Finite Group Databasebeta

← #14676885

Subgroups — #14676885

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×#67006C211yesmaximal, characteristic
2C2×#10622570C212yesmaximal, complemented
3C2×#10622826C211yesmaximal, characteristic, complemented
4C2×#10622826C211yesmaximal, characteristic, complemented
5C2×#10622823C211yesmaximal, characteristic, complemented
6C2×#10622860C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
8#13066859C212yesmaximal, complemented
9#13066855C212yesmaximal, complemented
10#13066853C212yesmaximal, complemented
11C23×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C26×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C22×C11×C22⋊C4—24no—
18C22×C11×C22⋊C4—28no—
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C2×#67006—24no—
22C2×#67006—24no—
23C2×#67006C418yescomplemented
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2212yes—
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
31C22×(C2×D11)⋊C4C2212yescomplemented
32C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
33C22×Dic11⋊C4C2212yescomplemented
34C22×C4×Dic11C2212yescomplemented
35#10622860—24no—
36#10622826—24no—
37#10622826—24no—
38#10622823—24no—
39C4×C22⋊Dic11—24no—
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2211yescharacteristic, complemented
42C2×C11⋊#95C2212yescomplemented
43C2×C11⋊#95C2212yescomplemented
44C2×C11⋊#95C2211yescharacteristic, complemented
45#10622570—28no—
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×C11C2312yes—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—24no—
64C23×C4×C11—24no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—42no—
68C23×C4×C11—42no—
69C23×C4×C11D414yescomplemented
70C23×C4×C11C2312yes—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—24no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—24no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11C2×C414yes—
86C22×C22⋊D11C2×C418yescomplemented
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2312yes—
91C23×Dic11C2312yes—
92C2×C11×C22⋊C4—232no—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4—24no—
98C2×C11×C22⋊C4D418yescomplemented
99#67006—232no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—24no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11—42no—
112C2×C22⋊Dic11—42no—
113C2×C22⋊Dic11C2×C414yes—
114C2×C22⋊Dic11C2×C418yescomplemented
115C2×C22⋊Dic11D414yes—
116C2×C22⋊Dic11D414yes—
117C2×C22⋊Dic11D414yescomplemented
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4—42no—
125C2×Dic11⋊C4—24no—
126C2×Dic11⋊C4—24no—
127C2×Dic11⋊C4—42no—
128C2×C4×Dic11—24no—
129C2×C4×Dic11—24no—
130C2×C4×Dic11—42no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—24no—
134C11⋊#95—24no—
135C11⋊#95—24no—
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—48no—
161C24×C11—48no—
162C24×C11—48no—
163C24×C11—48no—
164C24×C11—48no—
165C24×C11—48no—
166C24×C11—48no—
167C24×C11—48no—
168C24×C11—48no—
169C24×C11—44no—
170C24×C11—44no—
171C24×C11—48no—
172C24×C11—44no—
173C24×C11—44no—
174C24×C11—44no—
175C24×C11—44no—
176C24×C11C22×C414yes—
177C24×C11C22×C412yes—
178C24×C11C2×D414yes—
179C24×C11C2×D412yes—
180C24×C11C2×D412yes—
181C24×C11C2×D412yes—
182C24×C11C2×D412yes—
183C24×C11#4114yes—
184C24×C11#4112yes—
185C24×C11#4112yes—
186C24×C11C2411yescharacteristic
187C23×D11—21no—
188C23×D11—22no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11C22×C412yes—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—22no—
201C22×C4×C11—28no—
202C22×C4×C11—28no—
203C22×C4×C11—21no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—21no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—28no—
214C22×C4×C11—44no—
215C22×C4×C11—48no—
216C22×C4×C11—48no—
217C22×C4×C11—48no—
218C22×C4×C11—48no—
219C22×C4×C11—44no—
220C22×C4×C11—44no—
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2×D414yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×D414yes—
225C2×C22⋊D11—216no—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—216no—
230C2×C22⋊D11—48no—
231C2×C22⋊D11—48no—
232C2×C22⋊D11—48no—
233C2×C22⋊D11—48no—
