Finite Group Databasebeta

← #14676587

Subgroups — #14676587

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×(C2×D11)⋊C4C211yesmaximal, characteristic
2C2×#10622283C212yesmaximal, complemented
3C2×#10622563C211yesmaximal, characteristic, complemented
4C2×#10622568C211yesmaximal, characteristic
5C2×#10622568C211yesmaximal, characteristic
6C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#13066864C212yesmaximal, complemented
8#13066862C212yesmaximal, complemented
9#13066852C212yesmaximal, complemented
10#13066839C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4—24no—
20C22×(C2×D11)⋊C4—28no—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic, complemented
28C22×C4⋊Dic11C2211yescharacteristic, complemented
29C22×C4×Dic11C2212yescomplemented
30C2×C11×#95C2212yescomplemented
31C2×C11×#95C2212yescomplemented
32C2×C11⋊#95C2212yescomplemented
33C2×C11⋊#95C2211yescharacteristic, complemented
34C2×C11⋊#95C2212yescomplemented
35C2×C11⋊#95C2211yescharacteristic, complemented
36C2×C11⋊#95C2212yescomplemented
37#10622568—24no—
38#10622568C418yescomplemented
39#10622563—24no—
40C22⋊C4×Dic11—24no—
41#10622283—28no—
42C25×C11C2311yescharacteristic
43C24×D11—22no—
44C24×D11—22no—
45C24×D11—24no—
46C24×D11—24no—
47C24×D11—22no—
48C24×D11—22no—
49C24×D11—22no—
50C24×D11—22no—
51C24×D11—42no—
52C24×D11—42no—
53C24×D11C2×C414yes—
54C24×D11C2312yes—
55C23×C4×C11—22no—
56C23×C4×C11—24no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—42no—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C23×C4×C11C2312yes—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—24no—
67C23×Dic11—42no—
68C23×Dic11D414yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4C2×C414yes—
79C2×C11×C22⋊C4D414yes—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11C2×C414yes—
86C2×(C2×D11)⋊C4—232no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—42no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4—42no—
101C2×(C2×D11)⋊C4—42no—
102C2×(C2×D11)⋊C4C2×C418yescomplemented
103C2×(C2×D11)⋊C4C2×C418yescomplemented
104C2×(C2×D11)⋊C4D418yes—
105C2×C4⋊Dic11—24no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—42no—
109C2×C4×Dic11—24no—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—42no—
112C11×#95—24no—
113C11×#95—42no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—42no—
119#13971—111nomaximal, Sylow
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11C22×C412yes—
125C24×C11C2×D412yes—
126C24×C11C2×D412yes—
127C24×C11#4112yes—
128C24×C11#4112yes—
129C24×C11#4112yes—
130C24×C11#4112yes—
131C24×C11C2411yescharacteristic
132C23×D11—28no—
133C23×D11—216no—
134C23×D11—28no—
135C23×D11—28no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11—22no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—216no—
149C23×D11—28no—
150C23×D11—28no—
151C23×D11—48no—
152C23×D11—48no—
153C23×D11—48no—
154C23×D11—48no—
155C23×D11—48no—
156C23×D11—48no—
157C23×D11—48no—
158C23×D11—48no—
159C23×D11—48no—
160C23×D11—44no—
161C23×D11—44no—
162C23×D11—48no—
163C23×D11—44no—
164C23×D11—44no—
165C23×D11—44no—
166C23×D11—44no—
167C23×D11C22×C414yes—
168C23×D11C2×D414yes—
169C23×D11#4114yes—
170C22×C4×C11—28no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
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—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—48no—
192C22×C4×C11—48no—
193C22×C4×C11—44no—
194C22×C4×C11—44no—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C2×D414yes—
198C22×C4×C11C2×D414yes—
199C22×Dic11—28no—
200C22×Dic11—28no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—21no—
207C22×Dic11—22no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—21no—
215C22×Dic11—22no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—44no—
225C22×Dic11—48no—
226C22×Dic11—48no—
227C22×Dic11C22×C414yes—
228C22×Dic11C2×D412yes—
229C22×Dic11C2×D412yes—
230C22×Dic11C2×D414yes—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—28no—
