Finite Group Databasebeta

← #14676879

Subgroups — #14676879

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
1C22×#66935C211yesmaximal, characteristic
2C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
3C2×#10622552C212yesmaximal, complemented
4C2×#10622826C211yesmaximal, characteristic, complemented
5C2×#10622571C211yesmaximal, characteristic, complemented
6C2×#10622563C211yesmaximal, characteristic, complemented
7C2×#10622568C211yesmaximal, characteristic, complemented
8#13066862C212yesmaximal, complemented
9#13066856C212yesmaximal, complemented
10#13066854C212yesmaximal, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×D44C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2212yescomplemented
20C22×C22⋊Dic11C2211yescharacteristic
21C22×(C2×D11)⋊C4—24no—
22C22×(C2×D11)⋊C4—28no—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
29C22×(C2×D11)⋊C4C2212yescomplemented
30C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
31C22×C4⋊Dic11C2212yescomplemented
32C2×#66935—24no—
33C2×#66935—24no—
34C2×#66935C418yescomplemented
35C4×C11×C22⋊C4—24no—
36C2×C11×#95C2212yescomplemented
37#10622826—24no—
38C2×C11⋊#95C2211yescharacteristic, complemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2211yescharacteristic, complemented
42#10622571—24no—
43#10622568—24no—
44#10622563—24no—
45#10622552—28no—
46C25×C11C2311yescharacteristic
47C24×D11—22no—
48C24×D11—22no—
49C24×D11—24no—
50C24×D11—24no—
51C24×D11—22no—
52C24×D11—22no—
53C24×D11—22no—
54C24×D11—22no—
55C24×D11—42no—
56C24×D11—42no—
57C24×D11C2×C414yes—
58C24×D11C2311yescharacteristic
59C24×D11C2312yes—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—24no—
63C23×C4×C11—42no—
64C23×C4×C11D414yescomplemented
65C23×C4×C11C2312yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2312yes—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11C2×C414yes—
76C23×Dic11—22no—
77C23×Dic11—24no—
78C23×Dic11—22no—
79C23×Dic11—22no—
80C23×Dic11—42no—
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2312yes—
85C22×D44—24no—
86C22×D44—24no—
87C22×D44—24no—
88C22×D44—24no—
89C22×D44—42no—
90C22×D44—42no—
91C22×D44C2×C418yescomplemented
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4C2×C414yes—
95C2×C11×C22⋊C4D414yes—
96C2×C11×C22⋊C4D414yes—
97C2×C11×C22⋊C4D414yescomplemented
98C2×C42×C11—24no—
99C2×C42×C11—24no—
100C2×C42×C11—42no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×(C2×D11)⋊C4—232no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—24no—
107C2×(C2×D11)⋊C4—24no—
108C2×(C2×D11)⋊C4—24no—
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)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4C2×C418yescomplemented
126C2×(C2×D11)⋊C4D418yescomplemented
127C2×C4⋊Dic11—24no—
128C2×C4⋊Dic11—24no—
129C2×C4⋊Dic11—42no—
130#66935—232no—
131C11×#95—24no—
132C11⋊#95—24no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—24no—
136#13995—111nomaximal, Sylow
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—22no—
140C24×C11—22no—
141C24×C11C22×C412yes—
142C24×C11C2×D412yes—
143C24×C11C2×D412yes—
144C24×C11C2×D412yes—
145C24×C11C2×D412yes—
146C24×C11#4112yes—
147C24×C11#4112yes—
