Finite Group Databasebeta

← #14675687

Subgroups — #14675687

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Dic11C211yesmaximal, characteristic
2C2×#10622557C212yesmaximal, complemented
3C2×#10622555C211yesmaximal, characteristic, complemented
4C2×#10622860C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6#13066863C212yesmaximal, complemented
7#13066859C212yesmaximal, 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⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11—28no—
20C22×C22⋊Dic11C418yescomplemented
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2212yescomplemented
30C22×C4×Dic11C2212yescomplemented
31C11×#379—24no—
32#10622860—24no—
33C2×C11⋊#95C2212yescomplemented
34C2×C11⋊#95C2212yescomplemented
35C2×C11⋊#95C2212yescomplemented
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39#10622557—28no—
40#10622555—24no—
41C22⋊C4×Dic11—24no—
42C25×C11—24no—
43C25×C11—24no—
44C25×C11—22no—
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×C11C2311yescharacteristic
54C25×C11C2311yescharacteristic
55C25×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×Dic11—22no—
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11—42no—
65C23×Dic11—42no—
66C23×Dic11C2×C414yes—
67C23×Dic11C2×C414yes—
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—22no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—42no—
84C2×C11×C22⋊C4—42no—
85C2×C11×C22⋊C4D414yes—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—232no—
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—42no—
100C2×C22⋊Dic11—42no—
101C2×C22⋊Dic11C2×C414yes—
102C2×C22⋊Dic11C2×C414yes—
103C2×C22⋊Dic11C2×C414yes—
104C2×C22⋊Dic11C2×C414yes—
105C2×C22⋊Dic11D414yes—
106C2×C22⋊Dic11D418yes—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4—24no—
109C2×Dic11⋊C4—42no—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—24no—
112C2×C4×Dic11—42no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—42no—
118C11⋊#95—42no—
119#13873—111nomaximal, Sylow
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—216no—
125C24×C11—216no—
126C24×C11—28no—
127C24×C11—28no—
128C24×C11—28no—
129C24×C11—22no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—21no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C24×C11—22no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—22no—
144C24×C11—22no—
145C24×C11—22no—
146C24×C11—22no—
147C24×C11—28no—
148C24×C11—28no—
149C24×C11—44no—
150C24×C11—44no—
151C24×C11—48no—
152C24×C11—48no—
153C24×C11—48no—
154C24×C11—48no—
155C24×C11—48no—
156C24×C11—48no—
157C24×C11—48no—
158C24×C11—48no—
159C24×C11—48no—
160C24×C11—48no—
161C24×C11—44no—
162C24×C11—44no—
163C24×C11—44no—
164C24×C11—44no—
165C24×C11C22×C412yes—
166C24×C11C22×C412yes—
167C24×C11C22×C412yes—
168C24×C11C2×D414yes—
169C24×C11C2×D412yes—
170C24×C11C2×D412yes—
171C24×C11#4114yes—
172C24×C11#4112yes—
173C24×C11#4112yes—
174C24×C11#4112yes—
175C24×C11#4112yes—
176C24×C11C2411yescharacteristic
177C22×C4×C11—22no—
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×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11C2×D414yes—
191C22×Dic11—28no—
192C22×Dic11—28no—
193C22×Dic11—28no—
194C22×Dic11—28no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
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—44no—
223C22×Dic11—44no—
224C22×Dic11—48no—
225C22×Dic11—48no—
226C22×Dic11—48no—
227C22×Dic11—48no—
228C22×Dic11C22×C412yes—
229C22×Dic11C22×C412yes—
230C22×Dic11C22×C412yes—
231C22×Dic11C22×C412yes—
232C22×Dic11C2×D414yes—
233C22×Dic11C2×D414yes—
234C22×Dic11C2×D414yes—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—48no—
