Finite Group Databasebeta

← #14677183

Subgroups — #14677183

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×C4⋊Dic11C211yesmaximal, characteristic, complemented
2C2×#10622564C212yesmaximal, complemented
3C2×#10622833C211yesmaximal, characteristic
4C2×#10622833C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6#13066873C212yesmaximal, complemented
7#13066861C212yesmaximal, complemented
8#13066850C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C11×#386C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11—24no—
24C22×C4⋊Dic11—28no—
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2212yes—
27C22×C4×Dic11C2212yes—
28C11×#386C418yescomplemented
29C2×C11×#95C2212yes—
30#10622833—24no—
31#10622833—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—
40#10622564—28no—
41C22⋊C4×Dic11—24no—
42C25×C11C2311yescharacteristic
43C25×C11C2311yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11C2×C414yes—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—24no—
54C23×C4×C11—24no—
55C23×C4×C11C2×C414yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—42no—
67C23×Dic11—42no—
68C23×Dic11D414yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4C2×C414yes—
80C2×C11×C22⋊C4C2×C418yescomplemented
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—42no—
92C2×C22⋊Dic11—42no—
93C2×C22⋊Dic11D414yes—
94C2×C4⋊Dic11—232no—
95C2×C4⋊Dic11—24no—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11D418yescomplemented
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11—42no—
104C11×#95C2×C418yescomplemented
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C11⋊#95—42no—
113#14019—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—21no—
120C24×C11—21no—
121C24×C11—22no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11C22×C412yes—
129C24×C11C22×C412yes—
130C24×C11C2×D412yes—
131C24×C11C2×D412yes—
132C24×C11#4112yes—
133C24×C11#4112yes—
134C24×C11#4112yes—
135C24×C11#4112yes—
136C24×C11C2411yescharacteristic
137C2×D4×C11—28no—
138C2×D4×C11—28no—
139C2×D4×C11—28no—
140C2×D4×C11—44no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—44no—
144C22×C4×C11—28no—
145C22×C4×C11—216no—
146C22×C4×C11—28no—
147C22×C4×C11—28no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—216no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11C22×C412yes—
166C22×C4×C11C22×C414yes—
167C22×C4×C11C22×C414yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11#4114yes—
170C22×Dic11—28no—
171C22×Dic11—28no—
172C22×Dic11—28no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—44no—
203C22×Dic11—48no—
204C22×Dic11—48no—
205C22×Dic11—48no—
206C22×Dic11—48no—
207C22×Dic11—44no—
208C22×Dic11—44no—
209C22×Dic11C2×D414yes—
210C22×Dic11C2×D412yes—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×D412yes—
213C22×Dic11C2×D414yes—
214C11×C22⋊C4—28no—
215C11×C22⋊C4—216no—
216C22⋊Dic11—28no—
217C22⋊Dic11—48no—
218C22⋊Dic11—44no—
219C22⋊Dic11—44no—
220C22⋊Dic11—44no—
221C4⋊Dic11—216no—
222C4⋊Dic11—216no—
223C4×Dic11—48no—
224C23×C4⋊C4—111no—
225C2×#388—112no—
226C2×#386—111no—
227C2×#386—111no—
228C2×#386D1111yescharacteristic
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—22no—
252C23×C11—24no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—24no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—42no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11#11714yes—
275C23×C11C4×D414yes—
276C23×C11C4×D414yes—
277C23×C11#12114yes—
278C23×C11#12314yes—
279C23×C11#12414yes—
280C23×C11#12614yes—
281C23×C11C23×C411yescharacteristic
282C23×C11C22×D411yescharacteristic
283C23×C11C22×D412yes—
284C23×C11C22×D411yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11C2×#4111yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4112yes—
289C23×C11C2×#4111yescharacteristic
290C23×C11H(5,𝔽2)12yes—
291C23×C112−1+412yes—
292D4×C11—416no—