148C24×C11C2411yescharacteristic
149C23×D11—28no—
150C23×D11—216no—
151C23×D11—28no—
152C23×D11—28no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11—22no—
159C23×D11—22no—
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—216no—
166C23×D11—28no—
167C23×D11—28no—
168C23×D11—22no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—22no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—48no—
179C23×D11—48no—
180C23×D11—48no—
181C23×D11—48no—
182C23×D11—48no—
183C23×D11—48no—
184C23×D11—48no—
185C23×D11—48no—
186C23×D11—48no—
187C23×D11—44no—
188C23×D11—44no—
189C23×D11—48no—
190C23×D11—44no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—44no—
194C23×D11C22×C412yes—
195C23×D11C22×C414yes—
196C23×D11C2×D414yes—
197C23×D11#4114yes—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—22no—
201C22×C4×C11—21no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—28no—
206C22×C4×C11—21no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—21no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—28no—
217C22×C4×C11—44no—
218C22×C4×C11—48no—
219C22×C4×C11—48no—
220C22×C4×C11C22×C414yes—
221C22×C4×C11C2×D414yes—
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2×D414yes—
224C22×C4×C11C2×D414yes—
225C22×C4×C11C2×D412yes—
226C22×C4×C11C2×D414yes—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—28no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C22×Dic11—28no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—22no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—48no—
258C22×Dic11—48no—
259C22×Dic11—44no—
260C22×Dic11—44no—
261C22×Dic11C22×C412yes—
262C22×Dic11C2×D414yes—
263C2×D44—216no—
264C2×D44—216no—
265C2×D44—48no—
266C2×D44—48no—
267C2×D44—48no—
268C2×D44—48no—
269C2×D44—48no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4C22⋊C4116yescomplemented
272C42×C11—48no—
273C22⋊Dic11—44no—
274(C2×D11)⋊C4—216no—
275(C2×D11)⋊C4—216no—
276(C2×D11)⋊C4—216no—
277(C2×D11)⋊C4—48no—
278(C2×D11)⋊C4—48no—
279(C2×D11)⋊C4—48no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4—44no—
282C4⋊Dic11—48no—
283C22×#120—111no—
284C23×C22⋊C4—111no—
285C2×#390—112no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#385—111no—
289C2×#379—111no—
290C2×C4×C22⋊C4D1111yescharacteristic, complemented
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×C11C2×C22⋊C414yes—
311C23×C11C4×D414yes—
312C23×C11C4×D414yes—
313C23×C11#12114yes—
314C23×C11#12114yes—
315C23×C11#12414yes—
316C23×C11#12714yes—
317C23×C11C23×C411yescharacteristic
318C23×C11C22×D411yescharacteristic
319C23×C11C22×D411yescharacteristic
320C23×C11C22×D411yescharacteristic
321C23×C11C22×D412yes—
322C23×C11C22×D411yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4112yes—
326C23×C11H(5,𝔽2)12yes—
327C23×C11H(5,𝔽2)12yes—
328C22×D11—232no—
329C22×D11—24no—
330C22×D11—24no—
331C22×D11—24no—
332C22×D11—24no—
333C22×D11—24no—
334C22×D11—24no—
335C22×D11—24no—
336C22×D11—24no—
337C22×D11—24no—
338C22×D11—24no—
339C22×D11—24no—
340C22×D11—24no—
341C22×D11—24no—
342C22×D11—24no—
343C22×D11—24no—
344C22×D11—24no—
345C22×D11—24no—
346C22×D11—24no—
347C22×D11—22no—
348C22×D11—24no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—24no—
