Finite Group Databasebeta

← #14676865

Subgroups — #14676865

Order 2816.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C211yesmaximal, characteristic, complemented
2C2×#10622825C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic
5#13066878C212yesmaximal, complemented
6#13066861C212yesmaximal
7#13066853C212yesmaximal
8#13066850C212yesmaximal, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066845C211yesmaximal, characteristic, 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×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C11×#380C418yescomplemented
26C2×C11×#95C2212yes—
27#10622825—24no—
28C4×C22⋊Dic11—24no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622598—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×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
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⋊C4C2×C414yes—
63C2×C11×C4⋊C4C2×C414yes—
64C2×C11×C22⋊C4—42no—
65C2×C11×C22⋊C4—42no—
66C2×C11×C22⋊C4C2×C418yes—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11Q814yes—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11—42no—
84C2×C4⋊Dic11D414yes—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—24no—
91C2×C4×Dic11—42no—
92C2×C4×Dic11—42no—
93C2×C4×Dic11D414yes—
94C11×#95C2×C418yes—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104#13993—111nomaximal, Sylow
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×C11—21no—
116C24×C11—21no—
117C24×C11C22×C412yes—
118C24×C11C2×Q812yes—
119C24×C11#4112yes—
120C24×C11C2411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—28no—
140C22×C4×C11—28no—
141C22×C4×C11—28no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C414yes—
148C22×C4×C11C22×C414yes—
149C22×C4×C11C22×C412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11C2×D412yes—
192C22×Dic11C2×D414yes—
193C22×Dic11C2×D412yes—
194C22×Dic11C2×Q812yes—
195C22×Dic11C2×Q812yes—
196C22×Dic11#4112yes—
197C22×Dic11#4112yes—
198C11×C4⋊C4—28no—
199C11×C4⋊C4—28no—
200C11×C22⋊C4—48no—
201C22⋊Dic11—28no—
202C22⋊Dic11—28no—
203C22⋊Dic11—48no—
204C4⋊Dic11—28no—
205C4⋊Dic11—48no—
206C4⋊Dic11—44no—
207C4×Dic11—28no—
208C4×Dic11—48no—
209C4×Dic11—44no—
210C2×#389—111no—
211C2×#380—111no—
212C2×#380D1111yescharacteristic
213C2×C4×C4⋊C4—111no—
214C2×C4×C22⋊C4—111no—
215#1443—112no—
216#1439—112no—
217#1437—112no—
218#1436—112no—
219C4⋊#95—111no—
220C4⋊#95—111no—
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—22no—
237C23×C11—22no—
238C23×C11—22no—
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—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11C4×Q814yes—
256C23×C11C23×C411yescharacteristic
257C23×C11C22×D411yescharacteristic
258C23×C11C22×D411yescharacteristic
259C23×C11C22×Q811yescharacteristic
260C23×C11C2×#4111yescharacteristic
261C23×C11C2×#4111yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11H(5,𝔽2)11yescharacteristic
268C23×C11H(5,𝔽2)11yescharacteristic
269C23×C11H(5,𝔽2)11yescharacteristic
270C23×C112−1+411yescharacteristic
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
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—42no—
291C2×C4×C11—42no—
292C2×C4×C11—416no—
293C2×C4×C11#11714yes—
294C2×C4×C11C4×D414yes—
295C2×C4×C11C4×D414yes—
296C2×C4×C11#12114yes—
297C2×C4×C11#12314yes—
298C2×C4×C11#12414yes—
299C2×C4×C11#12614yes—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11C22⋊Q814yes—
342C24×C4C2×D1111yescharacteristic
343C22×C4⋊C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—112no—
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C22⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C22⋊C4—112no—
351C22×C22⋊C4C2×D1112yes—
352C22×C42—111no—
353C22×C42—111no—
354C22×C42—112no—
355#389—224no—
356#380—224no—
357#380Dic1118yescomplemented
358C4×C4⋊C4—224no—
359C4×C22⋊C4—224no—
360C2×#95—112no—
