Finite Group Databasebeta

← #14676887

Subgroups — #14676887

Order 2816.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Dic11C211yesmaximal, characteristic, complemented
2C2×#10622834C212yesmaximal, complemented
3C2×#10622833C211yesmaximal, characteristic, complemented
4C2×#10622833C211yesmaximal, characteristic, complemented
5C2×#10622563C211yesmaximal, characteristic, complemented
6C2×#10622860C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
8#13066861C212yesmaximal, complemented
9#13066857C212yesmaximal, complemented
10#13066853C212yesmaximal, complemented
11C22×C11×#120C211yesmaximal, characteristic
12C26×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C2×C11×#120—24no—
18C2×C11×#120—24no—
19C2×C11×#120C418yescomplemented
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11—24no—
23C22×C22⋊Dic11—28no—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2212yes—
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2212yes—
30C22×C22⋊Dic11C2211yescharacteristic, complemented
31C22×C22⋊Dic11C2212yescomplemented
32C22×C22⋊Dic11C2211yescharacteristic, complemented
33C22×C4⋊Dic11C2212yescomplemented
34C22×C4×Dic11C2212yescomplemented
35#10622860—24no—
36#10622834—28no—
37#10622833—24no—
38#10622833—24no—
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2211yescharacteristic, complemented
41C2×C11⋊#95C2212yescomplemented
42C2×C11⋊#95C2212yescomplemented
43C2×C11⋊#95C2211yescharacteristic, complemented
44#10622563—24no—
45C22⋊C4×Dic11—24no—
46C25×C11—24no—
47C25×C11—22no—
48C25×C11—24no—
49C25×C11—22no—
50C25×C11—22no—
51C25×C11—22no—
52C25×C11—22no—
53C25×C11—22no—
54C25×C11—42no—
55C25×C11—42no—
56C25×C11C2×C414yes—
57C25×C11C2311yescharacteristic
58C25×C11C2312yes—
59C25×C11C2311yescharacteristic
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—24no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—24no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—24no—
69C22×D4×C11—24no—
70C22×D4×C11—42no—
71C22×D4×C11—42no—
72C22×D4×C11C2×C414yes—
73C22×D4×C11C2×C418yescomplemented
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2312yes—
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11—24no—
80C23×Dic11—24no—
81C23×Dic11—22no—
82C23×Dic11—22no—
83C23×Dic11—42no—
84C23×Dic11—42no—
85C23×Dic11D414yescomplemented
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2312yes—
89C23×Dic11C2312yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C11×#120—232no—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4C2×C414yes—
96C2×C11×C22⋊C4C2×C418yescomplemented
97C2×C11×C22⋊C4D414yes—
98C2×C11×C22⋊C4D414yes—
99C2×C22⋊Dic11—232no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—24no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—42no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11—42no—
122C2×C22⋊Dic11—42no—
123C2×C22⋊Dic11D414yescomplemented
124C2×C22⋊Dic11D418yescomplemented
125C2×C4⋊Dic11—24no—
126C2×C4⋊Dic11—24no—
127C2×C4⋊Dic11—42no—
128C2×C4×Dic11—24no—
129C2×C4×Dic11—24no—
130C2×C4×Dic11—42no—
131C11⋊#95—24no—
132C11⋊#95—24no—
133C11⋊#95—24no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136#13995—111nomaximal, Sylow
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—28no—
142C24×C11—28no—
143C24×C11—216no—
144C24×C11—216no—
145C24×C11—28no—
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—22no—
150C24×C11—22no—
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—28no—
159C24×C11—28no—
160C24×C11—21no—
161C24×C11—22no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—48no—
171C24×C11—48no—
172C24×C11—48no—
173C24×C11—48no—
174C24×C11—48no—
175C24×C11—48no—
176C24×C11—48no—
177C24×C11—48no—
178C24×C11—48no—
179C24×C11—44no—
