Finite Group Databasebeta

← #14675713

Subgroups — #14675713

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×#10622549C211yesmaximal, characteristic, complemented
2C2×#10622825C211yesmaximal, characteristic
3C2×#10622825C211yesmaximal, characteristic
4C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13066878C212yesmaximal, complemented
6#13066865C212yesmaximal
7#13066853C212yesmaximal
8#13066846C211yesmaximal, characteristic, complemented
9#13066846C211yesmaximal, characteristic, complemented
10#13066841C212yesmaximal, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C4×C11×C22⋊C4C418yescomplemented
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27#10622825—24no—
28#10622825—24no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622549—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×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4C2×C414yes—
63C2×C11×C22⋊C4C2×C414yes—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11C2×C414yes—
69C2×C42×C11C2×C414yes—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11—42no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11D414yes—
87C2×C4⋊Dic11D414yes—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—24no—
90C2×C4×Dic11—42no—
91C11×#95C2×C414yes—
92C11×#95C2×C414yes—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—42no—
100C11⋊#95—42no—
101C11⋊#95—42no—
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—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—28no—
148C22×C4×C11—28no—
149C22×C4×C11—28no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×C4×C11#4112yes—
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×C4×C11#4112yes—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11C2×D414yes—
195C22×Dic11C2×D414yes—
196C11×C22⋊C4—28no—
197C11×C22⋊C4—28no—
198C42×C11—28no—
199C42×C11—28no—
200C22⋊Dic11—48no—
201C22⋊Dic11—48no—
202C4⋊Dic11—28no—
203C4⋊Dic11—28no—
204C4⋊Dic11—44no—
205C4⋊Dic11—44no—
206C4×Dic11—48no—
207C2×#382—111no—
208C2×#380—111no—
209C2×#380—111no—
210C2×C4×C4⋊C4—111no—
211C2×C4×C22⋊C4D1111yescharacteristic
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—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—416no—
303C2×C4×C11#11714yes—
304C2×C4×C11#11714yes—
305C2×C4×C11C4×D414yes—
306C2×C4×C11C4×D414yes—
307C2×C4×C11#12114yes—
308C2×C4×C11#12314yes—
309C2×C4×C11#12414yes—
310C2×C4×C11#12614yes—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
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—
338C2×Dic11—42no—
339C24×C4C2×D1111yescharacteristic
340C22×C4⋊C4—111no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4—111no—
343C22×C4⋊C4—111no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4C2×D1111yescharacteristic
347C22×C22⋊C4C2×D1111yescharacteristic
348C22×C42—112no—
349C22×C42C2×D1111yescharacteristic
350C22×C42C2×D1111yescharacteristic
351#382—224no—
352#380—224no—
353#380—224no—
354C4×C4⋊C4—224no—
355C4×C22⋊C4Dic1118yescomplemented
356C2×#95—112no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95C2×D1111yescharacteristic
366C2×#95C2×D1111yescharacteristic
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—24no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11—42no—
421C4×C11—42no—
422C4×C11#38818yes—
423Dic11—44no—
424Dic11—44no—
425Dic11—82no—
426Dic11—82no—
427C25C22×D1111yescharacteristic
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—112no—
435C23×C4—112no—
436C23×C4—112no—
437C23×C4—112no—
438C23×C4C2×Dic1114yes—
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C2×C4⋊C4—114no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—222no—
448C2×C4⋊C4—222no—
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⋊C4—222no—
456C2×C4⋊C4—222no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—224no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—224no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4C2×Dic1114yes—
468C2×C22⋊C4C2×Dic1114yes—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—224no—
474C2×C42—224no—
475C2×C42—442no—
476C2×C42C2×Dic1114yes—
477C2×C42C2×Dic1114yes—
478#95—224no—
479#95—224no—
480#95—224no—
481#95—224no—
482#95—224no—
483#95—224no—
484#95—442no—
485#95—442no—
486#95—442no—
487#95C2×Dic1114yes—
488#95C2×Dic1114yes—