361C2×#95—111no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—111no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95C2×D1112yes—
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—24no—
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×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11C2×#11711yescharacteristic
386C22×C11C2×C4×D411yescharacteristic
387C22×C11C2×C4×D411yescharacteristic
388C22×C11C2×C4×Q811yescharacteristic
389C22×C11C4×#4111yescharacteristic
390C22×C11#51811yescharacteristic
391C22×C11#52011yescharacteristic
392C22×C11C2×#12111yescharacteristic
393C22×C11C2×C22⋊Q811yescharacteristic
394C22×C11C2×#12311yescharacteristic
395C22×C11#52511yescharacteristic
396C22×C11C2×#12411yescharacteristic
397C22×C11C2×#12611yescharacteristic
398C22×C11#52911yescharacteristic
399C22×C11#53311yescharacteristic
400C22×C11#53511yescharacteristic
401C22×C11#53711yescharacteristic
402C22×C11#54011yescharacteristic
403C22×C11#54211yescharacteristic
404C22×C11#54611yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11D4×Q811yescharacteristic
407C22×C11#55011yescharacteristic
408C22×C11#55211yescharacteristic
409C22×C11#55311yescharacteristic
410C22×C11#55311yescharacteristic
411C22×C11#55311yescharacteristic
412C22×C11#55311yescharacteristic
413C22×C11#55311yescharacteristic
414C22×C11#55411yescharacteristic
415C22×C11#55411yescharacteristic
416C22×C11#55411yescharacteristic
417C22×C11#55511yescharacteristic
418C22×C11#55611yescharacteristic
419C22×C11#55611yescharacteristic
420C4×C11—44no—
421C4×C11—44no—
422C4×C11—42no—
423C4×C11#38818yes—
424Dic11—24no—
425Dic11—42no—
426Dic11—44no—
427Dic11—42no—
428Dic11—42no—
429Dic11—82no—
430C25C22×D1111yescharacteristic
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—112no—
443C23×C4C2×Dic1114yes—
444C23×C4C22×D1112yes—
445C23×C4C22×D1112yes—
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—442no—
461C2×C4⋊C4C2×Dic1114yes—
462C2×C4⋊C4C2×Dic1114yes—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—222no—
470C2×C22⋊C4—222no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4C2×Dic1118yes—
475C2×C42—114no—
476C2×C42—222no—
477C2×C42—222no—
478C2×C42—224no—
479C2×C42—222no—
480C2×C42—222no—
481C2×C42—222no—
482C2×C42—442no—
483C2×C42—442no—
484#95—224no—
485#95—222no—
486#95—222no—
487#95—224no—
488#95—224no—
489#95—224no—
490#95—442no—
491#95—442no—
492#95—442no—
493#95C2×Dic1118yes—
494C2×C11—44no—
495C2×C11C2×#38811yescharacteristic
496C2×C11C4×C22⋊Q811yescharacteristic
497C2×C11#232411yescharacteristic
498C2×C11#234511yescharacteristic
499C2×C11#234711yescharacteristic
500C2×C11#236011yescharacteristic
501C2×C11#236311yescharacteristic
502C2×C11#248511yescharacteristic
503C2×C11#248711yescharacteristic
504C2×C11#249011yescharacteristic
505C2×C11#249211yescharacteristic
506C2×C11#249411yescharacteristic
507C2×C11#249711yescharacteristic
508C2×C11#253511yescharacteristic
509C2×C11#253811yescharacteristic
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24Q8×D1112yes—
523C24#434312yes—
524C24C22×Dic1112yes—
525C24C23×D1111yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—112no—
552C22×C4—112no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—114no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—222no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—222no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—222no—
582C22×C4—221no—
583C22×C4—222no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4#433912yes—
594C22×C4#433912yes—
595C22×C4D4×D1112yes—
596C22×C4D4×D1112yes—
597C22×C4#434112yes—
598C22×C4#434112yes—
599C22×C4C22×Dic1112yes—
600C22×C4C22×Dic1114yes—
601C22×C4C22×Dic1114yes—
602C22×C4C22×Dic1112yes—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—228no—
606C4⋊C4—448no—
607C4⋊C4—444no—
608C22⋊C4—48no—
609C22⋊C4—228no—
