Finite Group Databasebeta

← #14675731

Subgroups — #14675731

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×#10622563C211yesmaximal, characteristic, complemented
4C2×#10622600C212yesmaximal, complemented
5C2×#10622568C211yesmaximal, characteristic
6#13066862C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic, complemented
9#13066838C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C2×C11×#385C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C22×C11×C4⋊C4C2212yescomplemented
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×(C2×D11)⋊C4—24no—
22C22×(C2×D11)⋊C4—28no—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2212yescomplemented
31C2×C22⋊C4×D11—24no—
32C2×C22⋊C4×D11—24no—
33C2×C22⋊C4×D11C418yescomplemented
34C11×#385—24no—
35C2×C11×#95C2212yescomplemented
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39C2×C11⋊#95C2212yescomplemented
40C2×C11⋊#95C2212yescomplemented
41#10622600—28no—
42#10622568—24no—
43#10622563—24no—
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×C4⋊C4—24no—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4—42no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4C2×C414yes—
90C2×C11×C22⋊C4D414yes—
91C2×C11×C22⋊C4D414yes—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11C2×C414yes—
98C2×(C2×D11)⋊C4—232no—
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—24no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—24no—
111C2×(C2×D11)⋊C4—24no—
112C2×(C2×D11)⋊C4—42no—
113C2×(C2×D11)⋊C4—42no—
114C2×(C2×D11)⋊C4C2×C418yescomplemented
115C2×(C2×D11)⋊C4D418yes—
116C2×C4⋊Dic11—24no—
117C2×C4⋊Dic11—24no—
118C2×C4⋊Dic11—42no—
119C22⋊C4×D11—232no—
120C11×#95—24no—
121C11⋊#95—24no—
122C11⋊#95—24no—
123C11⋊#95—24no—
124C11⋊#95—42no—
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—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—28no—
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—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—22no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—48no—
206C22×C4×C11—48no—
207C22×C4×C11—44no—
208C22×C4×C11—44no—
209C22×C4×C11C22×C414yes—
210C22×C4×C11C2×D414yes—
211C22×C4×C11C2×D414yes—
212C22×C4×C11C2×D414yes—
213C22×Dic11—28no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—21no—
221C22×Dic11—22no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—48no—
237C22×Dic11—48no—
238C22×Dic11—44no—
239C22×Dic11—44no—
240C22×Dic11C22×C414yes—
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×C4⋊C4—48no—
250C11×C22⋊C4—44no—
251C11×C22⋊C4C22⋊C4116yescomplemented
252C22⋊Dic11—28no—
253C22⋊Dic11—44no—
254(C2×D11)⋊C4—216no—
255(C2×D11)⋊C4—216no—
256(C2×D11)⋊C4—216no—
257(C2×D11)⋊C4—44no—
258(C2×D11)⋊C4—44no—
259(C2×D11)⋊C4—44no—
260(C2×D11)⋊C4—44no—
261C4⋊Dic11—48no—
262C23×C22⋊C4—111no—
263C23×C22⋊C4—111no—
264C2×#385—111no—
265C2×#385D1111yescharacteristic, complemented
266C2×#380—112no—
267C2×#379—111no—
268#1439—112no—
269#1439—112no—
270C22⋊#95—112no—
271C22⋊#95—111no—
272C22⋊#95—111no—
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×D412yes—
300C23×C11C22×D411yescharacteristic
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—24no—
371C2×C4×C11—24no—
372C2×C4×C11—24no—
373C2×C4×C11—416no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11C2×C22⋊C418yescomplemented
389C2×Dic11—24no—
390C2×Dic11—24no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—24no—
394C2×Dic11—24no—