233C22⋊Dic11—28no—
234C22⋊Dic11—44no—
235(C2×D11)⋊C4—216no—
236(C2×D11)⋊C4—216no—
237(C2×D11)⋊C4—216no—
238(C2×D11)⋊C4—48no—
239(C2×D11)⋊C4—48no—
240(C2×D11)⋊C4—48no—
241C4⋊Dic11—44no—
242C4⋊Dic11—44no—
243C4×Dic11—48no—
244C23×C22⋊C4—111no—
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⋊#95D1111yescharacteristic, complemented
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#11714yes—
272C23×C11C4×D414yes—
273C23×C11C4×D414yes—
274C23×C11#12114yes—
275C23×C11#12314yes—
276C23×C11#12414yes—
277C23×C11#12614yes—
278C23×C11C23×C411yescharacteristic
279C23×C11C22×D411yescharacteristic
280C23×C11C22×D411yescharacteristic
281C23×C11C22×D412yes—
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4111yescharacteristic
284C23×C11C2×#4111yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11C2×#4112yes—
287C23×C11H(5,𝔽2)12yes—
288C23×C11H(5,𝔽2)12yes—
289C22×D11—232no—
290C22×D11—24no—
291C22×D11—24no—
292C22×D11—24no—
293C22×D11—24no—
294C22×D11—24no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—24no—
301C22×D11—24no—
302C22×D11—24no—
303C22×D11—24no—
304C22×D11—24no—
305C22×D11—24no—
306C22×D11—24no—
307C22×D11—24no—
308C22×D11—432no—
309C22×D11—432no—
310C22×D11—416no—
311C22×D11—416no—
312C22×D11—416no—
313C22×D11—416no—
314C22×D11—432no—
315C22×D11—416no—
316C22×D11—432no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—416no—
334C22×D11C4×D418yes—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—24no—
339C2×C4×C11—24no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
344C2×C4×C11—24no—
345C2×C4×C11—416no—
346C2×C4×C11—41no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—41no—
350C2×C4×C11—42no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—24no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—416no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C2×Dic11—42no—
376C2×Dic11—42no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—42no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11#12014yes—
388C26—111no—
389C24×C4—111no—
390C24×C4C2×D1111yescharacteristic
391C22×C4⋊C4—111no—
392C22×C4⋊C4—111no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—112no—
395C22×C22⋊C4—112no—
396C22×C22⋊C4—112no—
397C22×C22⋊C4—111no—
398C22×C22⋊C4—112no—
399C22×C22⋊C4—112no—
400C22×C22⋊C4—112no—
401C22×C22⋊C4—228no—
402C22×C22⋊C4—224no—
403C22×C22⋊C4C2×D1111yescharacteristic
404C22×C22⋊C4C2×D1111yescharacteristic
405C22×C42—112no—
406#388—228no—
407#385—224no—
408#379—118no—
409#379—224no—
410C4×C22⋊C4—224no—
411C2×#95—112no—
412C2×#95—111no—
413C2×#95—112no—
414C2×#95—111no—
415C2×#95—112no—
416C2×#95C2×D1112yescomplemented
417C2×#95C2×D1112yescomplemented
418C22×C11—24no—
419C22×C11—24no—
420C22×C11—28no—
421C22×C11—28no—
422C22×C11—24no—
423C22×C11—24no—
424C22×C11—28no—
425C22×C11—24no—
426C22×C11—28no—
427C22×C11—24no—
428C22×C11#38818yescomplemented
429C22×C11C2×#11711yescharacteristic
430C22×C11C2×C4×D411yescharacteristic
431C22×C11C2×C4×D411yescharacteristic
432C22×C11C2×C4×D412yes—
433C22×C11#51812yes—
434C22×C11C2×#12011yescharacteristic
435C22×C11C2×#12111yescharacteristic
436C22×C11C2×#12311yescharacteristic
437C22×C11#52512yes—
438C22×C11#52511yescharacteristic
439C22×C11C2×#12411yescharacteristic
440C22×C11C2×#12611yescharacteristic
441C22×C11#53411yescharacteristic
442C22×C11#53511yescharacteristic
443C22×C11#53812yes—
444C22×C11D4212yes—
445C22×C11#54612yes—
446C22×C11#54612yes—
447C22×C11#54612yes—
448C22×C11#54612yes—
449C22×C11#55112yes—
450C22×C11#55112yes—
451C22×C11#55112yes—
452C2×D11—28no—
453C2×D11—28no—
454C2×D11—28no—
455C2×D11—464no—
456C2×D11—44no—
457C2×D11—44no—
458C2×D11—44no—
459C2×D11—44no—
460C2×D11—44no—
461C2×D11—44no—
462C2×D11—44no—
463C2×D11—44no—
464C2×D11—44no—
465C2×D11—44no—
466C2×D11—44no—
467C2×D11—44no—
468C4×C11—42no—
469C4×C11—44no—
470C4×C11—44no—
471C4×C11—42no—
472Dic11—24no—
473Dic11—44no—
474Dic11—42no—
