Finite Group Databasebeta

← #14677181

Subgroups — #14677181

Order 2816.

2538 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622603C212yesmaximal, complemented
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622826C211yesmaximal, characteristic
5C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#13066875C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066848C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066839C211yesmaximal, characteristic, complemented
11C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C22×C11×C4⋊C4—24no—
17C22×C11×C4⋊C4—28no—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28#10622826—24no—
29#10622826—24no—
30#10622826C418yescomplemented
31C4×C22⋊Dic11—24no—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622603—28no—
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—24no—
47C23×C4×C11—24no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—42no—
56C23×C4×C11—42no—
57C23×C4×C11C2×C414yes—
58C23×C4×C11D414yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—22no—
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11C2×C414yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2312yes—
75C2×C11×C4⋊C4—232no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4D418yescomplemented
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11C2×C414yes—
90C2×C22⋊Dic11D414yes—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—42no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4C2×C418yescomplemented
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11—42no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—42no—
112C11⋊#95C2×C418yescomplemented
113#14019—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11C22×C412yes—
119C24×C11C2×D412yes—
120C24×C11C2×D412yes—
121C24×C11#4112yes—
122C24×C11#4112yes—
123C24×C11#4112yes—
124C24×C11#4112yes—
125C24×C11C2411yescharacteristic
126C23×D11—22no—
127C23×D11—21no—
128C23×D11—21no—
129C23×D11—22no—
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11C22×C412yes—
137C22×C4×C11—28no—
138C22×C4×C11—216no—
139C22×C4×C11—28no—
140C22×C4×C11—28no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—216no—
149C22×C4×C11—28no—
150C22×C4×C11—28no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—28no—
162C22×C4×C11—44no—
163C22×C4×C11—48no—
164C22×C4×C11—48no—
165C22×C4×C11—48no—
166C22×C4×C11—48no—
167C22×C4×C11—44no—
168C22×C4×C11—44no—
169C22×C4×C11C22×C414yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D414yes—
172C22×C4×C11C2×D414yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D414yes—
175C22×C4×C11#4114yes—
176C2×C22⋊D11—28no—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—28no—
179C2×C22⋊D11—44no—
180C2×C22⋊D11—44no—
181C2×C22⋊D11—44no—
182C2×C22⋊D11—44no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—22no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11C22×C412yes—
212C22×Dic11C22×C414yes—
213C22×Dic11C2×D414yes—
214C11×C4⋊C4—216no—
215C11×C4⋊C4—216no—
216C22⋊Dic11—28no—
217C22⋊Dic11—28no—
218C22⋊Dic11—44no—
219(C2×D11)⋊C4—216no—
220(C2×D11)⋊C4—48no—
221(C2×D11)⋊C4—44no—
222(C2×D11)⋊C4—44no—
223C4×Dic11—48no—
224C23×C4⋊C4D1111yescharacteristic, complemented
225C2×#388—112no—
226C2×#386—111no—
227C2×#386—111no—
228C2×#386—111no—
229C2×C4×C22⋊C4—111no—
230#1442—112no—
231#1439—112no—
232#1436—112no—
233C22⋊#95—111no—
234C22⋊#95—111no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—24no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11#11714yes—
252C23×C11C4×D414yes—
253C23×C11C4×D414yes—
254C23×C11#12114yes—
255C23×C11#12314yes—
256C23×C11#12414yes—
257C23×C11#12614yes—
258C23×C11C23×C411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C22×D412yes—
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4112yes—
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11H(5,𝔽2)12yes—
268C23×C112−1+412yes—
269C22×D11—22no—
270C22×D11—24no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—24no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—42no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C2×C4×C11—232no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—22no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—22no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—24no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—416no—
