Finite Group Databasebeta

← #14685021

Subgroups — #14685021

Order 2816.

3366 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C23×C4×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622570C212yesmaximal, complemented
4C2×#10622833C211yesmaximal, characteristic, complemented
5C2×#10622826C211yesmaximal, characteristic, complemented
6C2×#10622571C211yesmaximal, characteristic, complemented
7C2×#10622555C211yesmaximal, characteristic, complemented
8#13066853C212yesmaximal, complemented
9#13066852C212yesmaximal, complemented
10Dic11⋊#95C212yesmaximal, complemented
11C2×C11×#386C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66992—24no—
24C2×#66992—24no—
25C2×#66992C418yescomplemented
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11—24no—
32C22×C4×Dic11—28no—
33C22×C4×Dic11C2212yes—
34C22×C4×Dic11C2212yes—
35C11×#386—24no—
36C2×C11×#95C2212yes—
37#10622833—24no—
38#10622826—24no—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622571—24no—
44#10622570—28no—
45#10622555—24no—
46C25×C11C2311yescharacteristic
47C25×C11C2311yescharacteristic
48C24×D11C2311yescharacteristic
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11C2×C414yes—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—24no—
59C23×C4×C11—24no—
60C23×C4×C11D414yescomplemented
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—24no—
73C22×C22⋊D11—24no—
74C22×C22⋊D11C2×C414yes—
75C22×C22⋊D11C2×C414yescomplemented
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—24no—
79C23×Dic11—24no—
80C23×Dic11—24no—
81C23×Dic11—24no—
82C23×Dic11C2×C414yes—
83C23×Dic11D414yes—
84C23×Dic11D414yes—
85C23×Dic11D414yescomplemented
86C23×Dic11C2312yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2312yes—
90C23×Dic11C2311yescharacteristic
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—24no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—24no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11C2×C414yescomplemented
106#66992—232no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4—24no—
111C2×(C2×D11)⋊C4—24no—
112C2×(C2×D11)⋊C4—24no—
113C2×(C2×D11)⋊C4—24no—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4C2×C414yescomplemented
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—24no—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4C2×C414yescomplemented
122C2×C4×Dic11—232no—
123C2×C4×Dic11—24no—
124C2×C4×Dic11—24no—
125C2×C4×Dic11—24no—
126C2×C4×Dic11—24no—
127C2×C4×Dic11—24no—
128C2×C4×Dic11D418yescomplemented
129C11×#95—24no—
130C11⋊#95—24no—
131C11⋊#95—24no—
132C11⋊#95—24no—
133C11⋊#95—24no—
134#14698—111nomaximal, Sylow
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—21no—
140C24×C11—22no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—22no—
145C24×C11—22no—
146C24×C11—22no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11C22×C412yes—
150C24×C11C22×C412yes—
151C24×C11C2×D412yes—
152C24×C11C2×D412yes—
153C24×C11C2×D412yes—
154C24×C11C2×D412yes—
155C24×C11#4112yes—
156C24×C11#4112yes—
157C24×C11C2411yescharacteristic
158C23×D11—22no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11C22×C412yes—
169C2×D4×C11—28no—
170C2×D4×C11—28no—
171C2×D4×C11—28no—
172C2×D4×C11—44no—
173C2×D4×C11—44no—
174C2×D4×C11—44no—
175C2×D4×C11—44no—
176C22×C4×C11—28no—
177C22×C4×C11—216no—
178C22×C4×C11—28no—
179C22×C4×C11—28no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—216no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D414yes—
