Finite Group Databasebeta

← #27320771

Subgroups — #27320771

Order 13568.

1762 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810550C212yesmaximal, complemented
2C2×#16810525C211yesmaximal, characteristic
3C2×#16810524C211yesmaximal, characteristic
4C2×#16810524C211yesmaximal, characteristic
5C2×#16810522C211yesmaximal, characteristic, complemented
6#20272963C212yesmaximal, complemented
7#20272963C212yesmaximal, complemented
8#20272961C212yesmaximal, complemented
9#20272944C211yesmaximal, characteristic, complemented
10C4×#13133124C211yesmaximal, characteristic, complemented
11C53×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D212C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2212yes—
15C22×#11719921C2212yes—
16C22×#11719921C2212yes—
17C22×#11719921C2212yes—
18C22×#11719921C2212yes—
19C22×#11719921C2212yes—
20C22×#11719921C2212yes—
21C22×C4×Dic53C2211yescharacteristic
22C22×C4×Dic53C2211yescharacteristic
23#16810550—28no—
24#16810525—24no—
25#16810524—24no—
26#16810524—24no—
27#16810522—24no—
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2211yescharacteristic
35C22×C4⋊C4×C53C2211yescharacteristic
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C42×C53C2211yescharacteristic
38C2×#95×C53C2212yes—
39C2×#95×C53C2212yes—
40C24×D53C2312yes—
41C22×D212—22no—
42C22×D212—22no—
43C22×D212—22no—
44C22×D212—22no—
45C22×D212—22no—
46C22×D212—22no—
47C22×D212D414yes—
48C23×Dic53C2312yes—
49C23×Dic53C2311yescharacteristic
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2311yescharacteristic
53C2×C4⋊Dic53—24no—
54C2×C4⋊Dic53—22no—
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—24no—
58C2×C4⋊Dic53—42no—
59C2×#11719921—24no—
60C2×#11719921—24no—
61C2×#11719921—24no—
62C2×#11719921—24no—
63C2×#11719921—24no—
64C2×#11719921—24no—
65C2×#11719921—24no—
66C2×#11719921—24no—
67C2×#11719921—24no—
68C2×#11719921—24no—
69C2×#11719921—24no—
70C2×#11719921—24no—
71C2×#11719921—42no—
72C2×#11719921—42no—
73C2×#11719921—42no—
74C2×#11719921—42no—
75C2×#11719921—42no—
76C2×#11719921—42no—
77C2×C4×Dic53—22no—
78C2×C4×Dic53—22no—
79C2×C4×Dic53—22no—
80C2×C4×Dic53—22no—
81C2×C4×Dic53—22no—
82C2×C4×Dic53—22no—
83#13133124—24no—
84#13133124—22no—
85#13133124—24no—
86#13133124—22no—
87#13133124—22no—
88#13133124—42no—
89#13133124D414yescomplemented
90C23×C4×C53C2312yes—
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2312yes—
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2311yescharacteristic
95C2×C4⋊C4×C53—22no—
96C2×C4⋊C4×C53—22no—
97C2×C4⋊C4×C53—22no—
98C2×C4⋊C4×C53—22no—
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53D414yes—
101C2×C42×C53—22no—
102C2×C42×C53—22no—
103C2×C42×C53—22no—
104#95×C53—24no—
105#95×C53—42no—
106C24×C53C2411yescharacteristic
107C23×D53—22no—
108C23×D53—22no—
109C23×D53—22no—
110C23×D53—22no—
111C23×D53—22no—
112C23×D53—22no—
113C23×D53—22no—
114C23×D53—22no—
115C23×D53—22no—
116C23×D53—22no—
117C23×D53—22no—
118C23×D53—22no—
119C23×D53—22no—
120C23×D53—22no—
121C23×D53C2×D414yes—
122C22×C4×C53—22no—
123C22×C4×C53—21no—
124C22×C4×C53—21no—
125C22×C4×C53—21no—