395C2×Dic11—416no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399C2×Dic11—42no—
400C2×Dic11—42no—
401C2×Dic11—42no—
402C2×Dic11—42no—
403C2×Dic11—42no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—42no—
411C2×Dic11—42no—
412C2×Dic11—42no—
413C2×Dic11—42no—
414C4×D11—432no—
415C26—111no—
416C24×C4—112no—
417C24×C4—111no—
418C24×C4C2×D1111yescharacteristic
419C22×C4⋊C4—112no—
420C22×C4⋊C4C2×D1112yescomplemented
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—228no—
432C22×C22⋊C4—224no—
433C22×C22⋊C4—224no—
434C22×C22⋊C4—224no—
435C22×C22⋊C4C2×D1111yescharacteristic
436C22×C22⋊C4C2×D1111yescharacteristic
437#385—24no—
438#385—224no—
439#380—228no—
440#379—224no—
441C2×#95—112no—
442C2×#95—112no—
443C2×#95—112no—
444C2×#95—112no—
445C2×#95—112no—
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—28no—
505C4×C11—44no—
506C4×C11—81no—
507C4×C11—81no—
508Dic11—44no—
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—222no—
540C23×C4—224no—
541C23×C4—224no—
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—24no—
552C2×C4⋊C4—24no—
553C2×C4⋊C4—42no—
554C2×C4⋊C4—224no—
555C2×C4⋊C4—224no—
556C2×C4⋊C4—442no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—118no—
562C2×C22⋊C4—118no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—2232no—
568C2×C22⋊C4—222no—
569C2×C22⋊C4—222no—
570C2×C22⋊C4—224no—
571C2×C22⋊C4—224no—
572C2×C22⋊C4—224no—
573C2×C22⋊C4—2232no—
574C2×C22⋊C4—222no—
575C2×C22⋊C4—222no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—222no—
578C2×C22⋊C4—224no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—222no—
581C2×C22⋊C4—222no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—442no—
584C2×C22⋊C4—442no—
585C2×C22⋊C4C4×D1114yes—
586C2×C22⋊C4D4414yes—
587C2×C22⋊C4C22⋊D1114yes—
588#95—24no—
589#95—224no—
590#95—224no—
591#95—224no—
592#95—442no—
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—222no—
628C24—221no—
629C24—222no—
630C24—221no—
631C24—228no—
632C24—228no—
633C24—228no—
634C24—228no—
635C24—228no—
636C24—228no—
637C24—221no—
638C24—222no—
639C24—221no—
640C24—222no—
641C24—221no—
642C24—222no—
643C24—222no—
644C24—221no—
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—
658C24C2×D4412yes—
659C24D4×D1112yes—
660C24#434112yes—
661C24Q8×D1112yes—
662C24#434312yes—
663C24C2×C22⋊D1112yes—
664C24C23×D1111yescharacteristic
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—114no—
691C22×C4—114no—
692C22×C4—2216no—
693C22×C4—228no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—2216no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—222no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—222no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—448no—
718C22×C4—448no—
719C22×C4—448no—
720C22×C4—448no—
721C22×C4—448no—
722C22×C4—448no—
723C22×C4—448no—
724C22×C4—444no—
725C22×C4—444no—
726C22×C4C2×C4×D1114yes—
727C22×C4C2×D4414yes—
728C22×C4D4×D1114yes—
729C22×C4C2×C22⋊D1114yes—
730C4⋊C4—48no—
731C4⋊C4—448no—
732C22⋊C4—44no—
733C22⋊C4—2216no—
734C22⋊C4—2216no—
735C22⋊C4—228no—
736C22⋊C4—2216no—
737C22⋊C4—444no—
738C22⋊C4—444no—
739C22⋊C4—444no—
740C22⋊C4—444no—
741C22⋊C4—444no—
742C22⋊C4(C2×D11)⋊C4116yescomplemented
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—222no—
772C23—224no—
773C23—224no—
774C23—224no—
775C23—224no—
776C23—222no—
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—224no—
790C23—222no—
791C23—224no—
792C23—222no—
793C23—2232no—
