D412yes—
204C23×C11C22×D411yescharacteristic
205C23×C11C22×D412yes—
206C23×C11C22×Q811yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11C2×#4112yes—
209C23×C11C2×#4112yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C11H(5,𝔽2)12yes—
212C22×D11—232no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—28no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—28no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—28no—
224C22×D11—28no—
225C22×D11—464no—
226C22×D11—416no—
227C22×D11—416no—
228C22×D11—416no—
229C22×D11—416no—
230C22×D11—416no—
231C22×D11—464no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—44no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—416no—
243C22×D11C22⋊Q818yescomplemented
244Q8×C11—416no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—28no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—28no—
254C2×C4×C11—28no—
255C2×C4×C11—416no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—44no—
261C2×C4×C11—44no—
262C2×C4×C11—44no—
263C2×C4×C11#12014yes—
264C2×Dic11—24no—
265C2×Dic11—28no—
266C2×Dic11—416no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C26—111no—
278C23×Q8C2×D1111yescharacteristic, complemented
279C24×C4—111no—
280C24×C4C2×D1111yescharacteristic
281C2×C22⋊Q8—24no—
282C2×C22⋊Q8—28no—
283C22×C4⋊C4C2×D1111yescharacteristic, complemented
284C22×C4⋊C4C2×D1112yescomplemented
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—114no—
289C22×C22⋊C4—114no—
290C22×C22⋊C4—228no—
291C22×C22⋊C4—224no—
292C22×C22⋊C4C2×D1112yes—
293#393—228no—
294#379—228no—
295C2×#95—114no—
296C2×#95—112no—
297C2×#95—114no—
298C2×#95—112no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—216no—
306C22×C11—216no—
307C22×C11#39318yescomplemented
308C22×C11C2×#12011yescharacteristic
309C22×C11C2×#12011yescharacteristic
310C22×C11C2×C22⋊Q811yescharacteristic
311C22×C11C2×C22⋊Q812yes—
312C22×C11C2×C22⋊Q812yes—
313C22×C11#52511yescharacteristic
314C22×C11#52512yes—
315C22×C11C2×#12411yescharacteristic
316C22×C11C2×#12412yes—
317C22×C11#53411yescharacteristic
318C22×C11#53511yescharacteristic
319C22×C11#53812yes—
320C22×C11#54312yes—
321C22×C11D4214yes—
322C22×C11#54614yes—
323C22×C11#54614yes—
324C22×C11#55114yes—
325C2×D11—28no—
326C2×D11—216no—
327C2×D11—464no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—48no—
335C2×D11—48no—
336C2×D11—48no—
337C4×C11—24no—
338C4×C11—42no—
339C4×C11—44no—
340C4×C11—44no—
341Dic11—44no—
342Dic11—84no—
343C25—112no—
344C25—114no—
345C25—224no—
346C25—224no—
347C25—222no—
348C25—222no—
349C25—224no—
350C25—224no—
351C25—442no—
352C25—442no—
353C25C22×D1111yescharacteristic
354C22×Q8—24no—
355C22×Q8—24no—
356C22×Q8—22no—
357C22×Q8—42no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—42no—
361C23×C4—112no—
362C23×C4—114no—
363C23×C4—224no—
364C23×C4—222no—
365C23×C4—224no—
366C23×C4—442no—
367C23×C4C22⋊D1114yes—
368C23×C4C22×D1112yes—
369C23×C4C22×D1112yes—
370C23×C4C22×D1111yescharacteristic
371C23×C4C22×D1111yescharacteristic
372C22⋊Q8—232no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—2232no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—228no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—228no—
393C2×C22⋊C4—228no—
394C2×C22⋊C4—444no—
395C2×C22⋊C4—444no—
396C2×C22⋊C4C22⋊D1118yes—
397#95—228no—
398#95—224no—
399#95—442no—
400#95—444no—
401C2×C11—28no—
402C2×C11C2×#39311yescharacteristic
403C2×C11#240311yescharacteristic
404C2×C11#240411yescharacteristic
405C2×C11#243511yescharacteristic
406C2×C11#243714yes—
407C2×C11#247214yes—
408C2×C11#256111yescharacteristic
409C2×C11#262611yescharacteristic
410C2×C11#284811yescharacteristic
411D11—48no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—114no—
417C24—114no—
418C24—114no—
419C24—2216no—
420C24—228no—
421C24—228no—
422C24—2216no—
423C24—228no—
424C24—222no—
425C24—224no—
426C24—222no—
427C24—224no—
428C24—222no—
429C24—224no—
430C24—222no—
431C24—224no—
432C24—2216no—
433C24—448no—
434C24—4416no—
435C24—4416no—
436C24—4416no—
437C24—4416no—
438C24—444no—
439C24—444no—
440C24—448no—
441C24—448no—
442C24—444no—
443C24—444no—
444C24Q8×D1112yes—
445C24#434312yes—
446C24#434314yes—
447C24C2×C22⋊D1112yes—
448C24C2×C22⋊D1114yes—
449C24C23×D1111yescharacteristic