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—22no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—22no—
139C22×C4×C53—21no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53C2×D414yes—
148C22×C4×C53C2×D412yes—
149C22×C4×C53C2×D412yes—
150C22×C4×C53C2×D412yes—
151C22×C4×C53#4112yes—
152C22×C4×C53#4112yes—
153C22×C4×C53#4112yes—
154C22×C4×C53#4112yes—
155C22×C4×C53#4112yes—
156C22×C4×C53#4112yes—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53C2×D412yes—
189C22×Dic53C2×D412yes—
190C22×Dic53#4112yes—
191C22×Dic53#4112yes—
192C2×D212—28no—
193C2×D212—28no—
194C2×D212—28no—
195C2×D212—44no—
196C2×D212—44no—
197C2×D212—44no—
198C2×D212—44no—
199C4⋊C4×C53—28no—
200C4⋊C4×C53—44no—
201C42×C53—44no—
202#11719921—48no—
203#11719921—48no—
204#11719921—48no—
205#11719921—48no—
206#11719921—48no—
207#11719921—48no—
208C4⋊Dic53—48no—
209C4⋊Dic53—44no—
210C4×Dic53—44no—
211C4×Dic53—44no—
212C23×C53C22×D411yescharacteristic
213C23×C53C22×D411yescharacteristic
214C23×C53C22×D411yescharacteristic
215C23×C53C2×#4111yescharacteristic
216C23×C53C2×#4111yescharacteristic
217C23×C53C2×#4111yescharacteristic
218C23×C53C2×#4111yescharacteristic
219C23×C53C2×#4111yescharacteristic
220C23×C53C2×#4111yescharacteristic
221C23×C53C2×#4111yescharacteristic
222C23×C53C2×#4111yescharacteristic
223C23×C53H(5,𝔽2)11yescharacteristic
224C23×C53H(5,𝔽2)11yescharacteristic
225C23×C53H(5,𝔽2)11yescharacteristic
226C23×C532−1+411yescharacteristic
227C22×D53—24no—
228C22×D53—24no—
229C22×D53—24no—
230C22×D53—24no—
231C22×D53—24no—
232C22×D53—24no—
233C22×D53—24no—
234C22×D53—42no—
235C22×D53—42no—
236C22×D53—42no—
237C22×D53—42no—
238C22×D53—42no—
239C22×D53—42no—
240C22×D53—42no—
241C22×D53—42no—
242C22×D53—42no—
243C22×D53—42no—
244C22×D53—42no—
245C22×D53—42no—
246C22×D53—42no—
247C22×D53—42no—
248C22×D53—42no—
249C22×D53—42no—
250C22×D53—42no—
251C22×D53—42no—
252C22×D53—42no—
253C22×D53—42no—
254C22×D53—42no—
255C22×D53—42no—
256C22×D53—42no—
257C22×D53—42no—
258C22×D53—42no—
259C22×D53—42no—
260C22×D53—42no—
261C22×D53—42no—
262C2×C4×C53—24no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—24no—
266C2×C4×C53—22no—
267C2×C4×C53—24no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—42no—
274C2×C4×C53—41no—
275C2×C4×C53—42no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—42no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53#12114yes—
291C2×C4×C53#12314yes—
292C2×C4×C53#12314yes—
293C2×C4×C53#12314yes—
294C2×C4×C53#12414yes—
295C2×C4×C53#12614yes—
296C2×C4×C53#12614yes—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332D212—416no—
333#15138—531nomaximal, Sylow
334C22×C53C2×#12111yescharacteristic
335C22×C53C2×#12311yescharacteristic
336C22×C53C2×#12311yescharacteristic
337C22×C53C2×#12311yescharacteristic
338C22×C53C2×#12411yescharacteristic
339C22×C53C2×#12611yescharacteristic
340C22×C53C2×#12611yescharacteristic
341C22×C53#52911yescharacteristic
342C22×C53#52911yescharacteristic
343C22×C53#52911yescharacteristic
344C22×C53#53211yescharacteristic
345C22×C53#53211yescharacteristic
346C22×C53#53211yescharacteristic
