Finite Group Databasebeta

← #14676842

Subgroups — #14676842

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
1C23×C22⋊Dic11C211yesmaximal, characteristic
2C2×#10622564C212yesmaximal, complemented
3C2×#10622563C211yesmaximal, characteristic, complemented
4C2×#10622860C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6#13066865C212yesmaximal, complemented
7#13066861C212yesmaximal, complemented
8#13066853C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C11×#379C211yesmaximal, characteristic
12C26×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11—24no—
20C22×C22⋊Dic11—28no—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2212yes—
27C22×C4⋊Dic11C2212yescomplemented
28C22×C4×Dic11C2211yescharacteristic, complemented
29C22×C4×Dic11C2211yescharacteristic, complemented
30C11×#379C418yescomplemented
31#10622860—24no—
32C2×C11⋊#95C2212yescomplemented
33C2×C11⋊#95C2212yescomplemented
34C2×C11⋊#95C2211yescharacteristic, complemented
35C2×C11⋊#95C2211yescharacteristic, complemented
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39#10622564—28no—
40#10622563—24no—
41C22⋊C4×Dic11—24no—
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×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×Dic11—22no—
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—24no—
62C23×Dic11—24no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—42no—
66C23×Dic11—42no—
67C23×Dic11D414yes—
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—42no—
81C2×C11×C22⋊C4—42no—
82C2×C11×C22⋊C4C2×C414yes—
83C2×C11×C22⋊C4C2×C414yes—
84C2×C11×C22⋊C4C2×C418yescomplemented
85C2×C11×C22⋊C4C2×C418yescomplemented
86C2×C22⋊Dic11—232no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—42no—
102C2×C22⋊Dic11—42no—
103C2×C22⋊Dic11D414yes—
104C2×C22⋊Dic11D418yes—
105C2×C4⋊Dic11—24no—
106C2×C4⋊Dic11—24no—
107C2×C4⋊Dic11—42no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—42no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—24no—
115C11⋊#95—24no—
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—22no—
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C22×C414yes—
186C22×C4×C11C22×C412yes—
187C22×Dic11—28no—
188C22×Dic11—28no—
189C22×Dic11—28no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—44no—
219C22×Dic11—48no—
220C22×Dic11—48no—
221C22×Dic11—48no—
222C22×Dic11—48no—
223C22×Dic11—44no—
224C22×Dic11—44no—
225C22×Dic11C2×D412yes—
226C22×Dic11C2×D412yes—
227C22×Dic11C2×D414yes—
228C22×Dic11C2×D412yes—
229C22×Dic11C2×D414yes—
230C22×Dic11C2×D412yes—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—28no—
233C11×C22⋊C4—216no—
234C11×C22⋊C4—48no—
235C22⋊Dic11—216no—
236C22⋊Dic11—216no—
237C22⋊Dic11—28no—
238C22⋊Dic11—48no—
239C22⋊Dic11—48no—
240C22⋊Dic11—44no—
241C4⋊Dic11—48no—
242C4×Dic11—44no—
243C4×Dic11—44no—
244C23×C22⋊C4—111no—
245C2×#388—112no—
246C2×#385—111no—
247C2×#379—111no—
248C2×#379D1111yescharacteristic
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×D418yes—
318C23×C11C4×D414yes—
319C23×C11C4×D414yes—
320C23×C11#12114yes—
321C23×C11#12314yes—
322C23×C11#12414yes—
323C23×C11#12614yes—
324C23×C11C23×C411yescharacteristic
325C23×C11C22×D411yescharacteristic
326C23×C11C22×D412yes—
327C23×C11C22×D411yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4112yes—
333C23×C11H(5,𝔽2)12yes—
334C23×C11H(5,𝔽2)12yes—
335C2×C4×C11—22no—
336C2×C4×C11—24no—
337C2×C4×C11—24no—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
342C2×C4×C11—41no—
343C2×C4×C11—42no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—24no—
355C2×Dic11—24no—
