Finite Group Databasebeta

← #14675691

Subgroups — #14675691

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
1C2×#10622564C212yesmaximal, complemented
2C2×#10622825C211yesmaximal, characteristic, complemented
3C2×#10622860C211yesmaximal, characteristic
4C2×#10622860C211yesmaximal, characteristic
5C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#13066865C212yesmaximal, complemented
7#13066861C212yesmaximal, 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—28no—
16C22×C11×C22⋊C4C418yescomplemented
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2212yescomplemented
30C22×C4×Dic11C2212yescomplemented
31#10622860—24no—
32#10622860—24no—
33#10622825—24no—
34C4×C22⋊Dic11—24no—
35C2×C11⋊#95C2212yescomplemented
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41#10622564—28no—
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×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—24no—
61C23×C4×C11—24no—
62C23×C4×C11—42no—
63C23×C4×C11—42no—
64C23×C4×C11C2×C414yes—
65C23×C4×C11C2×C414yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2312yes—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—232no—
78C2×C11×C22⋊C4C2×C414yes—
79C2×C11×C22⋊C4C2×C414yes—
80C2×C11×C22⋊C4C2×C414yes—
81C2×C11×C22⋊C4C2×C414yes—
82C2×C11×C22⋊C4D418yes—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—42no—
102C2×C22⋊Dic11—42no—
103C2×C22⋊Dic11—42no—
104C2×C22⋊Dic11—42no—
105C2×C22⋊Dic11D414yes—
106C2×C22⋊Dic11D414yes—
107C2×C4⋊Dic11—24no—
108C2×C4⋊Dic11—24no—
109C2×C4⋊Dic11—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—21no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—21no—
133C24×C11—22no—
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—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—28no—
184C22×C4×C11—28no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—28no—
194C22×C4×C11—28no—
195C22×C4×C11—44no—
196C22×C4×C11—44no—
197C22×C4×C11—48no—
198C22×C4×C11—48no—
199C22×C4×C11—48no—
200C22×C4×C11—48no—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C2×D414yes—
206C22×C4×C11C2×D414yes—
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—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11C2×D414yes—
234C22×Dic11C2×D414yes—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—28no—
237C11×C22⋊C4—28no—
238C11×C22⋊C4C22⋊C4116yescomplemented
239C22⋊Dic11—28no—
240C22⋊Dic11—28no—
241C22⋊Dic11—48no—
242C22⋊Dic11—48no—
243C22⋊Dic11—48no—
244C22⋊Dic11—48no—
245C22⋊Dic11—44no—
246C22⋊Dic11—44no—
247C4⋊Dic11—48no—
248C4×Dic11—48no—
249C23×C22⋊C4D1111yescharacteristic
250C2×#388—112no—
251C2×#380—111no—
252C2×#379—111no—
253C2×#379—111no—
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×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C22×D412yes—
344C23×C11C2×#4111yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11C2×#4112yes—
347C23×C11C2×#4111yescharacteristic
348C23×C11C2×#4111yescharacteristic
349C23×C11H(5,𝔽2)12yes—
350C23×C11H(5,𝔽2)12yes—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—24no—
356C2×C4×C11—24no—
357C2×C4×C11—24no—
358C2×C4×C11—24no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—416no—
366C2×C4×C11—416no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11—42no—
370C2×C4×C11—42no—
371C2×C4×C11C2×C22⋊C414yes—
372C2×C4×C11C2×C22⋊C414yes—
373C2×Dic11—24no—
374C2×Dic11—24no—
375C2×Dic11—24no—
376C2×Dic11—24no—
377C2×Dic11—24no—
378C2×Dic11—24no—
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—
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×Dic11—42no—
400C2×Dic11—42no—
401C26C2×D1111yescharacteristic
402C24×C4C2×D1111yescharacteristic
403C24×C4C2×D1111yescharacteristic
404C22×C4⋊C4—112no—
405C22×C22⋊C4—28no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
410C22×C22⋊C4—112no—
411C22×C22⋊C4—112no—
412C22×C22⋊C4—112no—
413C22×C22⋊C4—112no—
414C22×C22⋊C4Dic1118yescomplemented
415C22×C22⋊C4C2×D1111yescharacteristic
416C22×C22⋊C4C2×D1111yescharacteristic
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C42—112no—
420#388—228no—
421#380—224no—
422#379—224no—
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—24no—
489C4×C11—24no—
490C4×C11—42no—
491C4×C11—42no—
492Dic11—44no—
493Dic11—44no—
494Dic11—82no—
495Dic11—82no—
496C25—24no—
497C25—22no—
498C25—22no—
499C25—24no—
500C25—22no—
501C25—22no—
502C25—22no—
503C25—22no—
504C25—42no—
505C25—42no—
506C25C2×Dic1114yes—
507C25C22×D1111yescharacteristic
508C25C22×D1111yescharacteristic
509C25C22×D1111yescharacteristic
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—42no—
517C23×C4—42no—
518C23×C4—112no—
519C23×C4—112no—
520C23×C4—112no—
521C23×C4—112no—
522C23×C4C2×Dic1114yes—
523C23×C4C2×Dic1114yes—
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C2×C4⋊C4—224no—
529C2×C4⋊C4—224no—
530C2×C4⋊C4—442no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—232no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—222no—
538C2×C22⋊C4—222no—
539C2×C22⋊C4—222no—
540C2×C22⋊C4—222no—
541C2×C22⋊C4—224no—
542C2×C22⋊C4—224no—
543C2×C22⋊C4—224no—
544C2×C22⋊C4—224no—
545C2×C22⋊C4—224no—
546C2×C22⋊C4—224no—
