Finite Group Databasebeta

← #14677175

Subgroups — #14677175

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
1C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
2C2×#10622553C212yesmaximal, complemented
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622571C211yesmaximal, characteristic
5C2×#10622571C211yesmaximal, characteristic
6#13066871C212yesmaximal, complemented
7#13066860C212yesmaximal, complemented
8#13066849C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C42×C11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×Dic11⋊C4—24no—
25C22×Dic11⋊C4—28no—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C4×C11×C22⋊C4—24no—
29C2×C11×#95C2212yes—
30#10622826—24no—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622571—24no—
40#10622571C418yescomplemented
41#10622553—28no—
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—24no—
47C23×C4×C11—42no—
48C23×C4×C11D414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11C2×C414yes—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11—22no—
65C23×Dic11—24no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—42no—
69C23×Dic11C2×C414yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2312yes—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4C2×C414yes—
80C2×C11×C22⋊C4D414yes—
81C2×C42×C11—24no—
82C2×C42×C11—24no—
83C2×C42×C11—42no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—42no—
95C2×(C2×D11)⋊C4—42no—
96C2×(C2×D11)⋊C4C2×C418yescomplemented
97C2×Dic11⋊C4—232no—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4D418yescomplemented
104C11×#95—24no—
105C11⋊#95—22no—
106C11⋊#95—22no—
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—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—28no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—28no—
158C22×C4×C11—44no—
159C22×C4×C11—48no—
160C22×C4×C11—48no—
161C22×C4×C11C22×C414yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D414yes—
166C2×C22⋊D11—28no—
167C2×C22⋊D11—28no—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—44no—
170C2×C22⋊D11—44no—
171C2×C22⋊D11—44no—
172C2×C22⋊D11—44no—
173C22×Dic11—28no—
174C22×Dic11—28no—
175C22×Dic11—216no—
176C22×Dic11—216no—
177C22×Dic11—28no—
178C22×Dic11—28no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—22no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—48no—
206C22×Dic11—48no—
207C22×Dic11—44no—
208C22×Dic11—44no—
209C22×Dic11C22×C412yes—
210C22×Dic11C22×C414yes—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×D414yes—
213C22×Dic11#4114yes—
214C11×C22⋊C4—28no—
215C11×C22⋊C4—28no—
216C42×C11—48no—
217C22⋊Dic11—44no—
218(C2×D11)⋊C4—216no—
219(C2×D11)⋊C4—48no—
220(C2×D11)⋊C4—44no—
221(C2×D11)⋊C4—44no—
222Dic11⋊C4—216no—
223Dic11⋊C4—216no—
224C23×C4⋊C4—111no—
225C2×#388—112no—
226C2×#386—111no—
227C2×#386—111no—
228C2×#386—111no—
229C2×C4×C22⋊C4D1111yescharacteristic, complemented
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×D412yes—
261C23×C11C22×D411yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4112yes—
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—22no—
293C2×C4×C11—22no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—24no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—416no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11#12014yes—
317C22⋊D11—416no—
318C2×Dic11—232no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—416no—
332C2×Dic11—42no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11C4×D418yes—
351C23×D4—111no—
352C24×C4—111no—
353C24×C4—111no—
354C24×C4C2×D1111yescharacteristic
355C22×C4⋊C4—112no—
356C22×C4⋊C4—112no—
357C22×C4⋊C4—228no—
358C22×C4⋊C4—224no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4C2×D1111yescharacteristic
365C22×C22⋊C4C2×D1111yescharacteristic
366C22×C42C2×D1112yes—
367#388—228no—
368#386—118no—
369#386—224no—
370#386—224no—
371C4×C22⋊C4—24no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—111no—
377C2×#95—112no—
378C2×#95—111no—
379C2×#95—112no—
380C2×#95C2×D1112yes—
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—44no—
428C4×C11—42no—
429C4×C11—44no—
430Dic11—28no—
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—42no—
448C23×C4—112no—
449C23×C4—114no—
450C23×C4—112no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—224no—
455C23×C4—224no—
456C23×C4—224no—
457C23×C4—222no—
458C23×C4—222no—
459C23×C4—222no—
460C23×C4—222no—
461C23×C4—222no—
462C23×C4—442no—
463C23×C4D4414yes—
464C23×C4C22×D1112yes—
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1112yes—
467C23×C4C22×D1111yescharacteristic
468C2×C4⋊C4—118no—
469C2×C4⋊C4—224no—
470C2×C4⋊C4—224no—
471C2×C4⋊C4—2232no—
472C2×C4⋊C4—224no—
473C2×C4⋊C4—224no—
474C2×C4⋊C4—224no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—118no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—222no—
486C2×C22⋊C4—222no—