237C11×C22⋊C4—48no—
238C11×C22⋊C4—44no—
239C22⋊Dic11—28no—
240C22⋊Dic11—28no—
241C22⋊Dic11—28no—
242C22⋊Dic11—28no—
243C22⋊Dic11—48no—
244C22⋊Dic11—48no—
245C22⋊Dic11—44no—
246C22⋊Dic11C22⋊C4116yescomplemented
247Dic11⋊C4—48no—
248C4×Dic11—48no—
249C23×C22⋊C4—111no—
250C2×#388—112no—
251C2×#380—111no—
252C2×#379—111no—
253C2×#379D1111yescharacteristic
254C2×C4×C22⋊C4—111no—
255#1440—112no—
256#1439—112no—
257#1437—112no—
258C22⋊#95—111no—
259C22⋊#95—111no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11—24no—
272C23×C11—24no—
273C23×C11—24no—
274C23×C11—24no—
275C23×C11—24no—
276C23×C11—232no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—24no—
290C23×C11—24no—
291C23×C11—24no—
292C23×C11—24no—
293C23×C11—24no—
294C23×C11—24no—
295C23×C11—24no—
296C23×C11—24no—
297C23×C11—24no—
298C23×C11—24no—
299C23×C11—24no—
300C23×C11—24no—
301C23×C11—416no—
302C23×C11—416no—
303C23×C11—416no—
304C23×C11—416no—
305C23×C11—416no—
306C23×C11—432no—
307C23×C11—432no—
308C23×C11—432no—
309C23×C11—432no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—416no—
331C23×C11C2×C22⋊C414yes—
332C23×C11#11714yes—
333C23×C11#11714yes—
334C23×C11C4×D414yes—
335C23×C11C4×D414yes—
336C23×C11#12114yes—
337C23×C11#12314yes—
338C23×C11#12414yes—
339C23×C11#12614yes—
340C23×C11C23×C411yescharacteristic
341C23×C11C22×D412yes—
342C23×C11C22×D411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C23×C11C2×#4111yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11C2×#4111yescharacteristic
347C23×C11C2×#4112yes—
348C23×C11C2×#4111yescharacteristic
349C23×C11H(5,𝔽2)12yes—
350C23×C11H(5,𝔽2)12yes—
351C2×C4×C11—24no—
352C2×C4×C11—24no—
353C2×C4×C11—24no—
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×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—24no—
370C2×Dic11—24no—
371C2×Dic11—24no—
372C2×Dic11—24no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—24no—
380C2×Dic11—24no—
381C2×Dic11—24no—
382C2×Dic11—416no—
383C2×Dic11—416no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11—42no—
394C2×Dic11—42no—
395C2×Dic11—42no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399C2×Dic11C2×C22⋊C414yes—
400C2×Dic11C2×C22⋊C414yes—
401C26C2×D1111yescharacteristic
402C24×C4—111no—
403C24×C4—111no—
404C22×C4⋊C4—112no—
405C22×C22⋊C4—111no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—118no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—112no—
413C22×C22⋊C4—112no—
414C22×C22⋊C4—228no—
415C22×C22⋊C4C2×D1111yescharacteristic
416C22×C22⋊C4C2×D1112yes—
417C22×C22⋊C4C2×D1112yes—
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C42—112no—
420#388—228no—
421#380—224no—
422#379—24no—
423#379—224no—
424C4×C22⋊C4—224no—
425C2×#95—112no—
426C2×#95—112no—
427C2×#95—112no—
428C2×#95—112no—
429C2×#95—112no—
430C2×#95—112no—
431C22×C11—24no—
432C22×C11—24no—
433C22×C11—24no—
434C22×C11—24no—
435C22×C11—24no—
436C22×C11—28no—
437C22×C11—28no—
438C22×C11—28no—
439C22×C11—28no—
440C22×C11—24no—
441C22×C11—24no—
442C22×C11—24no—
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—464no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—44no—
455C22×C11—44no—
456C22×C11—44no—
457C22×C11—44no—
458C22×C11—44no—
459C22×C11—44no—
460C22×C11—44no—
461C22×C11—44no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11#38818yescomplemented
465C22×C11C22×C22⋊C411yescharacteristic
466C22×C11C2×#11711yescharacteristic
467C22×C11C2×#11711yescharacteristic
468C22×C11C2×C4×D411yescharacteristic
469C22×C11C2×C4×D411yescharacteristic
470C22×C11#51811yescharacteristic
471C22×C11#51811yescharacteristic
472C22×C11C2×#12111yescharacteristic
