Finite Group Databasebeta

← #14675733

Subgroups — #14675733

Order 2816.

4046 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D11)⋊C4C211yesmaximal, characteristic
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3C2×#10622823C211yesmaximal, characteristic, complemented
4C2×#10622559C211yesmaximal, characteristic, complemented
5C2×#10622280C212yesmaximal, complemented
6C2×#10622568C211yesmaximal, characteristic
7#13066860C212yesmaximal, complemented
8#13066860C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4—24no—
21C22×(C2×D11)⋊C4—28no—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2212yescomplemented
30C22×Dic11⋊C4C2212yescomplemented
31C2×C22⋊C4×D11—24no—
32C2×C22⋊C4×D11—24no—
33C2×C22⋊C4×D11C418yescomplemented
34C2×C11×#95C2212yescomplemented
35C2×C11×#95C2212yescomplemented
36#10622823—24no—
37C2×C11⋊#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41#10622568—24no—
42#10622559—24no—
43#10622280—28no—
44C25×C11C2311yescharacteristic
45C24×D11—22no—
46C24×D11—22no—
47C24×D11—22no—
48C24×D11—22no—
49C24×D11—24no—
50C24×D11—24no—
51C24×D11—42no—
52C24×D11—42no—
53C24×D11C2×C414yes—
54C24×D11D414yes—
55C24×D11Q814yes—
56C24×D11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11—22no—
59C23×C4×C11—24no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—42no—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2312yes—
66C23×C4×C11C2312yes—
67C23×Dic11—22no—
68C23×Dic11—24no—
69C23×Dic11—22no—
70C23×Dic11—22no—
71C23×Dic11—42no—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2312yes—
75C23×Dic11C2312yes—
76C22×C4×D11—24no—
77C22×C4×D11—24no—
78C22×C4×D11—24no—
79C22×C4×D11—24no—
80C22×C4×D11—42no—
81C22×C4×D11—42no—
82C22×C4×D11C2×C418yescomplemented
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4C2×C414yes—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11C2×C414yes—
93C2×C22⋊Dic11D414yes—
94C2×C22⋊Dic11D414yes—
95C2×(C2×D11)⋊C4—232no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—24no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—24no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—24no—
109C2×(C2×D11)⋊C4—42no—
110C2×(C2×D11)⋊C4—42no—
111C2×(C2×D11)⋊C4C2×C418yescomplemented
112C2×(C2×D11)⋊C4D418yes—
113C2×Dic11⋊C4—24no—
114C2×Dic11⋊C4—24no—
115C2×Dic11⋊C4—24no—
116C2×Dic11⋊C4—24no—
117C2×Dic11⋊C4—42no—
118C2×Dic11⋊C4—42no—
119C22⋊C4×D11—232no—
120C11×#95—24no—
121C11×#95—42no—
122C11⋊#95—24no—
123C11⋊#95—24no—
124C11⋊#95—24no—
125C11⋊#95—42no—
126#13877—111nomaximal, Sylow
127C24×C11—22no—
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11C22×C412yes—
132C24×C11C2×D412yes—
133C24×C11C2×D412yes—
134C24×C11C2×D412yes—
135C24×C11C2×Q812yes—
136C24×C11#4112yes—
137C24×C11#4112yes—
138C24×C11C2411yescharacteristic
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11—28no—
146C23×D11—28no—
147C23×D11—28no—
148C23×D11—28no—
149C23×D11—28no—
150C23×D11—28no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—22no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11—22no—
159C23×D11—216no—
160C23×D11—28no—
161C23×D11—216no—
162C23×D11—28no—
163C23×D11—48no—
164C23×D11—44no—
165C23×D11—44no—
166C23×D11—48no—
167C23×D11—48no—
168C23×D11—48no—
169C23×D11—48no—
170C23×D11—48no—
171C23×D11—48no—
172C23×D11—48no—
173C23×D11—48no—
174C23×D11—48no—
175C23×D11C4⋊C4116yescomplemented
176C23×D11C22×C412yes—
177C23×D11C22×C412yes—
178C23×D11C2×D412yes—
179C23×D11C2×D412yes—
