Finite Group Databasebeta

← #14690475

Subgroups — #14690475

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622561C212yesmaximal, complemented
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622834C211yesmaximal, characteristic
4C2×#10622598C211yesmaximal, characteristic, complemented
5C2×#10622541C211yesmaximal, characteristic, complemented
6C2×#10622586C211yesmaximal, characteristic, complemented
7#13066861C212yesmaximal, complemented
8#13066859C212yesmaximal, complemented
9#13066859C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#390C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C4⋊Dic11C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C11×#390—24no—
29#10622834—24no—
30#10622834—24no—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622598—24no—
39#10622586—24no—
40#10622561—28no—
41#10622541—24no—
42C25×C11C2312yes—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11Q814yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4D414yes—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4—42no—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11—42no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11—42no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11—42no—
91C2×C4⋊Dic11D414yes—
92C2×C4⋊Dic11D414yes—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—42no—
98C2×Dic11⋊C4—42no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C11⋊#95—24no—
106C11⋊#95—22no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95D414yescomplemented
112#15141—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11C2×Q814yes—
128C24×C11C2411yescharacteristic
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
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—22no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×Q812yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—21no—
193C22×Dic11—22no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11C2×D414yes—
201C22×Dic11C2×D414yes—
202C22×Dic11C2×D412yes—
203C22×Dic11C2×D412yes—
204C22×Dic11#4112yes—
205C22×Dic11#4112yes—
206C11×C4⋊C4—28no—
207C11×C22⋊C4—48no—
208C11×C22⋊C4—48no—
209C42×C11—44no—
210C22⋊Dic11—48no—
211C22⋊Dic11—48no—
212C22⋊Dic11—48no—
213C22⋊Dic11—48no—
214C4⋊Dic11—28no—
215C4⋊Dic11—28no—
216C4⋊Dic11—48no—
217Dic11⋊C4—48no—
218Dic11⋊C4—48no—
219C4×Dic11—44no—
220C4×Dic11—44no—
221C2×#396—112no—
222C2×#390—111no—
223C2×#390—111no—
224C2×#390D1111yescharacteristic
225C2×#389—111no—
226C2×#389—111no—
227C2×#389—111no—
228#1439—112no—
229#1439—112no—
230#1439—112no—
231C4×#95—111no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11C22×D411yescharacteristic
268C23×C11C22×D411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C23×C11C22×D411yescharacteristic
271C23×C11C22×Q811yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4111yescharacteristic
274C23×C11C2×#4111yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11H(5,𝔽2)11yescharacteristic
279C23×C11H(5,𝔽2)11yescharacteristic
280C23×C11H(5,𝔽2)11yescharacteristic
281C23×C112−1+411yescharacteristic
282D4×C11—416no—
283C2×C4×C11—24no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—24no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—24no—
291C2×C4×C11—22no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—42no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—42no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11#12114yes—
305C2×C4×C11#12114yes—
306C2×C4×C11#12114yes—
307C2×C4×C11C22⋊Q814yes—
308C2×C4×C11C22⋊Q814yes—
309C2×C4×C11C22⋊Q814yes—
310C2×C4×C11#12614yes—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—24no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—41no—
353C23×D4C2×D1111yescharacteristic
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—112no—
357C22×C4⋊C4—112no—
358C22×C4⋊C4—112no—
359C22×C4⋊C4C2×D1111yescharacteristic
360C22×C22⋊C4—112no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—112no—
364C22×C22⋊C4C2×D1112yes—
365C22×C22⋊C4C2×D1112yes—
366C22×C42—111no—
367C22×C42—111no—
368C22×C42C2×D1111yescharacteristic
369#396—228no—
370#390—24no—
371#390—224no—