234C2×C22⋊D11—48no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C22×Dic11—22no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—22no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11C22×C412yes—
266C22×Dic11C22×C414yes—
267C22×Dic11C2×D414yes—
268C22×Dic11C2×D414yes—
269C22×Dic11C2×D414yes—
270C11×C22⋊C4—216no—
271C11×C22⋊C4—216no—
272C22⋊Dic11—216no—
273C22⋊Dic11—28no—
274C22⋊Dic11—48no—
275C22⋊Dic11—48no—
276C22⋊Dic11—44no—
277C22⋊Dic11C22⋊C4116yescomplemented
278(C2×D11)⋊C4—48no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281Dic11⋊C4—48no—
282C4×Dic11—48no—
283C22×#120—111no—
284C23×C22⋊C4D1111yescharacteristic, complemented
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—432no—
330C23×C11—432no—
331C23×C11—416no—
332C23×C11—416no—
333C23×C11—416no—
334C23×C11—432no—
335C23×C11—416no—
336C23×C11—432no—
337C23×C11—416no—
338C23×C11—42no—
339C23×C11—42no—
340C23×C11—42no—
341C23×C11—42no—
342C23×C11—42no—
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—416no—
355C23×C11C2×C22⋊C414yes—
356C23×C11C4×D414yes—
357C23×C11C4×D418yes—
358C23×C11C4×D414yes—
359C23×C11#12114yes—
360C23×C11#12114yes—
361C23×C11#12414yes—
362C23×C11#12714yes—
363C23×C11C23×C411yescharacteristic
364C23×C11C22×D411yescharacteristic
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D412yes—
369C23×C11C2×#4111yescharacteristic
370C23×C11C2×#4112yes—
371C23×C11C2×#4111yescharacteristic
372C23×C11H(5,𝔽2)12yes—
373C23×C11H(5,𝔽2)12yes—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—24no—
378C22×D11—24no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—42no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
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×D11—42no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—24no—
400C2×C4×C11—24no—
401C2×C4×C11—22no—
402C2×C4×C11—24no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—24no—
406C2×C4×C11—24no—
407C2×C4×C11—416no—
408C2×C4×C11—416no—
409C2×C4×C11—42no—
410C2×C4×C11—42no—
411C2×C4×C11—42no—
412C2×C4×C11—42no—
413C2×C4×C11—42no—
414C2×C4×C11—42no—
415C2×C4×C11#12014yescomplemented
416C22⋊D11—432no—
417C22⋊D11—416no—
418C2×Dic11—24no—
419C2×Dic11—24no—
420C2×Dic11—24no—
421C2×Dic11—24no—
422C2×Dic11—24no—
423C2×Dic11—24no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—24no—
428C2×Dic11—24no—
429C2×Dic11—24no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—42no—
433C2×Dic11—41no—
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—
448C2×Dic11C2×C22⋊C418yescomplemented
449C26C2×D1111yescharacteristic
450C23×D4—111no—
451C23×D4—112no—
452C24×C4C2×D1111yescharacteristic
453C24×C4C2×D1111yescharacteristic
454C2×#120—118no—
455C2×#120—224no—
456C2×#120—224no—
457C22×C4⋊C4—112no—
458C22×C22⋊C4—24no—
459C22×C22⋊C4—28no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—112no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—112no—
466C22×C22⋊C4—112no—
467C22×C22⋊C4—112no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4C2×D1112yes—
470C22×C22⋊C4C2×D1112yes—
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#39018yescomplemented
510C22×C11C22×C22⋊C411yescharacteristic
511C22×C11C2×C4×D411yescharacteristic
512C22×C11C2×C4×D411yescharacteristic
513C22×C11C2×C4×D412yes—
514C22×C11#51812yes—
515C22×C11C2×#12011yescharacteristic
516C22×C11C2×#12111yescharacteristic
517C22×C11C2×#12111yescharacteristic
518C22×C11#52511yescharacteristic
519C22×C11#52512yes—
520C22×C11C2×#12411yescharacteristic
521C22×C11C2×#12711yescharacteristic
522C22×C11#53411yescharacteristic
523C22×C11#53511yescharacteristic
524C22×C11#53812yes—
525C22×C11D4212yes—
526C22×C11D4212yes—
527C22×C11D4212yes—
528C22×C11#54612yes—
529C22×C11#54612yes—
530C22×C11#54612yes—
531C22×C11#54612yes—
532C22×C11#55112yes—
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—24no—
545C4×C11—42no—
546C4×C11—44no—
547Dic11—28no—
548Dic11—44no—
549Dic11—42no—
550Dic11—81no—
551Dic11—81no—
552C25—24no—
553C25—22no—
554C25—24no—
555C25—22no—
556C25—22no—
557C25—22no—
558C25—22no—
559C25—22no—
560C25—42no—
561C25—42no—
562C25—111no—