180C23×D11C2×D414yes—
181C23×D11C2×Q812yes—
182C23×D11C2×Q812yes—
183C23×D11#4114yes—
184C22×C4×C11—28no—
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—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—21no—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—22no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—48no—
208C22×C4×C11—48no—
209C22×C4×C11—44no—
210C22×C4×C11—44no—
211C22×C4×C11C22×C414yes—
212C22×C4×C11C2×D414yes—
213C22×Dic11—28no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—21no—
219C22×Dic11—22no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—48no—
235C22×Dic11—48no—
236C22×Dic11—44no—
237C22×Dic11—44no—
238C22×Dic11C22×C414yes—
239C22×Dic11C2×D414yes—
240C22×Dic11C2×D414yes—
241C22×Dic11C2×D414yes—
242C2×C4×D11—216no—
243C2×C4×D11—216no—
244C2×C4×D11—48no—
245C2×C4×D11—48no—
246C2×C4×D11—48no—
247C2×C4×D11—48no—
248C2×C4×D11—48no—
249C11×C22⋊C4—28no—
250C11×C22⋊C4—44no—
251C22⋊Dic11—44no—
252C22⋊Dic11C22⋊C4116yescomplemented
253(C2×D11)⋊C4—216no—
254(C2×D11)⋊C4—216no—
255(C2×D11)⋊C4—216no—
256(C2×D11)⋊C4—44no—
257(C2×D11)⋊C4—44no—
258(C2×D11)⋊C4—44no—
259(C2×D11)⋊C4—44no—
260Dic11⋊C4—48no—
261Dic11⋊C4—48no—
262C23×C22⋊C4—111no—
263C23×C22⋊C4—111no—
264C2×#385—111no—
265C2×#385—111no—
266C2×#380—112no—
267C2×#379—111no—
268#1439—112no—
269#1439—112no—
270C22⋊#95—112no—
271C22⋊#95—111no—
272C22⋊#95D1111yescharacteristic, complemented
273C23×C11—24no—
274C23×C11—24no—
275C23×C11—22no—
276C23×C11—24no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
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×C11C2×C22⋊C414yes—
290C23×C11C2×C4⋊C414yes—
291C23×C11#11714yes—
292C23×C11#12114yes—
293C23×C11#12114yes—
294C23×C11C22⋊Q814yes—
295C23×C11C22⋊Q814yes—
296C23×C11C23×C411yescharacteristic
297C23×C11C22×D411yescharacteristic
298C23×C11C22×D411yescharacteristic
299C23×C11C22×D411yescharacteristic
300C23×C11C22×D412yes—
301C23×C11C22×Q811yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11C2×#4112yes—
305C23×C11H(5,𝔽2)12yes—
306C23×C11H(5,𝔽2)12yes—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—24no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—24no—
317C22×D11—24no—
318C22×D11—24no—
319C22×D11—24no—
320C22×D11—24no—
321C22×D11—24no—
322C22×D11—24no—
323C22×D11—24no—
324C22×D11—24no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—24no—
328C22×D11—24no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—24no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—24no—
339C22×D11—232no—
340C22×D11—232no—
341C22×D11—416no—
342C22×D11—432no—
343C22×D11—432no—
344C22×D11—416no—
345C22×D11—416no—
346C22×D11—416no—
347C22×D11—416no—
348C22×D11—432no—
349C22×D11—432no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11—42no—
358C22×D11C2×C4⋊C414yes—
359C22×D11C2×C4⋊C414yes—
360C22×D11C4×D418yes—
361C22×D11#12014yes—
362C22×D11C22⋊Q818yes—
363C22×D11#12314yes—
364C2×C4×C11—24no—
365C2×C4×C11—24no—
366C2×C4×C11—24no—
367C2×C4×C11—24no—
368C2×C4×C11—24no—
369C2×C4×C11—24no—
370C2×C4×C11—416no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11—42no—
389C2×Dic11—24no—
390C2×Dic11—24no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—24no—
394C2×Dic11—24no—
395C2×Dic11—24no—
396C2×Dic11—24no—
397C2×Dic11—24no—
398C2×Dic11—416no—
399C2×Dic11—42no—
400C2×Dic11—42no—
401C2×Dic11—42no—
402C2×Dic11—42no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—42no—
410C2×Dic11—42no—
