Finite Group Databasebeta

← #14676494

Subgroups — #14676494

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C212yesmaximal
2C2×#10622825C211yesmaximal, characteristic, complemented
3C22×C11⋊#95C211yesmaximal, characteristic, complemented
4#13066869C212yesmaximal, complemented
5#13066861C212yesmaximal, complemented
6#13066843C212yesmaximal, complemented
7#13066839C212yesmaximal, complemented
8#13066838C212yesmaximal, complemented
9C22×C4×D4×C11C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2212yes—
14C2×C4×D4×C11—24no—
15C2×C4×D4×C11—24no—
16C2×C4×D4×C11C418yescomplemented
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2214yes—
23C22×C4⋊Dic11C2212yes—
24#10622833—28no—
25#10622825—24no—
26C2×C11⋊#95—24no—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2214yes—
33C25×C11C2311yescharacteristic
34C25×C11C2311yescharacteristic
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2×C414yes—
40C22×D4×C11D414yes—
41C22×D4×C11Q814yes—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—44no—
45C23×C4×C11—44no—
46C23×C4×C11C2×C414yes—
47C23×C4×C11C2×C414yescomplemented
48C23×C4×C11D414yes—
49C23×C4×C11D414yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11—24no—
56C23×Dic11—28no—
57C23×Dic11—24no—
58C23×Dic11—24no—
59C23×Dic11—44no—
60C23×Dic11C2314yes—
61C23×Dic11C2314yes—
62C4×D4×C11—232no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2×C414yescomplemented
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4C2×C414yes—
71C2×C11×C22⋊C4C2×C414yescomplemented
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11C2×C414yescomplemented
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11—44no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—44no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—28no—
87C11⋊#95—28no—
88C11⋊#95—44no—
89#13960—111nomaximal, Sylow
90C24×C11—24no—
91C24×C11—24no—
92C24×C11—21no—
93C24×C11—21no—
94C24×C11—24no—
95C24×C11—21no—
96C24×C11—21no—
97C24×C11—24no—
98C24×C11C22×C412yes—
99C24×C11C22×C412yes—
100C24×C11C2×D412yes—
101C24×C11C2×D412yes—
102C24×C11C2×D412yes—
103C24×C11C2×D412yes—
104C24×C11C2×Q812yes—
105C24×C11C2×Q812yes—
106C24×C11#4112yes—
107C24×C11#4112yes—
108C24×C11C2411yescharacteristic
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—28no—
112C2×D4×C11—28no—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11C4⋊C4116yescomplemented
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—28no—
129C22×C4×C11—48no—
130C22×C4×C11—48no—
131C22×C4×C11—48no—
132C22×C4×C11—48no—
133C22×C4×C11—48no—
134C22×C4×C11—48no—
135C22×C4×C11C22⋊C4116yescomplemented
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×Q812yes—
147C22×Dic11—216no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—416no—
162C22×Dic11—416no—
163C22×Dic11—48no—
164C22×Dic11—48no—
165C22×Dic11#4118yes—
166C11×C4⋊C4—28no—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—28no—
169C42×C11—28no—
170C22⋊Dic11—416no—
171C22⋊Dic11—48no—
172C4⋊Dic11—48no—
173C22×C4×D4D1111yescharacteristic
174C2×#386—112no—
175C2×#380—111no—
176C22×#95—111no—
177#1441—112no—
178#1439—112no—
179#1434—112no—
180C22⋊#95—112no—
181C22⋊#95—112no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—28no—
189C23×C11—28no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—28no—
201C23×C11—28no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11C2×C22⋊C414yes—
209C23×C11C2×C4⋊C414yes—
210C23×C11C2×C4⋊C414yes—
211C23×C11#11714yes—
212C23×C11#12114yes—
213C23×C11#12114yes—
214C23×C11C22⋊Q814yes—
215C23×C11C22⋊Q814yes—
216C23×C11C23×C411yescharacteristic
217C23×C11C22×D411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C22×D411yescharacteristic
220C23×C11C22×Q811yescharacteristic
221C23×C11C2×#4111yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C23×C11C2×#4114yes—
224C23×C11H(5,𝔽2)14yes—
