Finite Group Databasebeta

← #14675707

Subgroups — #14675707

Order 2816.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622590C211yesmaximal, characteristic, complemented
2C2×#10622600C211yesmaximal, characteristic
3C2×#10622600C211yesmaximal, characteristic
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13066876C212yesmaximal, complemented
6#13066864C212yesmaximal
7#13066854C212yesmaximal
8#13066846C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066843C212yesmaximal, complemented
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C4×C11×C4⋊C4—24no—
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36#10622600—24no—
37#10622600—24no—
38#10622590—24no—
39C4×(C2×D11)⋊C4C418yescomplemented
40C24×D11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11C2×C414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4D414yes—
63C2×C11×C4⋊C4D414yes—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11—24no—
67C2×C42×C11—24no—
68C2×C42×C11—42no—
69C2×C42×C11C2×C414yes—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4C2×C414yes—
81C2×(C2×D11)⋊C4C2×C414yes—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11C2×C414yes—
91C11×#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95C2×C414yes—
101C11⋊#95C2×C414yes—
102#13875—111nomaximal, Sylow
103C24×C11C2411yescharacteristic
104C23×D11—21no—
105C23×D11—21no—
106C23×D11—21no—
107C23×D11—21no—
108C23×D11—21no—
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—21no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11C22×C412yes—
117C23×D11#4112yes—
118C23×D11#4112yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4112yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11C22×C412yes—
187C22×Dic11C22×C412yes—
188C22×Dic11C22×C412yes—
189C2×C4×D11—28no—
190C2×C4×D11—28no—
191C2×C4×D11—28no—
192C2×C4×D11—44no—
193C2×C4×D11—44no—
194C2×C4×D11—44no—
195C2×C4×D11—44no—
196C11×C4⋊C4—28no—
197C11×C4⋊C4—28no—
198C42×C11—28no—
199C42×C11—48no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—48no—
203(C2×D11)⋊C4—48no—
204C4⋊Dic11—44no—
205C4⋊Dic11—44no—
206C4×Dic11—28no—
207C2×#382—111no—
208C2×#380—111no—
209C2×#380—111no—
210C2×C4×C4⋊C4D1111yescharacteristic, complemented
211C2×C4×C22⋊C4—111no—
212#1443—112no—
213#1440—112no—
214#1437—112no—
215C4⋊#95—111no—
216C4⋊#95—111no—
217#1434—112no—
218C23×C11C23×C411yescharacteristic
219C23×C11C22×D411yescharacteristic
220C23×C11C22×D411yescharacteristic
221C23×C11C2×#4111yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C23×C11C2×#4111yescharacteristic
224C23×C11C2×#4111yescharacteristic
225C23×C11C2×#4111yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11H(5,𝔽2)11yescharacteristic
230C23×C11H(5,𝔽2)11yescharacteristic
231C23×C112−1+411yescharacteristic
232C23×C112−1+411yescharacteristic
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11#11714yes—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11#11714yes—
296C2×C4×C11#11714yes—
297C2×C4×C11C4×D414yes—
298C2×C4×C11C4×D414yes—
299C2×C4×C11#12114yes—
300C2×C4×C11#12314yes—
301C2×C4×C11#12414yes—
302C2×C4×C11#12614yes—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C4×D11—416no—
339C24×C4—111no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4C2×D1111yescharacteristic
343C22×C4⋊C4C2×D1111yescharacteristic
344C22×C22⋊C4—111no—
345C22×C22⋊C4—111no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C42—111no—
349C22×C42C2×D1112yes—
350C22×C42C2×D1111yescharacteristic
351#382—224no—
352#380—224no—
353#380—224no—
354C4×C4⋊C4—24no—
355C4×C22⋊C4—118no—
356C2×#95—111no—
357C2×#95—111no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95C2×D1112yes—
367C22×C11C2×#11711yescharacteristic
368C22×C11C2×#11711yescharacteristic
369C22×C11C2×#11711yescharacteristic
370C22×C11C2×C4×D411yescharacteristic
371C22×C11C2×C4×D411yescharacteristic