352C22×D11—432no—
353C22×D11—432no—
354C22×D11—416no—
355C22×D11—416no—
356C22×D11—416no—
357C22×D11—432no—
358C22×D11—416no—
359C22×D11—432no—
360C22×D11—416no—
361C22×D11—42no—
362C22×D11—42no—
363C22×D11—42no—
364C22×D11—42no—
365C22×D11—42no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—42no—
371C22×D11—42no—
372C22×D11—42no—
373C22×D11—42no—
374C22×D11—42no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—416no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—42no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—42no—
388C22×D11—42no—
389C22×D11—42no—
390C22×D11—42no—
391C22×D11—42no—
392C22×D11—42no—
393C22×D11—42no—
394C22×D11—42no—
395C22×D11—42no—
396C22×D11C4×D418yes—
397C2×C4×C11—24no—
398C2×C4×C11—24no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—24no—
402C2×C4×C11—24no—
403C2×C4×C11—24no—
404C2×C4×C11—24no—
405C2×C4×C11—24no—
406C2×C4×C11—24no—
407C2×C4×C11—22no—
408C2×C4×C11—24no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—24no—
412C2×C4×C11—24no—
413C2×C4×C11—416no—
414C2×C4×C11—42no—
415C2×C4×C11—42no—
416C2×C4×C11—42no—
417C2×C4×C11—42no—
418C2×C4×C11—42no—
419C2×C4×C11—42no—
420C2×C4×C11C2×C22⋊C418yescomplemented
421C2×C4×C11#12014yescomplemented
422C22⋊D11—416no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—24no—
427C2×Dic11—24no—
428C2×Dic11—24no—
429C2×Dic11—416no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—42no—
434C2×Dic11—41no—
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—
448D44—432no—
449C26—111no—
450C23×D4—111no—
451C23×D4—112no—
452C24×C4—111no—
453C24×C4C2×D1111yescharacteristic
454C2×#120—118no—
455C2×#120—224no—
456C2×#120—224no—
457C22×C4⋊C4—112no—
458C22×C22⋊C4—112no—
459C22×C22⋊C4—112no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—112no—
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×D1111yescharacteristic
470C22×C22⋊C4C2×D1111yescharacteristic
471C22×C42C2×D1112yescomplemented
472#390—228no—
473#386—224no—
474#386—224no—
475#385—224no—
476#379—224no—
477C4×C22⋊C4—24no—
478C2×#95—111no—
479C2×#95—112no—
480C2×#95—112no—
481C2×#95—111no—
482C2×#95C2×D1112yescomplemented
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#39018yescomplemented
494C22×C11C22×C22⋊C411yescharacteristic
495C22×C11C2×C4×D411yescharacteristic
496C22×C11C2×C4×D411yescharacteristic
497C22×C11C2×C4×D412yes—
498C22×C11#51812yes—
499C22×C11C2×#12011yescharacteristic
500C22×C11C2×#12111yescharacteristic
501C22×C11C2×#12111yescharacteristic
502C22×C11#52511yescharacteristic
503C22×C11#52512yes—
504C22×C11C2×#12411yescharacteristic
505C22×C11C2×#12711yescharacteristic
506C22×C11#53411yescharacteristic
507C22×C11#53511yescharacteristic
508C22×C11#53812yes—
509C22×C11D4212yes—
510C22×C11D4212yes—
511C22×C11D4212yes—
512C22×C11#54612yes—
513C22×C11#54612yes—
514C22×C11#54612yes—
515C22×C11#54612yes—
516C22×C11#55112yes—
517C2×D11—28no—
518C2×D11—28no—
519C2×D11—28no—
520C2×D11—464no—
521C2×D11—44no—
522C2×D11—44no—
523C2×D11—44no—
524C2×D11—44no—
525C2×D11—44no—
526C2×D11—44no—
527C2×D11—44no—
528C2×D11—44no—
529C2×D11—44no—
530C2×D11—44no—
531C2×D11—44no—
532C2×D11—44no—
533C2×D11—42no—