225D4×C11—232no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—416no—
243C2×C4×C11—416no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11C2×C22⋊C414yes—
249C2×C4×C11C2×C22⋊C414yes—
250C2×C4×C11C2×C4⋊C414yes—
251C2×Dic11—28no—
252C2×Dic11—28no—
253C2×Dic11—28no—
254C2×Dic11—432no—
255C2×Dic11—44no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C2×Dic11—44no—
260C2×Dic11—44no—
261C2×Dic11—44no—
262C2×Dic11—44no—
263C2×Dic11—44no—
264C2×Dic11—44no—
265C2×Dic11—44no—
266C23×D4C2×D1111yescharacteristic
267C24×C4—112no—
268C24×C4C2×D1111yescharacteristic
269C24×C4C2×D1111yescharacteristic
270C2×C4×D4—24no—
271C2×C4×D4—24no—
272C2×C4×D4Dic1118yescomplemented
273C22×C4⋊C4—112no—
274C22×C4⋊C4C2×D1111yescharacteristic
275C22×C22⋊C4—112no—
276C22×C22⋊C4—114no—
277C22×C22⋊C4C2×D1111yescharacteristic
278C22×C22⋊C4C2×D1111yescharacteristic
279C22×C42C2×D1111yescharacteristic
280#386—228no—
281#380—224no—
282C2×#95—114no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—114no—
286C2×#95—112no—
287C2×#95—114no—
288C2×#95—224no—
289C22×C11—24no—
290C22×C11—28no—
291C22×C11—28no—
292C22×C11—28no—
293C22×C11—28no—
294C22×C11—28no—
295C22×C11—28no—
296C22×C11—24no—
297C22×C11—28no—
298C22×C11—24no—
299C22×C11—42no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11#38018yes—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11C22×C4⋊C411yescharacteristic
309C22×C11C2×#11711yescharacteristic
310C22×C11C4×#4112yes—
311C22×C11#51812yes—
312C22×C11C2×#12111yescharacteristic
313C22×C11C2×#12111yescharacteristic
314C22×C11C2×C22⋊Q811yescharacteristic
315C22×C11C2×C22⋊Q811yescharacteristic
316C22×C11#52512yes—
317C22×C11#53212yes—
318C22×C11#53412yes—
319C22×C11#53412yes—
320C22×C11#54614yes—
321C22×C11#55114yes—
322C22×C11#55314yes—
323C22×C11#55414yes—
324C4×C11—24no—
325C4×C11—24no—
326C4×C11—24no—
327C4×C11—42no—
328C4×C11—42no—
329Dic11—48no—
330Dic11—84no—
331C25C22×D1111yescharacteristic
332C25C22×D1111yescharacteristic
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4Dic2214yes—
338C22×D4D4414yes—
339C22×D4C2×Dic1114yes—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—44no—
343C23×C4—44no—
344C23×C4—114no—
345C23×C4—114no—
346C23×C4—228no—
347C23×C4—224no—
348C23×C4—224no—
349C23×C4—224no—
350C23×C4—444no—
351C23×C4C2×Dic1114yes—
352C23×C4C2×Dic1114yescomplemented
353C23×C4C22⋊D1114yes—
354C23×C4C22⋊D1114yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1111yescharacteristic
360C4×D4—232no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—444no—
365C2×C4⋊C4C2×Dic1114yescomplemented
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—228no—
371C2×C22⋊C4—228no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—444no—
376C2×C22⋊C4C2×Dic1114yes—
377C2×C22⋊C4C2×Dic1114yescomplemented
378C2×C42—22no—
379C2×C42—22no—
380C2×C42C2×Dic1114yescomplemented
381#95—228no—
382#95—228no—
383#95—224no—
384#95—224no—
385#95—224no—
386#95—444no—
387C2×C11—28no—
388C2×C11—44no—
389C2×C11C2×#38011yescharacteristic
390C2×C11#229711yescharacteristic
391C2×C11#230811yescharacteristic
392C2×C11#234912yes—
393C2×C11#235312yes—
394C2×C11#253412yes—
395C2×C11#254312yes—
396C2×C11#256412yes—
397C2×C11#257912yes—
398C24—24no—
399C24—24no—
400C24—21no—
401C24—21no—
402C24—24no—
403C24—24no—
404C24—21no—
405C24—21no—
406C24C2×Dic2212yes—
407C24C2×Dic2212yes—
408C24C2×D4412yes—
409C24C2×D4412yes—
410C24#433912yes—
411C24#433912yes—
412C24C22×Dic1112yes—
413C24C22×Dic1112yes—
414C24C2×C22⋊D1112yes—
415C24C2×C22⋊D1112yes—
416C24C23×D1111yescharacteristic
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4C4⋊Dic11116yescomplemented
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—28no—
437C22×C4—48no—
438C22×C4—48no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4—48no—
442C22×C4—48no—
443C22×C4—118no—
