Finite Group Databasebeta

← #14676876

Subgroups — #14676876

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C211yesmaximal, characteristic, complemented
2C2×#10622564C212yesmaximal
3C2×#10622825C211yesmaximal, characteristic
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic11C211yesmaximal, characteristic
6#13066873C212yesmaximal, complemented
7#13066865C212yesmaximal
8#13066845C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066841C212yesmaximal, complemented
11C2×C11×#380C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C11×#380C418yescomplemented
26C2×C11×#95C2212yes—
27#10622825—24no—
28C4×C22⋊Dic11—24no—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622598—24no—
39C4⋊C4×Dic11—24no—
40#10622564—28no—
41C25×C11C2311yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11C2×C414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2×C414yes—
64C2×C11×C4⋊C4C2×C414yes—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4C2×C418yes—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11D414yes—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11—42no—
85C2×C4⋊Dic11D414yes—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11D414yes—
95C11×#95C2×C418yes—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—42no—
105#13994—111nomaximal, Sylow
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×C11—21no—
116C24×C11—21no—
117C24×C11—21no—
118C24×C11C22×C412yes—
119C24×C11C2×D412yes—
120C24×C11#4112yes—
121C24×C11C2411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—28no—
141C22×C4×C11—28no—
142C22×C4×C11—28no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11—44no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C22×C414yes—
149C22×C4×C11C22×C414yes—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
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—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×D412yes—
194C22×Dic11C2×D414yes—
195C22×Dic11C2×D412yes—
196C22×Dic11C2×D412yes—
197C22×Dic11#4112yes—
198C22×Dic11#4112yes—
199C11×C4⋊C4—28no—
200C11×C4⋊C4—28no—
201C11×C22⋊C4—216no—
202C22⋊Dic11—28no—
203C22⋊Dic11—28no—
204C22⋊Dic11—48no—
205C4⋊Dic11—28no—
206C4⋊Dic11—48no—
207C4⋊Dic11—44no—
208C4×Dic11—28no—
209C4×Dic11—48no—
210C4×Dic11—44no—
211C2×#389—111no—
212C2×#388—112no—
213C2×#380—111no—
214C2×#380D1111yescharacteristic
215C2×C4×C4⋊C4—111no—
216C2×C4×C22⋊C4—111no—
217#1442—112no—
218#1440—112no—
219C4⋊#95—111no—
220C4⋊#95—111no—
221#1434—112no—
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—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
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—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11C4×D414yes—
257C23×C11C23×C411yescharacteristic
258C23×C11C22×D411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C2×#4111yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11H(5,𝔽2)11yescharacteristic
269C23×C112−1+411yescharacteristic
270C23×C112−1+411yescharacteristic
271C23×C112−1+411yescharacteristic
272C2×C4×C11—22no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—42no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—42no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—416no—
294C2×C4×C11#11714yes—
295C2×C4×C11C4×D414yes—
296C2×C4×C11C4×D414yes—
297C2×C4×C11#12114yes—
298C2×C4×C11#12314yes—
299C2×C4×C11#12414yes—
300C2×C4×C11#12614yes—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—24no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—24no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—42no—
322C2×Dic11—41no—
323C2×Dic11—42no—
324C2×Dic11—41no—
325C2×Dic11—42no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—42no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11#12114yes—
343C24×C4C2×D1111yescharacteristic
344C22×C4⋊C4—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4—112no—
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C4⋊C4C2×D1111yescharacteristic
