Finite Group Databasebeta

← #14676839

Subgroups — #14676839

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622557C212yesmaximal, complemented
2C2×#10622823C211yesmaximal, characteristic, complemented
3C2×#10622860C211yesmaximal, characteristic
4C2×#10622860C211yesmaximal, characteristic
5C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#13066863C212yesmaximal, complemented
7#13066859C212yesmaximal, complemented
8#13066853C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066839C211yesmaximal, characteristic, complemented
11C23×C11×C22⋊C4C211yesmaximal, characteristic
12C26×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C22×C11×C22⋊C4—24no—
16C22×C11×C22⋊C4—28no—
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2212yes—
27C22×Dic11⋊C4C2212yescomplemented
28C22×C4×Dic11C2211yescharacteristic, complemented
29C22×C4×Dic11C2211yescharacteristic, complemented
30#10622860—24no—
31#10622860C418yescomplemented
32#10622823—24no—
33C4×C22⋊Dic11—24no—
34C2×C11⋊#95C2212yescomplemented
35C2×C11⋊#95C2212yescomplemented
36C2×C11⋊#95C2211yescharacteristic, complemented
37C2×C11⋊#95C2211yescharacteristic, complemented
38C2×C11⋊#95C2212yescomplemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41#10622557—28no—
42C25×C11—24no—
43C25×C11—22no—
44C25×C11—24no—
45C25×C11—22no—
46C25×C11—22no—
47C25×C11—22no—
48C25×C11—22no—
49C25×C11—22no—
50C25×C11—42no—
51C25×C11—42no—
52C25×C11C2×C414yes—
53C25×C11C2312yes—
54C25×C11C2311yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—24no—
59C23×C4×C11—24no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—42no—
63C23×C4×C11—42no—
64C23×C4×C11D414yes—
65C23×C4×C11C2312yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C2×C11×C22⋊C4—232no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4D418yes—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—42no—
97C2×C22⋊Dic11—42no—
98C2×C22⋊Dic11—42no—
99C2×C22⋊Dic11—42no—
100C2×C22⋊Dic11C2×C414yes—
101C2×C22⋊Dic11C2×C414yes—
102C2×C22⋊Dic11C2×C418yescomplemented
103C2×C22⋊Dic11C2×C418yescomplemented
104C2×C22⋊Dic11D414yes—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—24no—
107C2×Dic11⋊C4—42no—
108C2×C4×Dic11—24no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—42no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—24no—
117C11⋊#95—42no—
118C11⋊#95—42no—
119#13991—111nomaximal, Sylow
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—28no—
125C24×C11—28no—
126C24×C11—216no—
127C24×C11—216no—
128C24×C11—28no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—28no—
142C24×C11—28no—
143C24×C11—48no—
144C24×C11—48no—
145C24×C11—48no—
146C24×C11—48no—
147C24×C11—48no—
148C24×C11—48no—
149C24×C11—48no—
150C24×C11—48no—
151C24×C11—48no—
152C24×C11—44no—
153C24×C11—44no—
154C24×C11—48no—
155C24×C11—44no—
156C24×C11—44no—
157C24×C11—44no—
158C24×C11—44no—
159C24×C11C22×C414yes—
160C24×C11C22×C412yes—
161C24×C11C2×D414yes—
162C24×C11C2×D412yes—
163C24×C11C2×D412yes—
164C24×C11#4114yes—
165C24×C11#4112yes—
166C24×C11#4112yes—
167C24×C11#4112yes—
168C24×C11#4112yes—
169C24×C11C2411yescharacteristic
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—28no—
174C22×C4×C11—28no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—28no—
186C22×C4×C11—44no—
187C22×C4×C11—48no—
188C22×C4×C11—48no—
189C22×C4×C11—48no—
190C22×C4×C11—48no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2×D414yes—
195C22×C4×C11C2×D414yes—
196C22×C4×C11C2×D412yes—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11C22×C412yes—
227C22×Dic11C22×C414yes—
228C22×Dic11C22×C412yes—
229C22×Dic11C2×D412yes—
230C22×Dic11C2×D412yes—