356C2×Dic11—22no—
357C2×Dic11—24no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—24no—
365C2×Dic11—24no—
366C2×Dic11—416no—
367C2×Dic11—416no—
368C2×Dic11—41no—
369C2×Dic11—42no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—42no—
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#12014yes—
388C26C2×D1111yescharacteristic
389C24×C4—111no—
390C24×C4—111no—
391C22×C4⋊C4—112no—
392C22×C22⋊C4—112no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—112no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—112no—
397C22×C22⋊C4—112no—
398C22×C22⋊C4—228no—
399C22×C22⋊C4—224no—
400C22×C22⋊C4C2×D1111yescharacteristic
401C22×C22⋊C4C2×D1111yescharacteristic
402C22×C22⋊C4C2×D1112yes—
403C22×C22⋊C4C2×D1112yes—
404C22×C42—111no—
405C22×C42—111no—
406#388—228no—
407#385—224no—
408#379—224no—
409#379Dic1118yescomplemented
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×D412yes—
448C22×C11C2×C4×D411yescharacteristic
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—42no—
469C4×C11—44no—
470C4×C11—42no—
471Dic11—24no—
472Dic11—42no—
473Dic11—42no—
474Dic11—44no—
475Dic11—42no—
476Dic11—82no—
477C25—24no—
478C25—22no—
479C25—24no—
480C25—22no—
481C25—22no—
482C25—22no—
483C25—22no—
484C25—22no—
485C25—42no—
486C25—42no—
487C25C2×Dic1114yes—
488C25C22×D1112yes—
489C25C22×D1111yescharacteristic
490C23×C4—111no—
491C23×C4—111no—
492C23×C4—111no—
493C23×C4—112no—
494C23×C4—111no—
495C23×C4—114no—
496C23×C4—112no—
497C23×C4—224no—
498C23×C4—224no—
499C23×C4—222no—
500C23×C4—222no—
501C23×C4—222no—
502C23×C4—222no—
503C23×C4—222no—
504C23×C4—442no—
505C23×C4—442no—
506C23×C4C22×D1112yes—
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1111yescharacteristic
509C2×C4⋊C4—224no—
510C2×C4⋊C4—224no—
511C2×C4⋊C4—442no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—118no—
521C2×C22⋊C4—114no—
522C2×C22⋊C4—224no—
523C2×C22⋊C4—224no—
524C2×C22⋊C4—224no—
525C2×C22⋊C4—224no—
526C2×C22⋊C4—2232no—
527C2×C22⋊C4—222no—
528C2×C22⋊C4—224no—
529C2×C22⋊C4—222no—
530C2×C22⋊C4—224no—
531C2×C22⋊C4—224no—
532C2×C22⋊C4—222no—
533C2×C22⋊C4—222no—
534C2×C22⋊C4—224no—
535C2×C22⋊C4—224no—
536C2×C22⋊C4—222no—
537C2×C22⋊C4—442no—
538C2×C22⋊C4—442no—
539C2×C22⋊C4C2×Dic1114yes—
540C2×C22⋊C4C2×Dic1114yes—
541C2×C22⋊C4C2×Dic1118yescomplemented
542C2×C22⋊C4C2×Dic1118yescomplemented
543C2×C42—222no—
544C2×C42—222no—
545C2×C42—224no—
546C2×C42—442no—
547#95—222no—
548#95—222no—
549#95—224no—
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—28no—
573C24—216no—
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—44no—
600C24—44no—
601C24—48no—
602C24—44no—
603C24—44no—
604C24—44no—
605C24—44no—
606C24#433912yes—
607C24#433912yes—
608C24D4×D1114yes—
609C24D4×D1112yes—
610C24D4×D1112yes—
611C24#434114yes—
612C24#434112yes—
613C24#434112yes—
614C24C22×Dic1114yes—
615C24C22×Dic1112yes—
616C24C23×D1111yescharacteristic
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—114no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—114no—
636C22×C4—112no—
637C22×C4—228no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—222no—
641C22×C4—228no—
642C22×C4—228no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—222no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—221no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—444no—
669C22×C4—448no—
670C22×C4—448no—
671C22×C4—448no—
672C22×C4—448no—
673C22×C4—444no—
674C22×C4—444no—
675C22×C4C22×Dic1112yes—
676C22×C4C22×Dic1114yes—
677C22×C4C22×Dic1112yes—
678C4⋊C4—448no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—216no—
