Finite Group Databasebeta

← #14677258

Subgroups — #14677258

Order 2816.

2358 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622843C211yesmaximal, characteristic, complemented
3C2×#10622834C211yesmaximal, characteristic
4C2×#10622834C211yesmaximal, characteristic
5#13066861C214yesmaximal, complemented
6#13066853C214yesmaximal, complemented
7#13066846C211yesmaximal, characteristic, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C22×C11×#124C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C2×C11×#124—24no—
13C2×C11×#124—24no—
14C2×C11×#124C418yescomplemented
15C22×C11×C22⋊C4C2214yes—
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2214yes—
19C22×C22⋊Dic11C2212yes—
20C2×Q8×Dic11—24no—
21C2×Q8×Dic11—24no—
22C2×Q8×Dic11—24no—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29#10622843—24no—
30#10622834—24no—
31#10622834—24no—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2214yes—
35C2×C11⋊#95C2214yes—
36C25×C11C2312yes—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11C2×C414yes—
42C22×Q8×C11D414yes—
43C22×Q8×C11D414yes—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11C2×C414yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2312yes—
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C11×#124—232no—
60C2×C11×C22⋊C4—28no—
61C2×C11×C22⋊C4—28no—
62C2×C11×C22⋊C4C2×C4116yes—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C42×C11C2×C414yes—
66C2×C22⋊Dic11—28no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—28no—
70C2×C22⋊Dic11—28no—
71C2×C22⋊Dic11—44no—
72C2×C22⋊Dic11—44no—
73Q8×Dic11—232no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—24no—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11D414yes—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—24no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11D414yes—
92C11⋊#95—28no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—44no—
96#14026—111nomaximal, Sylow
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—24no—
102C24×C11—24no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—24no—
106C24×C11—24no—
107C24×C11C22×C414yes—
108C24×C11C2411yescharacteristic
109C2×Q8×C11—28no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—28no—
113C2×Q8×C11—28no—
114C2×Q8×C11—28no—
115C2×Q8×C11C22⋊C4116yescomplemented
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—28no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
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×C414yes—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4112yes—
143C22×C4×C11#4112yes—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—24no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11C2×D414yes—
167C22×Dic11C2×D412yes—
168C22×Dic11C2×D412yes—
169C22×Dic11#4114yes—
170C22×Dic11#4114yes—
171C11×C22⋊C4—232no—
172C42×C11—28no—
173C22⋊Dic11—416no—
174C22⋊Dic11—48no—
175C22⋊Dic11—48no—
176C4⋊Dic11—216no—
177C4⋊Dic11—28no—
178C4⋊Dic11—44no—
179C4×Dic11—216no—
180C4×Dic11—28no—
181C4×Dic11—44no—
182C22×#124D1111yescharacteristic
183C22×C4×Q8—111no—
184C2×#391—111no—
185C2×#390—111no—
186C2×#390—111no—
187#1439—114no—
188#1437—114no—
189C4⋊#95—111no—
190C4×#95—111no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—44no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—44no—
209C23×C11—44no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11C23×C411yescharacteristic
215C23×C11C22×D411yescharacteristic
216C23×C11C22×D411yescharacteristic
217C23×C11C22×D411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C2×#4111yescharacteristic
220C23×C11C2×#4111yescharacteristic
221C23×C11C2×#4112yes—
222C23×C11C2×#4112yes—
223C23×C11H(5,𝔽2)12yes—
224C23×C112−1+412yes—
225Q8×C11—232no—
226D4×C11—416no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11C2×C22⋊C418yes—