347C22×C53#54011yescharacteristic
348C22×C53#54011yescharacteristic
349C22×C53#54011yescharacteristic
350C22×C53#54211yescharacteristic
351C22×C53#54211yescharacteristic
352C22×C53#54211yescharacteristic
353C22×C53D4211yescharacteristic
354C22×C53D4211yescharacteristic
355C22×C53#54611yescharacteristic
356C22×C53#54611yescharacteristic
357C22×C53#54611yescharacteristic
358C22×C53#54711yescharacteristic
359C22×C53#54711yescharacteristic
360C22×C53#54811yescharacteristic
361C22×C53#55011yescharacteristic
362C22×C53#55011yescharacteristic
363C22×C53#55311yescharacteristic
364C22×C53#55311yescharacteristic
365C22×C53#55511yescharacteristic
366C22×C53#55611yescharacteristic
367C22×C53#55911yescharacteristic
368C22×C53#55911yescharacteristic
369C2×D53—44no—
370C2×D53—44no—
371C2×D53—44no—
372C2×D53—44no—
373C2×D53—44no—
374C2×D53—44no—
375C2×D53—44no—
376C2×D53—82no—
377C2×D53—82no—
378C2×D53—82no—
379C2×D53—82no—
380C2×D53—82no—
381C2×D53—82no—
382C2×D53—82no—
383C2×D53—82no—
384C4×C53—42no—
385C4×C53—42no—
386C4×C53—44no—
387C4×C53—82no—
388C4×C53#39718yescomplemented
389Dic53—42no—
390Dic53—42no—
391Dic53—42no—
392Dic53—42no—
393Dic53—82no—
394C2×#397—532no—
395C2×#390—531no—
396C2×#390—531no—
397C2×#390—531no—
398C2×#389—531no—
399#1440—532no—
400#1440—532no—
401#1439—532no—
402C4⋊#95—531no—
403C4⋊#95D5311yescharacteristic, complemented
404C4×#95—531no—
405C2×C53C2×#39711yescharacteristic
406C2×C53#242011yescharacteristic
407C2×C53#242211yescharacteristic
408C2×C53#242711yescharacteristic
409C2×C53#242811yescharacteristic
410C2×C53#244511yescharacteristic
411C2×C53#244511yescharacteristic
412C2×C53#244711yescharacteristic
413C2×C53#244811yescharacteristic
414C2×C53#249011yescharacteristic
415C2×C53#249111yescharacteristic
416C2×C53#251211yescharacteristic
417C2×C53#251311yescharacteristic
418C2×C53#264411yescharacteristic
419C2×C53#286011yescharacteristic
420D53—84no—
421C23×D4—531no—
422C22×C4⋊C4—531no—
423C22×C4⋊C4—532no—
424C22×C4⋊C4C2×D5311yescharacteristic
425C22×C4⋊C4C2×D5311yescharacteristic
426C22×C22⋊C4—532no—
427C22×C22⋊C4—532no—
428C22×C22⋊C4—532no—
429C22×C22⋊C4—532no—
430C22×C22⋊C4—532no—
431C22×C22⋊C4—532no—
432C22×C42—531no—
433C22×C42—531no—
434C22×C42C2×D5311yescharacteristic
435#397—1068no—
436#390—1064no—
437#390—1064no—
438#390—1064no—
439#389—1064no—
440C2×#95—531no—
441C2×#95—532no—
442C2×#95—531no—
443C2×#95—531no—
444C2×#95—531no—
445C2×#95—532no—
446C2×#95—532no—
447C2×#95C2×D5312yes—
448C2×#95C2×D5312yes—
449C53#1513811yescharacteristic, complemented, Sylow
450C25—532no—
451C22×D4—534no—
452C22×D4—1062no—
453C22×D4—1062no—
454C22×D4—1062no—
455C22×D4—1062no—
456C22×D4—1062no—
457C22×D4—1062no—
458C23×C4—531no—
459C23×C4—531no—
460C23×C4—531no—
461C23×C4—531no—
462C23×C4—532no—
463C23×C4C22×D5312yes—
464C23×C4C22×D5312yes—
465C23×C4C22×D5311yescharacteristic
466C23×C4C22×D5311yescharacteristic
467C23×C4C22×D5311yescharacteristic
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—1064no—
474C2×C4⋊C4—1064no—
475C2×C4⋊C4—1062no—
476C2×C4⋊C4—1062no—
477C2×C4⋊C4—1062no—
478C2×C4⋊C4—2122no—
479C2×C4⋊C4D21214yes—
