Finite Group Databasebeta

← #27306464

Subgroups — #27306464

Order 13568.

2458 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133179C211yesmaximal, characteristic
2C2×#16810525C211yesmaximal, characteristic
3C2×#16810524C211yesmaximal, characteristic
4C2×#16810522C211yesmaximal, characteristic, complemented
5C2×#16810480C212yesmaximal, complemented
6#20272961C212yesmaximal, complemented
7#20272957C212yesmaximal, complemented
8#20272944C211yesmaximal, characteristic, complemented
9#20272936C212yesmaximal, complemented
10C4×#13133124C211yesmaximal, characteristic, complemented
11C2×C53×#389C211yesmaximal, characteristic, complemented
12C23×D212C2211yescharacteristic
13C23×C4×D53C2212yes—
14C2×#13133179—24no—
15C2×#13133179—24no—
16C2×#13133179C418yescomplemented
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2212yes—
19C22×#11719921C2212yes—
20C22×#11719921C2212yes—
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×C4×Dic53C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26#16810525—24no—
27#16810524—24no—
28#16810522—24no—
29#16810480—28no—
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2211yescharacteristic
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2212yes—
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C42×C53C2211yescharacteristic
41C53×#389—24no—
42C2×#95×C53C2212yes—
43C24×D53C2312yes—
44C22×D212—22no—
45C22×D212—22no—
46C22×D212—22no—
47C22×D212—22no—
48C22×D212C2×C414yes—
49C22×D212D414yes—
50C22×D212Q814yes—
51C23×Dic53C2312yes—
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C22×C4×D53—24no—
57C22×C4×D53—24no—
58C22×C4×D53—24no—
59C22×C4×D53—24no—
60C22×C4×D53—42no—
61C22×C4×D53—42no—
62C22×C4×D53C2×C418yes—
63#13133179—232no—
64C2×C4⋊Dic53—24no—
65C2×C4⋊Dic53—22no—
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53—24no—
69C2×C4⋊Dic53—42no—
70C2×#11719921—24no—
71C2×#11719921—24no—
72C2×#11719921—24no—
73C2×#11719921—24no—
74C2×#11719921—24no—
75C2×#11719921—24no—
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—24no—
79C2×#11719921—24no—
80C2×#11719921—42no—
81C2×#11719921—42no—
82C2×#11719921—42no—
83C2×#11719921—42no—
84C2×#11719921C2×C418yes—
85C2×C4×Dic53—22no—
86C2×C4×Dic53—22no—
87C2×C4×Dic53—22no—
88C2×C4×Dic53—22no—
89C2×C4×Dic53—22no—
90C2×C4×Dic53C2×C414yes—
91#13133124—24no—
92#13133124—22no—
93#13133124—24no—
94#13133124—22no—
95#13133124—22no—
96#13133124—42no—
97#13133124D414yescomplemented
98C23×C4×C53C2312yes—
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2311yescharacteristic
101C23×C4×C53C2312yes—
102C23×C4×C53C2311yescharacteristic
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—24no—
105C2×C4⋊C4×C53—22no—
106C2×C4⋊C4×C53—24no—
107C2×C4⋊C4×C53—22no—
108C2×C4⋊C4×C53—42no—
109C2×C4⋊C4×C53C2×C414yes—
110C2×C4⋊C4×C53D414yes—
111C2×C4⋊C4×C53D414yes—
112C2×C42×C53—22no—
113C2×C42×C53—22no—
114C2×C42×C53—22no—
115#95×C53—24no—
116C24×C53C2411yescharacteristic
117C23×D53—22no—
118C23×D53—22no—
119C23×D53—22no—
120C23×D53—22no—
121C23×D53—22no—
122C23×D53—22no—
123C23×D53—22no—
124C23×D53—22no—
125C23×D53—22no—
126C23×D53—22no—
127C23×D53—22no—
128C23×D53—22no—
129C23×D53C22×C414yes—
130C23×D53C2×D414yes—
131C23×D53C2×Q814yes—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53C22×C414yes—
156C22×C4×C53C22×C412yes—