411C2×Dic11—42no—
412C2×Dic11—42no—
413C2×Dic11C2×C22⋊C418yescomplemented
414C4×D11—432no—
415C26—111no—
416C24×C4—112no—
417C24×C4—111no—
418C24×C4C2×D1111yescharacteristic
419C22×C4⋊C4—112no—
420C22×C4⋊C4—112no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—112no—
423C22×C22⋊C4—112no—
424C22×C22⋊C4—118no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—112no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—224no—
432C22×C22⋊C4—224no—
433C22×C22⋊C4—228no—
434C22×C22⋊C4—224no—
435C22×C22⋊C4C2×D1111yescharacteristic
436C22×C22⋊C4C2×D1111yescharacteristic
437#385—224no—
438#385—224no—
439#380—228no—
440#379—224no—
441C2×#95—112no—
442C2×#95—112no—
443C2×#95—112no—
444C2×#95—112no—
445C2×#95C2×D1112yescomplemented
446C2×#95C2×D1112yescomplemented
447C22×C11—24no—
448C22×C11—28no—
449C22×C11—28no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—24no—
454C22×C11—28no—
455C22×C11—28no—
456C22×C11—24no—
457C22×C11#38018yescomplemented
458C22×C11C22×C22⋊C411yescharacteristic
459C22×C11C22×C4⋊C411yescharacteristic
460C22×C11C2×#11711yescharacteristic
461C22×C11C2×C4×D412yes—
462C22×C11#51812yes—
463C22×C11C2×#12011yescharacteristic
464C22×C11C2×#12111yescharacteristic
465C22×C11C2×#12111yescharacteristic
466C22×C11C2×C22⋊Q811yescharacteristic
467C22×C11C2×C22⋊Q811yescharacteristic
468C22×C11C2×C22⋊Q812yes—
469C22×C11C2×#12311yescharacteristic
470C22×C11#53411yescharacteristic
471C22×C11#53411yescharacteristic
472C22×C11#54312yes—
473C22×C11D4212yes—
474C22×C11D4212yes—
475C22×C11#54612yes—
476C22×C11#54612yes—
477C22×C11#54612yes—
478C22×C11#54612yes—
479C22×C11#55112yes—
480C22×C11#55112yes—
481C2×D11—24no—
482C2×D11—28no—
483C2×D11—28no—
484C2×D11—24no—
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—28no—
489C2×D11—28no—
490C2×D11—24no—
491C2×D11—24no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—464no—
495C2×D11—44no—
496C2×D11—44no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—44no—
502C2×D11—44no—
503C2×D11#38518yescomplemented
504C4×C11—44no—
505C4×C11—44no—
506C4×C11—81no—
507C4×C11—81no—
508Dic11—28no—
509Dic11—44no—
510Dic11—81no—
511Dic11—81no—
512C25—111no—
513C25—111no—
514C25—114no—
515C25—114no—
516C25—114no—
517C25—224no—
518C25—224no—
519C25—222no—
520C25—222no—
521C25—222no—
522C25—222no—
523C25—442no—
524C25—442no—
525C25C22×D1111yescharacteristic
526C23×C4—22no—
527C23×C4—24no—
528C23×C4—22no—
529C23×C4—22no—
530C23×C4—42no—
531C23×C4—112no—
532C23×C4—112no—
533C23×C4—118no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—224no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4—224no—
540C23×C4—224no—
541C23×C4—222no—
542C23×C4—222no—
543C23×C4—222no—
544C23×C4—442no—
545C23×C4—442no—
546C23×C4—442no—
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1112yes—
550C23×C4C22×D1112yes—
551C2×C4⋊C4—224no—
552C2×C4⋊C4—224no—
553C2×C4⋊C4—224no—
554C2×C4⋊C4—224no—
555C2×C4⋊C4—442no—
556C2×C4⋊C4—442no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—114no—
564C2×C22⋊C4—114no—
565C2×C22⋊C4—118no—
566C2×C22⋊C4—118no—
567C2×C22⋊C4—2232no—
568C2×C22⋊C4—224no—
569C2×C22⋊C4—224no—
570C2×C22⋊C4—224no—
571C2×C22⋊C4—224no—
572C2×C22⋊C4—224no—
573C2×C22⋊C4—224no—
574C2×C22⋊C4—2232no—
575C2×C22⋊C4—224no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—222no—
578C2×C22⋊C4—222no—
579C2×C22⋊C4—222no—
580C2×C22⋊C4—224no—
581C2×C22⋊C4—224no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—442no—
