Finite Group Databasebeta

← #14680664

Subgroups — #14680664

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×#10622834C211yesmaximal, characteristic, complemented
2C2×#10622833C212yesmaximal, complemented
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
4#13066873C211yesmaximal, characteristic, complemented
5#13066865C212yesmaximal, complemented
6#13066861C211yesmaximal, characteristic, complemented
7#13066857C211yesmaximal, characteristic, complemented
8#13066857C212yesmaximal, complemented
9#13066853C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C2×C11×#392C211yesmaximal, characteristic
12C23×D4×C11C2212yes—
13C23×D4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C11×#392C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28#10622834—24no—
29#10622833—28no—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C22⋊C4×Dic11—24no—
39C25×C11C2312yes—
40C25×C11C2311yescharacteristic
41C22×D4×C11—24no—
42C22×D4×C11—24no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—42no—
46C22×D4×C11—42no—
47C22×D4×C11—42no—
48C22×D4×C11—42no—
49C22×D4×C11—42no—
50C22×D4×C11—42no—
51C22×D4×C11C2×C418yes—
52C22×D4×C11C2×C414yescomplemented
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—22no—
57C23×Dic11—22no—
58C23×Dic11—42no—
59C23×Dic11—42no—
60C23×Dic11D414yescomplemented
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4—42no—
71C2×C11×C22⋊C4C2×C414yes—
72C2×C11×C22⋊C4C2×C418yescomplemented
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—42no—
84C2×C22⋊Dic11—42no—
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×C4⋊Dic11—22no—
92C2×C4⋊Dic11—42no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—42no—
95C2×C4×Dic11—42no—
96C2×C4×Dic11D414yescomplemented
97C11×#95C2×C414yescomplemented
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95—42no—
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×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—22no—
129C24×C11C22×C414yes—
130C24×C11C22×C412yes—
131C24×C11C2×D412yes—
132C24×C11#4112yes—
133C24×C11C2411yescharacteristic
134C2×D4×C11—216no—
135C2×D4×C11—28no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11—48no—
142C2×D4×C11—48no—
143C2×D4×C11—48no—
144C2×D4×C11—48no—
145C2×D4×C11—48no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
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×C11C22×C412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11#4112yes—
163C22×Dic11—28no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
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—48no—
193C22×Dic11—44no—
194C22×Dic11—44no—
195C22×Dic11—48no—
196C22×Dic11C2×D412yes—
197C22×Dic11C2×D412yes—
198C22×Dic11C2×D412yes—
199C22×Dic11C2×D412yes—
200C22×Dic11#4112yes—
201C22×Dic11#4112yes—
202C11×C22⋊C4—28no—
203C11×C22⋊C4—48no—
204C22⋊Dic11—28no—
205C22⋊Dic11—48no—
206C22⋊Dic11—48no—
207C22⋊Dic11—48no—
208C22⋊Dic11—48no—
209C22⋊Dic11—48no—
210C4⋊Dic11—44no—
211C4×Dic11—44no—
212C4×Dic11—44no—
213C2×#392D1111yescharacteristic
214C2×#390—111no—
215C2×#386—112no—
216C2×C4×C22⋊C4—111no—
217#1442—111no—
218#1440—112no—
219#1439—111no—
220#1438—112no—
221#1438—111no—
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—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
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×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—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11C4×D414yes—
282C23×C11C23×C411yescharacteristic
283C23×C11C22×D411yescharacteristic
284C23×C11C22×D411yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11C2×#4111yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11H(5,𝔽2)12yes—
290C23×C11H(5,𝔽2)12yes—
291C23×C11H(5,𝔽2)12yes—
