Finite Group Databasebeta

← #14680528

Subgroups — #14680528

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic, complemented
2C2×#10622284C211yesmaximal, characteristic
3C2×#10622553C211yesmaximal, characteristic, complemented
4C2×#10622278C212yesmaximal, complemented
5#13066873C211yesmaximal, characteristic, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066860C212yesmaximal, complemented
8#13066856C212yesmaximal, complemented
9#13066856C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×D44C2212yes—
14C23×C4×D11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C2×C4×D44—28no—
27C2×C4×D44—24no—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11×#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622553—24no—
38#10622284C418yescomplemented
39#10622278—28no—
40C24×D11C2311yescharacteristic
41C24×D11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C22×D44—24no—
52C22×D44—24no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—24no—
56C22×D44—24no—
57C22×D44—42no—
58C22×D44—42no—
59C22×D44—42no—
60C22×D44—42no—
61C22×D44C2×C414yes—
62C22×D44C2×C418yescomplemented
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—42no—
66C22×C4×D11—42no—
67C22×C4×D11—42no—
68C22×C4×D11—42no—
69C22×C4×D11D418yescomplemented
70C2×C42×C11—24no—
71C2×C42×C11D414yescomplemented
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4C2×C414yescomplemented
93C2×(C2×D11)⋊C4C2×C418yescomplemented
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—24no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—42no—
98C4×D44—232no—
99C11×#95—24no—
100C11×#95—22no—
101C11×#95—42no—
102C11×#95C2×C414yescomplemented
103C11⋊#95—22no—
104C11⋊#95—22no—
105C11⋊#95—24no—
106C11⋊#95—42no—
107C11⋊#95—42no—
108#14299—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—21no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11—22no—
126C23×D11—21no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—21no—
130C23×D11—21no—
131C23×D11—21no—
132C23×D11C22×C412yes—
133C23×D11C22×C414yes—
134C23×D11C2×D414yes—
135C23×D11#4114yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11C22×C414yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11#4112yes—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11C22×C412yes—
186C22×Dic11C2×D414yes—
187C2×D44—28no—
188C2×D44—28no—
189C2×D44—216no—
190C2×D44—216no—
191C2×D44—216no—
192C2×D44—28no—
193C2×D44—48no—
194C2×D44—48no—
195C2×D44—48no—
196C2×D44—48no—
197C2×D44—48no—
198C2×D44—48no—
199C2×C4×D11—216no—
200C2×C4×D11—48no—
201C2×C4×D11—48no—
202C2×C4×D11—48no—
203C2×C4×D11—48no—
204C2×C4×D11—48no—
205C2×C4×D11—48no—
206C42×C11—28no—
207(C2×D11)⋊C4—216no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—48no—
210(C2×D11)⋊C4—44no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4—48no—
213(C2×D11)⋊C4—48no—
214(C2×D11)⋊C4—44no—
215C4⋊Dic11—28no—
216Dic11⋊C4—44no—
217C22×C4×D4—111no—
218C2×#392—111no—
219C2×#388—111no—
220C2×#386—112no—
221#1442—111no—
222#1439—112no—
223#1439—111no—
224#1438—112no—
225#1438—111no—
226#1434D1111yescharacteristic, complemented
227C22⋊#95—112no—
228C23×C11C23×C411yescharacteristic
229C23×C11C22×D411yescharacteristic
230C23×C11C22×D412yes—
231C23×C11C2×#4111yescharacteristic
232C23×C11C2×#4112yes—
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C11H(5,𝔽2)11yescharacteristic
235C23×C11H(5,𝔽2)12yes—
236C23×C11H(5,𝔽2)12yes—
237C23×C11H(5,𝔽2)11yescharacteristic
238C23×C112−1+411yescharacteristic
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—22no—
258C22×D11—24no—
259C22×D11—22no—
260C22×D11—24no—
261C22×D11—22no—
262C22×D11—42no—
263C22×D11—42no—
264C22×D11—42no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—41no—
284C22×D11—42no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C22×D11—42no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11C4×D418yes—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
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×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11C4×D414yes—
325C2×C4×C11#12014yes—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—41no—
337C2×Dic11—42no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—42no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348D44—232no—