480C2×C22⋊C4—1064no—
481C2×C22⋊C4—1064no—
482C2×C22⋊C4—1064no—
483C2×C22⋊C4—1064no—
484C2×C22⋊C4—1064no—
485C2×C22⋊C4—1064no—
486C2×C22⋊C4—1064no—
487C2×C22⋊C4—1064no—
488C2×C22⋊C4—1064no—
489C2×C22⋊C4—1064no—
490C2×C22⋊C4—1064no—
491C2×C22⋊C4—1064no—
492C2×C22⋊C4—2122no—
493C2×C22⋊C4—2122no—
494C2×C22⋊C4—2122no—
495C2×C22⋊C4—2122no—
496C2×C22⋊C4—2122no—
497C2×C22⋊C4—2122no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—1062no—
502C2×C42—1062no—
503C2×C42—1062no—
504C2×C42—1062no—
505C2×C42—1062no—
506C2×C42—1062no—
507#95—24no—
508#95—42no—
509#95—534no—
510#95—1062no—
511#95—1062no—
512#95—1064no—
513#95—1064no—
514#95—1062no—
515#95—2122no—
516C24—534no—
517C24—1062no—
518C24—1062no—
519C24—1062no—
520C24—1062no—
521C24—1062no—
522C24—1062no—
523C24—1062no—
524C24—1062no—
525C24—1062no—
526C24—1062no—
527C24—1062no—
528C24—1062no—
529C24—1062no—
530C24—1062no—
531C24C23×D5311yescharacteristic
532C2×D4—1068no—
533C2×D4—1068no—
534C2×D4—1068no—
535C2×D4—2124no—
536C2×D4—2124no—
537C2×D4—2124no—
538C2×D4—2124no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—532no—
565C22×C4—532no—
566C22×C4—532no—
567C22×C4—532no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4C2×D21214yes—
600C22×C4C2×D21212yes—
601C22×C4#1171994512yes—
602C22×C4#1171994512yes—
603C22×C4D4×D5312yes—
604C22×C4D4×D5312yes—
605C22×C4#1171994712yes—
606C22×C4#1171994712yes—
607C22×C4#1171994912yes—
608C22×C4#1171994912yes—
609C4⋊C4—28no—
610C4⋊C4—44no—
611C4⋊C4—2128no—
612C4⋊C4—2124no—
613C22⋊C4—2128no—
614C22⋊C4—2128no—
615C22⋊C4—2128no—
616C22⋊C4—2128no—
617C22⋊C4—2128no—
618C22⋊C4—2128no—
619C42—44no—
620C42—2124no—
621C42—2124no—
622C23—1064no—
623C23—1064no—
624C23—1064no—
625C23—1064no—
626C23—1064no—
627C23—1064no—
628C23—1064no—
629C23—2122no—
630C23—2122no—
631C23—2122no—
632C23—2122no—
633C23—2122no—
634C23—2122no—
635C23—2122no—
636C23—2122no—
637C23—2122no—
638C23—2122no—
639C23—2122no—
640C23—2122no—
641C23—2122no—
642C23—2122no—
643C23—2122no—
644C23—2122no—
645C23—2122no—
646C23—2122no—
647C23—2122no—
648C23—2122no—
649C23—2122no—
650C23—2122no—
651C23—2122no—
652C23—2122no—
653C23—2122no—
654C23—2122no—
655C23—2122no—
656C23—2122no—
657C23C2×D4×D5311yescharacteristic
658C23C2×D4×D5311yescharacteristic
659C23C22×D21211yescharacteristic
660C23#41×D5311yescharacteristic
661C23#41×D5311yescharacteristic
662C23C2×#1171994711yescharacteristic
663C23C2×#1171994711yescharacteristic
664C23C2×#1171994511yescharacteristic
665C23C2×#1171994511yescharacteristic
666C23C2×#1171994911yescharacteristic
667C23C2×#1171994911yescharacteristic
668C23#1313326211yescharacteristic
669C23#1313326311yescharacteristic
670C23#1313326311yescharacteristic
671C23#1313326511yescharacteristic
672D4—21216no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—2122no—
714C2×C4—2122no—
715C2×C4—2122no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4—2121no—
721C2×C4—2121no—
722C2×C4—2121no—
723C2×C4—2121no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4—2121no—
730C2×C4—2121no—
731C2×C4—2121no—
732C2×C4—2121no—
733C2×C4—2121no—
734C2×C4—2121no—