292C23×C11H(5,𝔽2)12yes—
293D4×C11—416no—
294D4×C11—432no—
295C2×C4×C11—24no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—42no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11C4×D414yes—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—416no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
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—
346C2×Dic11#12114yes—
347C23×D4C2×D1112yes—
348C23×D4C2×D1111yescharacteristic
349C24×C4—111no—
350C22×C4⋊C4—111no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—111no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4C2×D1112yes—
359C22×C42—111no—
360C22×C42—111no—
361#392Dic1118yescomplemented
362#390—224no—
363#386—228no—
364C4×C22⋊C4—224no—
365C2×#95—112no—
366C2×#95—111no—
367C2×#95—111no—
368C2×#95—111no—
369C2×#95—112no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95—112no—
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×C11—44no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—44no—
391C22×C11—44no—
392C22×C11—82no—
393C22×C11—82no—
394C22×C11—82no—
395C22×C11—82no—
396C22×C11—82no—
397C22×C11—82no—
398C22×C11—82no—
399C22×C11—82no—
400C22×C11C2×C4×D411yescharacteristic
401C22×C11C2×C4×D411yescharacteristic
402C22×C11C4×#4111yescharacteristic
403C22×C11#51812yes—
404C22×C11#51812yes—
405C22×C11C2×#12111yescharacteristic
406C22×C11#52511yescharacteristic
407C22×C11#52911yescharacteristic
408C22×C11#53211yescharacteristic
409C22×C11#53411yescharacteristic
410C22×C11#53412yes—
411C22×C11#53511yescharacteristic
412C22×C11#53511yescharacteristic
413C22×C11#53511yescharacteristic
414C22×C11#53512yes—
415C22×C11#53812yes—
416C22×C11#53812yes—
417C22×C11#53812yes—
418C22×C11#53812yes—
419C22×C11#53812yes—
420C22×C11#54012yes—
421C22×C11#54012yes—
422C22×C11#54012yes—
423C4×C11—24no—
424C4×C11—44no—
425C4×C11—42no—
426Dic11—24no—
427Dic11—42no—
428Dic11—42no—
429Dic11—42no—
430Dic11—82no—
431Dic11—82no—
432C25C22×D1112yes—
433C25C22×D1111yescharacteristic
434C22×D4—24no—
435C22×D4—24no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—42no—
439C22×D4—42no—
440C22×D4—42no—
441C22×D4—42no—
442C22×D4—42no—
443C22×D4—42no—
444C22×D4C2×Dic1118yes—
445C22×D4C2×Dic1114yescomplemented
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—114no—
451C23×C4—112no—
452C23×C4—112no—
453C23×C4—222no—
454C23×C4—222no—
455C23×C4—442no—
456C23×C4—442no—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1112yes—
459C23×C4C22×D1111yescharacteristic
460C2×C4⋊C4—222no—
461C2×C4⋊C4—442no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—222no—
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—224no—
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⋊C4C2×Dic1114yes—
485C2×C22⋊C4C2×Dic1118yescomplemented
486C2×C42—114no—
487C2×C42—222no—
488C2×C42—442no—
489C2×C42—442no—
490#95—222no—
491#95—224no—
492#95—224no—
493#95—222no—
494#95—222no—
495#95—442no—
496#95—442no—
497#95—442no—
498#95C2×Dic1114yescomplemented
499C2×C11—44no—
500C2×C11—84no—
501C2×C11C4×#12111yescharacteristic
502C2×C11#232111yescharacteristic
503C2×C11#232112yes—
504C2×C11#232811yescharacteristic
505C2×C11#233312yes—
506C2×C11#261711yescharacteristic
507C2×C11#261911yescharacteristic
508C2×C11#263111yescharacteristic
509C2×C11#263511yescharacteristic
510C2×C11#264812yes—
511C2×C11#266112yes—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24D4×D1112yes—
535C24#434112yes—
536C24C22×Dic1114yes—
537C24C22×Dic1112yes—
538C24C23×D1111yescharacteristic
539C2×D4—216no—
540C2×D4—28no—
541C2×D4—48no—
542C2×D4—48no—
543C2×D4—48no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—48no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—228no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—221no—