444C22×C4—2216no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—4416no—
459C22×C4—4416no—
460C22×C4—448no—
461C22×C4—448no—
462C22×C4C22⋊Dic11116yescomplemented
463C22×C4C2×Dic2212yes—
464C22×C4C2×D4412yes—
465C22×C4C22×Dic1112yes—
466C22×C4C22×Dic1112yes—
467C22×C4C22×Dic1112yes—
468C22×C4C22×Dic1112yes—
469C22×C4C22×Dic1112yes—
470C22×C4C2×C22⋊D1112yes—
471C22×C4C2×C22⋊D1112yes—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C2×C22⋊D1112yes—
474C4⋊C4—28no—
475C4⋊C4—448no—
476C22⋊C4—28no—
477C22⋊C4—28no—
478C22⋊C4—4416no—
479C22⋊C4—448no—
480C42—28no—
481C11#1396011yescharacteristic, complemented, Sylow
482C23—28no—
483C23—28no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—28no—
488C23—28no—
489C23—24no—
490C23—24no—
491C23—24no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—28no—
498C23—24no—
499C23—28no—
500C23—24no—
501C23—22no—
502C23—44no—
503C23—42no—
504C23—42no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23#6697714yes—
509C23#6697714yes—
510C23C2×C4⋊Dic1114yes—
511C23C2×C4⋊Dic1114yes—
512C23#6697914yes—
513C23#6698314yes—
514C23#6698314yes—
515C23C2×C22⋊Dic1114yes—
516C23C22×Dic2211yescharacteristic
517C23C22×D4411yescharacteristic
518C23C2×#433911yescharacteristic
519C23C2×#433911yescharacteristic
520C23#6703714yes—
521C23#41×D1114yes—
522C23C23×Dic1111yescharacteristic
523C23C22×C22⋊D1111yescharacteristic
524C23C22×C22⋊D1111yescharacteristic
525D4—232no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—416no—
543C2×C4—416no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—228no—
549C2×C4—228no—
550C2×C4—228no—
551C2×C4—4432no—
552C2×C4—444no—
553C2×C4—444no—
554C2×C4—444no—
555C2×C4—444no—
556C2×C4—444no—
557C2×C4—444no—
558C2×C4—444no—
559C2×C4—444no—
560C2×C4—444no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4C2×C4⋊Dic1114yes—
564C2×C4C2×C22⋊Dic1114yes—
565C2×C4C2×C22⋊Dic1114yes—
566C22—24no—
567C22—28no—
568C22—24no—
569C22—28no—
570C22—28no—
571C22—28no—
572C22—28no—
573C22—28no—
574C22—24no—
575C22—28no—
576C22—42no—
577C22—44no—
578C22—42no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22#1062282518yes—
584C22#1062307014yes—
585C22#1062307114yes—
586C22#1062308514yes—
587C22#1062308714yes—
588C22C2×#6697711yescharacteristic
589C22C2×#6697711yescharacteristic
590C22C22×C4⋊Dic1111yescharacteristic
591C22C2×#6697911yescharacteristic
592C22C2×#6698311yescharacteristic
593C22C2×#6698311yescharacteristic
594C22#1062332912yes—
595C22#1062333512yes—
596C22#1062333512yes—
597C22#41×Dic1112yes—
598C22#1062335912yes—
599C22#1062336312yes—
600C22C22×C22⋊Dic1111yescharacteristic
601C4—24no—
602C4—24no—
603C4—24no—
604C4—42no—
605C4—42no—
606C4—448no—
607C4—884no—
608C2—28no—
609C2—44no—
610C2C2×#1062282511yescharacteristic
611C2#1307110711yescharacteristic
612C2#1307119411yescharacteristic
613C2#1307152612yes—
614C2#1307155612yes—
615C2#1307350212yes—
616C2#1307357212yes—
617C2#1307379212yes—
618C2#1307395912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#13960
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#10622825C2semidirect
3. C22×C11⋊#95C2semidirect
4. #13066869C2semidirect
5. #13066861C2semidirect
6. #13066843C2semidirect
7. #13066839C2semidirect
8. #13066838C2semidirect
16. C2×C4×D4×C11C4semidirect
47. C23×C4×C11C2×C4semidirect
65. C2×C11×C4⋊C4C2×C4semidirect
71. C2×C11×C22⋊C4C2×C4semidirect
74. C2×C42×C11C2×C4semidirect
115. C2×D4×C11C4⋊C4semidirect
135. C22×C4×C11C22⋊C4semidirect
272. C2×C4×D4Dic11semidirect
352. C23×C4C2×Dic11semidirect
365. C2×C4⋊C4C2×Dic11semidirect
377. C2×C22⋊C4C2×Dic11semidirect
380. C2×C42C2×Dic11semidirect
423. C2×D4C4⋊Dic11semidirect
462. C22×C4C22⋊Dic11semidirect
481. C11#13960semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
C2×#106228252
C22×C11⋊#952
#130668692
#130668612
#130668432
#130668392
#130668382
C22×C4×D4×C112
#1396011