Finite Group Databasebeta

← #14681069

Subgroups — #14681069

Order 2816.

3538 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622834C212yesmaximal, complemented
2C2×#10622564C212yesmaximal, complemented
3C2×#10622860C212yesmaximal, complemented
4#13066861C212yesmaximal, complemented
5#13066857C212yesmaximal, complemented
6#13066857C211yesmaximal, characteristic, complemented
7#13066857C211yesmaximal, characteristic, complemented
8#13066853C212yesmaximal, complemented
9C22×C11×#120C211yesmaximal, characteristic
10C26×C11C2211yescharacteristic
11C23×D4×C11C2212yes—
12C23×D4×C11C2211yescharacteristic
13C2×C11×#120—28no—
14C2×C11×#120C418yescomplemented
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic, complemented
24C22×C22⋊Dic11C2212yescomplemented
25C22×C22⋊Dic11C2211yescharacteristic, complemented
26C22×C4⋊Dic11C2212yescomplemented
27C22×C4×Dic11C2212yescomplemented
28#10622860—28no—
29#10622834—28no—
30C2×C11⋊#95C2212yescomplemented
31C2×C11⋊#95C2212yescomplemented
32C2×C11⋊#95C2211yescharacteristic, complemented
33C2×C11⋊#95C2212yescomplemented
34C2×C11⋊#95C2211yescharacteristic, complemented
35#10622564—28no—
36C25×C11—24no—
37C25×C11—24no—
38C25×C11—24no—
39C25×C11—42no—
40C25×C11—42no—
41C25×C11—41no—
42C25×C11—41no—
43C25×C11—42no—
44C25×C11C2×C414yes—
45C25×C11C2311yescharacteristic
46C25×C11C2311yescharacteristic
47C25×C11C2312yes—
48C22×D4×C11—24no—
49C22×D4×C11—24no—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11—42no—
54C22×D4×C11—42no—
55C22×D4×C11—42no—
56C22×D4×C11—41no—
57C22×D4×C11—41no—
58C22×D4×C11C2×C418yes—
59C22×D4×C11C2×C414yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C11×#120—232no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4C2×C418yes—
70C2×C11×C22⋊C4C2×C414yes—
71C2×C11×C22⋊C4D418yes—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
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×C22⋊Dic11—41no—
92C2×C22⋊Dic11—42no—
93C2×C22⋊Dic11—42no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—42no—
96C2×C22⋊Dic11D418yescomplemented
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11—42no—
100C2×C4×Dic11—24no—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—42no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—41no—
106C11⋊#95—42no—
107C11⋊#95—41no—
108#14358—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—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—28no—
129C24×C11—216no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—22no—
138C24×C11—44no—
139C24×C11—48no—
140C24×C11—44no—
141C24×C11—44no—
142C24×C11—48no—
143C24×C11—48no—
144C24×C11—48no—
145C24×C11—48no—
146C24×C11—48no—
147C24×C11—44no—
148C24×C11—48no—
149C24×C11—48no—
150C24×C11—48no—
151C24×C11—48no—
152C24×C11—48no—
153C24×C11—48no—
154C24×C11—48no—
155C24×C11—44no—
156C24×C11—44no—
157C24×C11C22×C412yes—
158C24×C11C22×C412yes—
159C24×C11C22×C414yes—
160C24×C11C2×D414yes—
161C24×C11C2×D414yes—
162C24×C11#4114yes—
163C24×C11C2411yescharacteristic
164C2×D4×C11—28no—
165C2×D4×C11—216no—
166C2×D4×C11—216no—
167C2×D4×C11—48no—
168C2×D4×C11—44no—
169C2×D4×C11—44no—
170C2×D4×C11—48no—
171C2×D4×C11—48no—
172C2×D4×C11—48no—
173C2×D4×C11—48no—
174C2×D4×C11—48no—
175C2×D4×C11—48no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C22×C414yes—
186C22×C4×C11C2×D414yes—
187C22×C4×C11C2×D414yes—
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×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11C2×D414yes—