241C2×C4×C11C2×C22⋊C414yes—
242C2×C4×C11C4×D414yes—
243C2×C4×C11C4×D414yes—
244C2×C4×C11#12014yes—
245C2×C4×C11#12114yes—
246C2×C4×C11#12114yes—
247C2×C4×C11#12314yes—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—28no—
259C2×Dic11—24no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—44no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11#12414yescomplemented
275C23×Q8C2×D1111yescharacteristic
276C23×D4C2×D1111yescharacteristic
277C2×#124—24no—
278C2×#124—24no—
279C2×#124Dic1118yescomplemented
280C2×C4×Q8—224no—
281C2×C4×Q8—224no—
282C2×C4×Q8—224no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4—111no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—114no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4C2×D1114yes—
290C22×C42—111no—
291C22×C42—112no—
292C22×C42—111no—
293C22×C42C2×D1111yescharacteristic
294#391—224no—
295#390—224no—
296#390—224no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—114no—
300C2×#95—114no—
301C22×C11—44no—
302C22×C11—48no—
303C22×C11—48no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—84no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—84no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11C22×C22⋊C411yescharacteristic
313C22×C11C2×C4×D411yescharacteristic
314C22×C11C2×C4×D411yescharacteristic
315C22×C11C4×#4112yes—
316C22×C11#52012yes—
317C22×C11C2×#12011yescharacteristic
318C22×C11C2×#12111yescharacteristic
319C22×C11C2×#12111yescharacteristic
320C22×C11C2×#12311yescharacteristic
321C22×C11C2×#12411yescharacteristic
322C22×C11#52912yes—
323C22×C11#53211yescharacteristic
324C22×C11#53511yescharacteristic
325C22×C11#53611yescharacteristic
326C22×C11#54212yes—
327C22×C11#54612yes—
328C22×C11#54812yes—
329C22×C11#54812yes—
330C22×C11#54812yes—
331C22×C11#55012yes—
332C22×C11#55012yes—
333C22×C11#55612yes—
334C22×C11#55912yes—
335C4×C11—28no—
336C4×C11—44no—
337C4×C11#38618yes—
338Dic11—24no—
339Dic11—44no—
340Dic11—42no—
341Dic11—44no—
342Dic11—82no—
343C25C22×D1112yes—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8C2×Dic1114yes—
349C22×Q8C22⋊D1114yes—
350C22×Q8C22⋊D1114yes—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4C2×Dic1114yes—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—112no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4C22×D1112yes—
364C23×C4C22×D1112yes—
365C23×C4C22×D1111yescharacteristic
366#124—232no—
367C4×Q8—2232no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—228no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—228no—
383C2×C22⋊C4—228no—
384C2×C22⋊C4—444no—
385C2×C22⋊C4—444no—
386C2×C22⋊C4C2×Dic11116yes—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—114no—
390C2×C42—224no—
391C2×C42—224no—
392C2×C42—222no—
393C2×C42—224no—
394C2×C42—222no—
395C2×C42—222no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42C2×Dic1114yes—
399#95—224no—
400#95—224no—
401#95—228no—
402#95—444no—
403C2×C11—84no—
404C2×C11C2×#38611yescharacteristic
405C2×C11C4×#12411yescharacteristic
406C2×C11#232611yescharacteristic
407C2×C11#234112yes—
408C2×C11#236712yes—
409C2×C11#242612yes—
410C2×C11#243111yescharacteristic
411C2×C11#243611yescharacteristic
412C2×C11#244812yes—
413C2×C11#254511yescharacteristic
414C2×C11#254811yescharacteristic
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—22no—
425C24C22×Dic1114yes—
426C24C23×D1111yescharacteristic
427C2×Q8—28no—
428C2×Q8—28no—
429C2×Q8—28no—
430C2×Q8—28no—
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8C22⋊Dic11116yescomplemented
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—28no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—112no—
452C22×C4—114no—
453C22×C4—112no—
454C22×C4—114no—
455C22×C4—114no—
456C22×C4—221no—