180C24×C11—44no—
181C24×C11—48no—
182C24×C11—44no—
183C24×C11—44no—
184C24×C11—44no—
185C24×C11—44no—
186C24×C11C22×C412yes—
187C24×C11C22×C414yes—
188C24×C11C22×C412yes—
189C24×C11C2×D414yes—
190C24×C11C2×D412yes—
191C24×C11C2×D412yes—
192C24×C11C2×D412yes—
193C24×C11C2×D412yes—
194C24×C11#4114yes—
195C24×C11#4112yes—
196C24×C11#4112yes—
197C24×C11C2411yescharacteristic
198C2×D4×C11—28no—
199C2×D4×C11—28no—
200C2×D4×C11—28no—
201C2×D4×C11—216no—
202C2×D4×C11—216no—
203C2×D4×C11—48no—
204C2×D4×C11—48no—
205C2×D4×C11—48no—
206C2×D4×C11—48no—
207C2×D4×C11—48no—
208C2×D4×C11—44no—
209C2×D4×C11—44no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C22×C414yes—
224C22×C4×C11C2×D414yes—
225C22×C4×C11C2×D414yes—
226C22×Dic11—28no—
227C22×Dic11—28no—
228C22×Dic11—28no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—22no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—21no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—44no—
259C22×Dic11—48no—
260C22×Dic11—48no—
261C22×Dic11—48no—
262C22×Dic11—48no—
263C22×Dic11—44no—
264C22×Dic11—44no—
265C22×Dic11C2×D414yes—
266C22×Dic11C2×D412yes—
267C22×Dic11C2×D414yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×D414yes—
270C11×C22⋊C4—216no—
271C11×C22⋊C4C22⋊C4116yescomplemented
272C22⋊Dic11—216no—
273C22⋊Dic11—216no—
274C22⋊Dic11—28no—
275C22⋊Dic11—48no—
276C22⋊Dic11—48no—
277C22⋊Dic11—48no—
278C22⋊Dic11—44no—
279C22⋊Dic11—44no—
280C22⋊Dic11—44no—
281C4⋊Dic11—48no—
282C4×Dic11—48no—
283C22×#120D1111yescharacteristic
284C23×C22⋊C4—111no—
285C2×#390—112no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#385—111no—
289C2×#379—111no—
290C2×C4×C22⋊C4—111no—
291#1439—112no—
292#1438—112no—
293#1437—112no—
294C23×C11—24no—
295C23×C11—24no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—24no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—24no—
302C23×C11—24no—
303C23×C11—24no—
304C23×C11—24no—
305C23×C11—24no—
306C23×C11—24no—
307C23×C11—24no—
308C23×C11—24no—
309C23×C11—24no—
310C23×C11—232no—
311C23×C11—24no—
312C23×C11—24no—
313C23×C11—24no—
314C23×C11—24no—
315C23×C11—24no—
316C23×C11—24no—
317C23×C11—24no—
318C23×C11—24no—
319C23×C11—24no—
320C23×C11—24no—
321C23×C11—24no—
322C23×C11—24no—
323C23×C11—24no—
324C23×C11—24no—
325C23×C11—24no—
326C23×C11—24no—
327C23×C11—24no—
328C23×C11—24no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—24no—
332C23×C11—22no—
333C23×C11—24no—
334C23×C11—432no—
335C23×C11—432no—
336C23×C11—416no—
337C23×C11—416no—
338C23×C11—416no—
339C23×C11—432no—
340C23×C11—416no—
341C23×C11—432no—
342C23×C11—416no—
343C23×C11—42no—
344C23×C11—42no—
345C23×C11—42no—
346C23×C11—42no—
347C23×C11—42no—
348C23×C11—42no—
349C23×C11—42no—
350C23×C11—42no—
351C23×C11—42no—
352C23×C11—42no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11—42no—
359C23×C11—416no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—42no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—42no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11—42no—
373C23×C11—42no—
374C23×C11—42no—
375C23×C11—42no—
376C23×C11—42no—
377C23×C11—42no—
378C23×C11C2×C22⋊C414yes—
379C23×C11C4×D418yes—
380C23×C11C4×D414yes—
381C23×C11C4×D414yes—
382C23×C11#12114yes—
383C23×C11#12114yes—
384C23×C11#12414yes—
385C23×C11#12714yes—
386C23×C11C23×C411yescharacteristic
387C23×C11C22×D411yescharacteristic
388C23×C11C22×D412yes—
389C23×C11C22×D411yescharacteristic
390C23×C11C22×D411yescharacteristic
391C23×C11C22×D411yescharacteristic
392C23×C11C2×#4111yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11C2×#4112yes—
395C23×C11H(5,𝔽2)12yes—
396C23×C11H(5,𝔽2)12yes—
397D4×C11—432no—
398D4×C11—416no—
399C2×C4×C11—24no—
400C2×C4×C11—24no—
401C2×C4×C11—24no—
402C2×C4×C11—24no—
