Finite Group Databasebeta

← #14677184

Subgroups — #14677184

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×#10622282C212yesmaximal, complemented
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622571C211yesmaximal, characteristic
5C2×#10622571C211yesmaximal, characteristic
6C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#13066874C212yesmaximal, complemented
8#13066860C212yesmaximal, complemented
9#13066847C212yesmaximal, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×Dic11⋊C4—24no—
24C22×Dic11⋊C4—28no—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30#10622826—24no—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38#10622571—24no—
39#10622571C418yescomplemented
40C22⋊C4×Dic11—24no—
41#10622282—28no—
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—24no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—42no—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
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—22no—
66C23×Dic11—24no—
67C23×Dic11—42no—
68C23×Dic11C2×C414yes—
69C23×Dic11D414yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4C2×C414yes—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11D414yes—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4—42no—
93C2×(C2×D11)⋊C4C2×C418yescomplemented
94C2×Dic11⋊C4—232no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4—24no—
100C2×Dic11⋊C4D418yescomplemented
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11—42no—
104C11×#95—24no—
105C11×#95—42no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95—24no—
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—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
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—21no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—48no—
161C22×C4×C11—48no—
162C22×C4×C11—44no—
163C22×C4×C11—44no—
164C22×C4×C11C22×C414yes—
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—28no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—44no—
204C22×Dic11—48no—
205C22×Dic11—48no—
206C22×Dic11C22×C412yes—
207C22×Dic11C22×C414yes—
208C22×Dic11C2×D414yes—
209C22×Dic11C2×D412yes—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D412yes—
212C22×Dic11C2×D414yes—
213C22×Dic11#4114yes—
214C11×C22⋊C4—28no—
215C11×C22⋊C4—44no—
216C22⋊Dic11—28no—
217(C2×D11)⋊C4—216no—
218(C2×D11)⋊C4—48no—
219(C2×D11)⋊C4—44no—
220(C2×D11)⋊C4—44no—
221Dic11⋊C4—216no—
222Dic11⋊C4—216no—
223C4×Dic11—48no—
224C23×C4⋊C4—111no—
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⋊#95D1111yescharacteristic, complemented
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—42no—
278C22×D11—41no—
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—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—416no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C22⋊D11—416no—
318C2×Dic11—232no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—22no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—416no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—42no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11C4×D418yes—
350C2×Dic11#12014yes—
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—111no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4C2×D1111yescharacteristic
365C22×C22⋊C4C2×D1111yescharacteristic
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—111no—
376C2×#95—112no—
377C2×#95—112no—
378C2×#95—111no—
379C2×#95C2×D1112yes—
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#52512yes—
401C22×C11#52511yescharacteristic
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—44no—
427C4×C11—44no—
428C4×C11—81no—
429C4×C11—81no—
430Dic11—24no—
431Dic11—28no—
432Dic11—42no—
433Dic11—44no—
434Dic11—42no—
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—24no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—42no—
449C23×C4—112no—
450C23×C4—111no—
451C23×C4—114no—
452C23×C4—112no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—114no—
456C23×C4—224no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4—222no—
460C23×C4—222no—
461C23×C4—222no—
462C23×C4—222no—
463C23×C4—442no—
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1112yes—
467C23×C4C22×D1112yes—
468C2×C4⋊C4—118no—
469C2×C4⋊C4—224no—
470C2×C4⋊C4—224no—
471C2×C4⋊C4—224no—
472C2×C4⋊C4—224no—
473C2×C4⋊C4—2232no—
474C2×C4⋊C4—224no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—114no—
481C2×C22⋊C4—118no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—222no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—222no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—442no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4C4×D1114yes—