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—
517C24#433912yes—
518C24#433912yes—
519C24C22×Dic1112yes—
520C24C23×D1111yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—114no—
557C22×C4—114no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
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—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4#433912yes—
585C22×C4#433912yes—
586C22×C4#433912yes—
587C22×C4#433912yes—
588C22×C4D4×D1112yes—
589C22×C4D4×D1112yes—
590C22×C4#434112yes—
591C22×C4#434112yes—
592C22×C4C22×Dic1112yes—
593C22×C4C22×Dic1112yes—
594C22×C4C22×Dic1112yes—
595C22×C4C22×Dic1112yes—
596C22×C4C22×Dic1112yes—
597C22×C4C22×Dic1112yes—
598C4⋊C4—228no—
599C4⋊C4—228no—
600C4⋊C4—444no—
601C4⋊C4—444no—
602C22⋊C4—28no—
603C22⋊C4—28no—
604C22⋊C4—448no—
605C22⋊C4—448no—
606C42—28no—
607C42—28no—
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#6697914yes—
645C23C2×#433911yescharacteristic
646C23C2×#433911yescharacteristic
647C23C2×#433911yescharacteristic
648C23C2×#433911yescharacteristic
649C23C2×#433911yescharacteristic
650C23C2×#433911yescharacteristic
651C23C2×D4×D1111yescharacteristic
652C23C2×D4×D1111yescharacteristic
653C23C2×#434111yescharacteristic
654C23C2×#434111yescharacteristic
655C23#6704211yescharacteristic
656C23#6704211yescharacteristic
657C23#6704311yescharacteristic
658C23#6704311yescharacteristic
659C23C23×Dic1111yescharacteristic
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—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—416no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
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#6693214yes—
724C2×C4#6693614yes—
725C2×C4#6693714yes—
726C2×C4#6693814yes—
727C2×C4#6697914yes—
728C2×C4#6697914yes—
729C2×C4D4×Dic1114yes—
730C2×C4D4×Dic1114yes—
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—
746C22#1062301011yescharacteristic
747C22#1062301011yescharacteristic
748C22#1062301011yescharacteristic
749C22#1062301011yescharacteristic
750C22C2×#6693211yescharacteristic
751C22C2×#6693611yescharacteristic
752C22C2×#6693711yescharacteristic
753C22C2×#6693811yescharacteristic
754C22#1062304911yescharacteristic
755C22#1062306511yescharacteristic
756C22#1062306511yescharacteristic
757C22#1062306611yescharacteristic
758C22#1062307211yescharacteristic
759C22#1062307211yescharacteristic
760C22#1062307211yescharacteristic
761C22#1062307311yescharacteristic
762C22#1062308111yescharacteristic
763C22#1062308111yescharacteristic
764C22#1062308111yescharacteristic
765C22#1062308211yescharacteristic
766C22#1062308311yescharacteristic
767C22#1062308311yescharacteristic
768C22#1062308311yescharacteristic
769C22#1062308411yescharacteristic
770C22#1062309411yescharacteristic
771C22#1062309611yescharacteristic
772C22#1062309611yescharacteristic
773C22#1062309611yescharacteristic
774C22C2×#6697911yescharacteristic
775C22C2×#6697911yescharacteristic
776C22C2×#6697911yescharacteristic
777C22C2×D4×Dic1111yescharacteristic
778C22C2×D4×Dic1111yescharacteristic
779C22#1062335811yescharacteristic
780C22#1062335811yescharacteristic
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—444no—
787C4—444no—
788C4—882no—
789C4—882no—
790C4#1062256418yes—
791C2—44no—
792C2#1307101411yescharacteristic
793C2C2×#1062256411yescharacteristic
794C2#1307122511yescharacteristic
795C2#1307154511yescharacteristic
796C2#1307154511yescharacteristic
797C2#1307154511yescharacteristic
798C2#1307156511yescharacteristic
799C2#1307210811yescharacteristic
800C2#1307211911yescharacteristic
801C2#1307218211yescharacteristic
802C2#1307219311yescharacteristic
803C2#1307295711yescharacteristic
804C2#1307296811yescharacteristic
805C2#1307301611yescharacteristic
806C2#1307302711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13875
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622549C2semidirect
4. C2×C4×C4⋊Dic11C2semidirect
5. #13066878C2semidirect
8. #13066846C2semidirect
9. #13066846C2semidirect
10. #13066841C2semidirect
24. C4×C11×C22⋊C4C4semidirect
355. C4×C22⋊C4Dic11semidirect
609. C11#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
C2×#106228252
C2×C4×C4⋊Dic112
#130668782
#130668652
#130668532
#130668462
#130668412
C2×C4×C11×C22⋊C42
#1387511