200C22×C4×C11C2×D414yes—
201C22×C4×C11#4114yes—
202C2×C22⋊D11—28no—
203C2×C22⋊D11—216no—
204C2×C22⋊D11—28no—
205C2×C22⋊D11—28no—
206C2×C22⋊D11—28no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11—48no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C22×Dic11—28no—
215C22×Dic11—28no—
216C22×Dic11—216no—
217C22×Dic11—216no—
218C22×Dic11—28no—
219C22×Dic11—216no—
220C22×Dic11—216no—
221C22×Dic11—28no—
222C22×Dic11—28no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11C22⋊C4116yescomplemented
243C22×Dic11C22×C412yes—
244C22×Dic11C22×C412yes—
245C22×Dic11C22×C412yes—
246C22×Dic11C2×D412yes—
247C22×Dic11C2×D412yes—
248C22×Dic11C2×D414yes—
249C22×Dic11C2×D414yes—
250C22×Dic11C2×D412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×D414yes—
253C22×Dic11#4114yes—
254C22×Dic11#4114yes—
255C11×C22⋊C4—44no—
256C11×C22⋊C4—48no—
257C22⋊Dic11—28no—
258C22⋊Dic11—48no—
259C22⋊Dic11—44no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—48no—
262(C2×D11)⋊C4—48no—
263Dic11⋊C4—28no—
264Dic11⋊C4—48no—
265C4×Dic11—216no—
266C4×Dic11—216no—
267C22×#121—111no—
268C23×C42—111no—
269C2×#390—112no—
270C2×#386—111no—
271C2×#386—111no—
272C2×#386—111no—
273C2×#386D1111yescharacteristic, complemented
274C2×#380—111no—
275#1437—112no—
276#1437—112no—
277C4⋊#95—112no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—22no—
281C23×C11—24no—
282C23×C11—24no—
283C23×C11—24no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—24no—
287C23×C11—22no—
288C23×C11—24no—
289C23×C11—24no—
290C23×C11—24no—
291C23×C11—24no—
292C23×C11—24no—
293C23×C11—24no—
294C23×C11—22no—
295C23×C11—24no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—24no—
299C23×C11—41no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—42no—
307C23×C11—41no—
308C23×C11—42no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11—41no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11C2×C22⋊C414yes—
318C23×C11C4×D414yes—
319C23×C11C4×D414yes—
320C23×C11#12114yes—
321C23×C11#12114yes—
322C23×C11#12414yes—
323C23×C11#12714yes—
324C23×C11C23×C411yescharacteristic
325C23×C11C22×D411yescharacteristic
326C23×C11C22×D411yescharacteristic
327C23×C11C22×D412yes—
328C23×C11C22×D411yescharacteristic
329C23×C11C22×D411yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4112yes—
333C23×C11C2×#4112yes—
334C23×C11C2×#4112yes—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—24no—
339C22×D11—24no—
340C22×D11—41no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—42no—
346C22×D11—41no—
347C22×D11—42no—
348C22×D11—41no—
349C22×D11—42no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—41no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11—42no—
358D4×C11—416no—
359C2×C4×C11—232no—
360C2×C4×C11—24no—
361C2×C4×C11—24no—
362C2×C4×C11—24no—
363C2×C4×C11—24no—
364C2×C4×C11—24no—
365C2×C4×C11—24no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—42no—
380C2×C4×C11#12118yescomplemented
381C22⋊D11—416no—
382C22⋊D11—416no—
383C2×Dic11—232no—
384C2×Dic11—24no—
385C2×Dic11—24no—
386C2×Dic11—22no—
387C2×Dic11—24no—
388C2×Dic11—24no—
389C2×Dic11—24no—
390C2×Dic11—22no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—24no—
394C2×Dic11—232no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—42no—
403C2×Dic11—42no—
404C2×Dic11—42no—
405C2×Dic11—42no—
406C2×Dic11—42no—
407C2×Dic11—42no—
408C2×Dic11—42no—
409C2×Dic11C2×C22⋊C414yes—
410C2×Dic11C2×C22⋊C414yes—
411C2×Dic11C4×D418yes—
412C2×Dic11#12014yes—