487C2×C22⋊C4—222no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C22⋊C4C4×D1114yes—
493C2×C22⋊C4C22⋊D1114yes—
494C2×C42—24no—
495C2×C42—24no—
496C2×C42—42no—
497#95—24no—
498#95—118no—
499#95—224no—
500#95—224no—
501#95—224no—
502#95—222no—
503#95—222no—
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—221no—
525C24—221no—
526C24—221no—
527C24—221no—
528C24—221no—
529C24—222no—
530C24—222no—
531C24—222no—
532C24—222no—
533C24—221no—
534C24C2×C4×D1112yes—
535C24C2×D4412yes—
536C24#433912yes—
537C24#433912yes—
538C24#433912yes—
539C24#433912yes—
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—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—44no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—114no—
574C22×C4—114no—
575C22×C4—114no—
576C22×C4—112no—
577C22×C4—114no—
578C22×C4—2216no—
579C22×C4—228no—
580C22×C4—228no—
581C22×C4—2216no—
582C22×C4—228no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—228no—
588C22×C4—221no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—221no—
599C22×C4—222no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—448no—
611C22×C4—448no—
612C22×C4—444no—
613C22×C4—444no—
614C22×C4C2×C4×D1114yes—
615C22×C4C2×D4412yes—
616C22×C4C2×D4412yes—
617C22×C4D4×D1114yes—
618C22×C4C2×C22⋊D1114yes—
619C4⋊C4—2216no—
620C4⋊C4—2216no—
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—2216no—
624C22⋊C4—448no—
625C22⋊C4—444no—
626C22⋊C4—444no—
627C22⋊C4—444no—
628C42—48no—
629C11#1401911yescharacteristic, complemented, Sylow
630C23—22no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—222no—
647C23—222no—
648C23—222no—
649C23—224no—
650C23—224no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23—442no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23—442no—
659C23—441no—
660C23—441no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23#6692514yes—
670C23C4×D4414yes—
671C23#6692814yes—
672C23#6692914yes—
673C23C4×C22⋊D1114yes—
674C23#6698214yes—
675C23#6698314yes—
676C23C22×C4×D1111yescharacteristic
677C23C22×D4411yescharacteristic
678C23C2×#433911yescharacteristic
679C23C2×#433911yescharacteristic
680C23C2×#433911yescharacteristic
681C23C2×#433911yescharacteristic
682C23C2×D4×D1112yes—
683C23#6703712yes—
684C23#41×D1112yes—
685C23#6704312yes—
686C23C22×C22⋊D1111yescharacteristic
687D4—4416no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—416no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—118no—
713C2×C4—2232no—
714C2×C4—224no—
715C2×C4—224no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—222no—
725C2×C4—224no—
726C2×C4—4416no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—441no—
732C2×C4—442no—
733C2×C4—441no—
734C2×C4—442no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4#6693514yes—
746C22—24no—
747C22—28no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—28no—
753C22—24no—
754C22—28no—
755C22—28no—
756C22—442no—
757C22—444no—
758C22—444no—
759C22—442no—
760C22—442no—
761C22—881no—
762C22—881no—
763C22—881no—
764C22—881no—
765C22—882no—
766C22—882no—
767C22#1062255318yescomplemented
768C22C2×#6692511yescharacteristic
769C22C2×C4×D4411yescharacteristic
770C22C2×#6692811yescharacteristic
771C22C2×#6692911yescharacteristic
772C22C2×#6693511yescharacteristic
773C22#1062302112yes—
774C22#1062302411yescharacteristic
775C22#1062305511yescharacteristic
776C22#1062305711yescharacteristic
777C22#1062306212yes—
778C22#1062307112yes—
779C22#1062307112yes—
780C22C4×D4×D1112yes—
781C22#1062307712yes—
782C22#1062307812yes—
783C22#1062308312yes—
784C22#1062308312yes—
785C22#1062309512yes—
786C22C2×C4×C22⋊D1111yescharacteristic
787C22C2×#6698211yescharacteristic
788C22C2×#6698311yescharacteristic
789C22D4×C22⋊D1112yes—
790C22#1062335512yes—
791C4—24no—
792C4—44no—
793C4—42no—
794C4—44no—
795C4—228no—
796C4—444no—
797C4—442no—
798C4—881no—
799C4—881no—
800C2—28no—
801C2—882no—
802C2C2×#1062255311yescharacteristic
803C2C4×#6693511yescharacteristic
804C2#1307128711yescharacteristic
805C2#1307153912yes—
806C2#1307163312yes—
807C2#1307198411yescharacteristic
808C2#1307201711yescharacteristic
809C2#1307227411yescharacteristic
810C2#1307234512yes—
811C2#1307287712yes—
812C2#1307409111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14019
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×Dic11⋊C4C2semidirect
2. C2×#10622553C2semidirect
6. #13066871C2semidirect
7. #13066860C2semidirect
8. #13066849C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
11. C2×C4×C11×C22⋊C4C2semidirect
40. #10622571C4semidirect
96. C2×(C2×D11)⋊C4C2×C4semidirect
103. C2×Dic11⋊C4D4semidirect
112. C11⋊#95C2×C4semidirect
229. C2×C4×C22⋊C4D11semidirect
391. C22×C11#388semidirect
629. C11#14019semidirect
767. C22#10622553semidirect

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106225532
C2×#106228262
C2×#106225712
#130668712
#130668602
#130668492
#130668382
C2×C4×C11×C22⋊C42
#1401911