494C2×C42—224no—
495C2×C42—224no—
496C2×C42—442no—
497#95—24no—
498#95—42no—
499#95—118no—
500#95—224no—
501#95—224no—
502#95—224no—
503#95—222no—
504#95—222no—
505#95—224no—
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—222no—
527C24—221no—
528C24—221no—
529C24—221no—
530C24—222no—
531C24—221no—
532C24—222no—
533C24—222no—
534C24C2×C4×D1112yes—
535C24#433912yes—
536C24#433912yes—
537C24D4×D1112yes—
538C24D4×D1112yes—
539C24#434112yes—
540C24#434312yes—
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—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—114no—
577C22×C4—114no—
578C22×C4—112no—
579C22×C4—114no—
580C22×C4—114no—
581C22×C4—112no—
582C22×C4—114no—
583C22×C4—112no—
584C22×C4—2216no—
585C22×C4—228no—
586C22×C4—228no—
587C22×C4—2216no—
588C22×C4—228no—
589C22×C4—228no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—228no—
598C22×C4—222no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—221no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—444no—
615C22×C4—448no—
616C22×C4—448no—
617C22×C4C2×C4×D1114yes—
618C22×C4D4×D1114yes—
619C4⋊C4—2216no—
620C4⋊C4—2216no—
621C22⋊C4—28no—
622C22⋊C4—44no—
623C22⋊C4—2216no—
624C22⋊C4—228no—
625C22⋊C4—448no—
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—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—222no—
647C23—222no—
648C23—222no—
649C23—224no—
650C23—224no—
651C23—441no—
652C23—442no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—442no—
657C23—442no—
658C23—442no—
659C23—441no—
660C23—441no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—441no—
667C23—442no—
668C23—441no—
669C23#6692514yes—
670C23(C22⋊D11)⋊C414yes—
671C23#6693714yes—
672C23#6693814yes—
673C23#6694614yes—
674C23#6694714yes—
675C23#6695114yes—
676C23C22×C4×D1111yescharacteristic
677C23C2×#433911yescharacteristic
678C23C2×#433911yescharacteristic
679C23C2×D4×D1111yescharacteristic
680C23C2×D4×D1111yescharacteristic
681C23C2×D4×D1112yes—
682C23C2×#434111yescharacteristic
683C23#6703712yes—
684C23C2×#434311yescharacteristic
685C23#41×D1112yes—
686C23#6704312yes—
687D4—4416no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—416no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—118no—
714C2×C4—114no—
715C2×C4—2232no—
716C2×C4—222no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—224no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—4416no—
736C2×C4—441no—
737C2×C4—442no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C22—28no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—28no—
753C22—24no—
754C22—28no—
755C22—28no—
756C22—444no—
757C22—442no—
758C22—444no—
759C22—442no—
760C22—442no—
761C22—881no—
762C22—881no—
763C22—881no—
764C22—881no—
765C22—882no—
766C22—882no—
767C22#1062228218yescomplemented
768C22C2×#6692511yescharacteristic
769C22C2×(C22⋊D11)⋊C411yescharacteristic
770C22C2×#6693711yescharacteristic
771C22#1062302112yes—
772C22C2×#6693811yescharacteristic
773C22C2×#6694611yescharacteristic
774C22C2×#6694711yescharacteristic
775C22C2×#6695111yescharacteristic
776C22#1062306212yes—
777C22#1062307112yes—
778C22C4×D4×D1112yes—
779C22#1062307712yes—
780C22#1062308312yes—
781C22D11×#12011yescharacteristic
782C22#1062312011yescharacteristic
783C22#1062312112yes—
784C22#1062312912yes—
785C22#1062313212yes—
786C22#1062315812yes—
787C22#1062317612yes—
788C22#1062317911yescharacteristic
789C22#1062318612yes—
790C22#1062318711yescharacteristic
791C4—44no—
792C4—44no—
793C4—81no—
794C4—81no—
795C4—228no—
796C4—224no—
797C4—442no—
798C4—442no—
799C4—444no—
800C2—28no—
801C2—882no—
802C2C2×#1062228211yescharacteristic
803C2#1307111711yescharacteristic
804C2#1307128411yescharacteristic
805C2#1307153912yes—
806C2#1307162712yes—
807C2#1307199211yescharacteristic
808C2#1307202511yescharacteristic
809C2#1307227211yescharacteristic
810C2#1307235512yes—
811C2#1307288412yes—
812C2#1307409511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14019
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C23×Dic11⋊C4C2semidirect
2. C2×#10622282C2semidirect
6. C2×C22⋊C4×Dic11C2semidirect
7. #13066874C2semidirect
8. #13066860C2semidirect
9. #13066847C2semidirect
10. #13066838C2semidirect
11. C11×C22⋊#95C2semidirect
39. #10622571C4semidirect
93. C2×(C2×D11)⋊C4C2×C4semidirect
100. C2×Dic11⋊C4D4semidirect
112. C11⋊#95C2×C4semidirect
234. C22⋊#95D11semidirect
391. C22×C11#388semidirect
629. C11#14019semidirect
767. C22#10622282semidirect

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106222822
C2×#106228262
C2×#106225712
C2×C22⋊C4×Dic112
#130668742
#130668602
#130668472
#130668382
C11×C22⋊#952
#1401911