586C2×C22⋊C4—442no—
587C2×C22⋊C4C4×D1114yes—
588#95—24no—
589#95—42no—
590#95—224no—
591#95—224no—
592#95—224no—
593#95—442no—
594C2×C11—28no—
595C2×C11C2×#38011yescharacteristic
596C2×C11C2×#38511yescharacteristic
597C2×C11#231511yescharacteristic
598C2×C11D4×C22⋊C412yes—
599C2×C11#234212yes—
600C2×C11#241011yescharacteristic
601C2×C11#241011yescharacteristic
602C2×C11#241211yescharacteristic
603C2×C11#241211yescharacteristic
604C2×C11#243712yes—
605C2×C11#243712yes—
606D11—28no—
607D11—44no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—112no—
613C24—114no—
614C24—112no—
615C24—112no—
616C24—114no—
617C24—112no—
618C24—112no—
619C24—112no—
620C24—1116no—
621C24—228no—
622C24—2216no—
623C24—2216no—
624C24—228no—
625C24—221no—
626C24—221no—
627C24—221no—
628C24—221no—
629C24—222no—
630C24—222no—
631C24—228no—
632C24—228no—
633C24—228no—
634C24—228no—
635C24—228no—
636C24—228no—
637C24—221no—
638C24—221no—
639C24—221no—
640C24—221no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—448no—
646C24—444no—
647C24—448no—
648C24—444no—
649C24—448no—
650C24—448no—
651C24—448no—
652C24—448no—
653C24—448no—
654C24—448no—
655C24—448no—
656C24—448no—
657C24C2×C4×D1112yes—
658C24#433912yes—
659C24#433912yes—
660C24D4×D1112yes—
661C24D4×D1112yes—
662C24D4×D1112yes—
663C24Q8×D1112yes—
664C24C23×D1111yescharacteristic
665C22×C4—28no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—114no—
693C22×C4—114no—
694C22×C4—114no—
695C22×C4—114no—
696C22×C4—2216no—
697C22×C4—2216no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—228no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—222no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—222no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—448no—
720C22×C4—448no—
721C22×C4—448no—
722C22×C4—448no—
723C22×C4—448no—
724C22×C4—448no—
725C22×C4—448no—
726C22×C4—444no—
727C22×C4—444no—
728C22×C4C2×C4×D1114yes—
729C22×C4D4×D1114yes—
730C4⋊C4—448no—
731C4⋊C4—448no—
732C22⋊C4—28no—
733C22⋊C4—44no—
734C22⋊C4—1116no—
735C22⋊C4—2216no—
736C22⋊C4—2216no—
737C22⋊C4—2216no—
738C22⋊C4—444no—
739C22⋊C4—444no—
740C22⋊C4—444no—
741C22⋊C4—444no—
742C22⋊C4—444no—
743C11#1387711yescharacteristic, complemented, Sylow
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—22no—
751C23—22no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—22no—
758C23—22no—
759C23—24no—
760C23—114no—
761C23—118no—
762C23—114no—
763C23—118no—
764C23—114no—
765C23—114no—
766C23—2232no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—224no—
772C23—222no—
773C23—222no—
774C23—224no—
775C23—224no—
776C23—224no—
777C23—224no—
778C23—222no—
779C23—224no—
780C23—224no—
781C23—224no—
782C23—224no—
783C23—222no—
784C23—224no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—2232no—
792C23—224no—
793C23—224no—
794C23—222no—
795C23—222no—
796C23—224no—
797C23—224no—
798C23—222no—
799C23—222no—
800C23—4416no—
801C23—4432no—
802C23—4432no—
803C23—4416no—
804C23—4416no—
805C23—4416no—
806C23—4416no—
807C23—4432no—
808C23—4432no—
809C23—442no—
810C23—442no—
811C23—442no—
812C23—442no—
813C23—442no—
814C23—442no—
815C23—442no—
816C23—442no—
817C23#6692514yes—
818C23C22⋊C4×D1114yes—
819C23#6693714yes—
820C23#6693714yes—
821C23C4⋊C4×D1114yes—
822C23#6694914yes—
823C23#6694914yes—
824C23C22×C4×D1111yescharacteristic
825C23C2×#433911yescharacteristic
826C23C2×#433911yescharacteristic
827C23C2×D4×D1111yescharacteristic