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2×D414yes—
159C22×C4×C53C2×D414yes—
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×D412yes—
162C22×C4×C53C2×D412yes—
163C22×C4×C53C2×Q812yes—
164C22×C4×C53#4112yes—
165C22×C4×C53#4112yes—
166C22×C4×C53#4112yes—
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—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53C22×C412yes—
197C22×Dic53C22×C412yes—
198C22×Dic53C2×D412yes—
199C22×Dic53C2×D412yes—
200C22×Dic53#4112yes—
201C22×Dic53#4112yes—
202C2×D212—28no—
203C2×D212—28no—
204C2×D212—28no—
205C2×D212—28no—
206C2×D212—28no—
207C2×D212—28no—
208C2×D212C4⋊C4116yescomplemented
209C2×C4×D53—216no—
210C2×C4×D53—216no—
211C2×C4×D53—48no—
212C2×C4×D53—48no—
213C2×C4×D53—48no—
214C2×C4×D53—48no—
215C2×C4×D53—48no—
216C4⋊C4×C53—48no—
217C4⋊C4×C53—44no—
218C4⋊C4×C53C22⋊C4116yescomplemented
219C42×C53—44no—
220#11719921—216no—
221#11719921—48no—
222#11719921—48no—
223#11719921—48no—
224#11719921—48no—
225C4⋊Dic53—48no—
226C4⋊Dic53—44no—
227C4×Dic53—28no—
228C4×Dic53—44no—
229C23×C53C23×C411yescharacteristic
230C23×C53C22×D411yescharacteristic
231C23×C53C22×D411yescharacteristic
232C23×C53C22×D411yescharacteristic
233C23×C53C22×D411yescharacteristic
234C23×C53C22×Q811yescharacteristic
235C23×C53C2×#4111yescharacteristic
236C23×C53C2×#4111yescharacteristic
237C23×C53C2×#4111yescharacteristic
238C23×C53C2×#4111yescharacteristic
239C23×C53C2×#4111yescharacteristic
240C23×C53H(5,𝔽2)11yescharacteristic
241C23×C53H(5,𝔽2)11yescharacteristic
242C23×C53H(5,𝔽2)11yescharacteristic
243C23×C532−1+411yescharacteristic
244C22×D53—24no—
245C22×D53—24no—
246C22×D53—24no—
247C22×D53—24no—
248C22×D53—24no—
249C22×D53—24no—
250C22×D53—24no—
251C22×D53—24no—
252C22×D53—24no—
253C22×D53—24no—
254C22×D53—24no—
255C22×D53—24no—
256C22×D53—24no—
257C22×D53—24no—
258C22×D53—24no—
259C22×D53—24no—
260C22×D53—24no—
261C22×D53—24no—
262C22×D53—42no—
263C22×D53—42no—
264C22×D53—42no—
265C22×D53—42no—
266C22×D53—42no—
267C22×D53—42no—
268C22×D53—42no—
269C22×D53—42no—
270C22×D53—42no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C22×D53—42no—
277C22×D53—42no—
278C22×D53C2×C4⋊C418yes—
279C2×C4×C53—24no—
280C2×C4×C53—24no—
281C2×C4×C53—24no—
282C2×C4×C53—24no—
283C2×C4×C53—24no—
284C2×C4×C53—24no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53C2×C22⋊C418yes—
307C2×C4×C53C2×C22⋊C414yes—
308C2×C4×C53C2×C4⋊C414yes—
309C2×C4×C53#11714yes—
310C2×C4×C53#12114yes—
311C2×C4×C53#12114yes—
312C2×C4×C53C22⋊Q814yes—
313C2×C4×C53C22⋊Q814yes—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—41no—
330C2×Dic53—41no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—41no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53C4×D414yes—
349D212—232no—
350C4×D53—432no—
351#13920—531nomaximal, Sylow
352C22×C53C22×C22⋊C411yescharacteristic
353C22×C53C22×C4⋊C411yescharacteristic
354C22×C53C2×#11711yescharacteristic
355C22×C53C2×C4×D411yescharacteristic
356C22×C53C4×#4111yescharacteristic
357C22×C53#51811yescharacteristic
358C22×C53#52011yescharacteristic
359C22×C53C2×#12111yescharacteristic
360C22×C53C2×#12111yescharacteristic
361C22×C53C2×C22⋊Q811yescharacteristic
362C22×C53C2×C22⋊Q811yescharacteristic
363C22×C53#52911yescharacteristic
364C22×C53#52911yescharacteristic
365C22×C53#53211yescharacteristic
366C22×C53#53211yescharacteristic