610C22⋊C4—228no—
611C22⋊C4—448no—
612C42—228no—
613C42—448no—
614C42—444no—
615C11#1399311yescharacteristic, complemented, Sylow
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—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
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—
650C23Q8×Dic1114yes—
651C23C2×#433911yescharacteristic
652C23C2×#433911yescharacteristic
653C23C2×D4×D1111yescharacteristic
654C23C2×D4×D1111yescharacteristic
655C23C2×#434111yescharacteristic
656C23C2×#434111yescharacteristic
657C23#6703711yescharacteristic
658C23#6703711yescharacteristic
659C23C2×Q8×D1111yescharacteristic
660C23C2×#434311yescharacteristic
661C23#41×D1111yescharacteristic
662C23#41×D1111yescharacteristic
663C23#6704211yescharacteristic
664C23#6704311yescharacteristic
665C23C23×Dic1111yescharacteristic
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
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—416no—
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—224no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—222no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—442no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—442no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4#6693214yes—
731C2×C4#6693614yes—
732C2×C4#6693714yes—
733C2×C4#6693814yes—
734C2×C4#6697914yes—
735C2×C4D4×Dic1114yes—
736C2×C4D4×Dic1114yes—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×#6693211yescharacteristic
753C22C2×#6693611yescharacteristic
754C22C2×#6693711yescharacteristic
755C22C2×#6693811yescharacteristic
756C22#1062304211yescharacteristic
757C22#1062304211yescharacteristic
758C22#1062304511yescharacteristic
759C22#1062304511yescharacteristic
760C22#1062306111yescharacteristic
761C22#1062306111yescharacteristic
762C22#1062306411yescharacteristic
763C22#1062306411yescharacteristic
764C22#1062313011yescharacteristic
765C22#1062313411yescharacteristic
766C22#1062313811yescharacteristic
767C22#1062313911yescharacteristic
768C22#1062314311yescharacteristic
769C22#1062314511yescharacteristic
770C22#1062314711yescharacteristic
771C22#1062315011yescharacteristic
772C22#1062315311yescharacteristic
773C22#1062315511yescharacteristic
774C22D11×C22⋊Q811yescharacteristic
775C22#1062315811yescharacteristic
776C22#1062316111yescharacteristic
777C22#1062316311yescharacteristic
778C22#1062316611yescharacteristic
779C22#1062317311yescharacteristic
780C22C2×#6697911yescharacteristic
781C22C2×D4×Dic1111yescharacteristic
782C22C2×D4×Dic1111yescharacteristic
783C22#1062332911yescharacteristic
784C22C2×Q8×Dic1111yescharacteristic
785C22#41×Dic1111yescharacteristic
786C22#1062335811yescharacteristic
787C4—44no—
788C4—42no—
789C4—44no—
790C4—224no—
791C4—442no—
792C4—444no—
793C4—442no—
794C4—442no—
795C4—882no—
796C4#1062256418yes—
797C2—44no—
798C2C2×#1062256411yescharacteristic
799C2C22⋊Q8×Dic1111yescharacteristic
800C2#1307131111yescharacteristic
801C2#1307149311yescharacteristic
802C2#1307150911yescharacteristic
803C2#1307162511yescharacteristic
804C2#1307165811yescharacteristic
805C2#1307291511yescharacteristic
806C2#1307292911yescharacteristic
807C2#1307296411yescharacteristic
808C2#1307298611yescharacteristic
809C2#1307301811yescharacteristic
810C2#1307305111yescharacteristic
811C2#1307351911yescharacteristic
812C2#1307354011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#13993
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
3. C2×C4⋊C4×Dic11C2semidirect
5. #13066878C2semidirect
8. #13066850C2semidirect
9. #13066845C2semidirect
10. #13066845C2semidirect
25. C11×#380C4semidirect
357. #380Dic11semidirect
615. C11#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
C2×#106228252
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668782
#130668612
#130668532
#130668502
#130668452
C2×C11×#3802
#1399311