372C22×C11#52011yescharacteristic
373C22×C11#52011yescharacteristic
374C22×C11C2×#12111yescharacteristic
375C22×C11C2×#12311yescharacteristic
376C22×C11C2×#12411yescharacteristic
377C22×C11C2×#12611yescharacteristic
378C22×C11#52911yescharacteristic
379C22×C11#52911yescharacteristic
380C22×C11#52911yescharacteristic
381C22×C11#52911yescharacteristic
382C22×C11#54011yescharacteristic
383C22×C11#54111yescharacteristic
384C22×C11#54211yescharacteristic
385C22×C11#54211yescharacteristic
386C22×C11#54611yescharacteristic
387C22×C11#54611yescharacteristic
388C22×C11#54611yescharacteristic
389C22×C11#54711yescharacteristic
390C22×C11#54811yescharacteristic
391C22×C11#54811yescharacteristic
392C22×C11#54811yescharacteristic
393C22×C11#55011yescharacteristic
394C22×C11#55211yescharacteristic
395C22×C11#55211yescharacteristic
396C22×C11#55211yescharacteristic
397C22×C11#55311yescharacteristic
398C22×C11#55311yescharacteristic
399C22×C11#55311yescharacteristic
400C22×C11#55511yescharacteristic
401C22×C11#55611yescharacteristic
402C2×D11—24no—
403C2×D11—24no—
404C2×D11—24no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C4×C11—24no—
418C4×C11—42no—
419C4×C11—44no—
420C4×C11—44no—
421C4×C11#38818yes—
422Dic11—42no—
423Dic11—42no—
424Dic11—42no—
425Dic11—82no—
426Dic11—82no—
427C25—111no—
428C23×C4—111no—
429C23×C4—111no—
430C23×C4—111no—
431C23×C4—114no—
432C23×C4—112no—
433C23×C4—112no—
434C23×C4—222no—
435C23×C4—222no—
436C23×C4—222no—
437C23×C4—222no—
438C23×C4—222no—
439C23×C4—222no—
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1112yes—
442C23×C4C22×D1112yes—
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—222no—
450C2×C4⋊C4—222no—
451C2×C4⋊C4—222no—
452C2×C4⋊C4—222no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4D4414yes—
456C2×C4⋊C4C22⋊D1114yes—
457C2×C22⋊C4—114no—
458C2×C22⋊C4—114no—
459C2×C22⋊C4—222no—
460C2×C22⋊C4—222no—
461C2×C22⋊C4—222no—
462C2×C22⋊C4—222no—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—224no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4—442no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—24no—
472C2×C42—24no—
473C2×C42—42no—
474C2×C42—114no—
475C2×C42—222no—
476C2×C42—222no—
477C2×C42C4×D1114yes—
478#95—24no—
479#95—114no—
480#95—114no—
481#95—224no—
482#95—224no—
483#95—224no—
484#95—224no—
485#95—224no—
486#95—442no—
487#95—442no—
488#95—442no—
489C2×C11#228311yescharacteristic
490C2×C11C2×#38811yescharacteristic
491C2×C11#231411yescharacteristic
492C2×C11#235211yescharacteristic
493C2×C11#235211yescharacteristic
494C2×C11#235211yescharacteristic
495C2×C11#235411yescharacteristic
496C2×C11#242011yescharacteristic
497C2×C11#242111yescharacteristic
498C2×C11#242611yescharacteristic
499C2×C11#242711yescharacteristic
500C2×C11#248911yescharacteristic
501C2×C11#249011yescharacteristic
502C2×C11#249411yescharacteristic
503C2×C11#249511yescharacteristic
504D11—44no—
505C24—112no—
506C24—112no—
507C24—112no—
508C24—221no—
509C24—221no—
510C24—221no—
511C24—221no—
512C24—221no—
513C24—221no—
514C24—221no—
515C24—221no—
516C24—221no—
517C24—221no—
518C24—221no—
519C24—221no—
520C24C23×D1111yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—112no—
546C22×C4—221no—
547C22×C4—221no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—228no—
565C22×C4—228no—
566C22×C4—228no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—444no—
582C22×C4—444no—
583C22×C4—444no—
584C22×C4—444no—
585C22×C4C2×C4×D1112yes—
586C22×C4C2×C4×D1112yes—
587C22×C4C2×C4×D1112yes—
588C22×C4C2×D4414yes—
589C22×C4C2×D4412yes—
590C22×C4#433912yes—
591C22×C4#433912yes—
592C22×C4#433912yes—
593C22×C4#433912yes—
594C22×C4#434112yes—
595C22×C4#434312yes—
596C22×C4C2×C22⋊D1114yes—
597C22×C4C2×C22⋊D1112yes—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—444no—