310C2×C4×C11—416no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11C4×D418yes—
318C2×C4×C11#12014yes—
319C22⋊D11—416no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—42no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C23×D4—111no—
352C24×C4C2×D1111yescharacteristic
353C24×C4C2×D1111yescharacteristic
354C24×C4C2×D1111yescharacteristic
355C22×C4⋊C4—24no—
356C22×C4⋊C4—28no—
357C22×C4⋊C4C2×D1112yes—
358C22×C4⋊C4C2×D1112yes—
359C22×C22⋊C4—111no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—112no—
365C22×C22⋊C4—111no—
366C22×C42—112no—
367#388—228no—
368#386—118no—
369#386—224no—
370#386—224no—
371C4×C22⋊C4—224no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—111no—
377C2×#95—112no—
378C2×#95—112no—
379C2×#95—111no—
380C2×#95—112no—
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—28no—
384C22×C11—28no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—24no—
388C22×C11—28no—
389C22×C11—28no—
390C22×C11—24no—
391C22×C11#38818yescomplemented
392C22×C11C2×#11711yescharacteristic
393C22×C11C2×C4×D411yescharacteristic
394C22×C11C2×C4×D411yescharacteristic
395C22×C11C2×C4×D412yes—
396C22×C11#52012yes—
397C22×C11C2×#12011yescharacteristic
398C22×C11C2×#12111yescharacteristic
399C22×C11C2×#12311yescharacteristic
400C22×C11#52511yescharacteristic
401C22×C11#52512yes—
402C22×C11C2×#12411yescharacteristic
403C22×C11C2×#12611yescharacteristic
404C22×C11#53411yescharacteristic
405C22×C11#53611yescharacteristic
406C22×C11#53912yes—
407C22×C11D4212yes—
408C22×C11#54612yes—
409C22×C11#54712yes—
410C22×C11#54812yes—
411C22×C11#54812yes—
412C22×C11#55212yes—
413C22×C11#55312yes—
414C22×C11#55312yes—
415C2×D11—42no—
416C2×D11—44no—
417C2×D11—44no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—81no—
421C2×D11—81no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—82no—
425C2×D11—82no—
426C4×C11—24no—
427C4×C11—28no—
428C4×C11—42no—
429C4×C11—44no—
430Dic11—44no—
431Dic11—44no—
432Dic11—42no—
433Dic11—81no—
434Dic11—81no—
435C25—111no—
436C25C22×D1111yescharacteristic
437C22×D4—114no—
438C22×D4—222no—
439C22×D4—222no—
440C22×D4—222no—
441C22×D4—222no—
442C22×D4—222no—
443C22×D4—222no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—112no—
458C23×C4—112no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4—111no—
462C23×C4C4×D1114yes—
463C23×C4C22⋊D1114yes—
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1112yes—
466C23×C4C22×D1112yes—
467C23×C4C22×D1111yescharacteristic
468C2×C4⋊C4—232no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4C22⋊D1118yescomplemented
475C2×C22⋊C4—114no—
476C2×C22⋊C4—114no—
477C2×C22⋊C4—118no—
478C2×C22⋊C4—222no—
479C2×C22⋊C4—222no—
480C2×C22⋊C4—222no—
481C2×C22⋊C4—222no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—222no—
486C2×C22⋊C4—222no—
487C2×C22⋊C4—222no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—222no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4—442no—
494C2×C42—224no—
495C2×C42—224no—
496C2×C42—442no—
497#95—118no—
498#95—224no—
499#95—224no—
500#95—224no—
501#95—222no—
502#95—222no—
503#95—224no—
504#95—224no—
505#95—442no—
506C2×C11—28no—
507C2×C11C2×#38811yescharacteristic
508C2×C11C4×#12011yescharacteristic
509C2×C11#232211yescharacteristic
510C2×C11#235212yes—
511C2×C11#236112yes—
512C2×C11#241011yescharacteristic
513C2×C11#241311yescharacteristic
514C2×C11#243611yescharacteristic
515C2×C11#244312yes—
516C2×C11#248112yes—
517C2×C11#259111yescharacteristic
518D11—82no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—112no—
524C24—222no—
525C24—221no—
526C24—221no—
527C24—221no—
528C24—222no—
529C24—221no—
530C24—221no—
531C24—222no—
532C24—222no—
533C24—221no—
534C24C2×C4×D1112yes—
535C24#433912yes—
536C24D4×D1112yes—
537C24#434112yes—
538C24#434312yes—
539C24#434312yes—
540C24C2×C22⋊D1112yes—
541C24C23×D1111yescharacteristic
542C2×D4—228no—
543C2×D4—228no—
544C2×D4—228no—
545C2×D4—444no—
546C2×D4—444no—
547C2×D4—444no—
548C2×D4—444no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—216no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—216no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—44no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—112no—