403C2×C4×C11—24no—
404C2×C4×C11—24no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11C2×C22⋊C418yescomplemented
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—24no—
416C2×Dic11—24no—
417C2×Dic11—22no—
418C2×Dic11—24no—
419C2×Dic11—24no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—24no—
423C2×Dic11—24no—
424C2×Dic11—24no—
425C2×Dic11—24no—
426C2×Dic11—416no—
427C2×Dic11—416no—
428C2×Dic11—42no—
429C2×Dic11—42no—
430C2×Dic11—42no—
431C2×Dic11—42no—
432C2×Dic11—42no—
433C2×Dic11—42no—
434C2×Dic11—42no—
435C2×Dic11—42no—
436C2×Dic11—42no—
437C2×Dic11—42no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—42no—
445C2×Dic11—42no—
446C2×Dic11—42no—
447C2×Dic11—42no—
448C2×Dic11#12014yescomplemented
449C26C2×D1111yescharacteristic
450C23×D4C2×D1111yescharacteristic
451C23×D4C2×D1112yes—
452C24×C4—111no—
453C24×C4—111no—
454C2×#120—24no—
455C2×#120—24no—
456C2×#120Dic1118yescomplemented
457C22×C4⋊C4—112no—
458C22×C22⋊C4—112no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—112no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—112no—
464C22×C22⋊C4—112no—
465C22×C22⋊C4—112no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—228no—
468C22×C22⋊C4—224no—
469C22×C22⋊C4C2×D1112yes—
470C22×C22⋊C4C2×D1111yescharacteristic
471C22×C42—112no—
472#390—228no—
473#386—224no—
474#386—224no—
475#385—224no—
476#379—224no—
477C4×C22⋊C4—224no—
478C2×#95—111no—
479C2×#95—112no—
480C2×#95—112no—
481C2×#95—112no—
482C2×#95—111no—
483C22×C11—24no—
484C22×C11—28no—
485C22×C11—28no—
486C22×C11—24no—
487C22×C11—24no—
488C22×C11—28no—
489C22×C11—24no—
490C22×C11—28no—
491C22×C11—24no—
492C22×C11—24no—
493C22×C11—28no—
494C22×C11—28no—
495C22×C11—28no—
496C22×C11—464no—
497C22×C11—44no—
498C22×C11—44no—
499C22×C11—44no—
500C22×C11—44no—
501C22×C11—44no—
502C22×C11—44no—
503C22×C11—44no—
504C22×C11—44no—
505C22×C11—44no—
506C22×C11—44no—
507C22×C11—44no—
508C22×C11—44no—
509C22×C11—42no—
510C22×C11—44no—
511C22×C11—44no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—81no—
515C22×C11—81no—
516C22×C11—82no—
517C22×C11—81no—
518C22×C11—82no—
519C22×C11—81no—
520C22×C11#39018yescomplemented
521C22×C11C22×C22⋊C411yescharacteristic
522C22×C11C2×C4×D411yescharacteristic
523C22×C11C2×C4×D412yes—
524C22×C11C2×C4×D411yescharacteristic
525C22×C11#51812yes—
526C22×C11C2×#12011yescharacteristic
527C22×C11C2×#12111yescharacteristic
528C22×C11C2×#12111yescharacteristic
529C22×C11#52511yescharacteristic
530C22×C11#52512yes—
531C22×C11C2×#12411yescharacteristic
532C22×C11C2×#12711yescharacteristic
533C22×C11#53411yescharacteristic
534C22×C11#53511yescharacteristic
535C22×C11#53812yes—
536C22×C11D4212yes—
537C22×C11D4212yes—
538C22×C11D4212yes—
539C22×C11#54612yes—
540C22×C11#54612yes—
541C22×C11#54612yes—
542C22×C11#54612yes—
543C22×C11#55112yes—
544C4×C11—28no—
545C4×C11—42no—
546Dic11—24no—
547Dic11—42no—
548Dic11—44no—
549Dic11—44no—
550Dic11—81no—
551Dic11—81no—
552C25—24no—
553C25—22no—
554C25—24no—
555C25—22no—
556C25—22no—
557C25—22no—
558C25—22no—
559C25—22no—
560C25—42no—
561C25—42no—
562C25C2×Dic1114yes—
563C25C22×D1111yescharacteristic
564C25C22×D1112yes—
565C25C22×D1111yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—24no—
569C22×D4—24no—
570C22×D4—22no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—24no—
575C22×D4—24no—
576C22×D4—42no—
577C22×D4—42no—
578C22×D4C2×Dic1114yes—
579C22×D4C2×Dic1118yescomplemented
580C23×C4—111no—
581C23×C4—112no—
582C23×C4—112no—
583C23×C4—111no—
584C23×C4—114no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—224no—
588C23×C4—224no—
589C23×C4—222no—
590C23×C4—222no—
591C23×C4—222no—
592C23×C4—222no—
593C23×C4—222no—
594C23×C4—442no—
595C23×C4—442no—