413C2×Dic11#12118yes—
414C2×Dic11#12118yescomplemented
415C2×Dic11#12314yes—
416C23×D4—111no—
417C23×D4—111no—
418C23×D4C2×D1111yescharacteristic
419C24×C4—111no—
420C24×C4—111no—
421C24×C4C2×D1111yescharacteristic
422C2×#121—118no—
423C2×#121—224no—
424C2×#121—224no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—112no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—112no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—112no—
432C22×C22⋊C4—112no—
433C22×C22⋊C4C2×D1112yes—
434C22×C22⋊C4C2×D1111yescharacteristic
435C22×C42—112no—
436C22×C42—112no—
437C22×C42—228no—
438C22×C42—224no—
439#390—228no—
440#386—24no—
441#386—224no—
442#386—224no—
443#386—224no—
444#380—224no—
445C2×#95—112no—
446C2×#95—112no—
447C2×#95—112no—
448C2×#95—112no—
449C2×#95C2×D1112yes—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—28no—
453C22×C11—24no—
454C22×C11—24no—
455C22×C11—28no—
456C22×C11—24no—
457C22×C11—24no—
458C22×C11—28no—
459C22×C11—28no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—44no—
464C22×C11—44no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—82no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11—82no—
471C22×C11#39018yescomplemented
472C22×C11C22×C22⋊C411yescharacteristic
473C22×C11C2×C4×D411yescharacteristic
474C22×C11C2×C4×D411yescharacteristic
475C22×C11C2×C4×D412yes—
476C22×C11C4×#4112yes—
477C22×C11C2×#12011yescharacteristic
478C22×C11C2×#12111yescharacteristic
479C22×C11C2×#12111yescharacteristic
480C22×C11C2×#12112yes—
481C22×C11C2×#12112yes—
482C22×C11C2×#12112yes—
483C22×C11C2×#12311yescharacteristic
484C22×C11#52512yes—
485C22×C11#52512yes—
486C22×C11#52511yescharacteristic
487C22×C11#52511yescharacteristic
488C22×C11C2×#12411yescharacteristic
489C22×C11#52912yes—
490C22×C11#52912yes—
491C22×C11C2×#12711yescharacteristic
492C22×C11#53212yes—
493C22×C11#53212yes—
494C22×C11#53212yes—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—44no—
499C2×D11—44no—
500C2×D11—81no—
501C2×D11—81no—
502C2×D11—82no—
503C2×D11—81no—
504C2×D11—81no—
505C2×D11—82no—
506C4×C11—28no—
507C4×C11—42no—
508C4×C11—82no—
509Dic11—28no—
510Dic11—24no—
511Dic11—42no—
512Dic11—82no—
513Dic11#38618yescomplemented
514C25—111no—
515C25C22×D1111yescharacteristic
516C25C22×D1111yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—114no—
524C22×D4—114no—
525C22×D4—222no—
526C22×D4—222no—
527C22×D4—224no—
528C22×D4—224no—
529C22×D4—222no—
530C22×D4—222no—
531C22×D4—222no—
532C22×D4—222no—
533C22×D4—222no—
534C22×D4—222no—
535C22×D4C4×D1114yes—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—24no—
539C23×C4—24no—
540C23×C4—111no—
541C23×C4—114no—
542C23×C4—114no—
543C23×C4—114no—
544C23×C4—111no—
545C23×C4—112no—
546C23×C4—114no—
547C23×C4—111no—
548C23×C4—112no—
549C23×C4—224no—
550C23×C4—224no—
551C23×C4—224no—
552C23×C4—224no—
553C23×C4—222no—
554C23×C4—222no—
555C23×C4C22⋊D1114yescomplemented
556C23×C4C22×D1112yes—
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1112yes—
559#121—2232no—
560C2×C4⋊C4—114no—
561C2×C4⋊C4—222no—
562C2×C4⋊C4—222no—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4—224no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—222no—
575C2×C22⋊C4—222no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—222no—
578C2×C22⋊C4—224no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—224no—
581C2×C22⋊C4—224no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—224no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—222no—
