Finite Group Databasebeta

← #14680659

Subgroups — #14680659

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×#10622573C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622826C212yesmaximal, complemented
4#13066872C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066861C211yesmaximal, characteristic, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066854C212yesmaximal, complemented
10#13066843C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C23×D44C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C4×C11×C22⋊C4—24no—
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29#10622826—28no—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622573C418yescomplemented
38#10622552—24no—
39C25×C11C2311yescharacteristic
40C24×D11C2312yes—
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—42no—
44C23×C4×C11—42no—
45C23×C4×C11D414yescomplemented
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—24no—
53C22×C22⋊D11—24no—
54C22×C22⋊D11—42no—
55C22×C22⋊D11—42no—
56C22×C22⋊D11—42no—
57C22×C22⋊D11—42no—
58C22×C22⋊D11C2×C418yes—
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C22×D44—22no—
63C22×D44—22no—
64C22×D44—42no—
65C22×D44—42no—
66C22×D44C2×C414yescomplemented
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4C2×C414yes—
73C2×C42×C11—22no—
74C2×C42×C11—42no—
75C2×C42×C11—42no—
76C2×C42×C11D414yescomplemented
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11—42no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
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)⋊C4—42no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4C2×C418yescomplemented
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—42no—
97C11×#95—22no—
98C11×#95—22no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—22no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95C2×C414yescomplemented
106#14311—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11C22×C412yes—
116C24×C11C2×D412yes—
117C24×C11#4112yes—
118C24×C11C2411yescharacteristic
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—22no—
133C23×D11C22×C414yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
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×C11—28no—
155C22×C4×C11—48no—
156C22×C4×C11—44no—
157C22×C4×C11—44no—
158C22×C4×C11—48no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11#4112yes—
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C2×C22⋊D11—216no—
170C2×C22⋊D11—48no—
171C2×C22⋊D11—48no—
172C2×C22⋊D11—48no—
173C2×C22⋊D11—48no—
174C2×C22⋊D11—48no—
175C2×C22⋊D11—48no—
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×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11C22×C414yes—
197C2×D44—28no—
198C2×D44—48no—
199C2×D44—44no—
200C2×D44—44no—
201C2×D44—48no—
202C11×C22⋊C4—28no—
203C11×C22⋊C4—28no—
204C42×C11—44no—
205C42×C11—44no—
206C22⋊Dic11—48no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4—48no—
209(C2×D11)⋊C4—48no—
210(C2×D11)⋊C4—48no—
211(C2×D11)⋊C4—48no—
212C4⋊Dic11—44no—
213C2×#392—111no—
214C2×#390—111no—
215C2×#386—112no—
216C2×C4×C22⋊C4D1111yescharacteristic, complemented
217#1442—111no—
218#1440—112no—
219#1439—111no—
220#1438—111no—
221#1438—112no—
222#1437—112no—
223#1434—111no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11C4×D414yes—
247C23×C11C23×C411yescharacteristic
248C23×C11C22×D411yescharacteristic
249C23×C11C22×D411yescharacteristic
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4111yescharacteristic
252C23×C11C2×#4111yescharacteristic
253C23×C11C2×#4111yescharacteristic
254C23×C11H(5,𝔽2)12yes—
255C23×C11H(5,𝔽2)12yes—
256C23×C11H(5,𝔽2)12yes—
257C23×C11H(5,𝔽2)12yes—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
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—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—24no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—416no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11C4×D414yes—
323C2×C4×C11#12114yes—
324C22⋊D11—432no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
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—
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—
346D44—416no—
347C23×D4—112no—
348C23×D4—111no—
349C24×C4C2×D1111yescharacteristic
350C22×C4⋊C4—111no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4C2×D1111yescharacteristic
359C22×C42C2×D1111yescharacteristic
360C22×C42C2×D1111yescharacteristic
361#392—118no—
362#390—224no—
363#386—228no—
364C4×C22⋊C4—24no—
365C2×#95—111no—
366C2×#95—112no—
367C2×#95—111no—
368C2×#95—112no—
369C2×#95—112no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95C2×D1111yescharacteristic
373C2×#95C2×D1111yescharacteristic
374C22×C11—28no—
375C22×C11—24no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—44no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11C2×C4×D411yescharacteristic
386C22×C11C2×C4×D411yescharacteristic
387C22×C11C4×#4111yescharacteristic
388C22×C11#51812yes—
389C22×C11#51812yes—
390C22×C11C2×#12111yescharacteristic
391C22×C11#52511yescharacteristic
392C22×C11#52911yescharacteristic
393C22×C11#53211yescharacteristic
394C22×C11#53412yes—
395C22×C11#53411yescharacteristic
396C22×C11#53512yes—
397C22×C11#53511yescharacteristic
398C22×C11#53511yescharacteristic
399C22×C11#53511yescharacteristic
400C22×C11#53812yes—
401C22×C11#53812yes—
402C22×C11#53812yes—
403C22×C11#53812yes—
404C22×C11#53812yes—
405C22×C11#54012yes—
406C22×C11#54012yes—
407C22×C11#54012yes—
408C2×D11—44no—
409C2×D11—44no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—82no—
416C2×D11—82no—
417C2×D11—82no—
418C2×D11—82no—