367C22×C53#54011yescharacteristic
368C22×C53#54011yescharacteristic
369C22×C53#54211yescharacteristic
370C22×C53#54211yescharacteristic
371C22×C53D4211yescharacteristic
372C22×C53D4211yescharacteristic
373C22×C53D4211yescharacteristic
374C22×C53#54611yescharacteristic
375C22×C53#54611yescharacteristic
376C22×C53#54611yescharacteristic
377C22×C53#54611yescharacteristic
378C22×C53#54711yescharacteristic
379C22×C53#54811yescharacteristic
380C22×C53#54811yescharacteristic
381C22×C53D4×Q811yescharacteristic
382C22×C53#55011yescharacteristic
383C22×C53#55011yescharacteristic
384C22×C53#55411yescharacteristic
385C22×C53#55411yescharacteristic
386C22×C53#55411yescharacteristic
387C2×D53—28no—
388C2×D53—28no—
389C2×D53—28no—
390C2×D53—44no—
391C2×D53—44no—
392C2×D53—44no—
393C2×D53—44no—
394C2×D53—44no—
395C2×D53—44no—
396C2×D53—44no—
397C2×D53—44no—
398C2×D53—44no—
399C2×D53—44no—
400C2×D53—44no—
401C2×D53—44no—
402C4×C53—28no—
403C4×C53—42no—
404C4×C53—42no—
405C4×C53—82no—
406C4×C53#38018yescomplemented
407Dic53—24no—
408Dic53—42no—
409Dic53—42no—
410Dic53—42no—
411Dic53—82no—
412C22×C4×D4—531no—
413C2×#390—531no—
414C2×#390—531no—
415C2×#389—531no—
416C2×#389D5311yescharacteristic, complemented
417C2×#380—532no—
418#1439—532no—
419#1439—532no—
420C4⋊#95—531no—
421C22⋊#95—532no—
422C4×#95—531no—
423C2×C53C2×#38011yescharacteristic
424C2×C53#229311yescharacteristic
425C2×C53#231911yescharacteristic
426C2×C53D4×C22⋊C411yescharacteristic
427C2×C53#234111yescharacteristic
428C2×C53D4×C4⋊C411yescharacteristic
429C2×C53#234911yescharacteristic
430C2×C53#242711yescharacteristic
431C2×C53#242711yescharacteristic
432C2×C53#242811yescharacteristic
433C2×C53#242811yescharacteristic
434C2×C53#245211yescharacteristic
435C2×C53#245211yescharacteristic
436C2×C53#245411yescharacteristic
437C2×C53#245411yescharacteristic
438D53—48no—
439C23×D4—531no—
440C24×C4—532no—
441C2×C4×D4—538no—
442C2×C4×D4—1064no—
443C2×C4×D4—1064no—
444C22×C4⋊C4—531no—
445C22×C4⋊C4—532no—
446C22×C4⋊C4C2×D5311yescharacteristic
447C22×C4⋊C4C2×D5312yes—
448C22×C4⋊C4C2×D5311yescharacteristic
449C22×C22⋊C4—532no—
450C22×C22⋊C4—532no—
451C22×C22⋊C4—532no—
452C22×C22⋊C4—532no—
453C22×C22⋊C4—532no—
454C22×C42—531no—
455C22×C42—531no—
456C22×C42C2×D5311yescharacteristic
457#390—1064no—
458#390—1064no—
459#389—24no—
460#389—1064no—
461#380—1068no—
462C2×#95—531no—
463C2×#95—531no—
464C2×#95—531no—
465C2×#95—531no—
466C2×#95—532no—
467C2×#95—532no—
468C2×#95—532no—
469C2×#95C2×D5312yes—
470C53#1392011yescharacteristic, complemented, Sylow
471C25—532no—
472C22×D4—534no—
473C22×D4—534no—
474C22×D4—534no—
475C22×D4—1062no—
476C22×D4—1062no—
477C22×D4—1062no—
478C22×D4—1062no—
479C23×C4—531no—
480C23×C4—531no—
481C23×C4—531no—
482C23×C4—531no—
483C23×C4—538no—
484C23×C4—532no—
485C23×C4—1064no—
486C23×C4—1064no—
487C23×C4—1064no—
488C23×C4—1064no—
489C23×C4—2122no—
490C23×C4—2122no—
491C23×C4C22×D5312yes—
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5311yescharacteristic
494C23×C4C22×D5312yes—
495C23×C4C22×D5311yescharacteristic
496C4×D4—10632no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—42no—
503C2×C4⋊C4—1064no—
504C2×C4⋊C4—1064no—
505C2×C4⋊C4—1062no—
506C2×C4⋊C4—1062no—
507C2×C4⋊C4—1062no—
508C2×C4⋊C4—2122no—
509C2×C4⋊C4C4×D5314yes—
510C2×C4⋊C4D21214yes—
511C2×C4⋊C4C22⋊D5314yes—