372#390—224no—
373#389—224no—
374#389—224no—
375#389—224no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95—111no—
379C2×#95—111no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95—112no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—82no—
391C22×C11—82no—
392C22×C11—82no—
393C22×C11—82no—
394C22×C11—82no—
395C22×C11—82no—
396C22×C11—82no—
397C22×C11—82no—
398C22×C11C2×#12111yescharacteristic
399C22×C11C2×#12111yescharacteristic
400C22×C11C2×#12111yescharacteristic
401C22×C11C2×C22⋊Q811yescharacteristic
402C22×C11C2×C22⋊Q811yescharacteristic
403C22×C11C2×C22⋊Q811yescharacteristic
404C22×C11C2×#12611yescharacteristic
405C22×C11#52911yescharacteristic
406C22×C11#52911yescharacteristic
407C22×C11#52911yescharacteristic
408C22×C11#53211yescharacteristic
409C22×C11#53211yescharacteristic
410C22×C11#53211yescharacteristic
411C22×C11#54011yescharacteristic
412C22×C11#54011yescharacteristic
413C22×C11#54011yescharacteristic
414C22×C11#54211yescharacteristic
415C22×C11#54211yescharacteristic
416C22×C11#54211yescharacteristic
417C22×C11D4211yescharacteristic
418C22×C11D4211yescharacteristic
419C22×C11D4211yescharacteristic
420C22×C11#54611yescharacteristic
421C22×C11#54611yescharacteristic
422C22×C11#54611yescharacteristic
423C22×C11#54811yescharacteristic
424C22×C11#54811yescharacteristic
425C22×C11#54811yescharacteristic
426C22×C11D4×Q811yescharacteristic
427C22×C11#55011yescharacteristic
428C22×C11#55011yescharacteristic
429C22×C11#55011yescharacteristic
430C22×C11#55411yescharacteristic
431C22×C11#55411yescharacteristic
432C22×C11#55411yescharacteristic
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—44no—
436C4×C11#39618yescomplemented
437Dic11—42no—
438Dic11—42no—
439Dic11—44no—
440Dic11—44no—
441Dic11—42no—
442Dic11—42no—
443C25C22×D1112yes—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4Dic2214yes—
451C23×C4—112no—
452C23×C4—112no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1112yes—
460C23×C4C22×D1111yescharacteristic
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—222no—
466C2×C4⋊C4—222no—
467C2×C4⋊C4—222no—
468C2×C4⋊C4—222no—
469C2×C4⋊C4—224no—
470C2×C4⋊C4—224no—
471C2×C4⋊C4—224no—
472C2×C4⋊C4—224no—
473C2×C4⋊C4—224no—
474C2×C4⋊C4—224no—
475C2×C4⋊C4—442no—
476C2×C4⋊C4—442no—
477C2×C4⋊C4—442no—
478C2×C4⋊C4C22⋊D1114yes—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—442no—
494C2×C22⋊C4—442no—
495C2×C22⋊C4—442no—
496C2×C22⋊C4—442no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—222no—
501C2×C42—222no—
502C2×C42—222no—
503C2×C42—222no—
504C2×C42—222no—
505C2×C42—222no—
506#95—114no—
507#95—222no—
508#95—222no—
509#95—224no—
510#95—224no—
511#95—222no—
512#95—224no—
513C2×C11—84no—
514C2×C11C2×#39611yescharacteristic
515C2×C11#242611yescharacteristic
516C2×C11#242611yescharacteristic
517C2×C11#242611yescharacteristic
518C2×C11#242811yescharacteristic
519C2×C11#242811yescharacteristic
520C2×C11#242811yescharacteristic
521C2×C11#245211yescharacteristic
522C2×C11#245211yescharacteristic
523C2×C11#245211yescharacteristic
524C2×C11#245411yescharacteristic
525C2×C11#245411yescharacteristic
526C2×C11#245411yescharacteristic
527C2×C11#264411yescharacteristic
528C2×C11#286011yescharacteristic
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24C2×Dic2214yes—
544C24C23×D1111yescharacteristic
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—44no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—112no—
571C22×C4—112no—
572C22×C4—114no—
573C22×C4—114no—
574C22×C4—112no—
575C22×C4—112no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—222no—
579C22×C4—221no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—222no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—222no—
611C22×C4—221no—
612C22×C4C2×Dic2212yes—
613C22×C4#433912yes—
614C22×C4D4×D1112yes—
615C22×C4D4×D1112yes—
616C22×C4D4×D1112yes—
617C22×C4#434112yes—
618C22×C4#434112yes—
619C22×C4#434112yes—
620C22×C4C2×C22⋊D1114yes—
621C22×C4C2×C22⋊D1112yes—
622C4⋊C4—28no—
623C4⋊C4—228no—
624C4⋊C4—228no—
625C4⋊C4—448no—
626C4⋊C4—448no—