349D44—432no—
350C4×D11—432no—
351C23×D4—111no—
352C23×D4—112no—
353C24×C4—112no—
354C2×C4×D4—228no—
355C2×C4×D4—224no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C22⋊C4—111no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—112no—
365C22×C22⋊C4—112no—
366C22×C42C2×D1111yescharacteristic
367#392—118no—
368#388—224no—
369#386—228no—
370C2×#95—111no—
371C2×#95—111no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95C2×D1112yes—
376C2×#95C2×D1111yescharacteristic
377C2×#95C2×D1112yes—
378C2×#95C2×D1111yescharacteristic
379C22×C11C2×C4×D411yescharacteristic
380C22×C11C2×C4×D412yes—
381C22×C11#51812yes—
382C22×C11#51811yescharacteristic
383C22×C11#52011yescharacteristic
384C22×C11C2×#12011yescharacteristic
385C22×C11#52511yescharacteristic
386C22×C11#52512yes—
387C22×C11#53412yes—
388C22×C11#53412yes—
389C22×C11#53511yescharacteristic
390C22×C11#53511yescharacteristic
391C22×C11#53511yescharacteristic
392C22×C11#53512yes—
393C22×C11#53711yescharacteristic
394C22×C11#53712yes—
395C22×C11#53812yes—
396C22×C11#53812yes—
397C22×C11#53812yes—
398C22×C11#53912yes—
399C22×C11#54012yes—
400C22×C11#54011yescharacteristic
401C22×C11#54211yescharacteristic
402C2×D11—28no—
403C2×D11—28no—
404C2×D11—28no—
405C2×D11—44no—
406C2×D11—44no—
407C2×D11—44no—
408C2×D11—44no—
409C2×D11—44no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—44no—
416C2×D11—44no—
417C2×D11—44no—
418C2×D11—42no—
419C2×D11—44no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—82no—
425C2×D11—81no—
426C2×D11—82no—
427C2×D11—81no—
428C4×C11—24no—
429C4×C11—24no—
430C4×C11—44no—
431C4×C11—42no—
432C4×C11—82no—
433Dic11—42no—
434Dic11—44no—
435Dic11—81no—
436Dic11—81no—
437C25—112no—
438C25—111no—
439C22×D4—114no—
440C22×D4—118no—
441C22×D4—224no—
442C22×D4—224no—
443C22×D4—224no—
444C22×D4—224no—
445C22×D4—222no—
446C22×D4—222no—
447C22×D4—442no—
448C22×D4—442no—
449C22×D4—442no—
450C22×D4—442no—
451C23×C4—111no—
452C23×C4—112no—
453C23×C4—118no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—224no—
457C23×C4—224no—
458C23×C4—442no—
459C23×C4—442no—
460C23×C4—442no—
461C23×C4—442no—
462C23×C4C22×D1112yes—
463C23×C4C22×D1112yes—
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1111yescharacteristic
467C4×D4—2232no—
468C2×C4⋊C4—224no—
469C2×C4⋊C4—222no—
470C2×C4⋊C4—222no—
471C2×C4⋊C4—442no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4—118no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—222no—
478C2×C22⋊C4—222no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—222no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—442no—
486C2×C22⋊C4—442no—
487C2×C22⋊C4—442no—
488C2×C22⋊C4—442no—
489C2×C22⋊C4—442no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4—442no—
494C2×C42—24no—
495C2×C42D4414yescomplemented
496#95—22no—
497#95—24no—
498#95—42no—
499#95—224no—
500#95—222no—
501#95—222no—
502#95—442no—
503#95—442no—
504#95C4×D1114yescomplemented
505C2×C11C4×#12011yescharacteristic
506C2×C11#232112yes—
507C2×C11#232411yescharacteristic
508C2×C11#232512yes—
509C2×C11#232811yescharacteristic
510C2×C11#261311yescharacteristic
511C2×C11#261511yescharacteristic
512C2×C11#263012yes—
513C2×C11#263111yescharacteristic
514C2×C11#263512yes—
515C2×C11#263611yescharacteristic
516D11—48no—
517D11—82no—
518C24—114no—
519C24—114no—
520C24—114no—
521C24—112no—
522C24—222no—
523C24—222no—
524C24—222no—
525C24—222no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24—222no—
530C24—222no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—221no—
535C24—221no—
536C24—222no—
537C24—221no—
538C24—221no—
539C24—222no—
540C24—221no—
541C24—222no—
542C24—222no—
543C24—221no—
544C24C23×D1111yescharacteristic
545C2×D4—2216no—
546C2×D4—228no—
547C2×D4—228no—
548C2×D4—2216no—
549C2×D4—2216no—
550C2×D4—228no—
551C2×D4—448no—
552C2×D4—448no—
553C2×D4—448no—
554C2×D4—448no—
555C2×D4—448no—
556C2×D4—448no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—112no—
580C22×C4—114no—
581C22×C4—221no—
582C22×C4—222no—
583C22×C4—221no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—2216no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—222no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—222no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—448no—
