Finite Group Databasebeta

← #14680525

Subgroups — #14680525

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×D4×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622564C211yesmaximal, characteristic, complemented
3C2×#10622833C212yesmaximal, complemented
4#13066873C211yesmaximal, characteristic, complemented
5#13066861C211yesmaximal, characteristic, complemented
6#13066861C212yesmaximal, complemented
7#13066857C211yesmaximal, characteristic, complemented
8#13066857C212yesmaximal, complemented
9#13066841C211yesmaximal, characteristic, complemented
10#13066838C212yesmaximal, complemented
11C2×C11×#392C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C23×D4×C11C2212yes—
14C24×Dic11C2212yes—
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C2×D4×Dic11—28no—
24C2×D4×Dic11—24no—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C11×#392C418yescomplemented
29C2×C11×#95C2211yescharacteristic
30#10622833—28no—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622564—24no—
40C25×C11C2311yescharacteristic
41C25×C11C2312yes—
42C22×D4×C11—24no—
43C22×D4×C11—24no—
44C22×D4×C11—24no—
45C22×D4×C11—24no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—42no—
49C22×D4×C11—42no—
50C22×D4×C11—42no—
51C22×D4×C11—42no—
52C22×D4×C11C2×C414yes—
53C22×D4×C11C2×C418yescomplemented
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11—24no—
58C23×Dic11—24no—
59C23×Dic11—42no—
60C23×Dic11—42no—
61C23×Dic11—42no—
62C23×Dic11—42no—
63C23×Dic11D418yescomplemented
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4C2×C414yescomplemented
75C2×C11×C22⋊C4C2×C418yescomplemented
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—42no—
86C2×C22⋊Dic11—42no—
87C2×C22⋊Dic11—42no—
88C2×C22⋊Dic11—42no—
89C2×C22⋊Dic11—42no—
90C2×C22⋊Dic11—42no—
91C2×C22⋊Dic11—42no—
92D4×Dic11—232no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—42no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11D414yescomplemented
99C11×#95C2×C414yescomplemented
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—42no—
106C11⋊#95—42no—
107C11⋊#95—42no—
108#14299—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—21no—
122C24×C11—22no—
123C24×C11—21no—
124C24×C11—22no—
125C24×C11—21no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—21no—
129C24×C11—21no—
130C24×C11—21no—
131C24×C11C22×C412yes—
132C24×C11C22×C414yes—
133C24×C11C2×D414yes—
134C24×C11#4114yes—
135C24×C11C2411yescharacteristic
136C2×D4×C11—28no—
137C2×D4×C11—28no—
138C2×D4×C11—216no—
139C2×D4×C11—216no—
140C2×D4×C11—216no—
141C2×D4×C11—28no—
142C2×D4×C11—48no—
143C2×D4×C11—48no—
144C2×D4×C11—48no—
145C2×D4×C11—48no—
146C2×D4×C11—48no—
147C2×D4×C11—48no—
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—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11C22×C414yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C22×C412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11#4112yes—
165C22×Dic11—216no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—21no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—48no—
197C22×Dic11—48no—
198C22×Dic11—48no—
199C22×Dic11—48no—
200C22×Dic11—48no—
201C22×Dic11—48no—
202C22×Dic11C2×D414yes—
203C22×Dic11C2×D412yes—
204C22×Dic11C2×D414yes—
205C22×Dic11C2×D412yes—
206C11×C22⋊C4—28no—
207C11×C22⋊C4—48no—
208C22⋊Dic11—216no—
209C22⋊Dic11—48no—
210C22⋊Dic11—48no—
211C22⋊Dic11—48no—
212C22⋊Dic11—44no—
213C22⋊Dic11—44no—
214C4⋊Dic11—28no—
215C4⋊Dic11—44no—
216C4×Dic11—28no—
217C22×C4×D4—111no—
218C2×#392D1111yescharacteristic
219C2×#388—111no—
220C2×#386—112no—
221#1442—111no—
222#1439—112no—
223#1439—111no—
224#1438—112no—
225#1438—111no—
226#1434—111no—
227C22⋊#95—112no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—22no—
247C23×C11—24no—
248C23×C11—22no—
249C23×C11—24no—
250C23×C11—22no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—41no—
268C23×C11—42no—
269C23×C11—41no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—41no—
273C23×C11—42no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—42no—