450C2×Q8—28no—
451C2×Q8—416no—
452C2×Q8—44no—
453C2×Q8—44no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—28no—
469C22×C4—44no—
470C22×C4—416no—
471C22×C4—114no—
472C22×C4—228no—
473C22×C4—222no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—222no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—4416no—
485C22×C4—444no—
486C22×C4—444no—
487C22×C4D4×D1114yes—
488C22×C4C2×C22⋊D1114yes—
489C22×C4C2×C22⋊D1114yes—
490C22×C4C2×C22⋊D1112yes—
491C22×C4C2×C22⋊D1112yes—
492C4⋊C4—28no—
493C4⋊C4—216no—
494C22⋊C4—216no—
495C22⋊C4—2216no—
496C22⋊C4—2216no—
497C22⋊C4—4416no—
498C22⋊C4—4416no—
499C22⋊C4—448no—
500C11#1471711yescharacteristic, complemented, Sylow
501C23—22no—
502C23—28no—
503C23—22no—
504C23—22no—
505C23—28no—
506C23—22no—
507C23—24no—
508C23—24no—
509C23—28no—
510C23—24no—
511C23—28no—
512C23—24no—
513C23—118no—
514C23—2232no—
515C23—224no—
516C23—228no—
517C23—228no—
518C23—224no—
519C23—224no—
520C23—228no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—228no—
525C23—228no—
526C23—228no—
527C23—4464no—
528C23—4416no—
529C23—4416no—
530C23—4464no—
531C23—4416no—
532C23—4416no—
533C23—4416no—
534C23—444no—
535C23—442no—
536C23—444no—
537C23—442no—
538C23—4416no—
539C23—444no—
540C23—442no—
541C23—442no—
542C23—444no—
543C23—444no—
544C23—444no—
545C23#6699918yes—
546C23#6699914yes—
547C23#6700018yes—
548C23#6700014yes—
549C23#6700614yes—
550C23C2×D4×D1112yes—
551C23#6703712yes—
552C23C2×Q8×D1111yescharacteristic
553C23C2×#434311yescharacteristic
554C23C2×#434312yes—
555C23#41×D1112yes—
556C23#6704212yes—
557C23C22×C22⋊D1111yescharacteristic
558C23C22×C22⋊D1112yes—
559Q8—416no—
560C2×C4—28no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—28no—
565C2×C4—22no—
566C2×C4—28no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—416no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—42no—
578C2×C4—224no—
579C2×C4—228no—
580C2×C4—4416no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—444no—
584C2×C4—444no—
585C2×C4—444no—
586C2×C4—444no—
587C2×C4—444no—
588C2×C4—444no—
589C2×C4—444no—
590C2×C4—444no—
591C2×C4#6699014yes—
592C22—24no—
593C22—24no—
594C22—216no—
595C22—24no—
596C22—24no—
597C22—216no—
598C22—24no—
599C22—24no—
600C22—2216no—
601C22—228no—
602C22—4464no—
603C22—444no—
604C22—444no—
605C22—448no—
606C22—448no—
607C22—444no—
608C22—444no—
609C22—448no—
610C22—444no—
611C22—444no—
612C22#1062284418yescomplemented
613C22D11×C22⋊Q812yes—
614C22#1062315812yes—
615C22#1062316114yes—
616C22#1062316512yes—
617C22#1062316814yes—
618C22#1062317512yes—
619C22C2×#6699011yescharacteristic
620C22D4×C22⋊D1114yes—
621C22#1062333511yescharacteristic
622C22C2×#6699912yes—
623C22C2×#6699911yescharacteristic
624C22C2×#6700012yes—
625C22C2×#6700011yescharacteristic
626C22#1062335911yescharacteristic
627C22#1062336014yes—
628C22#1062336111yescharacteristic
629C22C2×#6700611yescharacteristic
630C4—24no—
631C4—42no—
632C4—44no—
633C4—44no—
634C4—444no—
635C4—884no—
636C2—28no—
637C2—448no—
638C2C2×#1062284411yescharacteristic
639C2#1307192611yescharacteristic
640C2#1307193111yescharacteristic
641C2#1307226811yescharacteristic
642C2#1307227914yes—
643C2#1307274914yes—
644C2#1307377511yescharacteristic
645C2#1307442311yescharacteristic
646C2#1307690011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC22×C11×C22⋊Q8C2
prime radicalC25×D11C22
hypercenterC22×C22⋊Q8D11
hypocenterC11#14717
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622844C2semidirect
4. #13066858C2semidirect
5. #13066858C2semidirect
6. #13066839C2semidirect
7. #13066838C2semidirect
8. C22×C11×C22⋊Q8C2semidirect
10. C23×Q8×C11C22semidirect
15. C22×C11×C4⋊C4C22semidirect
16. C22×C11×C4⋊C4C22semidirect
26. C2×C11⋊#95C22semidirect
27. C2×C11⋊#95C22semidirect
28. C2×C11⋊#95C22semidirect
29. C2×C11⋊#95C22semidirect
40. C24×D11Q8semidirect
178. C22×C22⋊Q8D11semidirect
243. C22×D11C22⋊Q8semidirect
278. C23×Q8C2×D11semidirect
283. C22×C4⋊C4C2×D11semidirect
284. C22×C4⋊C4C2×D11semidirect
307. C22×C11#393semidirect
500. C11#14717semidirect
612. C22#10622844semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D11)⋊C42
C2×#106228442
C2×#106225682
#130668582
#130668392
#130668382
C22×C11×C22⋊Q82
#1471711