475Dic11—81no—
476Dic11—81no—
477C25—112no—
478C25—114no—
479C25—224no—
480C25—224no—
481C25—222no—
482C25—222no—
483C25—222no—
484C25—222no—
485C25—222no—
486C25—222no—
487C25—442no—
488C25—442no—
489C25C22×D1111yescharacteristic
490C23×C4—22no—
491C23×C4—24no—
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—42no—
495C23×C4—111no—
496C23×C4—112no—
497C23×C4—111no—
498C23×C4—114no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—224no—
502C23×C4—222no—
503C23×C4—222no—
504C23×C4—442no—
505C23×C4C22×D1111yescharacteristic
506C23×C4C22×D1111yescharacteristic
507C23×C4C22×D1112yes—
508C23×C4C22×D1112yes—
509C2×C4⋊C4—222no—
510C2×C4⋊C4—222no—
511C2×C4⋊C4—224no—
512C2×C4⋊C4—442no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—118no—
519C2×C22⋊C4—118no—
520C2×C22⋊C4—118no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—224no—
523C2×C22⋊C4—224no—
524C2×C22⋊C4—224no—
525C2×C22⋊C4—224no—
526C2×C22⋊C4—224no—
527C2×C22⋊C4—2232no—
528C2×C22⋊C4—222no—
529C2×C22⋊C4—222no—
530C2×C22⋊C4—224no—
531C2×C22⋊C4—224no—
532C2×C22⋊C4—224no—
533C2×C22⋊C4—222no—
534C2×C22⋊C4—222no—
535C2×C22⋊C4—222no—
536C2×C22⋊C4—224no—
537C2×C22⋊C4—224no—
538C2×C22⋊C4—442no—
539C2×C22⋊C4—442no—
540C2×C22⋊C4—442no—
541C2×C22⋊C4—442no—
542C2×C22⋊C4C4×D1114yes—
543C2×C22⋊C4D4414yes—
544C2×C42—224no—
545C2×C42—224no—
546C2×C42—442no—
547#95—24no—
548#95—42no—
549#95—222no—
550#95—222no—
551#95—224no—
552#95—224no—
553#95—442no—
554C2×C11—28no—
555C2×C11C2×#38811yescharacteristic
556C2×C11C4×#12011yescharacteristic
557C2×C11#232111yescharacteristic
558C2×C11#234212yes—
559C2×C11#235812yes—
560C2×C11#241011yescharacteristic
561C2×C11#241111yescharacteristic
562C2×C11#241812yes—
563C2×C11#243511yescharacteristic
564C2×C11#248012yes—
565C2×C11#256111yescharacteristic
566D11—48no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—114no—
572C24—114no—
573C24—114no—
574C24—2216no—
575C24—228no—
576C24—2216no—
577C24—228no—
578C24—228no—
579C24—222no—
580C24—222no—
581C24—222no—
582C24—222no—
583C24—222no—
584C24—222no—
585C24—222no—
586C24—222no—
587C24—222no—
588C24—222no—
589C24—222no—
590C24—222no—
591C24—228no—
592C24—228no—
593C24—448no—
594C24—448no—
595C24—448no—
596C24—448no—
597C24—448no—
598C24—448no—
599C24—448no—
600C24—448no—
601C24—448no—
602C24—444no—
603C24—448no—
604C24—444no—
605C24—444no—
606C24—444no—
607C24—444no—
608C24—444no—
609C24C2×C4×D1112yes—
610C24C2×D4412yes—
611C24#433912yes—
612C24D4×D1112yes—
613C24#434112yes—
614C24#434112yes—
615C24#434312yes—
616C24C23×D1111yescharacteristic
617C22×C4—28no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—48no—
639C22×C4—48no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—112no—
643C22×C4—114no—
644C22×C4—114no—
645C22×C4—112no—
646C22×C4—228no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—222no—
650C22×C4—228no—
651C22×C4—221no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—221no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—222no—
665C22×C4—221no—
666C22×C4—222no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—444no—
672C22×C4—448no—
673C22×C4—448no—
674C22×C4C2×C4×D1112yes—
675C22×C4C2×C4×D1112yes—
676C22×C4C2×D4414yes—
677C22×C4D4×D1114yes—
678C4⋊C4—444no—
679C4⋊C4—444no—
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—2216no—
683C22⋊C4—2216no—
684C22⋊C4—2216no—
685C22⋊C4—228no—
686C22⋊C4—448no—
687C22⋊C4—448no—
688C22⋊C4—448no—
689C22⋊C4—444no—
690C42—448no—
691C11#1397111yescharacteristic, complemented, Sylow
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—22no—
699C23—24no—
700C23—22no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—24no—
708C23—118no—
709C23—2232no—
710C23—224no—
711C23—224no—
712C23—224no—
713C23—224no—
714C23—224no—
715C23—224no—
716C23—224no—
717C23—224no—
718C23—224no—
719C23—224no—
720C23—224no—
721C23—224no—
722C23—224no—
723C23—224no—
724C23—224no—
725C23—224no—
726C23—224no—
727C23—224no—