231C11×C22⋊C4—216no—
232C11×C22⋊C4—216no—
233C22⋊Dic11—28no—
234C22⋊Dic11—28no—
235C22⋊Dic11—216no—
236C22⋊Dic11—28no—
237C22⋊Dic11—48no—
238C22⋊Dic11—48no—
239C22⋊Dic11—48no—
240C22⋊Dic11—44no—
241Dic11⋊C4—48no—
242C4×Dic11—44no—
243C4×Dic11—44no—
244C23×C22⋊C4D1111yescharacteristic
245C2×#388—112no—
246C2×#385—111no—
247C2×#379—111no—
248C2×#379—111no—
249C2×C4×C22⋊C4—111no—
250#1440—112no—
251#1439—112no—
252#1437—112no—
253C22⋊#95—111no—
254C22⋊#95—111no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11—232no—
272C23×C11—24no—
273C23×C11—24no—
274C23×C11—24no—
275C23×C11—24no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—24no—
282C23×C11—24no—
283C23×C11—24no—
284C23×C11—24no—
285C23×C11—24no—
286C23×C11—24no—
287C23×C11—24no—
288C23×C11—24no—
289C23×C11—24no—
290C23×C11—432no—
291C23×C11—432no—
292C23×C11—416no—
293C23×C11—416no—
294C23×C11—416no—
295C23×C11—432no—
296C23×C11—432no—
297C23×C11—416no—
298C23×C11—416no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—416no—
316C23×C11#11714yes—
317C23×C11C4×D414yes—
318C23×C11C4×D418yes—
319C23×C11C4×D414yes—
320C23×C11#12114yes—
321C23×C11#12314yes—
322C23×C11#12414yes—
323C23×C11#12614yes—
324C23×C11C23×C411yescharacteristic
325C23×C11C22×D411yescharacteristic
326C23×C11C22×D411yescharacteristic
327C23×C11C22×D412yes—
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4112yes—
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11H(5,𝔽2)12yes—
334C23×C11H(5,𝔽2)12yes—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—24no—
338C2×C4×C11—24no—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—24no—
345C2×C4×C11—416no—
346C2×C4×C11—416no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11#12014yes—
354C2×Dic11—24no—
355C2×Dic11—22no—
356C2×Dic11—24no—
357C2×Dic11—22no—
358C2×Dic11—24no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—24no—
364C2×Dic11—24no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—42no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—42no—
375C2×Dic11—42no—
376C2×Dic11—42no—
377C2×Dic11—42no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—42no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383C2×Dic11—42no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C26C2×D1111yescharacteristic
389C24×C4C2×D1111yescharacteristic
390C24×C4C2×D1111yescharacteristic
391C22×C4⋊C4—112no—
392C22×C22⋊C4—24no—
393C22×C22⋊C4—28no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—112no—
397C22×C22⋊C4—111no—
398C22×C22⋊C4—112no—
399C22×C22⋊C4—111no—
400C22×C22⋊C4—112no—
401C22×C22⋊C4—112no—
402C22×C22⋊C4C2×D1112yes—
403C22×C22⋊C4C2×D1112yes—
404C22×C42—111no—
405C22×C42—111no—
406#388—228no—
407#385—224no—
408#379—118no—
409#379—224no—
410C4×C22⋊C4—224no—
411C2×#95—112no—
412C2×#95—112no—
413C2×#95—112no—
414C2×#95—111no—
415C2×#95—111no—
416C2×#95—112no—
417C2×#95—112no—
418C22×C11—24no—
419C22×C11—28no—
420C22×C11—28no—
421C22×C11—24no—
422C22×C11—24no—
423C22×C11—28no—
424C22×C11—28no—
425C22×C11—24no—
426C22×C11—24no—
427C22×C11—24no—
428C22×C11—28no—
429C22×C11—28no—
430C22×C11—28no—
431C22×C11—464no—
432C22×C11—44no—
433C22×C11—44no—
434C22×C11—44no—
435C22×C11—44no—
436C22×C11—44no—
437C22×C11—44no—
438C22×C11—44no—
439C22×C11—44no—
440C22×C11—44no—
441C22×C11—44no—
442C22×C11—44no—
443C22×C11—44no—
444C22×C11#38818yescomplemented
445C22×C11C2×#11711yescharacteristic
446C22×C11C2×C4×D411yescharacteristic
447C22×C11C2×C4×D411yescharacteristic
448C22×C11C2×C4×D412yes—
449C22×C11#51812yes—
450C22×C11C2×#12011yescharacteristic
451C22×C11C2×#12111yescharacteristic
452C22×C11C2×#12311yescharacteristic
453C22×C11#52512yes—