512C2×C22⋊C4—538no—
513C2×C22⋊C4—1064no—
514C2×C22⋊C4—1064no—
515C2×C22⋊C4—1064no—
516C2×C22⋊C4—1064no—
517C2×C22⋊C4—1064no—
518C2×C22⋊C4—1064no—
519C2×C22⋊C4—1064no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—1064no—
522C2×C22⋊C4—1064no—
523C2×C22⋊C4—2122no—
524C2×C22⋊C4—2122no—
525C2×C22⋊C4—2122no—
526C2×C22⋊C4—2122no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—534no—
531C2×C42—1062no—
532C2×C42—1062no—
533C2×C42—1062no—
534C2×C42—1062no—
535C2×C42—1062no—
536#95—24no—
537#95—534no—
538#95—1062no—
539#95—1062no—
540#95—1064no—
541#95—1064no—
542#95—1062no—
543#95—2122no—
544C24—534no—
545C24—534no—
546C24—534no—
547C24—1062no—
548C24—1062no—
549C24—1062no—
550C24—1062no—
551C24—1062no—
552C24—1062no—
553C24—1062no—
554C24—1062no—
555C24—1062no—
556C24—1062no—
557C24—1062no—
558C24—1062no—
559C24C23×D5311yescharacteristic
560C2×D4—5316no—
561C2×D4—1068no—
562C2×D4—1068no—
563C2×D4—1068no—
564C2×D4—1068no—
565C2×D4—1068no—
566C2×D4—1068no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—532no—
593C22×C4—532no—
594C22×C4—532no—
595C22×C4—532no—
596C22×C4—10616no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—1061no—
619C22×C4—10616no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—2128no—
628C22×C4—2128no—
629C22×C4—2128no—
630C22×C4—2128no—
631C22×C4—2128no—
632C22×C4C2×C4×D5314yes—
633C22×C4C2×C4×D5312yes—
634C22×C4C2×D21214yes—
635C22×C4C2×D21212yes—
636C22×C4D4×D5312yes—
637C22×C4D4×D5312yes—
638C22×C4#1171994712yes—
639C22×C4Q8×D5312yes—
640C22×C4#1171994912yes—
641C22×C4#1171994912yes—
642C22×C4C2×C22⋊D5314yes—
643C22×C4C2×C22⋊D5312yes—
644C4⋊C4—48no—
645C4⋊C4—44no—
646C4⋊C4—2128no—
647C4⋊C4—2124no—
648C4⋊C4#11719921116yescomplemented
649C22⋊C4—10616no—
650C22⋊C4—2128no—
651C22⋊C4—2128no—
652C22⋊C4—2128no—
653C22⋊C4—2128no—
654C42—44no—
655C42—1068no—
656C42—2124no—
657C23—538no—
658C23—1064no—
659C23—1064no—
660C23—1064no—
661C23—1064no—
662C23—1064no—
663C23—1064no—
664C23—1064no—
665C23—1064no—
666C23—1064no—
667C23—1064no—
668C23—1064no—
669C23—1064no—
670C23—1064no—
671C23—1064no—
672C23—1064no—
673C23—1064no—
674C23—1064no—
675C23—1064no—
676C23—2122no—
677C23—2122no—
678C23—2122no—
679C23—2122no—
680C23—2122no—
681C23—2122no—
682C23—2122no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23—2122no—
687C23—2122no—
688C23—2122no—
689C23—2122no—
690C23—2122no—
691C23—2122no—
692C23C22×C4×D5311yescharacteristic
693C23C2×D4×D5311yescharacteristic
694C23C2×D4×D5311yescharacteristic
695C23C22×C22⋊D5311yescharacteristic
696C23C22×D21211yescharacteristic
697C23C2×Q8×D5311yescharacteristic
698C23#41×D5311yescharacteristic
699C23#41×D5311yescharacteristic
700C23C2×#1171994711yescharacteristic
701C23C2×#1171994911yescharacteristic
702C23C2×#1171994911yescharacteristic
703C23#1313326211yescharacteristic
704C23#1313326311yescharacteristic
705C23#1313326311yescharacteristic
706C23#1313326511yescharacteristic
707D4—10632no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—534no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—21232no—
752C2×C4—2122no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2122no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4—2121no—
760C2×C4—2121no—
761C2×C4—2121no—
762C2×C4—2121no—
763C2×C4—2121no—
764C2×C4—2121no—
765C2×C4—2121no—
766C2×C4—2121no—