728C23—4432no—
729C23—4432no—
730C23—4416no—
731C23—4416no—
732C23—4416no—
733C23—4416no—
734C23—4416no—
735C23—4432no—
736C23—4432no—
737C23—442no—
738C23—442no—
739C23—442no—
740C23—442no—
741C23—442no—
742C23—4416no—
743C23—442no—
744C23—442no—
745C23—442no—
746C23—442no—
747C23—442no—
748C23—442no—
749C23—442no—
750C23—442no—
751C23—442no—
752C23—442no—
753C23—442no—
754C23C4×D4414yes—
755C23(C22⋊D11)⋊C414yes—
756C23#6693814yes—
757C23#6693914yes—
758C23#6694514yes—
759C23#6694814yes—
760C23#6695114yes—
761C23C22×C4×D1111yescharacteristic
762C23C22×D4411yescharacteristic
763C23C2×#433911yescharacteristic
764C23C2×D4×D1111yescharacteristic
765C23C2×D4×D1112yes—
766C23C2×#434111yescharacteristic
767C23C2×#434111yescharacteristic
768C23#6703712yes—
769C23C2×#434311yescharacteristic
770C23#41×D1112yes—
771C23#6704212yes—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—416no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—114no—
798C2×C4—222no—
799C2×C4—224no—
800C2×C4—224no—
801C2×C4—222no—
802C2×C4—224no—
803C2×C4—222no—
804C2×C4—224no—
805C2×C4—224no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—4416no—
809C2×C4—442no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4—442no—
813C2×C4—442no—
814C2×C4—442no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—442no—
818C2×C4—442no—
819C2×C4—441no—
820C2×C4—441no—
821C2×C4—442no—
822C2×C4—442no—
823C2×C4—441no—
824C2×C4—441no—
825C22—24no—
826C22—28no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—28no—
833C22—28no—
834C22—28no—
835C22—228no—
836C22—228no—
837C22—228no—
838C22—4464no—
839C22—444no—
840C22—444no—
841C22—444no—
842C22—444no—
843C22—444no—
844C22—444no—
845C22—444no—
846C22—444no—
847C22—444no—
848C22—444no—
849C22—444no—
850C22—444no—
851C22#1062228318yescomplemented
852C22C2×C4×D4411yescharacteristic
853C22C2×(C22⋊D11)⋊C411yescharacteristic
854C22#1062302112yes—
855C22C2×#6693811yescharacteristic
856C22C2×#6693911yescharacteristic
857C22C2×#6694511yescharacteristic
858C22C2×#6694811yescharacteristic
859C22C2×#6695111yescharacteristic
860C22#1062305812yes—
861C22C4×D4×D1112yes—
862C22#1062307612yes—
863C22D4×D4412yes—
864C22#1062308512yes—
865C22D11×#12011yescharacteristic
866C22#1062312212yes—
867C22#1062312311yescharacteristic
868C22#1062313712yes—
869C22#1062314812yes—
870C22#1062316112yes—
871C22#1062316812yes—
872C22#1062318411yescharacteristic
873C22#1062318711yescharacteristic
874C22#1062318912yes—
875C4—42no—
876C4—44no—
877C4—42no—
878C4—44no—
879C4—224no—
880C4—442no—
881C4—444no—
882C4—881no—
883C4—881no—
884C2—28no—
885C2—448no—
886C2C2×#1062228311yescharacteristic
887C2#1307112111yescharacteristic
888C2#1307127911yescharacteristic
889C2#1307146312yes—
890C2#1307159812yes—
891C2#1307198811yescharacteristic
892C2#1307199911yescharacteristic
893C2#1307207612yes—
894C2#1307226511yescharacteristic
895C2#1307286712yes—
896C2#1307377311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenterC22⋊#95D11
hypocenterC11#13971
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622283C2semidirect
3. C2×#10622563C2semidirect
6. C2×C22⋊C4×Dic11C2semidirect
7. #13066864C2semidirect
8. #13066862C2semidirect
9. #13066852C2semidirect
10. #13066839C2semidirect
11. C11×C22⋊#95C2semidirect
27. C22×C4⋊Dic11C22semidirect
28. C22×C4⋊Dic11C22semidirect
29. C22×C4×Dic11C22semidirect
30. C2×C11×#95C22semidirect
31. C2×C11×#95C22semidirect
32. C2×C11⋊#95C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
38. #10622568C4semidirect
102. C2×(C2×D11)⋊C4C2×C4semidirect
103. C2×(C2×D11)⋊C4C2×C4semidirect
254. C22⋊#95D11semidirect
416. C2×#95C2×D11semidirect
417. C2×#95C2×D11semidirect
428. C22×C11#388semidirect
691. C11#13971semidirect
851. C22#10622283semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D11)⋊C42
C2×#106222832
C2×#106225632
C2×#106225682
C2×C22⋊C4×Dic112
#130668642
#130668622
#130668522
#130668392
C11×C22⋊#952
#1397111