563C25C4×D1114yes—
564C25C22×D1112yes—
565C25C22×D1111yescharacteristic
566C22×D4—114no—
567C22×D4—118no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—224no—
571C22×D4—222no—
572C22×D4—222no—
573C22×D4—222no—
574C22×D4—222no—
575C22×D4—222no—
576C22×D4—222no—
577C22×D4—224no—
578C22×D4—442no—
579C22×D4—442no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—24no—
584C23×C4—24no—
585C23×C4—22no—
586C23×C4—22no—
587C23×C4—42no—
588C23×C4—42no—
589C23×C4—112no—
590C23×C4—112no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4C22⋊D1114yescomplemented
595C23×C4C22×D1112yes—
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598#120—2232no—
599C2×C4⋊C4—224no—
600C2×C4⋊C4—224no—
601C2×C4⋊C4—442no—
602C2×C22⋊C4—232no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—114no—
609C2×C22⋊C4—114no—
610C2×C22⋊C4—114no—
611C2×C22⋊C4—118no—
612C2×C22⋊C4—114no—
613C2×C22⋊C4—224no—
614C2×C22⋊C4—224no—
615C2×C22⋊C4—222no—
616C2×C22⋊C4—222no—
617C2×C22⋊C4—224no—
618C2×C22⋊C4—224no—
619C2×C22⋊C4—224no—
620C2×C22⋊C4—224no—
621C2×C22⋊C4—222no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—224no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—224no—
628C2×C22⋊C4—224no—
629C2×C22⋊C4—442no—
630C2×C22⋊C4—442no—
631C2×C22⋊C4—442no—
632C2×C22⋊C4—442no—
633C2×C22⋊C4C22⋊D1118yescomplemented
634C2×C42—224no—
635C2×C42—224no—
636C2×C42—442no—
637#95—224no—
638#95—224no—
639#95—224no—
640#95—222no—
641#95—222no—
642C2×C11—28no—
643C2×C11—48no—
644C2×C11C2×#39011yescharacteristic
645C2×C11C4×#12011yescharacteristic
646C2×C11#232111yescharacteristic
647C2×C11D4×C22⋊C412yes—
648C2×C11#235812yes—
649C2×C11#241011yescharacteristic
650C2×C11#241111yescharacteristic
651C2×C11#242412yes—
652C2×C11#243311yescharacteristic
653C2×C11#247212yes—
654C2×C11#253911yescharacteristic
655D11—82no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—28no—
661C24—216no—
662C24—28no—
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—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—44no—
690C24—44no—
691C24—44no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—112no—
696C24—221no—
697C24—222no—
698C24—221no—
699C24—221no—
700C24—221no—
701C24—221no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—221no—
706C24C2×C4×D1114yes—
707C24C2×C4×D1112yes—
708C24#433914yes—
709C24#433912yes—
710C24D4×D1112yes—
711C24D4×D1112yes—
712C24D4×D1112yes—
713C24#434112yes—
714C24C2×C22⋊D1114yes—
715C24C2×C22⋊D1112yes—
716C24C23×D1111yescharacteristic
717C2×D4—2216no—
718C2×D4—228no—
719C2×D4—228no—
720C2×D4—2216no—
721C2×D4—228no—
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—21no—
733C22×C4—22no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—28no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—48no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—114no—
755C22×C4—114no—
756C22×C4—114no—
757C22×C4—112no—
758C22×C4—114no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—222no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—221no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—222no—
785C22×C4C2×C22⋊D1112yes—
786C22×C4C2×C22⋊D1114yes—
787C22×C4C2×C22⋊D1112yes—
788C22×C4C2×C22⋊D1114yes—
789C4⋊C4—448no—
790C22⋊C4—216no—
791C22⋊C4—216no—
792C22⋊C4—1116no—
793C22⋊C4—2216no—
794C22⋊C4—228no—
795C22⋊C4—448no—
796C22⋊C4—444no—
797C22⋊C4—448no—
798C22⋊C4—448no—
799C22⋊C4—444no—
800C22⋊C4—444no—
801C42—448no—
802C11#1399511yescharacteristic, complemented, Sylow
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—22no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—22no—
816C23—22no—
817C23—24no—
818C23—22no—
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—432no—
839C23—432no—
840C23—432no—
841C23—432no—
842C23—416no—
843C23—416no—
844C23—416no—
845C23—416no—
846C23—416no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—416no—
864C23—222no—
865C23—222no—
866C23—224no—
867C23—224no—
868C23—222no—
869C23—441no—
870C23—442no—
871C23—442no—
872C23—442no—
873C23—441no—
874C23—442no—
875C23—442no—
876C23—442no—
877C23—441no—
878C23—442no—
879C23—442no—