586C2×C22⋊C4—222no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C42—118no—
591C2×C42—224no—
592C2×C42—224no—
593C2×C42—224no—
594C2×C42—224no—
595C2×C42—2232no—
596C2×C42—224no—
597#95—24no—
598#95—224no—
599#95—224no—
600#95—224no—
601#95—224no—
602C2×C11—28no—
603C2×C11—82no—
604C2×C11C2×#38611yescharacteristic
605C2×C11C2×#39011yescharacteristic
606C2×C11#229711yescharacteristic
607C2×C11C4×#12112yes—
608C2×C11C4×#12112yes—
609C2×C11#284711yescharacteristic
610C2×C11#284711yescharacteristic
611C2×C11#285012yes—
612C2×C11#285411yescharacteristic
613C2×C11#285411yescharacteristic
614C2×C11#285612yes—
615D11—82no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—22no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—22no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24—112no—
631C24—221no—
632C24—221no—
633C24—222no—
634C24—221no—
635C24—221no—
636C24—222no—
637C24—221no—
638C24—222no—
639C24—222no—
640C24—221no—
641C24C2×C4×D1112yes—
642C24C2×C4×D1112yes—
643C24#433912yes—
644C24D4×D1112yes—
645C24D4×D1112yes—
646C24D4×D1112yes—
647C24#434112yes—
648C24C2×C22⋊D1112yes—
649C24C23×D1111yescharacteristic
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—44no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—228no—
658C2×D4—2216no—
659C2×D4—228no—
660C2×D4—228no—
661C2×D4—228no—
662C2×D4—444no—
663C2×D4—448no—
664C2×D4—444no—
665C2×D4—444no—
666C2×D4—444no—
667C2×D4—444no—
668C2×D4—444no—
669C22×C4—28no—
670C22×C4—216no—
671C22×C4—28no—
672C22×C4—28no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—216no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—112no—
692C22×C4—114no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—114no—
696C22×C4—1116no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—114no—
700C22×C4—114no—
701C22×C4—112no—
702C22×C4—114no—
703C22×C4—112no—
704C22×C4—228no—
705C22×C4—2216no—
706C22×C4—2216no—
707C22×C4—228no—
708C22×C4—2216no—
709C22×C4—228no—
710C22×C4—2216no—
711C22×C4—228no—
712C22×C4—228no—
713C22×C4—222no—
714C22×C4—222no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4C2×C4×D1112yes—
733C22×C4D4×D1114yes—
734C22×C4#434114yes—
735C22×C4C2×C22⋊D1114yes—
736C4⋊C4—228no—
737C4⋊C4—448no—
738C22⋊C4—44no—
739C22⋊C4—48no—
740C22⋊C4—228no—
741C22⋊C4—228no—
742C22⋊C4—448no—
743C22⋊C4—448no—
744C22⋊C4—444no—
745C22⋊C4—448no—
746C42—2216no—
747C42—2216no—
748C11#1469811yescharacteristic, complemented, Sylow
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—22no—
756C23—24no—
757C23—22no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—24no—
769C23—24no—
770C23—41no—
771C23—41no—
772C23—42no—
773C23—42no—
774C23—41no—
775C23—42no—
776C23—41no—
777C23—42no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—41no—
787C23—41no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—224no—
792C23—224no—
793C23—441no—
794C23—441no—
795C23—442no—
796C23—442no—
797C23—441no—
798C23—442no—
799C23—441no—
800C23—442no—
801C23—442no—
802C23—441no—
803C23—441no—
804C23—442no—
805C23—442no—
806C23—442no—
807C23—442no—
808C23—442no—
809C23—441no—
810C23—441no—
811C23C22⋊C4×D1114yes—
812C23(C22⋊D11)⋊C414yes—
813C23#6693714yes—
814C23#6693814yes—
815C23C4×C22⋊D1114yes—
816C23#6699214yes—
817C23#6699314yes—
818C23C22×C4×D1111yescharacteristic
819C23C2×#433911yescharacteristic
820C23C2×D4×D1111yescharacteristic
821C23C2×D4×D1111yescharacteristic
822C23C2×D4×D1111yescharacteristic