534C2×D11—44no—
535C2×D11—44no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—81no—
539C2×D11—81no—
540C2×D11—82no—
541C2×D11—81no—
542C2×D11—82no—
543C2×D11—81no—
544C4×C11—28no—
545C4×C11—24no—
546C4×C11—42no—
547C4×C11—44no—
548Dic11—44no—
549Dic11—42no—
550Dic11—81no—
551Dic11—81no—
552C25—112no—
553C25—111no—
554C25—114no—
555C25—224no—
556C25—224no—
557C25—222no—
558C25—222no—
559C25—222no—
560C25—222no—
561C25—222no—
562C25—222no—
563C25—442no—
564C25—442no—
565C25C22×D1111yescharacteristic
566C22×D4—114no—
567C22×D4—118no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—222no—
571C22×D4—222no—
572C22×D4—222no—
573C22×D4—222no—
574C22×D4—222no—
575C22×D4—222no—
576C22×D4—224no—
577C22×D4—224no—
578C22×D4—442no—
579C22×D4—442no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—24no—
583C23×C4—42no—
584C23×C4—112no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—224no—
589C23×C4—222no—
590C23×C4—222no—
591C23×C4—222no—
592C23×C4—442no—
593C23×C4D4414yescomplemented
594C23×C4C22×D1112yes—
595C23×C4C22×D1111yescharacteristic
596C23×C4C22×D1112yes—
597C23×C4C22×D1111yescharacteristic
598#120—2232no—
599C2×C4⋊C4—224no—
600C2×C4⋊C4—224no—
601C2×C4⋊C4—442no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—118no—
605C2×C22⋊C4—118no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4—2232no—
609C2×C22⋊C4—224no—
610C2×C22⋊C4—224no—
611C2×C22⋊C4—224no—
612C2×C22⋊C4—224no—
613C2×C22⋊C4—224no—
614C2×C22⋊C4—224no—
615C2×C22⋊C4—224no—
616C2×C22⋊C4—224no—
617C2×C22⋊C4—222no—
618C2×C22⋊C4—222no—
619C2×C22⋊C4—222no—
620C2×C22⋊C4—224no—
621C2×C22⋊C4—224no—
622C2×C22⋊C4—224no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C22⋊C4—224no—
626C2×C22⋊C4—442no—
627C2×C22⋊C4—442no—
628C2×C22⋊C4—442no—
629C2×C22⋊C4—442no—
630C2×C22⋊C4C4×D1114yes—
631C2×C22⋊C4D4414yes—
632C2×C22⋊C4D4414yescomplemented
633C2×C22⋊C4C22⋊D1114yes—
634C2×C42—24no—
635C2×C42—24no—
636C2×C42—42no—
637#95—24no—
638#95—224no—
639#95—224no—
640#95—222no—
641#95—222no—
642C2×C11—28no—
643C2×C11C2×#39011yescharacteristic
644C2×C11C4×#12011yescharacteristic
645C2×C11#232111yescharacteristic
646C2×C11D4×C22⋊C412yes—
647C2×C11#235812yes—
648C2×C11#241011yescharacteristic
649C2×C11#241111yescharacteristic
650C2×C11#242412yes—
651C2×C11#243311yescharacteristic
652C2×C11#247212yes—
653C2×C11#253911yescharacteristic
654D11—48no—
655D11—82no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—114no—
661C24—114no—
662C24—114no—
663C24—112no—
664C24—2216no—
665C24—228no—
666C24—228no—
667C24—2216no—
668C24—228no—
669C24—222no—
670C24—222no—
671C24—222no—
672C24—222no—
673C24—222no—
674C24—222no—
675C24—222no—
676C24—222no—
677C24—222no—
678C24—222no—
679C24—222no—
680C24—222no—
681C24—228no—
682C24—228no—
683C24—221no—
684C24—221no—
685C24—221no—
686C24—221no—
687C24—221no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24—221no—
693C24—448no—
694C24—448no—
695C24—448no—
696C24—448no—
697C24—448no—
698C24—448no—
699C24—448no—
700C24—448no—
701C24—448no—
702C24—444no—
703C24—444no—
704C24—448no—
705C24—444no—
706C24—444no—
707C24—444no—
708C24—444no—
709C24C2×C4×D1112yes—
710C24C2×D4412yes—
711C24C2×D4412yes—