457C22×C4—222no—
458C22×C4—221no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—221no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—221no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—222no—
478C22×C4D4×D1112yes—
479C22×C4D4×D1112yes—
480C22×C4#434112yes—
481C22×C4#434112yes—
482C22×C4C22×Dic1114yes—
483C22×C4C22×Dic1114yes—
484C22×C4C22×Dic1112yes—
485C22×C4C2×C22⋊D1114yes—
486C22×C4C2×C22⋊D1114yes—
487C22×C4C2×C22⋊D1112yes—
488C22×C4C2×C22⋊D1112yes—
489C4⋊C4—2216no—
490C4⋊C4—228no—
491C4⋊C4—444no—
492C22⋊C4—232no—
493C22⋊C4—448no—
494C22⋊C4—4416no—
495C22⋊C4—448no—
496C42—28no—
497C42—2216no—
498C42—228no—
499C42—444no—
500C11#1402611yescharacteristic, complemented, Sylow
501C23—24no—
502C23—24no—
503C23—28no—
504C23—28no—
505C23—24no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—44no—
511C23—44no—
512C23—44no—
513C23—44no—
514C23—42no—
515C23—44no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23C2×D4×D1111yescharacteristic
525C23C2×D4×D1111yescharacteristic
526C23C2×#434111yescharacteristic
527C23C2×#434111yescharacteristic
528C23#41×D1112yes—
529C23#41×D1112yes—
530C23#6704212yes—
531C23#6704312yes—
532C23C23×Dic1111yescharacteristic
533C23C22×C22⋊D1111yescharacteristic
534C23C22×C22⋊D1111yescharacteristic
535Q8—232no—
536D4—416no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—114no—
551C2×C4—222no—
552C2×C4—224no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—228no—
562C2×C4—224no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—444no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—444no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—444no—
577C2×C4D4×Dic1114yes—
578C2×C4D4×Dic1114yes—
579C2×C4#6698814yes—
580C2×C4#6699014yes—
581C2×C4#6699214yes—
582C2×C4#6699214yes—
583C2×C4C2×C22⋊Dic1118yes—
584C2×C4C2×C22⋊Dic1114yes—
585C22—44no—
586C22—48no—
587C22—48no—
588C22—44no—
589C22—44no—
590C22—84no—
591C22—84no—
592C22—82no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22#1062319911yescharacteristic
597C22#1062320212yes—
598C22D11×#12411yescharacteristic
599C22#1062320511yescharacteristic
600C22#1062320611yescharacteristic
601C22#1062320712yes—
602C22#1062320812yes—
603C22#1062321112yes—
604C22#1062321212yes—
605C22#1062321312yes—
606C22C2×D4×Dic1111yescharacteristic
607C22C2×D4×Dic1111yescharacteristic
608C22C2×#6698811yescharacteristic
609C22C2×#6699011yescharacteristic
610C22C2×#6699211yescharacteristic
611C22C2×#6699211yescharacteristic
612C22#41×Dic1112yes—
613C22#1062335812yes—
614C22#1062336212yes—
615C22#1062336212yes—
616C22#1062336512yes—
617C22#1062336512yes—
618C22C22×C22⋊Dic1111yescharacteristic
619C4—28no—
620C4—44no—
621C4—224no—
622C4—444no—
623C4—442no—
624C4—444no—
625C4—882no—
626C4#1062283318yes—
627C2—84no—
628C2C2×#1062283311yescharacteristic
629C2#124×Dic1111yescharacteristic
630C2#1307132911yescharacteristic
631C2#1307145712yes—
632C2#1307169112yes—
633C2#1307218512yes—
634C2#1307223811yescharacteristic
635C2#1307227111yescharacteristic
636C2#1307241012yes—
637C2#1307359511yescharacteristic
638C2#1307361611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#124C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#124D11
hypocenterC11#14026
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic11C2semidirect
2. C2×#10622843C2semidirect
5. #13066861C2semidirect
6. #13066853C2semidirect
7. #13066846C2semidirect
8. C4×C11⋊#95C2semidirect
14. C2×C11×#124C4semidirect
115. C2×Q8×C11C22⋊C4semidirect
274. C2×Dic11#124semidirect
279. C2×#124Dic11semidirect
433. C2×Q8C22⋊Dic11semidirect
500. C11#14026semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×#106228432
C2×#106228342
#130668612
#130668532
#130668462
C4×C11⋊#952
C22×C11×#1242
#1402611