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—
817C23C4⋊C4×D1114yes—
818C23#6694514yes—
819C23#6694814yes—
820C23#6695014yes—
821C23C2×(C2×D11)⋊C414yes—
822C23#6699114yes—
823C23#6699914yes—
824C23C22×C4×D1111yescharacteristic
825C23C22×D4411yescharacteristic
826C23C2×D4×D1111yescharacteristic
827C23C2×D4×D1112yes—
828C23C2×#434111yescharacteristic
829C23#6703712yes—
830C23C2×Q8×D1111yescharacteristic
831C23C2×#434311yescharacteristic
832C23#41×D1112yes—
833C23#6704212yes—
834C23C22×C22⋊D1111yescharacteristic
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—416no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—224no—
860C2×C4—224no—
861C2×C4—224no—
862C2×C4—224no—
863C2×C4—224no—
864C2×C4—224no—
865C2×C4—4432no—
866C2×C4—4416no—
867C2×C4—442no—
868C2×C4—442no—
869C2×C4—442no—
870C2×C4—442no—
871C2×C4—442no—
872C2×C4—442no—
873C2×C4—442no—
874C2×C4—442no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—442no—
878C2×C4—442no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—442no—
882C2×C4—442no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4C2×(C2×D11)⋊C418yescomplemented
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#1062260018yescomplemented
920C22C2×C4⋊C4×D1111yescharacteristic
921C22C2×#6694511yescharacteristic
922C22C2×#6694811yescharacteristic
923C22C2×#6695011yescharacteristic
924C22C4×D4×D1112yes—
925C22#1062307612yes—
926C22D4×D4412yes—
927C22#1062308512yes—
928C22D11×#12011yescharacteristic
929C22#1062312011yescharacteristic
930C22#1062312212yes—
931C22D11×C22⋊Q812yes—
932C22#1062316112yes—
933C22#1062316512yes—
934C22#1062316812yes—
935C22D11×#12311yescharacteristic
936C22#1062318411yescharacteristic
937C22#1062318912yes—
938C22C22×(C2×D11)⋊C411yescharacteristic
939C22C2×#6699111yescharacteristic
940C22D4×C22⋊D1112yes—
941C22C2×#6699911yescharacteristic
942C22#1062336012yes—
943C4—28no—
944C4—44no—
945C4—81no—
946C4—81no—
947C4—444no—
948C4—444no—
949C4—881no—
950C4—881no—
951C2—28no—
952C2—228no—
953C2—444no—
954C2C2×#1062260011yescharacteristic
955C2D11×#38511yescharacteristic
956C2#1307122711yescharacteristic
957C2D4×(C2×D11)⋊C412yes—
958C2#1307146312yes—
959C2#1307198611yescharacteristic
960C2#1307198811yescharacteristic
961C2#1307200811yescharacteristic
962C2#1307201011yescharacteristic
963C2#1307227912yes—
964C2#1307228012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#385D11
hypocenterC11#13877
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×#10622563C2semidirect
4. C2×#10622600C2semidirect
6. #13066862C2semidirect
7. #13066858C2semidirect
8. #13066839C2semidirect
9. #13066838C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C2×C11×#385C2semidirect
16. C22×C11×C4⋊C4C22semidirect
30. C22×C4⋊Dic11C22semidirect
33. C2×C22⋊C4×D11C4semidirect
35. C2×C11×#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
82. C22×C4×D11C2×C4semidirect
114. C2×(C2×D11)⋊C4C2×C4semidirect
175. C23×D11C4⋊C4semidirect
251. C11×C22⋊C4C22⋊C4semidirect
265. C2×#385D11semidirect
388. C2×C4×C11C2×C22⋊C4semidirect
420. C22×C4⋊C4C2×D11semidirect
446. C2×#95C2×D11semidirect
457. C22×C11#380semidirect
503. C2×D11#385semidirect
742. C22⋊C4(C2×D11)⋊C4semidirect
743. C11#13877semidirect
885. C2×C4C2×(C2×D11)⋊C4semidirect
919. C22#10622600semidirect

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×#106225632
C2×#106226002
C2×#106225682
#130668622
#130668582
#130668392
#130668382
(C2×D11)⋊#952
C2×C11×#3852
#1387711