627C4⋊C4—448no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—448no—
631C22⋊C4—448no—
632C22⋊C4—448no—
633C22⋊C4—448no—
634C42—44no—
635C42—444no—
636C42—444no—
637C11#1514111yescharacteristic, complemented, Sylow
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23C22×Dic2211yescharacteristic
674C23C2×#433911yescharacteristic
675C23C2×D4×D1111yescharacteristic
676C23C2×D4×D1111yescharacteristic
677C23C2×D4×D1111yescharacteristic
678C23C2×#434111yescharacteristic
679C23C2×#434111yescharacteristic
680C23C2×#434111yescharacteristic
681C23#6703711yescharacteristic
682C23#6703711yescharacteristic
683C23#41×D1111yescharacteristic
684C23#41×D1111yescharacteristic
685C23#6704211yescharacteristic
686C23#6704311yescharacteristic
687C23C22×C22⋊D1111yescharacteristic
688D4—416no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—224no—
715C2×C4—224no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—224no—
722C2×C4—222no—
723C2×C4—224no—
724C2×C4—222no—
725C2×C4—224no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—442no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—442no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—442no—
741C2×C4—441no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—441no—
745C2×C4—442no—
746C2×C4—441no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4#6693114yes—
753C2×C4#6693114yes—
754C2×C4#6693214yes—
755C2×C4#6693714yes—
756C2×C4#6697714yes—
757C2×C4#6699114yes—
758C2×C4#6699214yes—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22C2×#6693111yescharacteristic
775C22C2×#6693111yescharacteristic
776C22C2×#6693211yescharacteristic
777C22C2×#6693711yescharacteristic
778C22D4×Dic2211yescharacteristic
779C22#1062307011yescharacteristic
780C22#1062307011yescharacteristic
781C22#1062307411yescharacteristic
782C22#1062307911yescharacteristic
783C22#1062308811yescharacteristic
784C22#1062309211yescharacteristic
785C22#1062309311yescharacteristic
786C22#1062312711yescharacteristic
787C22#1062312911yescharacteristic
788C22#1062313011yescharacteristic
789C22#1062313111yescharacteristic
790C22#1062313411yescharacteristic
791C22#1062314011yescharacteristic
792C22#1062314311yescharacteristic
793C22#1062315011yescharacteristic
794C22#1062320711yescharacteristic
795C22#1062320811yescharacteristic
796C22#1062321111yescharacteristic
797C22#1062321311yescharacteristic
798C22#1062324711yescharacteristic
799C22#1062324811yescharacteristic
800C22#1062324911yescharacteristic
801C22#1062325011yescharacteristic
802C22C2×#6697711yescharacteristic
803C22C2×#6699111yescharacteristic
804C22D4×C22⋊D1111yescharacteristic
805C22C2×#6699211yescharacteristic
806C22#1062333711yescharacteristic
807C22#1062336211yescharacteristic
808C22#1062336511yescharacteristic
809C4—42no—
810C4—42no—
811C4—44no—
812C4—442no—
813C4—442no—
814C4—444no—
815C4—444no—
816C4—442no—
817C4—442no—
818C4#1062256118yescomplemented
819C2—84no—
820C2C2×#1062256111yescharacteristic
821C2#1307217811yescharacteristic
822C2#1307218311yescharacteristic
823C2#1307218511yescharacteristic
824C2#1307220011yescharacteristic
825C2#1307220511yescharacteristic
826C2#1307220711yescharacteristic
827C2#1307246011yescharacteristic
828C2#1307246811yescharacteristic
829C2#1307246911yescharacteristic
830C2#1307248211yescharacteristic
831C2#1307249011yescharacteristic
832C2#1307249111yescharacteristic
833C2#1307457711yescharacteristic
834C2#1307698011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#390C2
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#15141
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#10622561C2semidirect
4. C2×#10622598C2semidirect
5. C2×#10622541C2semidirect
6. C2×#10622586C2semidirect
7. #13066861C2semidirect
8. #13066859C2semidirect
9. #13066859C2semidirect
10. C4×C11⋊#95C2semidirect
111. C11⋊#95D4semidirect
436. C4×C11#396semidirect
637. C11#15141semidirect
818. C4#10622561semidirect

Maximal subgroups

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

subgroupindex
C2×#106225612
C2×#106228342
C2×#106225982
C2×#106225412
C2×#106225862
#130668612
#130668592
C4×C11⋊#952
C2×C11×#3902
#1514111