349C22×C22⋊C4—111no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4C2×D1112yes—
353C22×C42—111no—
354C22×C42—112no—
355C22×C42—111no—
356#389—224no—
357#388—228no—
358#380—224no—
359#380Dic1118yescomplemented
360C4×C4⋊C4—224no—
361C4×C22⋊C4—224no—
362C2×#95—111no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—111no—
370C2×#95—112no—
371C2×#95C2×D1112yes—
372C22×C11—24no—
373C22×C11—24no—
374C22×C11—24no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11C2×#11711yescharacteristic
388C22×C11C2×C4×D411yescharacteristic
389C22×C11C2×C4×D411yescharacteristic
390C22×C11C2×C4×D411yescharacteristic
391C22×C11C4×#4111yescharacteristic
392C22×C11#51911yescharacteristic
393C22×C11#52011yescharacteristic
394C22×C11C2×#12111yescharacteristic
395C22×C11C2×#12111yescharacteristic
396C22×C11C2×#12311yescharacteristic
397C22×C11#52511yescharacteristic
398C22×C11C2×#12411yescharacteristic
399C22×C11C2×#12611yescharacteristic
400C22×C11#52911yescharacteristic
401C22×C11#53211yescharacteristic
402C22×C11#53611yescharacteristic
403C22×C11#53711yescharacteristic
404C22×C11#54111yescharacteristic
405C22×C11#54211yescharacteristic
406C22×C11D4211yescharacteristic
407C22×C11#54711yescharacteristic
408C22×C11#54711yescharacteristic
409C22×C11#54711yescharacteristic
410C22×C11#54711yescharacteristic
411C22×C11#54811yescharacteristic
412C22×C11#54811yescharacteristic
413C22×C11#55211yescharacteristic
414C22×C11#55211yescharacteristic
415C22×C11#55211yescharacteristic
416C22×C11#55211yescharacteristic
417C22×C11#55211yescharacteristic
418C22×C11#55311yescharacteristic
419C22×C11#55511yescharacteristic
420C22×C11#55511yescharacteristic
421C22×C11#55611yescharacteristic
422C4×C11—44no—
423C4×C11—42no—
424C4×C11—44no—
425C4×C11#38818yescomplemented
426Dic11—24no—
427Dic11—42no—
428Dic11—42no—
429Dic11—44no—
430Dic11—42no—
431Dic11—82no—
432C25C22×D1111yescharacteristic
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—112no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—112no—
445C23×C4C2×Dic1114yes—
446C23×C4C22×D1112yes—
447C23×C4C22×D1112yes—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4—442no—
463C2×C4⋊C4C2×Dic1114yes—
464C2×C4⋊C4C2×Dic1114yes—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—114no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—222no—
470C2×C22⋊C4—222no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—222no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—442no—
476C2×C22⋊C4C2×Dic1118yes—
477C2×C42—114no—
478C2×C42—222no—
479C2×C42—222no—
480C2×C42—224no—
481C2×C42—224no—
482C2×C42—224no—
483C2×C42—222no—
484C2×C42—222no—
485C2×C42—222no—
486#95—224no—
487#95—222no—
488#95—222no—
489#95—224no—
490#95—224no—
491#95—224no—
492#95—224no—
493#95—224no—
494#95—442no—
495#95C2×Dic1118yes—
496C2×C11—44no—
497C2×C11C2×#38811yescharacteristic
498C2×C11C4×#12111yescharacteristic
499C2×C11#232311yescharacteristic
500C2×C11#234411yescharacteristic
501C2×C11#234611yescharacteristic
502C2×C11#236111yescharacteristic
503C2×C11#236211yescharacteristic
504C2×C11#248511yescharacteristic
505C2×C11#248611yescharacteristic
506C2×C11#248911yescharacteristic
507C2×C11#249111yescharacteristic
508C2×C11#249511yescharacteristic
509C2×C11#249611yescharacteristic
510C2×C11#253611yescharacteristic
511C2×C11#253711yescharacteristic
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24D4×D1112yes—
525C24#434112yes—
526C24C22×Dic1112yes—
527C24C23×D1111yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—114no—
559C22×C4—112no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—221no—
581C22×C4—222no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—222no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4#433912yes—
596C22×C4#433912yes—
597C22×C4D4×D1112yes—
598C22×C4D4×D1112yes—
599C22×C4#434112yes—
600C22×C4#434112yes—
601C22×C4C22×Dic1112yes—
602C22×C4C22×Dic1114yes—
603C22×C4C22×Dic1114yes—
604C22×C4C22×Dic1112yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—228no—