215C22×Dic11C2×D414yes—
216C11×C22⋊C4—216no—
217C11×C22⋊C4C22⋊C4116yescomplemented
218C22⋊Dic11—48no—
219C22⋊Dic11—48no—
220C22⋊Dic11—48no—
221C22⋊Dic11—48no—
222C22⋊Dic11—48no—
223C22⋊Dic11—48no—
224C22⋊Dic11—44no—
225C22⋊Dic11—48no—
226C22⋊Dic11—44no—
227C4⋊Dic11—48no—
228C4×Dic11—48no—
229C22×#120D1111yescharacteristic
230C2×#390—112no—
231C2×#388—112no—
232C2×#379—112no—
233#1439—112no—
234#1438—112no—
235#1438—111no—
236#1438—111no—
237#1437—112no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—22no—
267C23×C11—24no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—24no—
271C23×C11—432no—
272C23×C11—416no—
273C23×C11—416no—
274C23×C11—432no—
275C23×C11—416no—
276C23×C11—432no—
277C23×C11—432no—
278C23×C11—432no—
279C23×C11—432no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—42no—
283C23×C11—42no—
284C23×C11—42no—
285C23×C11—42no—
286C23×C11—42no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11—42no—
290C23×C11—42no—
291C23×C11—42no—
292C23×C11—42no—
293C23×C11—42no—
294C23×C11—41no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—41no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—41no—
304C23×C11—42no—
305C23×C11—41no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11—41no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—41no—
319C23×C11—42no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11C2×C22⋊C414yes—
323C23×C11C4×D418yes—
324C23×C11C23×C411yescharacteristic
325C23×C11C22×D412yes—
326C23×C11C22×D412yes—
327C23×C11C2×#4112yes—
328C23×C11H(5,𝔽2)12yes—
329C23×C11H(5,𝔽2)12yes—
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C11H(5,𝔽2)12yes—
333D4×C11—432no—
334D4×C11—416no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—24no—
338C2×C4×C11—24no—
339C2×C4×C11—24no—
340C2×C4×C11—24no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11C2×C22⋊C418yes—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—24no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C26C2×D1111yescharacteristic
376C23×D4C2×D1112yes—
377C23×D4C2×D1111yescharacteristic
378C2×#120—28no—
379C2×#120Dic1118yescomplemented
380C22×C4⋊C4—112no—
381C22×C22⋊C4—112no—
382C22×C22⋊C4—112no—
383C22×C22⋊C4—112no—
384C22×C22⋊C4—112no—
385C22×C22⋊C4—112no—
386C22×C22⋊C4—111no—
387C22×C22⋊C4—112no—
388C22×C22⋊C4—112no—
389C22×C22⋊C4—111no—
390C22×C22⋊C4C2×D1112yes—
391C22×C22⋊C4C2×D1111yescharacteristic
392C22×C42—112no—
393#390—228no—
394#388—228no—
395#379—228no—
396C2×#95—112no—
397C2×#95—112no—
398C2×#95—111no—
399C2×#95—112no—
400C2×#95—111no—
401C22×C11—24no—
402C22×C11—28no—
403C22×C11—28no—
404C22×C11—28no—
405C22×C11—28no—
406C22×C11—464no—
407C22×C11—44no—
408C22×C11—44no—
409C22×C11—44no—
410C22×C11—44no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—44no—
414C22×C11—44no—
415C22×C11—44no—
416C22×C11—44no—
417C22×C11—44no—
418C22×C11—44no—
419C22×C11—44no—
420C22×C11—44no—
421C22×C11—44no—
422C22×C11—44no—
423C22×C11—44no—
424C22×C11—44no—
425C22×C11—44no—
426C22×C11—42no—
427C22×C11—44no—
428C22×C11—44no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—82no—
432C22×C11—82no—
433C22×C11—82no—
434C22×C11—82no—
435C22×C11C22×C22⋊C411yescharacteristic
436C22×C11C2×C4×D412yes—
437C22×C11#51811yescharacteristic
438C22×C11#51811yescharacteristic
439C22×C11#51812yes—
440C22×C11#53412yes—
441C22×C11#53512yes—
442C22×C11#53512yes—
443C22×C11#53512yes—