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—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—448no—
599C22×C4—444no—
600C22×C4—444no—
601C22×C4—448no—
602C22×C4D4×D1112yes—
603C22×C4#434112yes—
604C22×C4C22×Dic1114yes—
605C22×C4C22×Dic1112yes—
606C22×C4C22×Dic1112yes—
607C4⋊C4—444no—
608C22⋊C4—28no—
609C22⋊C4—48no—
610C22⋊C4—228no—
611C22⋊C4—448no—
612C22⋊C4—448no—
613C22⋊C4—448no—
614C22⋊C4—448no—
615C22⋊C4—448no—
616C42—444no—
617C42—444no—
618C11#1431111yescharacteristic, complemented, Sylow
619C23—22no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—41no—
639C23—41no—
640C23—42no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
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—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23D4×Dic1114yes—
677C23C2×D4×D1111yescharacteristic
678C23C2×D4×D1111yescharacteristic
679C23C2×#434111yescharacteristic
680C23C2×#434111yescharacteristic
681C23#6703712yes—
682C23#6703712yes—
683C23#6703712yes—
684C23#6703712yes—
685C23#41×D1111yescharacteristic
686C23#41×D1111yescharacteristic
687C23C23×Dic1111yescharacteristic
688D4—416no—
689D4—432no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—114no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—224no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—224no—
718C2×C4—4416no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
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×C4—442no—
741C2×C4D4×Dic1114yes—
742C22—24no—
743C22—28no—
744C22—44no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—44no—
751C22—42no—
752C22—42no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22#1062312012yes—
769C22#1062312011yescharacteristic
770C22#1062312311yescharacteristic
771C22#1062312312yes—
772C22#1062312412yes—
773C22#1062312412yes—
774C22#1062312412yes—
775C22#1062312711yescharacteristic
776C22#1062313111yescharacteristic
777C22D11×#12111yescharacteristic
778C22#1062313711yescharacteristic
779C22#1062314412yes—
780C22#1062314412yes—
781C22#1062314612yes—
782C22#1062314612yes—
783C22#1062324611yescharacteristic
784C22#1062324611yescharacteristic
785C22#1062325012yes—
786C22C2×D4×Dic1111yescharacteristic
787C22C2×D4×Dic1111yescharacteristic
788C22#1062332912yes—
789C22#1062332912yes—
790C22#41×Dic1111yescharacteristic
791C4—24no—
792C4—44no—
793C4—42no—
794C4—224no—
795C4—442no—
796C4—442no—
797C4—442no—
798C4—882no—
799C4—882no—
800C2—44no—
801C2—84no—
802C2#121×Dic1111yescharacteristic
803C2#1307127711yescharacteristic
804C2#1307127712yes—
805C2#1307134211yescharacteristic
806C2#1307138312yes—
807C2#1307434911yescharacteristic
808C2#1307436511yescharacteristic
809C2#1307447311yescharacteristic
810C2#1307450511yescharacteristic
811C2#1307460512yes—
812C2#1307474112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC2×C11×#392C2
socle, cosocleC24×C11C24
hypercenterC2×#392D11
hypocenterC11#14311
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#10622834C2semidirect
2. C2×#10622833C2semidirect
3. C2×C22⋊C4×Dic11C2semidirect
4. #13066873C2semidirect
5. #13066865C2semidirect
6. #13066861C2semidirect
7. #13066857C2semidirect
8. #13066857C2semidirect
9. #13066853C2semidirect
10. #13066841C2semidirect
26. C11×#392C4semidirect
52. C22×D4×C11C2×C4semidirect
60. C23×Dic11D4semidirect
72. C2×C11×C22⋊C4C2×C4semidirect
96. C2×C4×Dic11D4semidirect
97. C11×#95C2×C4semidirect
361. #392Dic11semidirect
445. C22×D4C2×Dic11semidirect
485. C2×C22⋊C4C2×Dic11semidirect
498. #95C2×Dic11semidirect
618. C11#14311semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106228332
C2×C22⋊C4×Dic112
#130668732
#130668652
#130668612
#130668572
#130668532
#130668412
C2×C11×#3922
#1431111