608C4⋊C4—448no—
609C4⋊C4—444no—
610C22⋊C4—216no—
611C22⋊C4—228no—
612C22⋊C4—228no—
613C22⋊C4—448no—
614C42—228no—
615C42—448no—
616C42—444no—
617C11#1399411yescharacteristic, complemented, Sylow
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23D4×Dic1114yes—
653C23C2×#433911yescharacteristic
654C23C2×#433911yescharacteristic
655C23C2×D4×D1111yescharacteristic
656C23C2×D4×D1111yescharacteristic
657C23C2×D4×D1111yescharacteristic
658C23C2×#434111yescharacteristic
659C23C2×#434111yescharacteristic
660C23C2×#434111yescharacteristic
661C23#6704011yescharacteristic
662C23#6704011yescharacteristic
663C23#41×D1111yescharacteristic
664C23#41×D1111yescharacteristic
665C23#6704211yescharacteristic
666C23#6704311yescharacteristic
667C23C23×Dic1111yescharacteristic
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—416no—
690C2×C4—114no—
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—222no—
703C2×C4—222no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—224no—
708C2×C4—222no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—442no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—442no—
717C2×C4—441no—
718C2×C4—442no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—442no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4#6693214yes—
733C2×C4#6693614yes—
734C2×C4#6693714yes—
735C2×C4#6693814yes—
736C2×C4#6697914yes—
737C2×C4D4×Dic1114yes—
738C2×C4D4×Dic1114yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×#6693211yescharacteristic
755C22C2×#6693611yescharacteristic
756C22C2×#6693711yescharacteristic
757C22C2×#6693811yescharacteristic
758C22#1062303811yescharacteristic
759C22#1062303811yescharacteristic
760C22#1062304411yescharacteristic
761C22#1062304411yescharacteristic
762C22#1062306011yescharacteristic
763C22#1062306011yescharacteristic
764C22#1062306311yescharacteristic
765C22#1062306311yescharacteristic
766C22#1062312711yescharacteristic
767C22#1062312911yescharacteristic
768C22#1062313111yescharacteristic
769C22D11×#12111yescharacteristic
770C22#1062313711yescharacteristic
771C22#1062314011yescharacteristic
772C22#1062314211yescharacteristic
773C22#1062314911yescharacteristic
774C22#1062315611yescharacteristic
775C22#1062315911yescharacteristic
776C22#1062316011yescharacteristic
777C22#1062316211yescharacteristic
778C22#1062316411yescharacteristic
779C22#1062317011yescharacteristic
780C22#1062317211yescharacteristic
781C22#1062317411yescharacteristic
782C22C2×#6697911yescharacteristic
783C22C2×D4×Dic1111yescharacteristic
784C22C2×D4×Dic1111yescharacteristic
785C22C2×D4×Dic1111yescharacteristic
786C22#1062334311yescharacteristic
787C22#41×Dic1111yescharacteristic
788C22#1062335811yescharacteristic
789C4—44no—
790C4—44no—
791C4—42no—
792C4—224no—
793C4—442no—
794C4—442no—
795C4—444no—
796C4—442no—
797C4—882no—
798C4#1062256418yescomplemented
799C2—44no—
800C2C2×#1062256411yescharacteristic
801C2#121×Dic1111yescharacteristic
802C2#1307130011yescharacteristic
803C2#1307148511yescharacteristic
804C2#1307150111yescharacteristic
805C2#1307163611yescharacteristic
806C2#1307164711yescharacteristic
807C2#1307290911yescharacteristic
808C2#1307292011yescharacteristic
809C2#1307295311yescharacteristic
810C2#1307297511yescharacteristic
811C2#1307302911yescharacteristic
812C2#1307304011yescharacteristic
813C2#1307352711yescharacteristic
814C2#1307353111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#13994
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#10622598C2semidirect
4. C2×C4⋊C4×Dic11C2semidirect
6. #13066873C2semidirect
8. #13066845C2semidirect
9. #13066845C2semidirect
10. #13066841C2semidirect
25. C11×#380C4semidirect
359. #380Dic11semidirect
425. C4×C11#388semidirect
617. C11#13994semidirect
798. C4#10622564semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
C2×#106225642
C2×#106228252
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668732
#130668652
#130668452
#130668412
C2×C11×#3802
#1399411