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1112yes—
598#120—232no—
599C2×C4⋊C4—224no—
600C2×C4⋊C4—224no—
601C2×C4⋊C4—442no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—118no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4—224no—
609C2×C22⋊C4—224no—
610C2×C22⋊C4—2232no—
611C2×C22⋊C4—224no—
612C2×C22⋊C4—222no—
613C2×C22⋊C4—222no—
614C2×C22⋊C4—224no—
615C2×C22⋊C4—224no—
616C2×C22⋊C4—222no—
617C2×C22⋊C4—224no—
618C2×C22⋊C4—222no—
619C2×C22⋊C4—224no—
620C2×C22⋊C4—224no—
621C2×C22⋊C4—222no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—224no—
624C2×C22⋊C4—224no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—442no—
627C2×C22⋊C4—442no—
628C2×C22⋊C4—442no—
629C2×C22⋊C4—442no—
630C2×C22⋊C4C2×Dic1114yes—
631C2×C22⋊C4C2×Dic1118yescomplemented
632C2×C22⋊C4C22⋊D1114yes—
633C2×C22⋊C4C22⋊D1114yes—
634C2×C42—224no—
635C2×C42—224no—
636C2×C42—442no—
637#95—222no—
638#95—224no—
639#95—222no—
640#95—224no—
641#95—224no—
642C2×C11—28no—
643C2×C11—48no—
644C2×C11—82no—
645C2×C11C2×#39011yescharacteristic
646C2×C11C4×#12011yescharacteristic
647C2×C11#232111yescharacteristic
648C2×C11D4×C22⋊C412yes—
649C2×C11#235812yes—
650C2×C11#241011yescharacteristic
651C2×C11#241111yescharacteristic
652C2×C11#242412yes—
653C2×C11#243311yescharacteristic
654C2×C11#247212yes—
655C2×C11#253911yescharacteristic
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—28no—
661C24—28no—
662C24—216no—
663C24—216no—
664C24—28no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—28no—
678C24—28no—
679C24—21no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—21no—
688C24—21no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—44no—
699C24—44no—
700C24—48no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24D4×D1114yes—
706C24D4×D1112yes—
707C24D4×D1112yes—
708C24#434114yes—
709C24#434112yes—
710C24#434112yes—
711C24C22×Dic1112yes—
712C24C22×Dic1114yes—
713C24C22×Dic1112yes—
714C24C2×C22⋊D1112yes—
715C24C2×C22⋊D1112yes—
716C24C23×D1111yescharacteristic
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—216no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—112no—
742C22×C4—114no—
743C22×C4—114no—
744C22×C4—112no—
745C22×C4—114no—
746C22×C4—228no—
747C22×C4—221no—
748C22×C4—222no—
749C22×C4—221no—
750C22×C4—228no—
751C22×C4—228no—
752C22×C4—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—221no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—221no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—444no—
779C22×C4—448no—
780C22×C4—448no—
781C22×C4—448no—
782C22×C4—448no—
783C22×C4—444no—
784C22×C4—444no—
785C22×C4C22×Dic1112yes—
786C22×C4C22×Dic1114yes—
787C22×C4C2×C22⋊D1114yes—
788C22×C4C2×C22⋊D1114yes—
789C4⋊C4—448no—
790C22⋊C4—216no—
791C22⋊C4—2216no—
792C22⋊C4—2216no—
793C22⋊C4—228no—
794C22⋊C4—444no—
795C22⋊C4—448no—
796C22⋊C4—448no—
797C22⋊C4—448no—
798C22⋊C4—444no—
799C22⋊C4—444no—
800C22⋊C4C22⋊Dic11116yescomplemented
801C42—448no—
802C11#1399511yescharacteristic, complemented, Sylow
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—22no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—22no—
843C23—432no—
844C23—432no—
845C23—432no—
846C23—432no—
847C23—416no—
848C23—416no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—41no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—41no—
879C23—42no—
880C23—41no—
881C23—41no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—41no—
886C23—42no—
887C23D4×Dic1118yes—
888C23D4×Dic1114yes—
889C23D4×Dic1114yes—
890C23#6698914yes—
891C23#6699114yes—
892C23#6699114yes—
893C23#6699314yes—
894C23C2×C22⋊Dic1114yes—
895C23C2×D4×D1111yescharacteristic
896C23C2×D4×D1111yescharacteristic
897C23C2×D4×D1112yes—
898C23C2×#434111yescharacteristic
