Finite Group Databasebeta

← #14684432

Subgroups — #14684432

Order 2816.

1910 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3#13066875C211yesmaximal, characteristic, complemented
4#13066863C212yesmaximal, complemented
5#13066859C212yesmaximal, complemented
6#13066858C211yesmaximal, characteristic, complemented
7#13066857C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066855C212yesmaximal, complemented
10#13066843C211yesmaximal, characteristic, complemented
11C2×C11×#390C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×Dic11⋊C4C2211yescharacteristic
26C11×#390—24no—
27#10622836C418yescomplemented
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622553—24no—
38C25×C11C2312yes—
39C24×D11C2311yescharacteristic
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—42no—
43C22×D4×C11—42no—
44C22×D4×C11C2×C414yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—42no—
50C22×C22⋊D11—42no—
51C22×C22⋊D11—42no—
52C22×C22⋊D11—42no—
53C22×C22⋊D11—42no—
54C22×C22⋊D11—42no—
55C22×C22⋊D11C2×C418yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—42no—
66C2×C11×C22⋊C4—42no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4—42no—
69C2×C42×C11—42no—
70C2×C42×C11D414yescomplemented
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11—42no—
77C2×C22⋊Dic11—42no—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11C2×C418yes—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yes—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—42no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—42no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95C2×C414yes—
101#14623—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
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×C11C22×C414yes—
117C24×C11C2411yescharacteristic
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11C22×C412yes—
129C2×D4×C11—28no—
130C2×D4×C11—48no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—48no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
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×C11C22×C412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4112yes—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—48no—
162C2×C22⋊D11—48no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—21no—
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—21no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11C22×C414yes—
191C22×Dic11C22×C412yes—
192C11×C4⋊C4—44no—
193C11×C22⋊C4—48no—
194C11×C22⋊C4—48no—
195C42×C11—44no—
196C22⋊Dic11—48no—
197C22⋊Dic11—48no—
198C22⋊Dic11—48no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—44no—
201(C2×D11)⋊C4—44no—
202(C2×D11)⋊C4—48no—
203Dic11⋊C4—44no—
204C2×#392—111no—
205C2×#390D1111yescharacteristic, complemented
206C2×#388—111no—
207#1442—111no—
208#1440—112no—
209#1439—111no—
210#1439—112no—
211#1438—111no—
212#1438—112no—
213#1438—112no—
214#1434—111no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
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×C11C23×C411yescharacteristic
251C23×C11C22×D411yescharacteristic
252C23×C11C2×#4111yescharacteristic
253C23×C11H(5,𝔽2)12yes—
254C23×C11H(5,𝔽2)12yes—
255C23×C11H(5,𝔽2)12yes—
256C23×C11H(5,𝔽2)11yescharacteristic
257C23×C11H(5,𝔽2)11yescharacteristic
258C23×C11H(5,𝔽2)12yes—
259C23×C11H(5,𝔽2)11yescharacteristic
260C23×C112−1+411yescharacteristic
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—22no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—42no—
273C22×D11—41no—
274C22×D11—42no—
275C22×D11—41no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284D4×C11—416no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
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×C11C4×D414yes—
307C22⋊D11—432no—
308C2×Dic11—22no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C23×D4—112no—
338C23×D4C2×D1111yescharacteristic
339C22×C4⋊C4—111no—
340C22×C4⋊C4C2×D1111yescharacteristic
341C22×C22⋊C4—111no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—111no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4C2×D1112yes—
349C22×C22⋊C4C2×D1112yes—
350C22×C42C2×D1111yescharacteristic
351#392—118no—
352#390—24no—
353#388—224no—
354C2×#95—111no—
355C2×#95—111no—
356C2×#95—111no—
357C2×#95—111no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C22×C11—44no—
364C22×C11—44no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—44no—
369C22×C11—44no—
370C22×C11—82no—
371C22×C11—82no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11—82no—
375C22×C11—82no—
376C22×C11—82no—
377C22×C11—82no—
378C22×C11C2×C4×D411yescharacteristic
379C22×C11#51812yes—
380C22×C11#51811yescharacteristic
381C22×C11#51812yes—
382C22×C11#52011yescharacteristic
383C22×C11#53411yescharacteristic
384C22×C11#53511yescharacteristic
385C22×C11#53511yescharacteristic
386C22×C11#53511yescharacteristic
387C22×C11#53511yescharacteristic
388C22×C11#53711yescharacteristic
389C22×C11#53812yes—
390C22×C11#54011yescharacteristic
391C22×C11#54012yes—
392C22×C11#54211yescharacteristic
393C22×C11#56012yes—
394C22×C11#56012yes—
395C22×C11#56012yes—
396C22×C11#56012yes—
397C22×C11#56012yes—
398C22×C11H(3,𝔽4)12yes—
399C22×C11#56212yes—
400C22×C11#56212yes—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—81no—
407C2×D11—81no—
408C2×D11—82no—
409C2×D11—82no—
410C2×D11—81no—
411C2×D11—81no—
412C4×C11—24no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—82no—