880C23—442no—
881C23—441no—
882C23—441no—
883C23—441no—
884C23—441no—
885C23—442no—
886C23—441no—
887C23C22⋊C4×D1114yes—
888C23(C22⋊D11)⋊C414yes—
889C23#6693714yes—
890C23#6693814yes—
891C23C4×C22⋊D1118yes—
892C23C4×C22⋊D1114yes—
893C23#6699214yes—
894C23#6699314yes—
895C23C22×C4×D1111yescharacteristic
896C23C2×#433911yescharacteristic
897C23C2×#433912yes—
898C23C2×D4×D1111yescharacteristic
899C23C2×D4×D1111yescharacteristic
900C23C2×D4×D1111yescharacteristic
901C23C2×#434111yescharacteristic
902C23#6703712yes—
903C23#6703712yes—
904C23C22×C22⋊D1112yes—
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—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—416no—
919C2×C4—416no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—118no—
927C2×C4—224no—
928C2×C4—224no—
929C2×C4—224no—
930C2×C4—224no—
931C2×C4—224no—
932C2×C4—224no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—224no—
936C2×C4—224no—
937C2×C4—222no—
938C2×C4—224no—
939C2×C4—441no—
940C2×C4—442no—
941C2×C4—441no—
942C2×C4—442no—
943C2×C4—442no—
944C2×C4—442no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—442no—
948C2×C4—442no—
949C2×C4—441no—
950C2×C4—442no—
951C2×C4—442no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4#6700614yescomplemented
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—442no—
985C22—444no—
986C22—442no—
987C22—442no—
988C22—444no—
989C22—882no—
990C22—882no—
991C22—881no—
992C22—881no—
993C22—881no—
994C22—881no—
995C22#1062257018yescomplemented
996C22C2×C22⋊C4×D1111yescharacteristic
997C22C2×(C22⋊D11)⋊C411yescharacteristic
998C22#1062301712yes—
999C22C2×#6693711yescharacteristic
1000C22#1062302112yes—
1001C22#1062302112yes—
1002C22#1062302112yes—
1003C22C2×#6693811yescharacteristic
1004C22#1062302512yes—
1005C22#1062302612yes—
1006C22C2×C4×C22⋊D1112yes—
1007C22C2×C4×C22⋊D1111yescharacteristic
1008C22#1062332212yes—
1009C22#1062332211yescharacteristic
1010C22D4×C22⋊D1112yes—
1011C22D4×C22⋊D1112yes—
1012C22D4×C22⋊D1112yes—
1013C22C2×#6699211yescharacteristic
1014C22C2×#6699311yescharacteristic
1015C22#1062333511yescharacteristic
1016C22#1062333611yescharacteristic
1017C22#1062333712yes—
1018C22C2×#6700611yescharacteristic
1019C4—24no—
1020C4—42no—
1021C4—44no—
1022C4—228no—
1023C4—444no—
1024C4—442no—
1025C4—881no—
1026C4—881no—
1027C2—28no—
1028C2—48no—
1029C2—882no—
1030C2C2×#1062257011yescharacteristic
1031C2C4×#6700611yescharacteristic
1032C2#1307127411yescharacteristic
1033C2C22⋊C4×C22⋊D1112yes—
1034C2#1307159512yes—
1035C2#1307199011yescharacteristic
1036C2#1307200111yescharacteristic
1037C2#1307215212yes—
1038C2#1307224911yescharacteristic
1039C2#1307273612yes—
1040C2#1307354711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC22×#67006C2
hypercenterC23×C22⋊C4D11
hypocenterC11#13995
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622826C2semidirect
4. C2×#10622826C2semidirect
5. C2×#10622823C2semidirect
6. C2×#10622860C2semidirect
7. C2×C4×C22⋊Dic11C2semidirect
8. #13066859C2semidirect
9. #13066855C2semidirect
10. #13066853C2semidirect
11. C23×C11×C22⋊C4C2semidirect
23. C2×#67006C4semidirect
30. C22×(C2×D11)⋊C4C22semidirect
31. C22×(C2×D11)⋊C4C22semidirect
32. C22×(C2×D11)⋊C4C22semidirect
33. C22×Dic11⋊C4C22semidirect
34. C22×C4×Dic11C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
42. C2×C11⋊#95C22semidirect
43. C2×C11⋊#95C22semidirect
44. C2×C11⋊#95C22semidirect
69. C23×C4×C11D4semidirect
86. C22×C22⋊D11C2×C4semidirect
98. C2×C11×C22⋊C4D4semidirect
114. C2×C22⋊Dic11C2×C4semidirect
117. C2×C22⋊Dic11D4semidirect
277. C22⋊Dic11C22⋊C4semidirect
284. C23×C22⋊C4D11semidirect
415. C2×C4×C11#120semidirect
448. C2×Dic11C2×C22⋊C4semidirect
509. C22×C11#390semidirect
594. C23×C4C22⋊D11semidirect
633. C2×C22⋊C4C22⋊D11semidirect
802. C11#13995semidirect
957. C2×C4#67006semidirect
995. C22#10622570semidirect

Maximal subgroups

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

subgroupindex
C22×#670062
C2×#106225702
C2×#106228262
C2×#106228232
C2×#106228602
C2×C4×C22⋊Dic112
#130668592
#130668552
#130668532
C23×C11×C22⋊C42
#1399511