444C22×C11#53812yes—
445C22×C11#53812yes—
446C22×C11D4212yes—
447C22×C11D4212yes—
448C22×C11D4211yescharacteristic
449C22×C11#54612yes—
450C22×C11#54612yes—
451C22×C11#54612yes—
452C22×C11#55111yescharacteristic
453C22×C11#56012yes—
454C22×C11#56011yescharacteristic
455C22×C11H(3,𝔽4)11yescharacteristic
456C4×C11—28no—
457C4×C11—42no—
458Dic11—44no—
459Dic11—44no—
460Dic11—82no—
461Dic11—82no—
462C25—24no—
463C25—24no—
464C25—24no—
465C25—42no—
466C25—42no—
467C25—41no—
468C25—41no—
469C25—42no—
470C25C2×Dic1114yes—
471C25C22×D1111yescharacteristic
472C25C22×D1112yes—
473C25C22×D1111yescharacteristic
474C22×D4—24no—
475C22×D4—24no—
476C22×D4—24no—
477C22×D4—24no—
478C22×D4—24no—
479C22×D4—42no—
480C22×D4—42no—
481C22×D4—41no—
482C22×D4—42no—
483C22×D4—41no—
484C22×D4C2×Dic1118yes—
485C22×D4C2×Dic1114yes—
486C23×C4—112no—
487C23×C4—112no—
488C23×C4—112no—
489C23×C4—112no—
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1112yes—
492#120—232no—
493C2×C4⋊C4—224no—
494C2×C4⋊C4—224no—
495C2×C4⋊C4—442no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—118no—
499C2×C22⋊C4—224no—
500C2×C22⋊C4—224no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—224no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—224no—
505C2×C22⋊C4—224no—
506C2×C22⋊C4—224no—
507C2×C22⋊C4—224no—
508C2×C22⋊C4—224no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—442no—
511C2×C22⋊C4—442no—
512C2×C22⋊C4—441no—
513C2×C22⋊C4—442no—
514C2×C22⋊C4—442no—
515C2×C22⋊C4—442no—
516C2×C22⋊C4—442no—
517C2×C22⋊C4—442no—
518C2×C22⋊C4—442no—
519C2×C22⋊C4—442no—
520C2×C22⋊C4—442no—
521C2×C22⋊C4—442no—
522C2×C22⋊C4—441no—
523C2×C22⋊C4C2×Dic1118yes—
524C2×C22⋊C4C2×Dic1114yes—
525C2×C22⋊C4C22⋊D1118yes—
526C2×C42—224no—
527C2×C42—224no—
528C2×C42—442no—
529#95—224no—
530#95—224no—
531#95—441no—
532#95—442no—
533#95—441no—
534C2×C11—44no—
535C2×C11—48no—
536C2×C11—82no—
537C2×C11#230911yescharacteristic
538C2×C11#232112yes—
539C2×C11D4×C22⋊C412yes—
540C2×C11#235811yescharacteristic
541C2×C11#237511yescharacteristic
542C2×C11#266912yes—
543C2×C11#267012yes—
544C2×C11#267812yes—
545C2×C11#268512yes—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—21no—
561C24—22no—
562C24—21no—
563C24—22no—
564C24—22no—
565C24—216no—
566C24—28no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—21no—
572C24—22no—
573C24—21no—
574C24—22no—
575C24—48no—
576C24—44no—
577C24—44no—
578C24—48no—
579C24—48no—
580C24—48no—
581C24—48no—
582C24—44no—
583C24—44no—
584C24—48no—
585C24—48no—
586C24—48no—
587C24—48no—
588C24—48no—
589C24—48no—
590C24—48no—
591C24—44no—
592C24—48no—
593C24—44no—
594C24D4×D1114yes—
595C24#434114yes—
596C24C22×Dic1112yes—
597C24C22×Dic1114yes—
598C24C22×Dic1112yes—
599C24C2×C22⋊D1114yes—
600C24C23×D1111yescharacteristic
601C2×D4—216no—
602C2×D4—28no—
603C2×D4—216no—
604C2×D4—48no—
605C2×D4—44no—
606C2×D4—44no—
607C2×D4—48no—
608C2×D4—48no—
609C2×D4—48no—
610C2×D4—48no—
611C2×D4—48no—
612C2×D4—48no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—114no—
622C22×C4—114no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4C22×Dic1112yes—
650C22×C4C22×Dic1114yes—
651C22×C4C2×C22⋊D1114yes—
652C22×C4C2×C22⋊D1114yes—
653C4⋊C4—448no—
654C22⋊C4—216no—
655C22⋊C4—448no—
656C22⋊C4—444no—
657C22⋊C4—448no—
658C22⋊C4—448no—
659C22⋊C4—448no—
660C22⋊C4—448no—
661C22⋊C4—448no—
662C22⋊C4—448no—
663C22⋊C4—444no—
664C22⋊C4C22⋊Dic11116yescomplemented
665C42—448no—