416Dic11—42no—
417Dic11—44no—
418Dic11—81no—
419Dic11—82no—
420Dic11—81no—
421C25—111no—
422C25C22×D1112yes—
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—42no—
426C22×D4—42no—
427C22×D4—118no—
428C22×D4—442no—
429C22×D4—442no—
430C22×D4—442no—
431C22×D4—442no—
432C22×D4—442no—
433C22×D4—442no—
434C22×D4C4×D1114yes—
435C23×C4—111no—
436C23×C4—112no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4—111no—
440C23×C4C22×D1112yes—
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C2×C4⋊C4—22no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—222no—
447C2×C4⋊C4—442no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—118no—
456C2×C22⋊C4—222no—
457C2×C22⋊C4—222no—
458C2×C22⋊C4—222no—
459C2×C22⋊C4—222no—
460C2×C22⋊C4—442no—
461C2×C22⋊C4—442no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C42—42no—
474C2×C42C22⋊D1114yescomplemented
475#95—114no—
476#95—222no—
477#95—222no—
478#95—222no—
479#95—442no—
480#95—442no—
481#95—442no—
482#95—442no—
483#95—442no—
484C2×C11—84no—
485C2×C11#232111yescharacteristic
486C2×C11#232411yescharacteristic
487C2×C11#232811yescharacteristic
488C2×C11#237512yes—
489C2×C11#237712yes—
490C2×C11#281311yescharacteristic
491C2×C11#281511yescharacteristic
492C2×C11#281811yescharacteristic
493C2×C11#281911yescharacteristic
494C2×C11#282812yes—
495C2×C11#282912yes—
496D11—82no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—112no—
512C24—221no—
513C24—221no—
514C24—222no—
515C24—222no—
516C24—222no—
517C24—221no—
518C24—222no—
519C24—221no—
520C24—221no—
521C24—221no—
522C24C2×C4×D1114yes—
523C24C23×D1111yescharacteristic
524C2×D4—28no—
525C2×D4—48no—
526C2×D4—48no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—448no—
530C2×D4—448no—
531C2×D4—448no—
532C2×D4—448no—
533C2×D4—448no—
534C2×D4—448no—
535C2×D4—448no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—114no—
554C22×C4—112no—
555C22×C4—221no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—221no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—221no—
578C22×C4—222no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4C2×C4×D1112yes—
583C22×C4#433912yes—
584C22×C4C2×C22⋊D1112yes—
585C22×C4C2×C22⋊D1112yes—
586C22×C4C2×C22⋊D1112yes—
587C4⋊C4—44no—
588C4⋊C4—444no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—228no—
592C22⋊C4—444no—
593C22⋊C4—444no—
594C22⋊C4—448no—
595C22⋊C4—448no—
596C22⋊C4—448no—
597C22⋊C4—448no—
598C42—44no—
599C11#1462311yescharacteristic, complemented, Sylow
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—224no—
636C23—222no—
637C23—222no—
638C23—224no—
639C23—222no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—442no—
650C23—441no—
651C23—441no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23C22×C4×D1111yescharacteristic
659C23C2×#433911yescharacteristic
660C23#6703712yes—
661C23#6703711yescharacteristic
662C23#6703712yes—
663C23#6703711yescharacteristic
664C23#6703712yes—
665C23#6704212yes—
666C23#6704211yescharacteristic
667C23#6704311yescharacteristic
668C23C22×C22⋊D1111yescharacteristic
669D4—416no—
670D4—4432no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—224no—
693C2×C4—222no—
694C2×C4—224no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—442no—
698C2×C4—441no—
699C2×C4—442no—
700C2×C4—441no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4C4×C22⋊D1114yes—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—444no—
738C22—444no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—882no—
743C22—881no—
744C22—881no—
745C22—881no—
746C22—881no—
747C22—882no—
748C22#1062301712yes—
749C22#1062302512yes—
750C22#1062307611yescharacteristic
751C22#1062307612yes—
752C22#1062307711yescharacteristic
753C22#1062309211yescharacteristic
754C22#1062309312yes—
755C22#1062309311yescharacteristic
756C22#1062315112yes—
757C22#1062315112yes—
758C22#1062315112yes—
759C22#1062315212yes—
760C22#1062321412yes—
761C22#1062321512yes—
762C22#1062325112yes—
763C22#1062325112yes—
764C22C2×C4×C22⋊D1111yescharacteristic
765C22#1062333511yescharacteristic
766C22#1062333611yescharacteristic
767C22#1062333611yescharacteristic
768C22#1062333611yescharacteristic
769C22#1062336111yescharacteristic
770C22#1062336411yescharacteristic
771C4—24no—
772C4—42no—
773C4—42no—
774C4—82no—
775C4—444no—
776C4—442no—
777C4—881no—
778C4—881no—
779C4—882no—
780C2—84no—
781C2—882no—
782C2#1307127411yescharacteristic
783C2#1307130311yescharacteristic
784C2#1307133811yescharacteristic
785C2#1307175312yes—
786C2#1307176712yes—
787C2#1307661611yescharacteristic
788C2#1307663811yescharacteristic
789C2#1307665711yescharacteristic
790C2#1307666111yescharacteristic
791C2#1307673512yes—
792C2#1307674412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#390D11
hypocenterC11#14623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. #13066875C2semidirect
4. #13066863C2semidirect
5. #13066859C2semidirect
6. #13066858C2semidirect
7. #13066857C2semidirect
8. #13066855C2semidirect
9. #13066855C2semidirect
10. #13066843C2semidirect
11. C2×C11×#390C2semidirect
27. #10622836C4semidirect
70. C2×C42×C11D4semidirect
205. C2×#390D11semidirect
474. C2×C42C22⋊D11semidirect
599. C11#14623semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106225532
#130668752
#130668632
#130668592
#130668582
#130668572
#130668552
#130668432
C2×C11×#3902
#1462311