473C22×C11C2×#12311yescharacteristic
474C22×C11#52512yes—
475C22×C11#52512yes—
476C22×C11C2×#12411yescharacteristic
477C22×C11C2×#12611yescharacteristic
478C22×C11#53812yes—
479C22×C11#53812yes—
480C22×C11D4212yes—
481C22×C11D4212yes—
482C22×C11#54612yes—
483C22×C11#54612yes—
484C22×C11#54612yes—
485C22×C11#54612yes—
486C22×C11#55112yes—
487C22×C11#55112yes—
488C4×C11—44no—
489C4×C11—82no—
490Dic11—24no—
491Dic11—24no—
492Dic11—42no—
493Dic11—42no—
494Dic11—44no—
495Dic11—82no—
496C25—24no—
497C25—24no—
498C25—22no—
499C25—22no—
500C25—22no—
501C25—22no—
502C25—22no—
503C25—22no—
504C25—42no—
505C25—42no—
506C25C4×D1114yes—
507C25C22×D1111yescharacteristic
508C25C22×D1111yescharacteristic
509C25C22×D1111yescharacteristic
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—112no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—114no—
516C23×C4—114no—
517C23×C4—112no—
518C23×C4—224no—
519C23×C4—224no—
520C23×C4—222no—
521C23×C4—222no—
522C23×C4—222no—
523C23×C4—222no—
524C23×C4—442no—
525C23×C4—442no—
526C23×C4C22×D1112yes—
527C23×C4C22×D1112yes—
528C2×C4⋊C4—224no—
529C2×C4⋊C4—224no—
530C2×C4⋊C4—442no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—118no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—2232no—
549C2×C22⋊C4—224no—
550C2×C22⋊C4—224no—
551C2×C22⋊C4—224no—
552C2×C22⋊C4—222no—
553C2×C22⋊C4—222no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—222no—
557C2×C22⋊C4—222no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—222no—
561C2×C22⋊C4—442no—
562C2×C22⋊C4—442no—
563C2×C22⋊C4C22⋊D1114yes—
564C2×C42—224no—
565C2×C42—224no—
566C2×C42—442no—
567#95—224no—
568#95—224no—
569#95—224no—
570#95—224no—
571#95—442no—
572#95—442no—
573C2×C11—28no—
574C2×C11—44no—
575C2×C11—44no—
576C2×C11#228011yescharacteristic
577C2×C11C2×#38811yescharacteristic
578C2×C11#231211yescharacteristic
579C2×C11D4×C22⋊C411yescharacteristic
580C2×C11D4×C22⋊C411yescharacteristic
581C2×C11#234211yescharacteristic
582C2×C11#234211yescharacteristic
583C2×C11#241812yes—
584C2×C11#242412yes—
585C2×C11#247212yes—
586C2×C11#248012yes—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—216no—
592C24—216no—
593C24—28no—
594C24—28no—
595C24—28no—
596C24—21no—
597C24—21no—
598C24—22no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—22no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—28no—
615C24—28no—
616C24—44no—
617C24—44no—
618C24—48no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—44no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24C2×C4×D1112yes—
633C24C2×C4×D1112yes—
634C24C2×C4×D1112yes—
635C24#433912yes—
636C24D4×D1114yes—
637C24D4×D1112yes—
638C24#434114yes—
639C24#434112yes—
640C24#434112yes—
641C24#434112yes—
642C24C2×C22⋊D1112yes—
643C24C23×D1111yescharacteristic
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—114no—
660C22×C4—114no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—114no—
664C22×C4—228no—
665C22×C4—228no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—221no—
672C22×C4—228no—
673C22×C4—228no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—221no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—221no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—444no—
696C22×C4—444no—
697C22×C4—448no—
698C22×C4—448no—
699C22×C4—448no—
700C22×C4—448no—
701C22×C4C2×C22⋊D1114yes—
702C4⋊C4—448no—
703C22⋊C4—28no—
704C22⋊C4—48no—
705C22⋊C4—48no—
706C22⋊C4—44no—
707C22⋊C4—1116no—
708C22⋊C4—228no—
709C22⋊C4—228no—
710C22⋊C4—228no—
711C22⋊C4—228no—
712C22⋊C4—448no—
713C22⋊C4—448no—
714C22⋊C4—444no—
715C42—448no—
716C11#1387311yescharacteristic, complemented, Sylow
