Finite Group Databasebeta

← #14675716

Subgroups — #14675716

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×#10622600C211yesmaximal, characteristic
2C2×#10622600C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13066877C212yesmaximal, complemented
6#13066864C212yesmaximal
7#13066852C212yesmaximal
8#13066846C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066842C212yesmaximal, complemented
11C2×C11×#382C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C11×#382—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—
38C4⋊C4×Dic11—24no—
39C4×(C2×D11)⋊C4C418yescomplemented
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
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⋊C4—22no—
63C2×C11×C4⋊C4D414yes—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11C2×C414yes—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4—42no—
77C2×(C2×D11)⋊C4C2×C414yes—
78C2×(C2×D11)⋊C4C2×C414yes—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11D414yes—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—42no—
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—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
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—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—22no—
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—21no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11C22×C412yes—
184C22×Dic11C22×C412yes—
185C22×Dic11C22×C412yes—
186C22×Dic11C2×D414yes—
187C22×Dic11#4112yes—
188C22×Dic11#4112yes—
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—44no—
198C42×C11—28no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—48no—
202(C2×D11)⋊C4—48no—
203C4⋊Dic11—28no—
204C4⋊Dic11—44no—
205C4×Dic11—28no—
206C4×Dic11—48no—
207C2×#382D1111yescharacteristic, complemented
208C2×#380—111no—
209C2×#380—111no—
210C2×C4×C4⋊C4—111no—
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—24no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—42no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
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—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—42no—
328C2×Dic11—41no—
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#11714yes—
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×C42—112no—
350C22×C42C2×D1111yescharacteristic
351#382—24no—
352#380—224no—
353#380—224no—
354C4×C4⋊C4—224no—
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×#95C2×D1112yes—
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—42no—
418C4×C11—42no—
419C4×C11—44no—
420C4×C11—82no—
421C4×C11#38818yes—
422Dic11—24no—
423Dic11—42no—
424Dic11—44no—
425Dic11—42no—
426Dic11—82no—
427C25—111no—
428C23×C4—111no—
429C23×C4—112no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—114no—
433C23×C4—112no—
434C23×C4—222no—
435C23×C4—222no—
436C23×C4—222no—
437C23×C4—222no—
438C23×C4—222no—
439C23×C4—222no—
440C23×C4C22×D1112yes—
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1112yes—
444C23×C4C22×D1111yescharacteristic
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—222no—
452C2×C4⋊C4—222no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—222no—
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—114no—
472C2×C42—222no—
473C2×C42—222no—
474C2×C42—224no—
475C2×C42—224no—
476C2×C42—442no—
477C2×C42C4×D1114yes—
478#95—24no—
479#95—24no—
480#95—114no—
481#95—114no—
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—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—112no—
547C22×C4—112no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—112no—
551C22×C4—114no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—222no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—222no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—222no—
569C22×C4—221no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—228no—
575C22×C4—228no—
576C22×C4—228no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—444no—
585C22×C4—444no—
586C22×C4—444no—
587C22×C4—444no—
588C22×C4C2×C4×D1112yes—
589C22×C4C2×C4×D1112yes—
590C22×C4C2×C4×D1112yes—
591C22×C4#433912yes—
592C22×C4D4×D1112yes—
593C22×C4#434112yes—
594C22×C4#434312yes—
595C22×C4#434312yes—
596C22×C4C2×C22⋊D1114yes—
597C22×C4C2×C22⋊D1112yes—
598C4⋊C4—28no—
599C4⋊C4—44no—
600C4⋊C4—228no—
601C4⋊C4—444no—
602C22⋊C4—228no—
603C22⋊C4—228no—
604C22⋊C4—448no—
605C22⋊C4—448no—
606C42—28no—
607C42—228no—
608C42—448no—
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
646C23C2×#433911yescharacteristic
647C23C2×D4×D1111yescharacteristic
648C23C2×#434111yescharacteristic
649C23C2×#434311yescharacteristic
650C23C2×#434311yescharacteristic
651C23#41×D1111yescharacteristic
652C23#41×D1111yescharacteristic
653C23#41×D1111yescharacteristic
654C23#41×D1111yescharacteristic
655C23#6704211yescharacteristic
656C23#6704211yescharacteristic
657C23#6704311yescharacteristic
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—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
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—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—114no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—224no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—442no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—442no—
716C2×C4—4416no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4#6694514yes—
725C2×C4#6694614yes—
726C2×C4#6694714yes—
727C2×C4#6695114yes—
728C2×C4C4×C22⋊D1114yes—
729C2×C4#6699214yes—
730C2×C4#6700014yes—
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×#6694511yescharacteristic
747C22C2×#6694611yescharacteristic
748C22C2×#6694711yescharacteristic
749C22C2×#6695111yescharacteristic
750C22D11×#11711yescharacteristic
751C22D11×#11711yescharacteristic
752C22#1062305411yescharacteristic
753C22#1062305411yescharacteristic
754C22#1062306011yescharacteristic
755C22#1062306111yescharacteristic
756C22#1062306311yescharacteristic
757C22#1062306411yescharacteristic
758C22#1062320711yescharacteristic
759C22#1062320711yescharacteristic
760C22#1062320811yescharacteristic
761C22#1062320811yescharacteristic
762C22#1062321111yescharacteristic
763C22#1062321111yescharacteristic
764C22#1062321311yescharacteristic
765C22#1062321311yescharacteristic
766C22#1062322211yescharacteristic
767C22#1062322211yescharacteristic
768C22#1062322511yescharacteristic
769C22#1062322511yescharacteristic
770C22#1062322611yescharacteristic
771C22#1062322611yescharacteristic
772C22#1062322811yescharacteristic
773C22#1062322911yescharacteristic
774C22C2×C4×C22⋊D1111yescharacteristic
775C22C2×#6699211yescharacteristic
776C22C2×#6700011yescharacteristic
777C22#1062335511yescharacteristic
778C22#1062336011yescharacteristic
779C22#1062336211yescharacteristic
780C22#1062336511yescharacteristic
781C4—44no—
782C4—42no—
783C4—42no—
784C4—82no—
785C4—224no—
786C4—442no—
787C4—442no—
788C4—444no—
789C4—882no—
790C4#1062260318yes—
791C2—444no—
792C2#1307100911yescharacteristic
793C2C2×#1062260311yescharacteristic
794C2#1307122611yescharacteristic
795C2#1307154211yescharacteristic
796C2#1307154211yescharacteristic
797C2#1307154611yescharacteristic
798C2#1307156611yescharacteristic
799C2#1307211111yescharacteristic
800C2#1307212211yescharacteristic
801C2#1307218511yescharacteristic
802C2#1307219611yescharacteristic
803C2#1307296011yescharacteristic
804C2#1307297111yescharacteristic
805C2#1307301911yescharacteristic
806C2#1307303011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#382C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#382D11
hypocenterC11#13875
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic11C2semidirect
5. #13066877C2semidirect
8. #13066846C2semidirect
9. #13066845C2semidirect
10. #13066842C2semidirect
11. C2×C11×#382C2semidirect
39. C4×(C2×D11)⋊C4C4semidirect
207. C2×#382D11semidirect
609. C11#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#106226002
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
#130668772
#130668642
#130668522
#130668462
#130668452
#130668422
C2×C11×#3822
#1387511