666C11#1435811yescharacteristic, complemented, Sylow
667C23—24no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—432no—
701C23—416no—
702C23—416no—
703C23—432no—
704C23—432no—
705C23—416no—
706C23—432no—
707C23—432no—
708C23—432no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—42no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—42no—
743C23—41no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—41no—
749C23—42no—
750C23—41no—
751C23D4×Dic1118yes—
752C23C2×C22⋊Dic1114yes—
753C23C2×D4×D1112yes—
754C23C2×#434112yes—
755C23#6703712yes—
756C23#6703712yes—
757C23#6703711yescharacteristic
758C23#6703712yes—
759C23#6703711yescharacteristic
760C23C23×Dic1111yescharacteristic
761C23C22×C22⋊D1112yes—
762D4—432no—
763D4—416no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—224no—
778C2×C4—224no—
779C2×C4—224no—
780C2×C4—224no—
781C2×C4—442no—
782C2×C4—442no—
783C2×C4—442no—
784C2×C4—442no—
785C2×C4—442no—
786C2×C4—442no—
787C2×C4—442no—
788C2×C4—442no—
789C2×C4—442no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—442no—
793C2×C4—442no—
794C2×C4—442no—
795C2×C4—442no—
796C2×C4—442no—
797C2×C4—442no—
798C2×C4—442no—
799C2×C4—442no—
800C2×C4—442no—
801C2×C4—442no—
802C2×C4—442no—
803C2×C4C2×C22⋊Dic1118yes—
804C22—28no—
805C22—28no—
806C22—24no—
807C22—28no—
808C22—28no—
809C22—464no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—42no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—42no—
832C22—44no—
833C22—42no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22#1062311811yescharacteristic
839C22#1062312012yes—
840C22#1062312111yescharacteristic
841C22#1062312212yes—
842C22#1062312312yes—
843C22#1062312412yes—
844C22#1062312412yes—
845C22#1062312511yescharacteristic
846C22#1062312612yes—
847C22#1062312611yescharacteristic
848C22C2×D4×Dic1112yes—
849C22#1062332912yes—
850C22#1062332911yescharacteristic
851C22#1062332911yescharacteristic
852C22D4×C22⋊D1112yes—
853C22D4×C22⋊D1112yes—
854C22#1062333612yes—
855C22#1062333612yes—
856C22#1062333712yes—
857C22#1062333712yes—
858C22C22×C22⋊Dic1111yescharacteristic
859C4—28no—
860C4—42no—
861C4—444no—
862C4—444no—
863C4—882no—
864C4—882no—
865C2—48no—
866C2—44no—
867C2—82no—
868C2#1307119811yescharacteristic
869C2#1307127712yes—
870C2D4×C22⋊Dic1112yes—
871C2#1307160011yescharacteristic
872C2#1307175711yescharacteristic
873C2#1307483012yes—
874C2#1307483812yes—
875C2#1307493712yes—
876C2#1307500312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC22×C11×#120C2
socle, cosocleC24×C11C24
hypercenterC22×#120D11
hypocenterC11#14358
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10622834C2semidirect
2. C2×#10622564C2semidirect
3. C2×#10622860C2semidirect
4. #13066861C2semidirect
5. #13066857C2semidirect
6. #13066857C2semidirect
7. #13066857C2semidirect
8. #13066853C2semidirect
14. C2×C11×#120C4semidirect
23. C22×C22⋊Dic11C22semidirect
24. C22×C22⋊Dic11C22semidirect
25. C22×C22⋊Dic11C22semidirect
26. C22×C4⋊Dic11C22semidirect
27. C22×C4×Dic11C22semidirect
30. C2×C11⋊#95C22semidirect
31. C2×C11⋊#95C22semidirect
32. C2×C11⋊#95C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
96. C2×C22⋊Dic11D4semidirect
217. C11×C22⋊C4C22⋊C4semidirect
379. C2×#120Dic11semidirect
664. C22⋊C4C22⋊Dic11semidirect
666. C11#14358semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225642
C2×#106228602
#130668612
#130668572
#130668532
C22×C11×#1202
#1435811