Finite Group Databasebeta

← #14680660

Subgroups — #14680660

Order 2816.

2198 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
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622569C212yesmaximal, complemented
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4#13066875C211yesmaximal, characteristic, complemented
5#13066863C212yesmaximal, complemented
6#13066858C211yesmaximal, characteristic, complemented
7#13066857C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066853C212yesmaximal, complemented
10#13066843C211yesmaximal, characteristic, complemented
11C2×C11×#390C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C11×#390—24no—
27#10622836C418yescomplemented
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622569—28no—
38C4×(C2×D11)⋊C4—24no—
39C25×C11C2312yes—
40C24×D11C2311yescharacteristic
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—42no—
44C22×D4×C11—42no—
45C22×D4×C11C2×C414yescomplemented
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—24no—
51C22×C22⋊D11—24no—
52C22×C22⋊D11—42no—
53C22×C22⋊D11—42no—
54C22×C22⋊D11—42no—
55C22×C22⋊D11—42no—
56C22×C22⋊D11C2×C418yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—42no—
65C22×C4×D11—42no—
66C22×C4×D11D414yescomplemented
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—42no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4—42no—
75C2×C42×C11—42no—
76C2×C42×C11D414yescomplemented
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11—42no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11—42no—
84C2×C22⋊Dic11—42no—
85C2×C22⋊Dic11C2×C418yescomplemented
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—42no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4C2×C414yes—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—42no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—22no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95C2×C414yescomplemented
106#14311—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
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×C11C22×C414yes—
122C24×C11C2411yescharacteristic
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11C22×C412yes—
132C23×D11C2×D412yes—
133C23×D11#4112yes—
134C2×D4×C11—28no—
135C2×D4×C11—48no—
136C2×D4×C11—44no—
137C2×D4×C11—44no—
138C2×D4×C11—48no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
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—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—48no—
165C2×C22⋊D11—48no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—48no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11C22×C414yes—
194C22×Dic11C22×C412yes—
195C22×Dic11C2×D412yes—
196C22×Dic11#4112yes—
197C2×C4×D11—28no—
198C2×C4×D11—48no—
199C2×C4×D11—44no—
200C2×C4×D11—44no—
201C2×C4×D11—48no—
202C11×C4⋊C4—44no—
203C11×C22⋊C4—48no—
204C11×C22⋊C4—48no—
205C42×C11—44no—
206C22⋊Dic11—48no—
207C22⋊Dic11—48no—
208C22⋊Dic11—48no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—48no—
212C4×Dic11—44no—
213C2×#392—111no—
214C2×#390D1111yescharacteristic, complemented
215C2×#386—112no—
216C2×C4×C22⋊C4—111no—
217#1442—111no—
218#1440—112no—
219#1439—111no—
220#1438—111no—
221#1438—112no—
222#1437—112no—
223#1434—111no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
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×C11C23×C411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C22×D411yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11H(5,𝔽2)12yes—
267C23×C11H(5,𝔽2)12yes—
268C23×C11H(5,𝔽2)12yes—
269C23×C11H(5,𝔽2)12yes—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—24no—
273C22×D11—24no—
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—24no—
279C22×D11—24no—
280C22×D11—24no—
281C22×D11—24no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11C4×D414yes—
293D4×C11—416no—
294C2×C4×C11—24no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—42no—
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×C11C4×D414yes—
315C2×C4×C11#12114yes—
316C22⋊D11—432no—