682C22⋊C4—48no—
683C22⋊C4—2216no—
684C22⋊C4—2216no—
685C22⋊C4—228no—
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—22no—
699C23—24no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—22no—
707C23—24no—
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#6693214yes—
754C23#6693614yes—
755C23#6693714yes—
756C23#6693814yes—
757C23#6697914yes—
758C23D4×Dic1118yes—
759C23D4×Dic1114yes—
760C23D4×Dic1114yes—
761C23C2×#433911yescharacteristic
762C23C2×#433911yescharacteristic
763C23C2×D4×D1111yescharacteristic
764C23C2×D4×D1111yescharacteristic
765C23C2×D4×D1112yes—
766C23C2×#434111yescharacteristic
767C23C2×#434111yescharacteristic
768C23C2×#434112yes—
769C23#6703712yes—
770C23#6703712yes—
771C23C23×Dic1111yescharacteristic
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—114no—
790C2×C4—222no—
791C2×C4—224no—
792C2×C4—222no—
793C2×C4—224no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—224no—
798C2×C4—222no—
799C2×C4—224no—
800C2×C4—222no—
801C2×C4—224no—
802C2×C4—224no—
803C2×C4—224no—
804C2×C4—4416no—
805C2×C4—4416no—
806C2×C4—442no—
807C2×C4—442no—
808C2×C4—442no—
809C2×C4—442no—
810C2×C4—442no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—442no—
815C2×C4—442no—
816C2×C4—442no—
817C2×C4—441no—
818C2×C4—442no—
819C2×C4—442no—
820C2×C4—442no—
821C2×C4—442no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4—442no—
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#1062256418yescomplemented
852C22C2×#6693211yescharacteristic
853C22C2×#6693611yescharacteristic
854C22C2×#6693711yescharacteristic
855C22#1062302112yes—
856C22#1062302112yes—
857C22C2×#6693811yescharacteristic
858C22#1062302612yes—
859C22#1062302612yes—
860C22#1062311712yes—
861C22#1062311711yescharacteristic
862C22#1062311812yes—
863C22D11×#12011yescharacteristic
864C22#1062312011yescharacteristic
865C22#1062312112yes—
866C22#1062312212yes—
867C22#1062312212yes—
868C22#1062312311yescharacteristic
869C22#1062312412yes—
870C22C2×#6697911yescharacteristic
871C22C2×D4×Dic1112yes—
872C22C2×D4×Dic1111yescharacteristic
873C22C2×D4×Dic1111yescharacteristic
874C22#1062332912yes—
875C4—42no—
876C4—42no—
877C4—44no—
878C4—224no—
879C4—442no—
880C4—444no—
881C4—442no—
882C4—442no—
883C4—882no—
884C2—28no—
885C2—48no—
886C2C2×#1062256411yescharacteristic
887C2#120×Dic1111yescharacteristic
888C2#1307127711yescharacteristic
889C2#1307146512yes—
890C2#1307160012yes—
891C2#1307194111yescharacteristic
892C2#1307197111yescharacteristic
893C2#1307273912yes—
894C2#1307285912yes—
895C2#1307288711yescharacteristic
896C2#1307350911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#379C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11#13991
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C2×#10622564C2semidirect
3. C2×#10622563C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. #13066865C2semidirect
7. #13066861C2semidirect
8. #13066853C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
27. C22×C4⋊Dic11C22semidirect
28. C22×C4×Dic11C22semidirect
29. C22×C4×Dic11C22semidirect
30. C11×#379C4semidirect
32. C2×C11⋊#95C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
84. C2×C11×C22⋊C4C2×C4semidirect
85. C2×C11×C22⋊C4C2×C4semidirect
409. #379Dic11semidirect
444. C22×C11#388semidirect
541. C2×C22⋊C4C2×Dic11semidirect
542. C2×C22⋊C4C2×Dic11semidirect
691. C11#13991semidirect
851. C22#10622564semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Dic112
C2×#106225642
C2×#106225632
C2×#106228602
C2×C22⋊C4×Dic112
#130668652
#130668612
#130668532
#130668382
C2×C11×#3792
#1399111