277C23×C11—41no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—42no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11C4×D418yes—
286C23×C11C23×C411yescharacteristic
287C23×C11C22×D412yes—
288C23×C11C22×D411yescharacteristic
289C23×C11C2×#4112yes—
290C23×C11C2×#4111yescharacteristic
291C23×C11H(5,𝔽2)11yescharacteristic
292C23×C11H(5,𝔽2)12yes—
293C23×C11H(5,𝔽2)12yes—
294C23×C11H(5,𝔽2)11yescharacteristic
295C23×C11H(5,𝔽2)11yescharacteristic
296C23×C112−1+411yescharacteristic
297D4×C11—232no—
298D4×C11—432no—
299C2×C4×C11—24no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—42no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11C4×D414yes—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—432no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—41no—
342C2×Dic11—42no—
343C2×Dic11—41no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11#12014yes—
351C23×D4C2×D1111yescharacteristic
352C23×D4C2×D1112yes—
353C24×C4—112no—
354C2×C4×D4—224no—
355C2×C4×D4—228no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C22⋊C4—112no—
359C22×C22⋊C4—111no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—112no—
364C22×C22⋊C4C2×D1111yescharacteristic
365C22×C22⋊C4C2×D1112yes—
366C22×C42—111no—
367#392Dic1118yescomplemented
368#388—224no—
369#386—228no—
370C2×#95—111no—
371C2×#95—112no—
372C2×#95—111no—
373C2×#95—111no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—112no—
377C2×#95—112no—
378C2×#95C2×D1111yescharacteristic
379C22×C11—28no—
380C22×C11—28no—
381C22×C11—28no—
382C22×C11—44no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—44no—
391C22×C11—44no—
392C22×C11—44no—
393C22×C11—44no—
394C22×C11—44no—
395C22×C11—42no—
396C22×C11—44no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—82no—
402C22×C11—81no—
403C22×C11—82no—
404C22×C11—81no—
405C22×C11C2×C4×D412yes—
406C22×C11C2×C4×D411yescharacteristic
407C22×C11#51811yescharacteristic
408C22×C11#51812yes—
409C22×C11#52011yescharacteristic
410C22×C11C2×#12011yescharacteristic
411C22×C11#52512yes—
412C22×C11#52511yescharacteristic
413C22×C11#53412yes—
414C22×C11#53412yes—
415C22×C11#53511yescharacteristic
416C22×C11#53511yescharacteristic
417C22×C11#53512yes—
418C22×C11#53511yescharacteristic
419C22×C11#53712yes—
420C22×C11#53711yescharacteristic
421C22×C11#53812yes—
422C22×C11#53812yes—
423C22×C11#53812yes—
424C22×C11#53912yes—
425C22×C11#54012yes—
426C22×C11#54011yescharacteristic
427C22×C11#54211yescharacteristic
428C4×C11—24no—
429C4×C11—44no—
430C4×C11—42no—
431Dic11—24no—
432Dic11—44no—
433Dic11—42no—
434Dic11—81no—
435Dic11—81no—
436Dic11—82no—
437C25C22×D1111yescharacteristic
438C25C22×D1112yes—
439C22×D4—24no—
440C22×D4—24no—
441C22×D4—24no—
442C22×D4—24no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—42no—
446C22×D4—42no—
447C22×D4—42no—
448C22×D4—42no—
449C22×D4C2×Dic1114yes—
450C22×D4C2×Dic1118yescomplemented
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—112no—
454C23×C4—118no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—112no—
458C23×C4—224no—
459C23×C4—224no—
460C23×C4—442no—
461C23×C4—442no—
462C23×C4—442no—
463C23×C4—442no—
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1112yes—
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—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—222no—
482C2×C22⋊C4—222no—
483C2×C22⋊C4—224no—
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⋊C4C2×Dic1114yescomplemented
493C2×C22⋊C4C2×Dic1118yescomplemented
494C2×C42—114no—
495C2×C42—224no—
496#95—224no—
497#95—224no—
498#95—222no—
499#95—222no—
500#95—222no—
501#95—442no—
502#95—442no—
503#95—442no—
504#95C2×Dic1114yescomplemented
505C2×C11—48no—
506C2×C11—82no—
507C2×C11C4×#12011yescharacteristic
508C2×C11#232112yes—
509C2×C11#232411yescharacteristic
510C2×C11#232512yes—
511C2×C11#232811yescharacteristic
512C2×C11#261311yescharacteristic
513C2×C11#261511yescharacteristic
514C2×C11#263012yes—
515C2×C11#263111yescharacteristic
516C2×C11#263512yes—
517C2×C11#263611yescharacteristic
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—21no—
531C24—22no—