317C2×Dic11—22no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—41no—
327C2×Dic11—42no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C4×D11—416no—
347C23×D4—112no—
348C23×D4C2×D1111yescharacteristic
349C24×C4—111no—
350C22×C4⋊C4C2×D1111yescharacteristic
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—111no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4C2×D1112yes—
358C22×C22⋊C4C2×D1112yes—
359C22×C42—111no—
360C22×C42C2×D1111yescharacteristic
361#392—118no—
362#390—24no—
363#386—228no—
364C4×C22⋊C4—224no—
365C2×#95—111no—
366C2×#95—112no—
367C2×#95—111no—
368C2×#95—111no—
369C2×#95—111no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95—112no—
373C2×#95—112no—
374C22×C11—44no—
375C22×C11—44no—
376C22×C11—44no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—44no—
381C22×C11—82no—
382C22×C11—82no—
383C22×C11—82no—
384C22×C11—82no—
385C22×C11—82no—
386C22×C11—82no—
387C22×C11—82no—
388C22×C11—82no—
389C22×C11C2×C4×D411yescharacteristic
390C22×C11C2×C4×D411yescharacteristic
391C22×C11C4×#4111yescharacteristic
392C22×C11#51812yes—
393C22×C11#51812yes—
394C22×C11C2×#12111yescharacteristic
395C22×C11#52511yescharacteristic
396C22×C11#52911yescharacteristic
397C22×C11#53211yescharacteristic
398C22×C11#53411yescharacteristic
399C22×C11#53412yes—
400C22×C11#53512yes—
401C22×C11#53511yescharacteristic
402C22×C11#53511yescharacteristic
403C22×C11#53511yescharacteristic
404C22×C11#53812yes—
405C22×C11#53812yes—
406C22×C11#53812yes—
407C22×C11#53812yes—
408C22×C11#53812yes—
409C22×C11#54012yes—
410C22×C11#54012yes—
411C22×C11#54012yes—
412C2×D11—28no—
413C2×D11—24no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—44no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—44no—
422C2×D11—44no—
423C4×C11—24no—
424C4×C11—24no—
425C4×C11—42no—
426C4×C11—82no—
427Dic11—44no—
428Dic11—42no—
429Dic11—42no—
430Dic11—42no—
431Dic11—82no—
432C25—111no—
433C25C22×D1112yes—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—42no—
437C22×D4—42no—
438C22×D4—118no—
439C22×D4—224no—
440C22×D4—224no—
441C22×D4—442no—
442C22×D4—442no—
443C22×D4—442no—
444C22×D4—442no—
445C22×D4C4×D1114yescomplemented
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—112no—
450C23×C4—114no—
451C23×C4—112no—
452C23×C4—222no—
453C23×C4—222no—
454C23×C4—442no—
455C23×C4—442no—
456C23×C4C22×D1112yes—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C2×C4⋊C4—22no—
461C2×C4⋊C4—42no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—118no—
470C2×C22⋊C4—222no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—222no—
473C2×C22⋊C4—222no—
474C2×C22⋊C4—222no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—442no—
479C2×C22⋊C4—442no—
480C2×C22⋊C4—442no—
481C2×C22⋊C4—442no—
482C2×C22⋊C4—442no—
483C2×C22⋊C4—442no—
484C2×C22⋊C4—442no—
485C2×C22⋊C4—442no—
486C2×C42—42no—
487C2×C42—222no—
488C2×C42—442no—
489C2×C42C22⋊D1114yescomplemented
490#95—114no—
491#95—224no—
492#95—222no—
493#95—224no—
494#95—222no—
495#95—222no—
496#95—442no—
497#95—442no—
498#95—442no—
499C2×C11—84no—
500C2×C11C4×#12111yescharacteristic
501C2×C11#232111yescharacteristic
502C2×C11#232112yes—
503C2×C11#232811yescharacteristic
504C2×C11#233312yes—
505C2×C11#261711yescharacteristic
506C2×C11#261911yescharacteristic
507C2×C11#263111yescharacteristic
508C2×C11#263511yescharacteristic
509C2×C11#264812yes—
510C2×C11#266112yes—
511D11—44no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—112no—
527C24—112no—
528C24—112no—
529C24—221no—
530C24—221no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—221no—
535C24—222no—
536C24—221no—
537C24C2×C4×D1114yes—
538C24C23×D1111yescharacteristic
539C2×D4—28no—
540C2×D4—48no—
541C2×D4—48no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—2216no—
545C2×D4—448no—
546C2×D4—448no—
547C2×D4—448no—
548C2×D4—448no—
549C2×D4—448no—