454C22×C11#52511yescharacteristic
455C22×C11C2×#12411yescharacteristic
456C22×C11C2×#12611yescharacteristic
457C22×C11#53411yescharacteristic
458C22×C11#53511yescharacteristic
459C22×C11#53812yes—
460C22×C11D4212yes—
461C22×C11#54612yes—
462C22×C11#54612yes—
463C22×C11#54612yes—
464C22×C11#54612yes—
465C22×C11#55112yes—
466C22×C11#55112yes—
467C22×C11#55112yes—
468C4×C11—24no—
469C4×C11—42no—
470C4×C11—44no—
471Dic11—42no—
472Dic11—44no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—82no—
477C25—24no—
478C25—22no—
479C25—24no—
480C25—22no—
481C25—22no—
482C25—22no—
483C25—22no—
484C25—22no—
485C25—42no—
486C25—42no—
487C25C4×D1114yes—
488C25C22×D1112yes—
489C25C22×D1111yescharacteristic
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—22no—
493C23×C4—24no—
494C23×C4—24no—
495C23×C4—22no—
496C23×C4—22no—
497C23×C4—42no—
498C23×C4—42no—
499C23×C4—111no—
500C23×C4—112no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—112no—
505C23×C4C22⋊D1114yes—
506C23×C4C22×D1112yes—
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1111yescharacteristic
509C2×C4⋊C4—224no—
510C2×C4⋊C4—224no—
511C2×C4⋊C4—442no—
512C2×C22⋊C4—232no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—118no—
521C2×C22⋊C4—114no—
522C2×C22⋊C4—118no—
523C2×C22⋊C4—224no—
524C2×C22⋊C4—222no—
525C2×C22⋊C4—222no—
526C2×C22⋊C4—222no—
527C2×C22⋊C4—222no—
528C2×C22⋊C4—222no—
529C2×C22⋊C4—222no—
530C2×C22⋊C4—224no—
531C2×C22⋊C4—224no—
532C2×C22⋊C4—224no—
533C2×C22⋊C4—224no—
534C2×C22⋊C4—222no—
535C2×C22⋊C4—222no—
536C2×C22⋊C4—222no—
537C2×C22⋊C4—224no—
538C2×C22⋊C4—442no—
539C2×C22⋊C4—442no—
540C2×C22⋊C4—442no—
541C2×C22⋊C4—442no—
542C2×C22⋊C4C22⋊D1118yes—
543C2×C42—222no—
544C2×C42—222no—
545C2×C42—224no—
546C2×C42—442no—
547#95—224no—
548#95—222no—
549#95—222no—
550#95—224no—
551#95—224no—
552#95—442no—
553#95—442no—
554C2×C11—28no—
555C2×C11—48no—
556C2×C11C2×#38811yescharacteristic
557C2×C11C4×#12011yescharacteristic
558C2×C11#232111yescharacteristic
559C2×C11#234212yes—
560C2×C11#235812yes—
561C2×C11#240511yescharacteristic
562C2×C11#240811yescharacteristic
563C2×C11#247212yes—
564C2×C11#248012yes—
565C2×C11#248211yescharacteristic
566C2×C11#253411yescharacteristic
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—28no—
572C24—216no—
573C24—28no—
574C24—216no—
575C24—28no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—28no—
589C24—28no—
590C24—48no—
591C24—48no—
592C24—48no—
593C24—48no—
594C24—48no—
595C24—48no—
596C24—48no—
597C24—48no—
598C24—48no—
599C24—48no—
600C24—44no—
601C24—44no—
602C24—44no—
603C24—44no—
604C24—44no—
605C24—44no—
606C24C2×C4×D1114yes—
607C24C2×C4×D1112yes—
608C24#433914yes—
609C24#433912yes—
610C24D4×D1112yes—
611C24#434112yes—
612C24#434112yes—
613C24#434112yes—
614C24C2×C22⋊D1114yes—
615C24C2×C22⋊D1112yes—
616C24C23×D1111yescharacteristic
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—28no—
633C22×C4—44no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—114no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—221no—
661C22×C4—222no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4C2×C22⋊D1112yes—
675C22×C4C2×C22⋊D1114yes—
676C22×C4C2×C22⋊D1114yes—
677C22×C4C2×C22⋊D1112yes—
678C4⋊C4—448no—
679C22⋊C4—216no—
680C22⋊C4—216no—
681C22⋊C4—228no—
682C22⋊C4—2216no—
683C22⋊C4—228no—
684C22⋊C4—228no—
685C22⋊C4—448no—
686C22⋊C4—448no—
687C22⋊C4—448no—
688C22⋊C4—444no—
689C42—444no—
690C42—444no—
691C11#1399111yescharacteristic, complemented, Sylow
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—22no—
708C23—232no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—432no—
728C23—432no—
729C23—416no—