293C2×C4×C11—232no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
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—22no—
305C2×C4×C11—24no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11C4×D418yes—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—22no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—416no—
329C2×Dic11—416no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
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×Dic11#12014yes—
351C23×D4C2×D1111yescharacteristic
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—111no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4C2×D1111yescharacteristic
365C22×C22⋊C4C2×D1112yes—
366C22×C42—112no—
367#388—228no—
368#386—224no—
369#386—224no—
370#386Dic1118yescomplemented
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×#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—42no—
392C22×C11—44no—
393C22×C11—44no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—82no—
401C22×C11—82no—
402C22×C11#38818yescomplemented
403C22×C11C2×#11711yescharacteristic
404C22×C11C2×C4×D411yescharacteristic
405C22×C11C2×C4×D412yes—
406C22×C11C2×C4×D411yescharacteristic
407C22×C11#52012yes—
408C22×C11C2×#12011yescharacteristic
409C22×C11C2×#12111yescharacteristic
410C22×C11C2×#12311yescharacteristic
411C22×C11#52511yescharacteristic
412C22×C11#52512yes—
413C22×C11C2×#12411yescharacteristic
414C22×C11C2×#12611yescharacteristic
415C22×C11#53411yescharacteristic
416C22×C11#53611yescharacteristic
417C22×C11#53912yes—
418C22×C11D4212yes—
419C22×C11#54612yes—
420C22×C11#54712yes—
421C22×C11#54812yes—
422C22×C11#54812yes—
423C22×C11#55212yes—
424C22×C11#55312yes—
425C22×C11#55312yes—
426C4×C11—28no—
427C4×C11—44no—
428C4×C11—42no—
429Dic11—24no—
430Dic11—42no—
431Dic11—44no—
432Dic11—44no—
433Dic11—81no—
434Dic11—81no—
435C25C22×D1111yescharacteristic
436C25C22×D1111yescharacteristic
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4C2×Dic1114yes—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—111no—
449C23×C4—112no—
450C23×C4—112no—
451C23×C4—111no—
452C23×C4—114no—
453C23×C4—111no—
454C23×C4—111no—
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×C4—442no—
464C23×C4C2×Dic1114yes—
465C23×C4C22×D1112yes—
466C23×C4C22×D1111yescharacteristic
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—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—114no—
480C2×C22⋊C4—222no—
481C2×C22⋊C4—222no—
482C2×C22⋊C4—222no—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—222no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—222no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C22⋊C4C2×Dic1114yes—
493C2×C22⋊C4C2×Dic1118yescomplemented
494C2×C42—224no—
495C2×C42—224no—
496C2×C42—442no—
497#95—224no—
498#95—222no—
499#95—224no—
500#95—222no—
501#95—224no—
502#95—224no—
503#95—224no—
504#95—442no—
505#95C2×Dic1118yescomplemented
506C2×C11—28no—
507C2×C11—82no—
508C2×C11C2×#38811yescharacteristic
509C2×C11C4×#12011yescharacteristic
510C2×C11#232211yescharacteristic
511C2×C11#235212yes—
512C2×C11#236112yes—
513C2×C11#241011yescharacteristic
514C2×C11#241311yescharacteristic
515C2×C11#243611yescharacteristic
516C2×C11#244312yes—
517C2×C11#248112yes—
518C2×C11#259111yescharacteristic
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—22no—
529C24—21no—
530C24—21no—
531C24—22no—
532C24—22no—
533C24#433912yes—
534C24#433912yes—
535C24D4×D1112yes—
536C24D4×D1112yes—
537C24#434112yes—
538C24#434112yes—
539C24C22×Dic1112yes—
540C24C22×Dic1112yes—
541C24C23×D1111yescharacteristic
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C22×C4—28no—
550C22×C4—216no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—216no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—112no—
571C22×C4—114no—
572C22×C4—114no—
573C22×C4—114no—
574C22×C4—112no—
575C22×C4—228no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—222no—