582C22×C4—114no—
583C22×C4—114no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—222no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—221no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4C2×C4×D1114yes—
613C22×C4#433914yes—
614C22×C4C2×C22⋊D1112yes—
615C22×C4C2×C22⋊D1114yes—
616C22×C4C2×C22⋊D1114yes—
617C22×C4C2×C22⋊D1112yes—
618C22×C4C2×C22⋊D1114yes—
619C4⋊C4—216no—
620C4⋊C4—216no—
621C22⋊C4—228no—
622C22⋊C4—228no—
623C22⋊C4—2216no—
624C22⋊C4—448no—
625C22⋊C4—444no—
626C22⋊C4—444no—
627C22⋊C4—444no—
628C42—448no—
629C11#1401911yescharacteristic, complemented, Sylow
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—222no—
647C23—222no—
648C23—224no—
649C23—224no—
650C23—222no—
651C23—441no—
652C23—442no—
653C23—441no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23—441no—
659C23—442no—
660C23—442no—
661C23—441no—
662C23—441no—
663C23—442no—
664C23—441no—
665C23—441no—
666C23—442no—
667C23—442no—
668C23—441no—
669C23#6694514yes—
670C23#6694614yes—
671C23#6694714yes—
672C23#6695114yes—
673C23C4×C22⋊D1114yes—
674C23#6699214yes—
675C23#6700014yes—
676C23C22×C4×D1111yescharacteristic
677C23C2×#433911yescharacteristic
678C23C2×#433912yes—
679C23C2×D4×D1111yescharacteristic
680C23C2×#434111yescharacteristic
681C23#6703712yes—
682C23C2×#434311yescharacteristic
683C23C2×#434311yescharacteristic
684C23#6704012yes—
685C23C22×C22⋊D1112yes—
686C23C22×C22⋊D1111yescharacteristic
687D4—4416no—
688C2×C4—232no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—416no—
706C2×C4—416no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—222no—
714C2×C4—224no—
715C2×C4—222no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—222no—
721C2×C4—224no—
722C2×C4—441no—
723C2×C4—442no—
724C2×C4—441no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—441no—
744C2×C4C4×C22⋊D1118yes—
745C2×C4#6700614yes—
746C22—24no—
747C22—28no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—28no—
754C22—28no—
755C22—28no—
756C22—442no—
757C22—444no—
758C22—442no—
759C22—444no—
760C22—442no—
761C22—881no—
762C22—881no—
763C22—881no—
764C22—881no—
765C22—882no—
766C22—882no—
767C22#1062260318yescomplemented
768C22C2×#6694511yescharacteristic
769C22C2×#6694611yescharacteristic
770C22#1062303512yes—
771C22C2×#6694711yescharacteristic
772C22#1062303812yes—
773C22C2×#6695111yescharacteristic
774C22#1062304412yes—
775C22#1062304512yes—
776C22#1062304512yes—
777C22#1062304612yes—
778C22C2×C4×C22⋊D1112yes—
779C22C2×C4×C22⋊D1111yescharacteristic
780C22#1062332211yescharacteristic
781C22#1062332212yes—
782C22D4×C22⋊D1112yes—
783C22C2×#6699211yescharacteristic
784C22#1062333511yescharacteristic
785C22#1062333712yes—
786C22C2×#6700011yescharacteristic
787C22#1062334711yescharacteristic
788C22#1062334812yes—
789C22#1062334812yes—
790C22C2×#6700611yescharacteristic
791C4—28no—
792C4—24no—
793C4—44no—
794C4—42no—
795C4—444no—
796C4—442no—
797C4—444no—
798C4—881no—
799C4—881no—
800C2—28no—
801C2—882no—
802C2C2×#1062260311yescharacteristic
803C2C4×#6700611yescharacteristic
804C2#1307128511yescharacteristic
805C2#1307154112yes—
806C2#1307163212yes—
807C2#1307199011yescharacteristic
808C2#1307202311yescharacteristic
809C2#1307227011yescharacteristic
810C2#1307235112yes—
811C2#1307287112yes—
812C2#1307409611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC23×C4⋊C4D11
hypocenterC11#14019
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622603C2semidirect
5. C2×C4×C22⋊Dic11C2semidirect
6. #13066875C2semidirect
7. #13066858C2semidirect
8. #13066848C2semidirect
9. #13066839C2semidirect
10. #13066839C2semidirect
11. C23×C11×C4⋊C4C2semidirect
30. #10622826C4semidirect
81. C2×C11×C4⋊C4D4semidirect
100. C2×(C2×D11)⋊C4C2×C4semidirect
112. C11⋊#95C2×C4semidirect
224. C23×C4⋊C4D11semidirect
391. C22×C11#388semidirect
474. C2×C4⋊C4C22⋊D11semidirect
629. C11#14019semidirect
767. C22#10622603semidirect

Maximal subgroups

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

subgroupindex
C2×#106226032
C2×#106228262
C2×C4×C22⋊Dic112
#130668752
#130668582
#130668482
#130668392
C23×C11×C4⋊C42
#1401911