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—24no—
745C23—24no—
746C23—22no—
747C23—22no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—432no—
764C23—416no—
765C23—432no—
766C23—432no—
767C23—41no—
768C23—41no—
769C23—42no—
770C23—41no—
771C23—41no—
772C23—42no—
773C23—416no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23#6693014yes—
789C23#6693014yes—
790C23#6693214yes—
791C23C22⋊C4×D1114yes—
792C23(C22⋊D11)⋊C414yes—
793C23#6693814yes—
794C23C4×C22⋊D1114yes—
795C23#6698814yes—
796C23#6699114yes—
797C23C22×C4×D1111yescharacteristic
798C23C2×#433911yescharacteristic
799C23C2×D4×D1112yes—
800C23C2×D4×D1111yescharacteristic
801C23C2×#434111yescharacteristic
802C23C2×#434111yescharacteristic
803C23C2×#434112yes—
804C23C2×#434111yescharacteristic
805C23#6703712yes—
806C23#6703712yes—
807C23C22×C22⋊D1111yescharacteristic
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—114no—
823C2×C4—114no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—224no—
828C2×C4—222no—
829C2×C4—224no—
830C2×C4—224no—
831C2×C4—224no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—224no—
839C2×C4—224no—
840C2×C4—224no—
841C2×C4—4416no—
842C2×C4—4416no—
843C2×C4—442no—
844C2×C4—442no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4—442no—
848C2×C4—442no—
849C2×C4—442no—
850C2×C4—442no—
851C2×C4—442no—
852C2×C4—442no—
853C2×C4—442no—
854C2×C4—442no—
855C2×C4—442no—
856C2×C4—442no—
857C2×C4—442no—
858C22—28no—
859C22—24no—
860C22—24no—
861C22—28no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—42no—
879C22—44no—
880C22—44no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22#1062255718yescomplemented
892C22C2×#6693011yescharacteristic
893C22C2×#6693011yescharacteristic
894C22C2×#6693211yescharacteristic
895C22C2×C22⋊C4×D1111yescharacteristic
896C22C2×(C22⋊D11)⋊C411yescharacteristic
897C22#1062301711yescharacteristic
898C22#1062301711yescharacteristic
899C22#1062302112yes—
900C22C2×#6693811yescharacteristic
901C22#1062302612yes—
902C22#1062311712yes—
903C22#1062311712yes—
904C22#1062311812yes—
905C22#1062312112yes—
906C22#1062312212yes—
907C22#1062312212yes—
908C22#1062312412yes—
909C22#1062312412yes—
910C22C2×C4×C22⋊D1111yescharacteristic
911C22C2×#6698811yescharacteristic
912C22C2×#6699111yescharacteristic
913C22D4×C22⋊D1112yes—
914C22#1062333712yes—
915C4—44no—
916C4—82no—
917C4—224no—
918C4—224no—
919C4—444no—
920C4—442no—
921C4—442no—
922C4—882no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2#1307099411yescharacteristic
927C2C2×#1062255711yescharacteristic
928C2#1307121211yescharacteristic
929C2#1307143211yescharacteristic
930C2C22⋊C4×C22⋊D1111yescharacteristic
931C2#1307146111yescharacteristic
932C2#1307146711yescharacteristic
933C2#1307207412yes—
934C2#1307214812yes—
935C2#1307273912yes—
936C2#1307286112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#379C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11#13873
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C2×#10622557C2semidirect
3. C2×#10622555C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. #13066863C2semidirect
7. #13066859C2semidirect
8. #13066853C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
20. C22×C22⋊Dic11C4semidirect
29. C22×Dic11⋊C4C22semidirect
30. C22×C4×Dic11C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
246. C22⋊Dic11C22⋊C4semidirect
464. C22×C11#388semidirect
716. C11#13873semidirect
891. C22#10622557semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Dic112
C2×#106225572
C2×#106225552
C2×#106228602
C2×C22⋊C4×Dic112
#130668632
#130668592
#130668532
#130668382
C2×C11×#3792
#1387311