550C2×D4—448no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—114no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—112no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—221no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—221no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—228no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—448no—
597C22×C4—444no—
598C22×C4—444no—
599C22×C4—448no—
600C22×C4C2×C4×D1112yes—
601C22×C4#433912yes—
602C22×C4D4×D1112yes—
603C22×C4#434112yes—
604C22×C4C2×C22⋊D1112yes—
605C22×C4C2×C22⋊D1112yes—
606C22×C4C2×C22⋊D1112yes—
607C4⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—228no—
611C22⋊C4—228no—
612C22⋊C4—448no—
613C22⋊C4—448no—
614C22⋊C4—448no—
615C22⋊C4—448no—
616C42—44no—
617C42—444no—
618C11#1431111yescharacteristic, complemented, Sylow
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—114no—
655C23—224no—
656C23—224no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—224no—
661C23—222no—
662C23—222no—
663C23—222no—
664C23—224no—
665C23—224no—
666C23—224no—
667C23—442no—
668C23—442no—
669C23—441no—
670C23—441no—
671C23—441no—
672C23—442no—
673C23—441no—
674C23—442no—
675C23—442no—
676C23—442no—
677C23C22×C4×D1111yescharacteristic
678C23C2×#433911yescharacteristic
679C23C2×D4×D1111yescharacteristic
680C23C2×#434111yescharacteristic
681C23#6703712yes—
682C23#6703712yes—
683C23#6703712yes—
684C23#41×D1111yescharacteristic
685C23#41×D1111yescharacteristic
686C23#6704212yes—
687C23C22×C22⋊D1111yescharacteristic
688D4—416no—
689D4—4432no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
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—224no—
711C2×C4—222no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—224no—
715C2×C4—224no—
716C2×C4—222no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—4416no—
720C2×C4—442no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—442no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4C4×C22⋊D1114yes—
741C2×C4#6699114yes—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—224no—
758C22—228no—
759C22—444no—
760C22—442no—
761C22—444no—
762C22—442no—
763C22—442no—
764C22—442no—
765C22—444no—
766C22—442no—
767C22—442no—
768C22#1062301712yes—
769C22#1062302512yes—
770C22C4×#434111yescharacteristic
771C22C4×D4×D1111yescharacteristic
772C22#1062307612yes—
773C22#1062307911yescharacteristic
774C22#1062308811yescharacteristic
775C22#1062309312yes—
776C22#1062313612yes—
777C22#1062314412yes—
778C22#1062314612yes—
779C22#1062314812yes—
780C22#1062320912yes—
781C22#1062320912yes—
782C22#1062324612yes—
783C22#1062325012yes—
784C22C2×C4×C22⋊D1111yescharacteristic
785C22C2×#6699111yescharacteristic
786C22#1062333511yescharacteristic
787C22#1062333611yescharacteristic
788C22#1062333611yescharacteristic
789C22#1062335911yescharacteristic
790C22#1062336111yescharacteristic
791C4—24no—
792C4—24no—
793C4—42no—
794C4—82no—
795C4—442no—
796C4—444no—
797C4—442no—
798C4—442no—
799C4—882no—
800C2—84no—
801C2—444no—
802C2C4×#6699111yescharacteristic
803C2#1307127411yescharacteristic
804C2#1307127512yes—
805C2#1307133811yescharacteristic
806C2#1307137512yes—
807C2#1307435211yescharacteristic
808C2#1307436711yescharacteristic
809C2#1307446911yescharacteristic
810C2#1307450111yescharacteristic
811C2#1307460812yes—
812C2#1307474612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#390D11
hypocenterC11#14311
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622569C2semidirect
3. C2×C4×(C2×D11)⋊C4C2semidirect
4. #13066875C2semidirect
5. #13066863C2semidirect
6. #13066858C2semidirect
7. #13066857C2semidirect
8. #13066855C2semidirect
9. #13066853C2semidirect
10. #13066843C2semidirect
11. C2×C11×#390C2semidirect
27. #10622836C4semidirect
45. C22×D4×C11C2×C4semidirect
66. C22×C4×D11D4semidirect
76. C2×C42×C11D4semidirect
85. C2×C22⋊Dic11C2×C4semidirect
105. C11⋊#95C2×C4semidirect
214. C2×#390D11semidirect
445. C22×D4C4×D11semidirect
489. C2×C42C22⋊D11semidirect
618. C11#14311semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106225692
C2×C4×(C2×D11)⋊C42
#130668752
#130668632
#130668582
#130668572
#130668552
#130668532
#130668432
C2×C11×#3902
#1431111