579C22×C4—228no—
580C22×C4—228no—
581C22×C4—222no—
582C22×C4—221no—
583C22×C4—222no—
584C22×C4—221no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—222no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—222no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—444no—
608C22×C4—448no—
609C22×C4—448no—
610C22×C4—448no—
611C22×C4—448no—
612C22×C4—444no—
613C22×C4—444no—
614C22×C4D4×D1114yes—
615C22×C4#434114yes—
616C22×C4C22×Dic1112yes—
617C22×C4C22×Dic1114yes—
618C22×C4C22×Dic1114yes—
619C4⋊C4—2216no—
620C4⋊C4—2216no—
621C22⋊C4—28no—
622C22⋊C4—216no—
623C22⋊C4—228no—
624C22⋊C4—444no—
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—24no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—41no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23#6693214yes—
670C23#6693614yes—
671C23#6693714yes—
672C23#6693814yes—
673C23#6697914yes—
674C23D4×Dic1114yes—
675C23D4×Dic1114yes—
676C23C2×#433911yescharacteristic
677C23C2×#433911yescharacteristic
678C23C2×D4×D1111yescharacteristic
679C23C2×D4×D1111yescharacteristic
680C23C2×D4×D1112yes—
681C23C2×#434111yescharacteristic
682C23C2×#434111yescharacteristic
683C23C2×#434112yes—
684C23#6704212yes—
685C23#6704312yes—
686C23C23×Dic1111yescharacteristic
687D4—416no—
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—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—114no—
710C2×C4—222no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—224no—
715C2×C4—222no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—222no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—222no—
723C2×C4—4416no—
724C2×C4—4416no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4D4×Dic1118yes—
746C22—24no—
747C22—28no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—28no—
754C22—28no—
755C22—28no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22—44no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—82no—
766C22—82no—
767C22#1062256418yescomplemented
768C22C2×#6693211yescharacteristic
769C22C2×#6693611yescharacteristic
770C22C2×#6693711yescharacteristic
771C22C2×#6693811yescharacteristic
772C22#1062307212yes—
773C22#1062308112yes—
774C22#1062308312yes—
775C22#1062309612yes—
776C22#1062311711yescharacteristic
777C22#1062311712yes—
778C22D11×#12011yescharacteristic
779C22#1062312912yes—
780C22#1062314012yes—
781C22#1062314212yes—
782C22#1062314912yes—
783C22#1062317911yescharacteristic
784C22#1062318411yescharacteristic
785C22#1062319612yes—
786C22C2×#6697911yescharacteristic
787C22C2×D4×Dic1112yes—
788C22C2×D4×Dic1111yescharacteristic
789C22C2×D4×Dic1111yescharacteristic
790C22#1062335812yes—
791C4—28no—
792C4—44no—
793C4—42no—
794C4—224no—
795C4—442no—
796C4—444no—
797C4—444no—
798C4—881no—
799C4—881no—
800C2—28no—
801C2—82no—
802C2C2×#1062256411yescharacteristic
803C2#120×Dic1111yescharacteristic
804C2#1307128811yescharacteristic
805C2#1307154512yes—
806C2#1307163612yes—
807C2#1307199311yescharacteristic
808C2#1307202611yescharacteristic
809C2#1307227211yescharacteristic
810C2#1307235712yes—
811C2#1307287612yes—
812C2#1307409311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14019
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊Dic11C2semidirect
2. C2×#10622564C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. #13066873C2semidirect
7. #13066861C2semidirect
8. #13066850C2semidirect
9. #13066839C2semidirect
10. #13066838C2semidirect
28. C11×#386C4semidirect
80. C2×C11×C22⋊C4C2×C4semidirect
100. C2×C4⋊Dic11D4semidirect
104. C11×#95C2×C4semidirect
370. #386Dic11semidirect
402. C22×C11#388semidirect
493. C2×C22⋊C4C2×Dic11semidirect
505. #95C2×Dic11semidirect
629. C11#14019semidirect
767. C22#10622564semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic112
C2×#106225642
C2×#106228332
C2×C22⋊C4×Dic112
#130668732
#130668612
#130668502
#130668392
#130668382
C2×C11×#3862
#1401911