532C24—21no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24D4×D1114yes—
541C24#434114yes—
542C24C22×Dic1112yes—
543C24C22×Dic1114yes—
544C24C23×D1111yescharacteristic
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—216no—
548C2×D4—216no—
549C2×D4—216no—
550C2×D4—28no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—112no—
570C22×C4—114no—
571C22×C4—114no—
572C22×C4—112no—
573C22×C4—2216no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—221no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—221no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—221no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—448no—
605C22×C4—448no—
606C22×C4—448no—
607C22×C4—448no—
608C22×C4—448no—
609C22×C4—448no—
610C22×C4D4×D1112yes—
611C22×C4#434112yes—
612C22×C4C22×Dic1114yes—
613C22×C4C22×Dic1112yes—
614C22×C4C22×Dic1112yes—
615C4⋊C4—228no—
616C4⋊C4—444no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—2216no—
620C22⋊C4—444no—
621C22⋊C4—444no—
622C22⋊C4—448no—
623C22⋊C4—448no—
624C22⋊C4—448no—
625C42—228no—
626C11#1429911yescharacteristic, complemented, Sylow
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23D4×Dic1118yes—
685C23C2×D4×D1111yescharacteristic
686C23C2×D4×D1112yes—
687C23C2×#434111yescharacteristic
688C23C2×#434112yes—
689C23#6703712yes—
690C23#6703712yes—
691C23#6703711yescharacteristic
692C23#6703711yescharacteristic
693C23#6704211yescharacteristic
694C23#6704311yescharacteristic
695C23C23×Dic1111yescharacteristic
696D4—232no—
697D4—432no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—114no—
715C2×C4—222no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—222no—
725C2×C4—4432no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—442no—
735C2×C4—441no—
736C2×C4—442no—
737C2×C4—441no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4D4×Dic1114yes—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—42no—
770C22—82no—
771C22—81no—
772C22—82no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22#1062311712yes—
777C22#1062311711yescharacteristic
778C22D11×#12011yescharacteristic
779C22#1062312012yes—
780C22#1062312312yes—
781C22#1062312412yes—
782C22#1062312412yes—
783C22#1062312812yes—
784C22#1062313312yes—
785C22#1062313411yescharacteristic
786C22#1062313612yes—
787C22#1062313811yescharacteristic
788C22#1062313911yescharacteristic
789C22#1062314812yes—
790C22#1062315011yescharacteristic
791C22#1062324611yescharacteristic
792C22#1062324611yescharacteristic
793C22#1062325012yes—
794C22C2×D4×Dic1112yes—
795C22C2×D4×Dic1111yescharacteristic
796C22#1062332911yescharacteristic
797C22#1062332912yes—
798C22#1062335811yescharacteristic
799C4—24no—
800C4—44no—
801C4—42no—
802C4—224no—
803C4—444no—
804C4—442no—
805C4—881no—
806C4—882no—
807C4—881no—
808C2—48no—
809C2—82no—
810C2#120×Dic1111yescharacteristic
811C2#1307127712yes—
812C2#1307131111yescharacteristic
813C2#1307132112yes—
814C2#1307134211yescharacteristic
815C2#1307432711yescharacteristic
816C2#1307433911yescharacteristic
817C2#1307445212yes—
818C2#1307446711yescharacteristic
819C2#1307449912yes—
820C2#1307451011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC2×C11×#392C2
socle, cosocleC24×C11C24
hypercenterC2×#392D11
hypocenterC11#14299
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
2. C2×#10622564C2semidirect
3. C2×#10622833C2semidirect
4. #13066873C2semidirect
5. #13066861C2semidirect
6. #13066861C2semidirect
7. #13066857C2semidirect
8. #13066857C2semidirect
9. #13066841C2semidirect
10. #13066838C2semidirect
28. C11×#392C4semidirect
53. C22×D4×C11C2×C4semidirect
63. C23×Dic11D4semidirect
74. C2×C11×C22⋊C4C2×C4semidirect
75. C2×C11×C22⋊C4C2×C4semidirect
98. C2×C4×Dic11D4semidirect
99. C11×#95C2×C4semidirect
367. #392Dic11semidirect
450. C22×D4C2×Dic11semidirect
492. C2×C22⋊C4C2×Dic11semidirect
493. C2×C22⋊C4C2×Dic11semidirect
504. #95C2×Dic11semidirect
626. C11#14299semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106225642
C2×#106228332
#130668732
#130668612
#130668572
#130668412
#130668382
C2×C11×#3922
#1429911