603C22×C4—448no—
604C22×C4—448no—
605C22×C4—448no—
606C22×C4—448no—
607C22×C4—448no—
608C22×C4C2×C4×D1114yes—
609C22×C4C2×C4×D1112yes—
610C22×C4C2×D4412yes—
611C22×C4C2×D4412yes—
612C22×C4C2×D4412yes—
613C22×C4#433912yes—
614C22×C4D4×D1114yes—
615C4⋊C4—228no—
616C4⋊C4—444no—
617C22⋊C4—2216no—
618C22⋊C4—228no—
619C22⋊C4—448no—
620C22⋊C4—444no—
621C22⋊C4—448no—
622C22⋊C4—448no—
623C22⋊C4—448no—
624C22⋊C4—444no—
625C42—28no—
626C11#1429911yescharacteristic, complemented, Sylow
627C23—118no—
628C23—224no—
629C23—224no—
630C23—224no—
631C23—224no—
632C23—224no—
633C23—224no—
634C23—224no—
635C23—224no—
636C23—224no—
637C23—224no—
638C23—224no—
639C23—224no—
640C23—224no—
641C23—224no—
642C23—224no—
643C23—224no—
644C23—224no—
645C23—224no—
646C23—222no—
647C23—224no—
648C23—224no—
649C23—222no—
650C23—222no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23—442no—
659C23—442no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23—441no—
670C23—441no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—442no—
676C23—442no—
677C23—441no—
678C23—441no—
679C23—442no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23C22×C4×D1111yescharacteristic
686C23C22×D4411yescharacteristic
687C23C2×#433911yescharacteristic
688C23C2×D4×D1112yes—
689C23#6703711yescharacteristic
690C23#6704011yescharacteristic
691C23#41×D1112yes—
692C23#6704212yes—
693C23#6704211yescharacteristic
694C23#6704211yescharacteristic
695C23#6704212yes—
696D4—2232no—
697D4—4432no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—222no—
726C2×C4—224no—
727C2×C4—224no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—4432no—
731C2×C4—441no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—441no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4C4×D4414yes—
749C2×C4#6693514yes—
750C22—228no—
751C22—228no—
752C22—228no—
753C22—444no—
754C22—444no—
755C22—444no—
756C22—444no—
757C22—444no—
758C22—444no—
759C22—444no—
760C22—444no—
761C22—444no—
762C22—444no—
763C22—444no—
764C22—444no—
765C22—442no—
766C22—444no—
767C22—442no—
768C22—444no—
769C22—442no—
770C22—882no—
771C22—881no—
772C22—882no—
773C22—881no—
774C22—881no—
775C22—881no—
776C22C2×C4×D4411yescharacteristic
777C22C2×#6693511yescharacteristic
778C22#1062304111yescharacteristic
779C22#1062305212yes—
780C22#1062305511yescharacteristic
781C22#1062305611yescharacteristic
782C22#1062305611yescharacteristic
783C22#1062305611yescharacteristic
784C22#1062306612yes—
785C22C4×D4×D1112yes—
786C22#1062307611yescharacteristic
787C22#1062307812yes—
788C22#1062309311yescharacteristic
789C22#1062310511yescharacteristic
790C22#1062311311yescharacteristic
791C22#1062313812yes—
792C22#1062316012yes—
793C22#1062318412yes—
794C22#1062318412yes—
795C22#1062320912yes—
796C22#1062322312yes—
797C22#1062323512yes—
798C22#1062323512yes—
799C4—24no—
800C4—24no—
801C4—42no—
802C4—44no—
803C4—82no—
804C4—444no—
805C4—442no—
806C4—881no—
807C4—881no—
808C2—448no—
809C2—882no—
810C2C4×#6693511yescharacteristic
811C2#1307127812yes—
812C2#1307131011yescharacteristic
813C2#1307131512yes—
814C2#1307134111yescharacteristic
815C2#1307433311yescharacteristic
816C2#1307434211yescharacteristic
817C2#1307446512yes—
818C2#1307447111yescharacteristic
819C2#1307450712yes—
820C2#1307451511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC2×#10622284C2
hypercenter#1434D11
hypocenterC11#14299
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C22×C4×D44C2semidirect
3. C2×#10622553C2semidirect
4. C2×#10622278C2semidirect
5. #13066873C2semidirect
6. #13066862C2semidirect
7. #13066860C2semidirect
8. #13066856C2semidirect
9. #13066856C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×#1434C2semidirect
38. #10622284C4semidirect
62. C22×D44C2×C4semidirect
69. C22×C4×D11D4semidirect
71. C2×C42×C11D4semidirect
92. C2×(C2×D11)⋊C4C2×C4semidirect
93. C2×(C2×D11)⋊C4C2×C4semidirect
102. C11×#95C2×C4semidirect
226. #1434D11semidirect
495. C2×C42D44semidirect
504. #95C4×D11semidirect
626. C11#14299semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C2×#106222842
C2×#106225532
C2×#106222782
#130668732
#130668622
#130668602
#130668562
(C2×D11)⋊#952
C11×#14342
#1429911