601C4⋊C4—444no—
602C22⋊C4—228no—
603C22⋊C4—228no—
604C22⋊C4—448no—
605C22⋊C4—448no—
606C42—28no—
607C42—48no—
608C42—228no—
609C11#1387511yescharacteristic, complemented, Sylow
610C23—114no—
611C23—222no—
612C23—222no—
613C23—222no—
614C23—222no—
615C23—222no—
616C23—222no—
617C23—222no—
618C23—222no—
619C23—222no—
620C23—222no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—222no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23C22×C4×D1111yescharacteristic
646C23C22×D4411yescharacteristic
647C23C2×#433911yescharacteristic
648C23C2×#433911yescharacteristic
649C23C2×#433911yescharacteristic
650C23C2×#433911yescharacteristic
651C23C2×#434111yescharacteristic
652C23#6703711yescharacteristic
653C23C2×#434311yescharacteristic
654C23#6704011yescharacteristic
655C23#41×D1111yescharacteristic
656C23#41×D1111yescharacteristic
657C23#6704211yescharacteristic
658C23#6704311yescharacteristic
659C23C22×C22⋊D1111yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—4416no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4#6692514yes—
724C2×C4C4×D4414yes—
725C2×C4#6692814yes—
726C2×C4#6692914yes—
727C2×C4#6694514yes—
728C2×C4C4×C22⋊D1114yes—
729C2×C4#6698214yes—
730C2×C4#6698314yes—
731C22—224no—
732C22—224no—
733C22—224no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—442no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22C2×#6692511yescharacteristic
747C22C2×C4×D4411yescharacteristic
748C22C2×#6692811yescharacteristic
749C22C2×#6692911yescharacteristic
750C22C2×#6694511yescharacteristic
751C22#1062303511yescharacteristic
752C22#1062304411yescharacteristic
753C22#1062304511yescharacteristic
754C22D11×#11711yescharacteristic
755C22#1062305411yescharacteristic
756C22#1062306011yescharacteristic
757C22#1062306111yescharacteristic
758C22#1062308511yescharacteristic
759C22#1062308611yescharacteristic
760C22#1062308811yescharacteristic
761C22#1062308811yescharacteristic
762C22#1062308911yescharacteristic
763C22#1062309211yescharacteristic
764C22#1062309311yescharacteristic
765C22#1062309411yescharacteristic
766C22#1062310711yescharacteristic
767C22#1062310811yescharacteristic
768C22#1062311111yescharacteristic
769C22#1062311111yescharacteristic
770C22#1062311211yescharacteristic
771C22#1062311311yescharacteristic
772C22#1062311411yescharacteristic
773C22#1062311511yescharacteristic
774C22C2×C4×C22⋊D1111yescharacteristic
775C22C2×#6698211yescharacteristic
776C22C2×#6698311yescharacteristic
777C22#1062333711yescharacteristic
778C22#1062334811yescharacteristic
779C22#1062336011yescharacteristic
780C22#1062336211yescharacteristic
781C4—24no—
782C4—44no—
783C4—42no—
784C4—44no—
785C4—442no—
786C4—442no—
787C4—442no—
788C4—882no—
789C4—882no—
790C4#1062255318yes—
791C2—444no—
792C2#1307101211yescharacteristic
793C2C2×#1062255311yescharacteristic
794C2#1307122111yescharacteristic
795C2#1307154111yescharacteristic
796C2#1307154611yescharacteristic
797C2#1307154811yescharacteristic
798C2#1307156311yescharacteristic
799C2#1307210211yescharacteristic
800C2#1307211311yescharacteristic
801C2#1307217611yescharacteristic
802C2#1307218711yescharacteristic
803C2#1307295111yescharacteristic
804C2#1307296211yescharacteristic
805C2#1307301011yescharacteristic
806C2#1307302111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13875
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622590C2semidirect
5. #13066876C2semidirect
8. #13066846C2semidirect
9. #13066845C2semidirect
10. #13066843C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
39. C4×(C2×D11)⋊C4C4semidirect
210. C2×C4×C4⋊C4D11semidirect
609. C11#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#106225902
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668762
#130668642
#130668542
#130668462
#130668452
#130668432
C2×C4×C11×C4⋊C42
#1387511