735C2×C4—2121no—
736C2×C4#1313319214yes—
737C2×C4#1313319914yes—
738C2×C4#1313319914yes—
739C2×C4#1313320114yes—
740C2×C4#1313320514yes—
741C2×C4#1313321214yes—
742C2×C4#1313321214yes—
743C22—4242no—
744C22—4242no—
745C22—4242no—
746C22—4242no—
747C22—4242no—
748C22—4242no—
749C22—4242no—
750C22—4242no—
751C22—2124no—
752C22—2124no—
753C22—2124no—
754C22—2124no—
755C22—2124no—
756C22—2124no—
757C22—2124no—
758C22C2×#1313319211yescharacteristic
759C22C2×#1313319911yescharacteristic
760C22C2×#1313319911yescharacteristic
761C22C2×#1313320111yescharacteristic
762C22C2×#1313320511yescharacteristic
763C22C2×#1313321211yescharacteristic
764C22C2×#1313321211yescharacteristic
765C22#1681115811yescharacteristic
766C22#1681115911yescharacteristic
767C22#1681116011yescharacteristic
768C22#1681116811yescharacteristic
769C22#1681117011yescharacteristic
770C22#1681117411yescharacteristic
771C22#1681122411yescharacteristic
772C22#1681122611yescharacteristic
773C22#1681122911yescharacteristic
774C22#1681124511yescharacteristic
775C22#1681124611yescharacteristic
776C22#1681124711yescharacteristic
777C22#1681125711yescharacteristic
778C22D4×D21211yescharacteristic
779C22#1681126411yescharacteristic
780C22#1681126811yescharacteristic
781C22#1681127011yescharacteristic
782C22#1681127411yescharacteristic
783C22#1681127511yescharacteristic
784C22#1681128511yescharacteristic
785C22#1681129311yescharacteristic
786C22#1681129511yescharacteristic
787C22#1681131711yescharacteristic
788C22#1681132111yescharacteristic
789C22#1681133611yescharacteristic
790C22#1681134711yescharacteristic
791C22#1681135511yescharacteristic
792C22#1681135511yescharacteristic
793C4—42no—
794C4—44no—
795C4—42no—
796C4—82no—
797C4—4242no—
798C4—2122no—
799C4—2122no—
800C4—2122no—
801C4—2122no—
802C4#1681055018yescomplemented
803C2—4244no—
804C2C2×#1681055011yescharacteristic
805C2#2027820911yescharacteristic
806C2#2027823111yescharacteristic
807C2#2027829011yescharacteristic
808C2#2027830111yescharacteristic
809C2#2027847811yescharacteristic
810C2#2027848111yescharacteristic
811C2#2027850311yescharacteristic
812C2#2027851111yescharacteristic
813C2#2027906111yescharacteristic
814C2#2027907211yescharacteristic
815C2#2027929711yescharacteristic
816C2#2027930811yescharacteristic
817C2#2028067811yescharacteristic
818C2#2028308311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, cosocleC24×C53C24
FittingC53×C4⋊#95C2
prime radicalC23×D212C22
hypercenterC4⋊#95D53
hypocenterC53#15138
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#16810550C2semidirect
5. C2×#16810522C2semidirect
6. #20272963C2semidirect
7. #20272963C2semidirect
8. #20272961C2semidirect
9. #20272944C2semidirect
10. C4×#13133124C2semidirect
11. C53×C4⋊#95C2semidirect
89. #13133124D4semidirect
388. C4×C53#397semidirect
403. C4⋊#95D53semidirect
449. C53#15138semidirect
802. C4#16810550semidirect

Maximal subgroups

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

subgroupindex
C2×#168105502
C2×#168105252
C2×#168105242
C2×#168105222
#202729632
#202729612
#202729442
C4×#131331242
C53×C4⋊#952
#1513853