547C2×C22⋊C4—222no—
548C2×C22⋊C4—222no—
549C2×C22⋊C4—222no—
550C2×C22⋊C4—222no—
551C2×C22⋊C4—222no—
552C2×C22⋊C4—222no—
553C2×C22⋊C4—224no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—442no—
556C2×C22⋊C4—442no—
557C2×C22⋊C4—442no—
558C2×C22⋊C4—442no—
559C2×C22⋊C4C2×Dic1114yes—
560C2×C22⋊C4C2×Dic1114yes—
561C2×C22⋊C4C2×Dic1114yes—
562C2×C22⋊C4C2×Dic1114yes—
563C2×C22⋊C4C22⋊D1118yes—
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—21no—
599C24—21no—
600C24—22no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
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—
632C24#433914yes—
633C24#433912yes—
634C24#433912yes—
635C24D4×D1112yes—
636C24D4×D1112yes—
637C24#434112yes—
638C24#434112yes—
639C24C22×Dic1112yes—
640C24C22×Dic1112yes—
641C24C22×Dic1112yes—
642C24C2×C22⋊D1114yes—
643C24C23×D1111yescharacteristic
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—48no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—114no—
669C22×C4—114no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
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—222no—
696C22×C4C22×Dic1112yes—
697C22×C4C22×Dic1112yes—
698C22×C4C22×Dic1112yes—
699C22×C4C22×Dic1112yes—
700C22×C4C2×C22⋊D1114yes—
701C22×C4C2×C22⋊D1114yes—
702C4⋊C4—448no—
703C22⋊C4—28no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—228no—
707C22⋊C4—228no—
708C22⋊C4—448no—
709C22⋊C4—448no—
710C22⋊C4—448no—
711C22⋊C4—448no—
712C22⋊C4—444no—
713C22⋊C4—444no—
714C22⋊C4C22⋊Dic11116yescomplemented
715C42—448no—
716C11#1387311yescharacteristic, complemented, Sylow
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—22no—
724C23—24no—
725C23—24no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—22no—
733C23—232no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—22no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—432no—
764C23—416no—
765C23—432no—
766C23—432no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—42no—
774C23—42no—
775C23—41no—
776C23—41no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—416no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23#6693214yes—
789C23#6693614yes—
790C23#6693714yes—
791C23#6693814yes—
792C23#6697914yes—
793C23#6697914yes—
794C23D4×Dic1114yes—
795C23D4×Dic1114yes—
796C23C2×C22⋊Dic1114yes—
797C23C2×#433911yescharacteristic
798C23C2×#433911yescharacteristic
799C23C2×#433912yes—
800C23C2×D4×D1111yescharacteristic
801C23C2×D4×D1111yescharacteristic
802C23C2×#434111yescharacteristic
803C23C2×#434111yescharacteristic
804C23#6703712yes—
805C23#6703712yes—
806C23C23×Dic1111yescharacteristic
807C23C22×C22⋊D1112yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—416no—
823C2×C4—416no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—224no—
829C2×C4—224no—
830C2×C4—224no—
831C2×C4—224no—
832C2×C4—224no—
833C2×C4—224no—
834C2×C4—442no—
835C2×C4—442no—
836C2×C4—442no—
837C2×C4—442no—
838C2×C4—442no—
839C2×C4—442no—
840C2×C4—442no—
841C2×C4—442no—
842C2×C4—442no—
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×C4C2×C22⋊Dic1114yes—
857C2×C4C2×C22⋊Dic1114yes—
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#1062256418yescomplemented
892C22C2×#6693211yescharacteristic
893C22C2×#6693611yescharacteristic
894C22C2×#6693711yescharacteristic
895C22#1062302112yes—
896C22#1062302112yes—
897C22C2×#6693811yescharacteristic
898C22#1062302512yes—
899C22#1062302512yes—
900C22#1062302612yes—
901C22#1062302612yes—
902C22C2×#6697911yescharacteristic
903C22C2×#6697911yescharacteristic
904C22#1062332212yes—
905C22#1062332212yes—
906C22C2×D4×Dic1111yescharacteristic
907C22C2×D4×Dic1111yescharacteristic
908C22#1062332911yescharacteristic
909C22#1062332911yescharacteristic
910C22D4×C22⋊D1112yes—
911C22D4×C22⋊D1112yes—
912C22#1062333712yes—
913C22#1062333712yes—
914C22C22×C22⋊Dic1111yescharacteristic
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—444no—
920C4—444no—
921C4—882no—
922C4—882no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2#1307099911yescharacteristic
927C2C2×#1062256411yescharacteristic
928C2#1307121411yescharacteristic
929C2D4×C22⋊Dic1111yescharacteristic
930C2D4×C22⋊Dic1111yescharacteristic
931C2#1307146511yescharacteristic
932C2#1307146511yescharacteristic
933C2#1307207812yes—
934C2#1307215212yes—
935C2#1307273612yes—
936C2#1307285612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11#13873
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×#10622564C2semidirect
2. C2×#10622825C2semidirect
5. C2×C4×C22⋊Dic11C2semidirect
6. #13066865C2semidirect
7. #13066861C2semidirect
8. #13066853C2semidirect
9. #13066839C2semidirect
10. #13066839C2semidirect
16. C22×C11×C22⋊C4C4semidirect
29. C22×C4⋊Dic11C22semidirect
30. C22×C4×Dic11C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
238. C11×C22⋊C4C22⋊C4semidirect
414. C22×C22⋊C4Dic11semidirect
464. C22×C11#388semidirect
714. C22⋊C4C22⋊Dic11semidirect
716. C11#13873semidirect
891. C22#10622564semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106228252
C2×#106228602
C2×C4×C22⋊Dic112
#130668652
#130668612
#130668532
#130668392
C23×C11×C22⋊C42
#1387311