419C2×D11—82no—
420C2×D11—82no—
421C2×D11—82no—
422C2×D11—82no—
423C4×C11—24no—
424C4×C11—24no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11—42no—
429Dic11—44no—
430Dic11—82no—
431Dic11—82no—
432C25—112no—
433C25C22×D1111yescharacteristic
434C22×D4—118no—
435C22×D4—114no—
436C22×D4—224no—
437C22×D4—224no—
438C22×D4—222no—
439C22×D4—222no—
440C22×D4—442no—
441C22×D4—442no—
442C22×D4—442no—
443C22×D4—442no—
444C22×D4—442no—
445C22×D4—442no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4—112no—
451C23×C4—112no—
452C23×C4—112no—
453C23×C4D4414yescomplemented
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C2×C4⋊C4—222no—
461C2×C4⋊C4—442no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—118no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—442no—
476C2×C22⋊C4—442no—
477C2×C22⋊C4—442no—
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⋊C4C4×D1114yes—
486C2×C42—22no—
487C2×C42—42no—
488C2×C42—42no—
489C2×C42C22⋊D1114yescomplemented
490#95—22no—
491#95—22no—
492#95—114no—
493#95—224no—
494#95—224no—
495#95—222no—
496#95—442no—
497#95—442no—
498#95—442no—
499C2×C11—44no—
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—84no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—21no—
520C24—114no—
521C24—222no—
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—222no—
535C24C2×C4×D1112yes—
536C24C2×D4412yes—
537C24#433912yes—
538C24C23×D1111yescharacteristic
539C2×D4—2216no—
540C2×D4—228no—
541C2×D4—448no—
542C2×D4—444no—
543C2×D4—448no—
544C2×D4—444no—
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—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—28no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—114no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
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×C4C2×C4×D1112yes—
598C22×C4C2×C4×D1112yes—
599C22×C4C2×D4412yes—
600C22×C4C2×D4412yes—
601C22×C4#433912yes—
602C22×C4#433912yes—
603C22×C4#433912yes—
604C22×C4C2×C22⋊D1112yes—
605C22×C4C2×C22⋊D1112yes—
606C22×C4C2×C22⋊D1112yes—
607C4⋊C4—444no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—448no—
611C22⋊C4—448no—
612C22⋊C4—448no—
613C22⋊C4—448no—
614C22⋊C4—448no—
615C22⋊C4—448no—
616C42—44no—
617C42—44no—
618C11#1431111yescharacteristic, complemented, Sylow
619C23—22no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—42no—
632C23—42no—
633C23—41no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—41no—
640C23—41no—
641C23—224no—
642C23—224no—
643C23—224no—
644C23—224no—
645C23—224no—
646C23—224no—
647C23—224no—
648C23—442no—
649C23—442no—
650C23—442no—
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—442no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23C4×D4414yes—
677C23C22×C4×D1111yescharacteristic
678C23C22×D4411yescharacteristic
679C23C2×#433911yescharacteristic
680C23C2×#433911yescharacteristic
681C23C2×#433911yescharacteristic
682C23C2×#433911yescharacteristic
683C23#6703712yes—
684C23#6703712yes—
685C23#6704212yes—
686C23#6704212yes—
687C23C22×C22⋊D1111yescharacteristic
688D4—4416no—
689D4—4432no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—416no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
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—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4C4×C22⋊D1114yes—
741C2×C4#6698314yes—
742C22—24no—
743C22—28no—
744C22—44no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—42no—
749C22—44no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—444no—
754C22—444no—
755C22—444no—
756C22—444no—
757C22—444no—
758C22—444no—
759C22—444no—
760C22—882no—
761C22—882no—
762C22—882no—
763C22—882no—
764C22—882no—
765C22—882no—
766C22—882no—
767C22—882no—
768C22C2×C4×D4411yescharacteristic
769C22C4×#433911yescharacteristic
770C22#1062300811yescharacteristic
771C22#1062301011yescharacteristic
772C22#1062302412yes—
773C22#1062302512yes—
774C22#1062305612yes—
775C22#1062306612yes—
776C22#1062307612yes—
777C22#1062307612yes—
778C22#1062309112yes—
779C22#1062309112yes—
780C22#1062309112yes—
781C22#1062309112yes—
782C22#1062309312yes—
783C22#1062309312yes—
784C22C2×C4×C22⋊D1111yescharacteristic
785C22C2×#6698311yescharacteristic
786C22#1062332211yescharacteristic
787C22#1062333511yescharacteristic
788C22#1062333611yescharacteristic
789C22#1062336111yescharacteristic
790C22#1062336111yescharacteristic
791C4—24no—
792C4—24no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—444no—
798C4—882no—
799C4—882no—
800C2—44no—
801C2—884no—
802C2C4×#6698311yescharacteristic
803C2#1307127011yescharacteristic
804C2#1307127612yes—
805C2#1307133811yescharacteristic
806C2#1307137612yes—
807C2#1307435011yescharacteristic
808C2#1307436611yescharacteristic
809C2#1307446811yescharacteristic
810C2#1307450011yescharacteristic
811C2#1307459812yes—
812C2#1307474212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14311
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622826C2semidirect
4. #13066872C2semidirect
5. #13066864C2semidirect
6. #13066861C2semidirect
7. #13066856C2semidirect
8. #13066855C2semidirect
9. #13066854C2semidirect
10. #13066843C2semidirect
11. C2×C4×C11×C22⋊C4C2semidirect
37. #10622573C4semidirect
45. C23×C4×C11D4semidirect
66. C22×D44C2×C4semidirect
76. C2×C42×C11D4semidirect
94. C2×(C2×D11)⋊C4C2×C4semidirect
105. C11⋊#95C2×C4semidirect
216. C2×C4×C22⋊C4D11semidirect
453. C23×C4D44semidirect
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×#106225732
C2×#106225522
C2×#106228262
#130668722
#130668642
#130668612
#130668562
#130668552
#130668542
#130668432
C2×C4×C11×C22⋊C42
#1431111