828C23C2×D4×D1111yescharacteristic
829C23C2×D4×D1111yescharacteristic
830C23C2×D4×D1112yes—
831C23#6703712yes—
832C23C2×Q8×D1111yescharacteristic
833C23#41×D1112yes—
834C23#6704212yes—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—416no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—118no—
861C2×C4—224no—
862C2×C4—224no—
863C2×C4—224no—
864C2×C4—224no—
865C2×C4—224no—
866C2×C4—224no—
867C2×C4—224no—
868C2×C4—224no—
869C2×C4—224no—
870C2×C4—4432no—
871C2×C4—4416no—
872C2×C4—442no—
873C2×C4—442no—
874C2×C4—442no—
875C2×C4—442no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—442no—
879C2×C4—442no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—442no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4—442no—
886C22—28no—
887C22—28no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—28no—
894C22—28no—
895C22—24no—
896C22—118no—
897C22—228no—
898C22—228no—
899C22—224no—
900C22—224no—
901C22—224no—
902C22—224no—
903C22—224no—
904C22—224no—
905C22—228no—
906C22—228no—
907C22—224no—
908C22—224no—
909C22—224no—
910C22—4464no—
911C22—444no—
912C22—444no—
913C22—442no—
914C22—442no—
915C22—442no—
916C22—442no—
917C22—444no—
918C22—444no—
919C22#1062228018yescomplemented
920C22C2×#6692511yescharacteristic
921C22C2×C22⋊C4×D1111yescharacteristic
922C22C2×#6693711yescharacteristic
923C22C2×#6693711yescharacteristic
924C22#1062302112yes—
925C22C2×C4⋊C4×D1111yescharacteristic
926C22C2×#6694911yescharacteristic
927C22C2×#6694911yescharacteristic
928C22#1062305812yes—
929C22C4×D4×D1112yes—
930C22#1062307612yes—
931C22#1062308112yes—
932C22#1062308712yes—
933C22D11×#12011yescharacteristic
934C22#1062312011yescharacteristic
935C22#1062312112yes—
936C22#1062314012yes—
937C22#1062314112yes—
938C22D11×C22⋊Q812yes—
939C22#1062316512yes—
940C22D11×#12311yescharacteristic
941C22#1062318411yescharacteristic
942C22#1062318512yes—
943C4—44no—
944C4—44no—
945C4—81no—
946C4—81no—
947C4—228no—
948C4—444no—
949C4—881no—
950C4—881no—
951C2—28no—
952C2—228no—
953C2—444no—
954C2C2×#1062228011yescharacteristic
955C2D11×#38511yescharacteristic
956C2#1307122711yescharacteristic
957C2#1307143412yes—
958C2#1307145912yes—
959C2#1307199211yescharacteristic
960C2#1307199311yescharacteristic
961C2#1307201411yescharacteristic
962C2#1307201511yescharacteristic
963C2#1307228112yes—
964C2#1307228412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenterC22⋊#95D11
hypocenterC11#13877
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622823C2semidirect
4. C2×#10622559C2semidirect
5. C2×#10622280C2semidirect
7. #13066860C2semidirect
8. #13066860C2semidirect
9. #13066838C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×C22⋊#95C2semidirect
29. C22×Dic11⋊C4C22semidirect
30. C22×Dic11⋊C4C22semidirect
33. C2×C22⋊C4×D11C4semidirect
34. C2×C11×#95C22semidirect
35. C2×C11×#95C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
82. C22×C4×D11C2×C4semidirect
111. C2×(C2×D11)⋊C4C2×C4semidirect
175. C23×D11C4⋊C4semidirect
252. C22⋊Dic11C22⋊C4semidirect
272. C22⋊#95D11semidirect
413. C2×Dic11C2×C22⋊C4semidirect
445. C2×#95C2×D11semidirect
446. C2×#95C2×D11semidirect
457. C22×C11#380semidirect
503. C2×D11#385semidirect
743. C11#13877semidirect
919. C22#10622280semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D11)⋊C42
C22×C22⋊C4×D112
C2×#106228232
C2×#106225592
C2×#106222802
C2×#106225682
#130668602
#130668382
(C2×D11)⋊#952
C11×C22⋊#952
#1387711