Finite Group Databasebeta

← #14675715

Subgroups — #14675715

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×#10622825C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic
5#13066876C212yesmaximal, complemented
6#13066863C212yesmaximal
7#13066853C212yesmaximal
8#13066845C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066842C212yesmaximal, complemented
11C2×C11×#380C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C11×#380—24no—
25C2×C11×#95C2212yes—
26#10622825—24no—
27C4×C22⋊Dic11C418yescomplemented
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38#10622590—24no—
39C4⋊C4×Dic11—24no—
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11C2×C414yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2312yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
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×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—42no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11C2×C414yes—
75C2×C22⋊Dic11C2×C414yes—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11D414yes—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—24no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—42no—
89C2×C4×Dic11C2×C414yes—
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×C11—21no—
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11C22×C412yes—
116C24×C11#4112yes—
117C24×C11#4112yes—
118C24×C11C2411yescharacteristic
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—28no—
132C22×C4×C11—28no—
133C22×C4×C11—28no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
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—22no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11C22×C412yes—
190C22×Dic11C22×C412yes—
191C22×Dic11C22×C412yes—
192C22×Dic11C22×C412yes—
193C22×Dic11C2×D414yes—
194C22×Dic11#4112yes—
195C22×Dic11#4112yes—
196C11×C4⋊C4—28no—
197C11×C4⋊C4—44no—
198C11×C22⋊C4—48no—
199C22⋊Dic11—28no—
200C22⋊Dic11—28no—
201C22⋊Dic11—48no—
202C4⋊Dic11—28no—
203C4⋊Dic11—44no—
204C4×Dic11—28no—
205C4×Dic11—28no—
206C4×Dic11—48no—
207C2×#382—111no—
208C2×#380—111no—
209C2×#380D1111yescharacteristic
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×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11#11714yes—
253C23×C11C23×C411yescharacteristic
254C23×C11C22×D411yescharacteristic
255C23×C11C22×D411yescharacteristic
256C23×C11C2×#4111yescharacteristic
257C23×C11C2×#4111yescharacteristic
258C23×C11C2×#4111yescharacteristic
259C23×C11C2×#4111yescharacteristic
260C23×C11C2×#4111yescharacteristic
261C23×C11C2×#4111yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11H(5,𝔽2)11yescharacteristic
265C23×C11H(5,𝔽2)11yescharacteristic
266C23×C112−1+411yescharacteristic
267C23×C112−1+411yescharacteristic
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—416no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11#11714yes—
291C2×C4×C11C4×D414yes—
292C2×C4×C11C4×D414yes—
293C2×C4×C11#12114yes—
294C2×C4×C11#12314yes—
295C2×C4×C11#12414yes—
296C2×C4×C11#12614yes—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
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—24no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—42no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—42no—
330C2×Dic11—41no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11#11714yes—
339C24×C4C2×D1111yescharacteristic
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⋊C4C2×D1112yes—
348C22×C42—111no—
349C22×C42—111no—
350C22×C42—112no—
351#382—224no—
352#380—24no—
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×#95—112no—
366C2×#95C2×D1112yes—
367C22×C11—24no—
368C22×C11—24no—
369C22×C11—24no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11C2×#11711yescharacteristic
383C22×C11C2×#11711yescharacteristic
384C22×C11C2×#11711yescharacteristic
385C22×C11C2×C4×D411yescharacteristic
386C22×C11C2×C4×D411yescharacteristic
387C22×C11#52011yescharacteristic
388C22×C11#52011yescharacteristic
389C22×C11C2×#12111yescharacteristic
390C22×C11C2×#12311yescharacteristic
391C22×C11C2×#12411yescharacteristic
392C22×C11C2×#12611yescharacteristic
393C22×C11#52911yescharacteristic
394C22×C11#52911yescharacteristic
395C22×C11#52911yescharacteristic
396C22×C11#52911yescharacteristic
397C22×C11#54011yescharacteristic
398C22×C11#54111yescharacteristic
399C22×C11#54211yescharacteristic
400C22×C11#54211yescharacteristic
401C22×C11#54611yescharacteristic
402C22×C11#54611yescharacteristic
403C22×C11#54611yescharacteristic
404C22×C11#54711yescharacteristic
405C22×C11#54811yescharacteristic
406C22×C11#54811yescharacteristic
407C22×C11#54811yescharacteristic
408C22×C11#55011yescharacteristic
409C22×C11#55211yescharacteristic
410C22×C11#55211yescharacteristic
411C22×C11#55211yescharacteristic
412C22×C11#55311yescharacteristic
413C22×C11#55311yescharacteristic
414C22×C11#55311yescharacteristic
415C22×C11#55511yescharacteristic
416C22×C11#55611yescharacteristic
417C4×C11—44no—
418C4×C11—42no—
419C4×C11—82no—
420C4×C11#38818yes—
421Dic11—24no—
422Dic11—42no—
423Dic11—42no—
424Dic11—42no—
425Dic11—44no—
426Dic11—82no—
427C25C22×D1111yescharacteristic
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—111no—
435C23×C4—112no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—111no—
439C23×C4—112no—