730C23—416no—
731C23—432no—
732C23—416no—
733C23—416no—
734C23—432no—
735C23—416no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—416no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23#6693014yes—
754C23#6693214yes—
755C23(C22⋊D11)⋊C414yes—
756C23#6693814yes—
757C23C4×C22⋊D1118yes—
758C23C4×C22⋊D1114yes—
759C23#6698814yes—
760C23#6699114yes—
761C23C22×C4×D1111yescharacteristic
762C23C2×#433911yescharacteristic
763C23C2×#433912yes—
764C23C2×D4×D1111yescharacteristic
765C23C2×#434111yescharacteristic
766C23C2×#434111yescharacteristic
767C23C2×#434111yescharacteristic
768C23#6703712yes—
769C23#6703712yes—
770C23C22×C22⋊D1111yescharacteristic
771C23C22×C22⋊D1112yes—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—416no—
783C2×C4—416no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—224no—
791C2×C4—224no—
792C2×C4—224no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—224no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—224no—
801C2×C4—442no—
802C2×C4—442no—
803C2×C4—442no—
804C2×C4—442no—
805C2×C4—442no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—442no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—442no—
814C2×C4—442no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—442no—
818C2×C4—442no—
819C2×C4—442no—
820C2×C4—442no—
821C2×C4—442no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4#6700614yes—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—28no—
829C22—24no—
830C22—28no—
831C22—24no—
832C22—28no—
833C22—28no—
834C22—24no—
835C22—28no—
836C22—28no—
837C22—28no—
838C22—464no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22#1062255718yescomplemented
852C22C2×#6693011yescharacteristic
853C22C2×#6693211yescharacteristic
854C22C2×(C22⋊D11)⋊C411yescharacteristic
855C22#1062301712yes—
856C22#1062302112yes—
857C22C2×#6693811yescharacteristic
858C22#1062302512yes—
859C22#1062302612yes—
860C22#1062302612yes—
861C22#1062302612yes—
862C22C2×C4×C22⋊D1112yes—
863C22C2×C4×C22⋊D1111yescharacteristic
864C22#1062332212yes—
865C22#1062332211yescharacteristic
866C22C2×#6698811yescharacteristic
867C22C2×#6699111yescharacteristic
868C22D4×C22⋊D1112yes—
869C22#1062333511yescharacteristic
870C22#1062333611yescharacteristic
871C22#1062333712yes—
872C22#1062333712yes—
873C22#1062333712yes—
874C22C2×#6700611yescharacteristic
875C4—24no—
876C4—42no—
877C4—44no—
878C4—442no—
879C4—442no—
880C4—442no—
881C4—442no—
882C4—444no—
883C4—882no—
884C2—28no—
885C2—48no—
886C2C2×#1062255711yescharacteristic
887C2C4×#6700611yescharacteristic
888C2#1307127411yescharacteristic
889C2#1307146112yes—
890C2#1307159512yes—
891C2#1307193911yescharacteristic
892C2#1307196611yescharacteristic
893C2#1307273612yes—
894C2#1307285612yes—
895C2#1307289011yescharacteristic
896C2#1307350611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11#13991
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622557C2semidirect
2. C2×#10622823C2semidirect
5. C2×C4×C22⋊Dic11C2semidirect
6. #13066863C2semidirect
7. #13066859C2semidirect
8. #13066853C2semidirect
9. #13066839C2semidirect
10. #13066839C2semidirect
27. C22×Dic11⋊C4C22semidirect
28. C22×C4×Dic11C22semidirect
29. C22×C4×Dic11C22semidirect
31. #10622860C4semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
102. C2×C22⋊Dic11C2×C4semidirect
103. C2×C22⋊Dic11C2×C4semidirect
444. C22×C11#388semidirect
691. C11#13991semidirect
851. C22#10622557semidirect

Maximal subgroups

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

subgroupindex
C2×#106225572
C2×#106228232
C2×#106228602
C2×C4×C22⋊Dic112
#130668632
#130668592
#130668532
#130668392
C23×C11×C22⋊C42
#1399111