767C2×C4—2121no—
768C2×C4—2121no—
769C2×C4—2121no—
770C2×C4—2121no—
771C2×C4C2×#1171992118yes—
772C2×C4C2×#1171992114yes—
773C2×C4C4⋊C4×D5314yes—
774C2×C4#1313317514yes—
775C2×C4#1313318814yes—
776C2×C4#1313319214yes—
777C2×C4#1313319314yes—
778C2×C4#1313319714yes—
779C22—1068no—
780C22—1068no—
781C22—1068no—
782C22—2124no—
783C22—2124no—
784C22—2124no—
785C22—2124no—
786C22—2124no—
787C22—2124no—
788C22—2124no—
789C22—2124no—
790C22—2124no—
791C22—2124no—
792C22—2124no—
793C22—2124no—
794C22C22×#1171992111yescharacteristic
795C22C2×C4⋊C4×D5311yescharacteristic
796C22C2×#1313317511yescharacteristic
797C22C4×D4×D5311yescharacteristic
798C22C4×#1171994911yescharacteristic
799C22#1681109511yescharacteristic
800C22#1681110511yescharacteristic
801C22C2×#1313318811yescharacteristic
802C22C2×#1313319211yescharacteristic
803C22C2×#1313319311yescharacteristic
804C22C2×#1313319711yescharacteristic
805C22#1681115811yescharacteristic
806C22#1681115911yescharacteristic
807C22#1681116811yescharacteristic
808C22#1681117411yescharacteristic
809C22#1681122611yescharacteristic
810C22#1681122911yescharacteristic
811C22#1681124611yescharacteristic
812C22#1681124711yescharacteristic
813C22D4×C22⋊D5311yescharacteristic
814C22#1681125711yescharacteristic
815C22D4×D21211yescharacteristic
816C22#1681126111yescharacteristic
817C22#1681126411yescharacteristic
818C22#1681126811yescharacteristic
819C22#1681127011yescharacteristic
820C22#1681127511yescharacteristic
821C22#1681128411yescharacteristic
822C22#1681128511yescharacteristic
823C22#1681128811yescharacteristic
824C22#1681129211yescharacteristic
825C22#1681129511yescharacteristic
826C22#1681132911yescharacteristic
827C22#1681132911yescharacteristic
828C22#1681133411yescharacteristic
829C4—28no—
830C4—42no—
831C4—42no—
832C4—82no—
833C4—1064no—
834C4—4242no—
835C4—2122no—
836C4—2122no—
837C4—2122no—
838C4#1681048018yescomplemented
839C2—2128no—
840C2C2×#1681048011yescharacteristic
841C2#2027717311yescharacteristic
842C2#2027735411yescharacteristic
843C2D4×#1171992111yescharacteristic
844C2#2027755311yescharacteristic
845C2#2027761611yescharacteristic
846C2#2027762411yescharacteristic
847C2#2027828811yescharacteristic
848C2#2027829011yescharacteristic
849C2#2027829911yescharacteristic
850C2#2027830111yescharacteristic
851C2#2027856111yescharacteristic
852C2#2027856311yescharacteristic
853C2#2027858311yescharacteristic
854C2#2027858511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#389C2
socle, cosocleC24×C53C24
prime radicalC23×D212C22
hypercenterC2×#389D53
hypocenterC53#13920
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#16810522C2semidirect
5. C2×#16810480C2semidirect
6. #20272961C2semidirect
7. #20272957C2semidirect
8. #20272944C2semidirect
9. #20272936C2semidirect
10. C4×#13133124C2semidirect
11. C2×C53×#389C2semidirect
16. C2×#13133179C4semidirect
97. #13133124D4semidirect
208. C2×D212C4⋊C4semidirect
218. C4⋊C4×C53C22⋊C4semidirect
406. C4×C53#380semidirect
416. C2×#389D53semidirect
470. C53#13920semidirect
648. C4⋊C4#11719921semidirect
838. C4#16810480semidirect

Maximal subgroups

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

subgroupindex
C22×#131331792
C2×#168105252
C2×#168105242
C2×#168105222
C2×#168104802
#202729612
#202729572
#202729442
#202729362
C4×#131331242
C2×C53×#3892
#1392053