712C24C2×D4412yes—
713C24#433912yes—
714C24#433912yes—
715C24C2×C22⋊D1112yes—
716C24C23×D1111yescharacteristic
717C2×D4—2216no—
718C2×D4—228no—
719C2×D4—228no—
720C2×D4—228no—
721C2×D4—2216no—
722C2×D4—448no—
723C2×D4—448no—
724C2×D4—448no—
725C2×D4—448no—
726C2×D4—448no—
727C2×D4—444no—
728C2×D4—444no—
729C2×D4—444no—
730C2×D4—444no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—28no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—44no—
751C22×C4—48no—
752C22×C4—48no—
753C22×C4—112no—
754C22×C4—114no—
755C22×C4—228no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—448no—
779C22×C4—448no—
780C22×C4—444no—
781C22×C4—444no—
782C22×C4C2×C4×D1114yes—
783C22×C4C2×D4414yes—
784C22×C4C2×D4412yes—
785C22×C4C2×D4412yes—
786C22×C4C2×D4414yes—
787C22×C4D4×D1114yes—
788C22×C4C2×C22⋊D1114yes—
789C4⋊C4—448no—
790C22⋊C4—28no—
791C22⋊C4—2216no—
792C22⋊C4—2216no—
793C22⋊C4—2216no—
794C22⋊C4—448no—
795C22⋊C4—448no—
796C22⋊C4—448no—
797C22⋊C4—444no—
798C22⋊C4—444no—
799C22⋊C4—444no—
800C22⋊C4(C2×D11)⋊C4116yescomplemented
801C42—48no—
802C11#1399511yescharacteristic, complemented, Sylow
803C23—22no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—118no—
820C23—2232no—
821C23—224no—
822C23—224no—
823C23—224no—
824C23—224no—
825C23—224no—
826C23—224no—
827C23—224no—
828C23—224no—
829C23—224no—
830C23—224no—
831C23—224no—
832C23—224no—
833C23—224no—
834C23—224no—
835C23—224no—
836C23—224no—
837C23—224no—
838C23—224no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—224no—
843C23—224no—
844C23—4432no—
845C23—4432no—
846C23—4432no—
847C23—4432no—
848C23—4416no—
849C23—4416no—
850C23—4416no—
851C23—4416no—
852C23—4416no—
853C23—442no—
854C23—442no—
855C23—442no—
856C23—442no—
857C23—442no—
858C23—442no—
859C23—4416no—
860C23—442no—
861C23—442no—
862C23—442no—
863C23—442no—
864C23—442no—
865C23—442no—
866C23—442no—
867C23—442no—
868C23—442no—
869C23—442no—
870C23—441no—
871C23—441no—
872C23—441no—
873C23—442no—
874C23—441no—
875C23—441no—
876C23—441no—
877C23—442no—
878C23—441no—
879C23—441no—
880C23—442no—
881C23—442no—
882C23—442no—
883C23—442no—
884C23—442no—
885C23—442no—
886C23—442no—
887C23—442no—
888C23C4×D4414yes—
889C23C4×D4414yes—
890C23#6692714yes—
891C23#6692814yes—
892C23C2×(C2×D11)⋊C414yes—
893C23#6698314yes—
894C23#6698314yes—
895C23C22×C4×D1111yescharacteristic
896C23C22×D4411yescharacteristic
897C23C22×D4411yescharacteristic
898C23C22×D4411yescharacteristic
899C23C2×#433911yescharacteristic
900C23C2×#433911yescharacteristic
901C23C2×D4×D1112yes—
902C23#6703712yes—
903C23#41×D1112yes—
904C23#6704212yes—
905C23C22×C22⋊D1111yescharacteristic
906D4—4432no—
907D4—4416no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—416no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—224no—
934C2×C4—222no—
935C2×C4—224no—
936C2×C4—224no—
937C2×C4—4416no—
938C2×C4—442no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—442no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—442no—
945C2×C4—442no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—442no—
953C2×C4—442no—
954C2×C4—442no—
955C2×C4—442no—
956C2×C4#6693514yescomplemented
957C2×C4C2×(C2×D11)⋊C418yescomplemented