899C23C2×#434111yescharacteristic
900C23C2×#434112yes—
901C23#6703712yes—
902C23#6703712yes—
903C23C23×Dic1111yescharacteristic
904C23C22×C22⋊D1111yescharacteristic
905C23C22×C22⋊D1111yescharacteristic
906D4—432no—
907D4—416no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—114no—
922C2×C4—222no—
923C2×C4—224no—
924C2×C4—222no—
925C2×C4—224no—
926C2×C4—224no—
927C2×C4—222no—
928C2×C4—224no—
929C2×C4—222no—
930C2×C4—224no—
931C2×C4—222no—
932C2×C4—224no—
933C2×C4—224no—
934C2×C4—224no—
935C2×C4—4416no—
936C2×C4—4416no—
937C2×C4—442no—
938C2×C4—442no—
939C2×C4—442no—
940C2×C4—442no—
941C2×C4—442no—
942C2×C4—442no—
943C2×C4—442no—
944C2×C4—442no—
945C2×C4—442no—
946C2×C4—442no—
947C2×C4—442no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—442no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—442no—
955C2×C4—442no—
956C2×C4—441no—
957C2×C4C2×C22⋊Dic1118yescomplemented
958C22—24no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—44no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—82no—
990C22—82no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22#1062283418yescomplemented
996C22#1062311712yes—
997C22#1062311711yescharacteristic
998C22#1062311812yes—
999C22D11×#12011yescharacteristic
1000C22#1062312011yescharacteristic
1001C22#1062312112yes—
1002C22#1062312212yes—
1003C22#1062312212yes—
1004C22#1062312311yescharacteristic
1005C22#1062312412yes—
1006C22C2×D4×Dic1112yes—
1007C22C2×D4×Dic1111yescharacteristic
1008C22C2×D4×Dic1111yescharacteristic
1009C22C2×#6698911yescharacteristic
1010C22#1062332912yes—
1011C22C2×#6699111yescharacteristic
1012C22C2×#6699111yescharacteristic
1013C22D4×C22⋊D1112yes—
1014C22D4×C22⋊D1112yes—
1015C22C2×#6699311yescharacteristic
1016C22#1062333712yes—
1017C22#1062333712yes—
1018C22C22×C22⋊Dic1111yescharacteristic
1019C4—28no—
1020C4—42no—
1021C4—224no—
1022C4—444no—
1023C4—442no—
1024C4—444no—
1025C4—881no—
1026C4—881no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×#1062283411yescharacteristic
1031C2#120×Dic1111yescharacteristic
1032C2#1307127711yescharacteristic
1033C2D4×C22⋊Dic1112yes—
1034C2#1307160012yes—
1035C2#1307198611yescharacteristic
1036C2#1307199711yescharacteristic
1037C2#1307214812yes—
1038C2#1307225111yescharacteristic
1039C2#1307274112yes—
1040C2#1307354411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC22×C11×#120C2
socle, cosocleC24×C11C24
hypercenterC22×#120D11
hypocenterC11#13995
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊Dic11C2semidirect
2. C2×#10622834C2semidirect
3. C2×#10622833C2semidirect
4. C2×#10622833C2semidirect
5. C2×#10622563C2semidirect
6. C2×#10622860C2semidirect
7. C2×C22⋊C4×Dic11C2semidirect
8. #13066861C2semidirect
9. #13066857C2semidirect
10. #13066853C2semidirect
19. C2×C11×#120C4semidirect
30. C22×C22⋊Dic11C22semidirect
31. C22×C22⋊Dic11C22semidirect
32. C22×C22⋊Dic11C22semidirect
33. C22×C4⋊Dic11C22semidirect
34. C22×C4×Dic11C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
42. C2×C11⋊#95C22semidirect
43. C2×C11⋊#95C22semidirect
73. C22×D4×C11C2×C4semidirect
85. C23×Dic11D4semidirect
96. C2×C11×C22⋊C4C2×C4semidirect
123. C2×C22⋊Dic11D4semidirect
124. C2×C22⋊Dic11D4semidirect
271. C11×C22⋊C4C22⋊C4semidirect
412. C2×C4×C11C2×C22⋊C4semidirect
448. C2×Dic11#120semidirect
456. C2×#120Dic11semidirect
520. C22×C11#390semidirect
579. C22×D4C2×Dic11semidirect
631. C2×C22⋊C4C2×Dic11semidirect
800. C22⋊C4C22⋊Dic11semidirect
802. C11#13995semidirect
957. C2×C4C2×C22⋊Dic11semidirect
995. C22#10622834semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Dic112
C2×#106228342
C2×#106228332
C2×#106225632
C2×#106228602
C2×C22⋊C4×Dic112
#130668612
#130668572
#130668532
C22×C11×#1202
#1399511