440C23×C4C4×D1114yes—
441C23×C4C22×D1112yes—
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—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—222no—
463C2×C22⋊C4—222no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4—222no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—442no—
469C2×C42—114no—
470C2×C42—114no—
471C2×C42—222no—
472C2×C42—222no—
473C2×C42—222no—
474C2×C42—222no—
475C2×C42—224no—
476C2×C42—224no—
477C2×C42—442no—
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—44no—
490C2×C11#228311yescharacteristic
491C2×C11C2×#38811yescharacteristic
492C2×C11#231411yescharacteristic
493C2×C11#235211yescharacteristic
494C2×C11#235211yescharacteristic
495C2×C11#235211yescharacteristic
496C2×C11#235411yescharacteristic
497C2×C11#242011yescharacteristic
498C2×C11#242111yescharacteristic
499C2×C11#242611yescharacteristic
500C2×C11#242711yescharacteristic
501C2×C11#248911yescharacteristic
502C2×C11#249011yescharacteristic
503C2×C11#249411yescharacteristic
504C2×C11#249511yescharacteristic
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24C2×C4×D1112yes—
518C24#434112yes—
519C24#434312yes—
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—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—112no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—112no—
551C22×C4—112no—
552C22×C4—112no—
553C22×C4—114no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—222no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—221no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—222no—
571C22×C4—221no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4C2×C4×D1112yes—
590C22×C4C2×C4×D1112yes—
591C22×C4#433912yes—
592C22×C4D4×D1112yes—
593C22×C4#434112yes—
594C22×C4#434112yes—
595C22×C4#434112yes—
596C22×C4C2×C22⋊D1114yes—
597C22×C4C2×C22⋊D1112yes—
598C4⋊C4—28no—
599C4⋊C4—44no—
600C4⋊C4—228no—
601C4⋊C4—444no—
602C22⋊C4—48no—
603C22⋊C4—228no—
604C22⋊C4—228no—
605C22⋊C4—448no—
606C42—228no—
607C42—228no—
608C42—448no—
609C11#1387511yescharacteristic, complemented, Sylow
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#6694514yes—
645C23C22×C4×D1111yescharacteristic
646C23C2×#433911yescharacteristic
647C23C2×D4×D1111yescharacteristic
648C23C2×#434111yescharacteristic
649C23C2×#434111yescharacteristic
650C23C2×#434111yescharacteristic
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—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—416no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—114no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—224no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—442no—
704C2×C4—441no—
705C2×C4—442no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4#6693014yes—
725C2×C4#6693214yes—
726C2×C4(C22⋊D11)⋊C414yes—
727C2×C4#6693614yes—
728C2×C4C4×C22⋊D1114yes—
729C2×C4#6698914yes—
730C2×C4#6699214yes—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×#6693011yescharacteristic
747C22C2×#6693211yescharacteristic
748C22C2×(C22⋊D11)⋊C411yescharacteristic
749C22C2×#6693611yescharacteristic
750C22C2×#6694511yescharacteristic
751C22#1062303511yescharacteristic
752C22#1062304411yescharacteristic
753C22#1062304511yescharacteristic
754C22D11×#11711yescharacteristic
755C22#1062305411yescharacteristic
756C22#1062306311yescharacteristic
757C22#1062306411yescharacteristic
758C22#1062312911yescharacteristic
759C22#1062313111yescharacteristic
760C22#1062313111yescharacteristic
761C22#1062313411yescharacteristic
762C22#1062314311yescharacteristic
763C22#1062314511yescharacteristic
764C22#1062314911yescharacteristic
765C22#1062315011yescharacteristic
766C22#1062315511yescharacteristic
767C22#1062315511yescharacteristic
768C22#1062315611yescharacteristic
769C22#1062316111yescharacteristic
770C22#1062316411yescharacteristic
771C22#1062317011yescharacteristic
772C22#1062317311yescharacteristic
773C22#1062317411yescharacteristic
774C22C2×C4×C22⋊D1111yescharacteristic
775C22C2×#6698911yescharacteristic
776C22C2×#6699211yescharacteristic
777C22#1062333711yescharacteristic
778C22#1062334811yescharacteristic
779C22#1062335511yescharacteristic
780C22#1062336511yescharacteristic
781C4—44no—
782C4—42no—
783C4—82no—
784C4—224no—
785C4—442no—
786C4—442no—
787C4—442no—
788C4—444no—
789C4—882no—
790C4#1062255818yes—
791C2—44no—
792C2#1307101111yescharacteristic
793C2C2×#1062255811yescharacteristic
794C2#1307122311yescharacteristic
795C2#1307153811yescharacteristic
796C2#1307154111yescharacteristic
797C2#1307154711yescharacteristic
798C2#1307156611yescharacteristic
799C2#1307211011yescharacteristic
800C2#1307212111yescharacteristic
801C2#1307218411yescharacteristic
802C2#1307219511yescharacteristic
803C2#1307295911yescharacteristic
804C2#1307297011yescharacteristic
805C2#1307301811yescharacteristic
806C2#1307302911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#13875
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#10622590C2semidirect
3. C2×C4⋊C4×Dic11C2semidirect
5. #13066876C2semidirect
8. #13066845C2semidirect
9. #13066845C2semidirect
10. #13066842C2semidirect
27. C4×C22⋊Dic11C4semidirect
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×#106228252
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668762
#130668632
#130668532
#130668452
#130668422
C2×C11×#3802
#1387511