958C22—24no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—28no—
968C22—228no—
969C22—228no—
970C22—228no—
971C22—4464no—
972C22—444no—
973C22—444no—
974C22—444no—
975C22—444no—
976C22—444no—
977C22—444no—
978C22—444no—
979C22—444no—
980C22—444no—
981C22—444no—
982C22—444no—
983C22—444no—
984C22—442no—
985C22—444no—
986C22—442no—
987C22—442no—
988C22—444no—
989C22—882no—
990C22—882no—
991C22—881no—
992C22—881no—
993C22—881no—
994C22—881no—
995C22#1062255218yescomplemented
996C22C2×C4×D4411yescharacteristic
997C22C2×C4×D4411yescharacteristic
998C22C2×#6692711yescharacteristic
999C22C2×#6692811yescharacteristic
1000C22C2×#6693511yescharacteristic
1001C22#1062302112yes—
1002C22#1062302411yescharacteristic
1003C22#1062305511yescharacteristic
1004C22#1062305611yescharacteristic
1005C22#1062305812yes—
1006C22C4×D4×D1112yes—
1007C22#1062307612yes—
1008C22#1062307812yes—
1009C22D4×D4412yes—
1010C22D4×D4412yes—
1011C22#1062308512yes—
1012C22#1062308512yes—
1013C22#1062309112yes—
1014C22C22×(C2×D11)⋊C411yescharacteristic
1015C22C2×#6698311yescharacteristic
1016C22C2×#6698311yescharacteristic
1017C22D4×C22⋊D1112yes—
1018C22#1062336012yes—
1019C4—28no—
1020C4—24no—
1021C4—44no—
1022C4—42no—
1023C4—444no—
1024C4—442no—
1025C4—881no—
1026C4—881no—
1027C2—28no—
1028C2—448no—
1029C2—882no—
1030C2C2×#1062255211yescharacteristic
1031C2C4×#6693511yescharacteristic
1032C2#1307127611yescharacteristic
1033C2D4×(C2×D11)⋊C412yes—
1034C2#1307159812yes—
1035C2#1307198411yescharacteristic
1036C2#1307199511yescharacteristic
1037C2#1307214612yes—
1038C2#1307225311yescharacteristic
1039C2#1307274212yes—
1040C2#1307354211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC22×#66935C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13995
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×(C2×D11)⋊C4C2semidirect
3. C2×#10622552C2semidirect
4. C2×#10622826C2semidirect
5. C2×#10622571C2semidirect
6. C2×#10622563C2semidirect
7. C2×#10622568C2semidirect
8. #13066862C2semidirect
9. #13066856C2semidirect
10. #13066854C2semidirect
11. C2×C4×C11×C22⋊C4C2semidirect
19. C22×C42×C11C22semidirect
28. C22×(C2×D11)⋊C4C22semidirect
29. C22×(C2×D11)⋊C4C22semidirect
30. C22×(C2×D11)⋊C4C22semidirect
31. C22×C4⋊Dic11C22semidirect
34. C2×#66935C4semidirect
36. C2×C11×#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
64. C23×C4×C11D4semidirect
91. C22×D44C2×C4semidirect
97. C2×C11×C22⋊C4D4semidirect
125. C2×(C2×D11)⋊C4C2×C4semidirect
126. C2×(C2×D11)⋊C4D4semidirect
271. C11×C22⋊C4C22⋊C4semidirect
290. C2×C4×C22⋊C4D11semidirect
420. C2×C4×C11C2×C22⋊C4semidirect
421. C2×C4×C11#120semidirect
471. C22×C42C2×D11semidirect
482. C2×#95C2×D11semidirect
493. C22×C11#390semidirect
593. C23×C4D44semidirect
632. C2×C22⋊C4D44semidirect
800. C22⋊C4(C2×D11)⋊C4semidirect
802. C11#13995semidirect
956. C2×C4#66935semidirect
957. C2×C4C2×(C2×D11)⋊C4semidirect
995. C22#10622552semidirect

Maximal subgroups

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

subgroupindex
C22×#669352
C23×(C2×D11)⋊C42
C2×#106225522
C2×#106228262
C2×#106225712
C2×#106225632
C2×#106225682
#130668622
#130668562
#130668542
C2×C4×C11×C22⋊C42
#1399511