823C23C2×D4×D1112yes—
824C23C2×#434111yescharacteristic
825C23C2×#434112yes—
826C23#41×D1112yes—
827C23#41×D1112yes—
828C23C22×C22⋊D1111yescharacteristic
829D4—416no—
830D4—4416no—
831D4—4416no—
832C2×C4—232no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—114no—
854C2×C4—118no—
855C2×C4—114no—
856C2×C4—118no—
857C2×C4—114no—
858C2×C4—114no—
859C2×C4—118no—
860C2×C4—2232no—
861C2×C4—2232no—
862C2×C4—224no—
863C2×C4—224no—
864C2×C4—224no—
865C2×C4—224no—
866C2×C4—224no—
867C2×C4—222no—
868C2×C4—224no—
869C2×C4—224no—
870C2×C4—222no—
871C2×C4—224no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—442no—
880C2×C4—442no—
881C2×C4—442no—
882C2×C4—442no—
883C2×C4—442no—
884C2×C4—442no—
885C2×C4—442no—
886C2×C4#6699218yescomplemented
887C22—28no—
888C22—28no—
889C22—24no—
890C22—24no—
891C22—28no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—28no—
896C22—24no—
897C22—44no—
898C22—44no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—81no—
903C22—81no—
904C22—82no—
905C22—81no—
906C22—81no—
907C22—82no—
908C22—444no—
909C22—444no—
910C22—442no—
911C22—442no—
912C22—442no—
913C22—881no—
914C22—881no—
915C22—882no—
916C22—881no—
917C22—881no—
918C22—882no—
919C22#1062257018yescomplemented
920C22C2×C22⋊C4×D1111yescharacteristic
921C22C2×(C22⋊D11)⋊C411yescharacteristic
922C22C2×#6693711yescharacteristic
923C22C2×#6693811yescharacteristic
924C22C4×#434112yes—
925C22#1062306912yes—
926C22C4×D4×D1112yes—
927C22#1062307812yes—
928C22#1062311712yes—
929C22#1062311711yescharacteristic
930C22D11×#12011yescharacteristic
931C22#1062312712yes—
932C22#1062312712yes—
933C22D11×#12112yes—
934C22D11×#12112yes—
935C22#1062318012yes—
936C22D11×#12311yescharacteristic
937C22#1062318711yescharacteristic
938C22C2×C4×C22⋊D1111yescharacteristic
939C22C2×#6699212yes—
940C22C2×#6699211yescharacteristic
941C22C2×#6699311yescharacteristic
942C22#1062336312yes—
943C4—28no—
944C4—42no—
945C4—82no—
946C4—118no—
947C4—228no—
948C4—224no—
949C4—442no—
950C4—882no—
951C2—28no—
952C2—82no—
953C2—882no—
954C2D11×#38611yescharacteristic
955C2C2×#1062257011yescharacteristic
956C2#1307110111yescharacteristic
957C2C4×#6699212yes—
958C2#1307112612yes—
959C2#1307689611yescharacteristic
960C2#1307689711yescharacteristic
961C2#1307691312yes—
962C2#1307694411yescharacteristic
963C2#1307694511yescharacteristic
964C2#1307695912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#386D11
hypocenterC11#14698
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic11C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622833C2semidirect
5. C2×#10622826C2semidirect
6. C2×#10622571C2semidirect
7. C2×#10622555C2semidirect
8. #13066853C2semidirect
9. #13066852C2semidirect
10. Dic11⋊#95C2semidirect
11. C2×C11×#386C2semidirect
25. C2×#66992C4semidirect
60. C23×C4×C11D4semidirect
75. C22×C22⋊D11C2×C4semidirect
85. C23×Dic11D4semidirect
105. C2×C22⋊Dic11C2×C4semidirect
115. C2×(C2×D11)⋊C4C2×C4semidirect
121. C2×Dic11⋊C4C2×C4semidirect
128. C2×C4×Dic11D4semidirect
242. C22×Dic11C22⋊C4semidirect
273. C2×#386D11semidirect
380. C2×C4×C11#121semidirect
414. C2×Dic11#121semidirect
471. C22×C11#390semidirect
513. Dic11#386semidirect
555. C23×C4C22⋊D11semidirect
748. C11#14698semidirect
886. C2×C4#66992semidirect
919. C22#10622570semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
C23×C4×Dic112
C2×#106225702
C2×#106228332
C2×#106228262
C2×#106225712
C2×#106225552
#130668532
#130668522
Dic11⋊#952
C2×C11×#3862
#1469811