Finite Group Databasebeta

← #27313263

Subgroups — #27313263

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810526C211yesmaximal, characteristic
2C2×#16810503C211yesmaximal, characteristic
3#20272968C212yesmaximal, complemented
4#20272964C212yesmaximal, complemented
5#20272964C212yesmaximal, complemented
6#20272947C212yesmaximal, complemented
7#20272938C212yesmaximal, complemented
8#20272937C212yesmaximal, complemented
9C22×#123×C53C211yesmaximal, characteristic
10C24×Dic53C2211yescharacteristic
11C22×C4⋊Dic53C2211yescharacteristic
12C22×C22⋊Dic53C2212yes—
13C22×C22⋊Dic53C2212yes—
14C22×C22⋊Dic53C2212yes—
15C22×C22⋊Dic53C2211yescharacteristic
16C22×C4×Dic53C2211yescharacteristic
17#16810526—24no—
18#16810503—24no—
19C2×#13133124C2212yes—
20C2×#13133124C2212yes—
21C2×#13133124C2212yes—
22C2×#13133124C2212yes—
23C2×#13133124C2212yes—
24C2×#13133124C2212yes—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C23×D4×C53C2211yescharacteristic
29C24×C4×C53C2211yescharacteristic
30C2×#123×C53—24no—
31C2×#123×C53—24no—
32C2×#123×C53C418yescomplemented
33C22×C4⋊C4×C53C2212yes—
34C22×C22⋊C4×C53C2212yes—
35C22×C22⋊C4×C53C2211yescharacteristic
36C23×Dic53—22no—
37C23×Dic53—24no—
38C23×Dic53—41no—
39C23×Dic53—41no—
40C23×Dic53—42no—
41C23×Dic53C2312yes—
42C23×Dic53C2312yes—
43C23×Dic53C2312yes—
44C23×Dic53C2312yes—
45C2×C4⋊Dic53—22no—
46C2×C4⋊Dic53—41no—
47C2×C4⋊Dic53—41no—
48C2×C22⋊Dic53—24no—
49C2×C22⋊Dic53—22no—
50C2×C22⋊Dic53—24no—
51C2×C22⋊Dic53—24no—
52C2×C22⋊Dic53—24no—
53C2×C22⋊Dic53—24no—
54C2×C22⋊Dic53—24no—
55C2×C22⋊Dic53—42no—
56C2×C22⋊Dic53—42no—
57C2×C22⋊Dic53—42no—
58C2×C22⋊Dic53—41no—
59C2×C22⋊Dic53—41no—
60C2×C4×Dic53—22no—
61C2×C4×Dic53—41no—
62C2×C4×Dic53—41no—
63#13133124—24no—
64#13133124—24no—
65#13133124—24no—
66#13133124—42no—
67#13133124—42no—
68#13133124—42no—
69#13133124—42no—
70#13133124—42no—
71#13133124—42no—
72C25×C53C2311yescharacteristic
73C25×C53C2311yescharacteristic
74C22×D4×C53—41no—
75C22×D4×C53—41no—
76C22×D4×C53—41no—
77C22×D4×C53—41no—
78C22×D4×C53C2×C414yes—
79C22×D4×C53D414yes—
80C22×D4×C53D414yes—
81C23×C4×C53—22no—
82C23×C4×C53—22no—
83C23×C4×C53—41no—
84C23×C4×C53—41no—
85C23×C4×C53—41no—
86C23×C4×C53—41no—
87C23×C4×C53C2×C414yescomplemented
88C23×C4×C53C2312yes—
89C23×C4×C53C2312yes—
90C23×C4×C53C2311yescharacteristic
91#123×C53—232no—
92C2×C4⋊C4×C53—24no—
93C2×C4⋊C4×C53—24no—
94C2×C4⋊C4×C53C2×C418yescomplemented
95C2×C22⋊C4×C53—22no—
96C2×C22⋊C4×C53—22no—
97C2×C22⋊C4×C53—24no—
98C2×C22⋊C4×C53—24no—
99C2×C22⋊C4×C53C2×C418yes—
100C2×C22⋊C4×C53C2×C414yescomplemented
101C24×C53—22no—
102C24×C53—22no—
103C24×C53—22no—
104C24×C53—22no—
105C24×C53—21no—
106C24×C53—21no—
107C24×C53—21no—
108C24×C53—21no—
109C24×C53—21no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—22no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53C22×C412yes—
118C24×C53C22×C412yes—
119C24×C53C2×D412yes—
120C24×C53C2×D412yes—
121C24×C53C2×D412yes—
122C24×C53C2×D412yes—
123C24×C53C2411yescharacteristic
124C2×D4×C53—44no—
125C2×D4×C53—44no—
126C2×D4×C53—44no—
127C2×D4×C53—44no—
128C2×D4×C53—44no—
129C2×D4×C53—44no—
130C2×D4×C53C22⋊C4116yes—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—28no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
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×C53—22no—
148C22×C4×C53—44no—
149C22×C4×C53—44no—
150C22×C4×C53—44no—
151C22×C4×C53—44no—
152C22×C4×C53—44no—
153C22×C4×C53—44no—
154C22×C4×C53C22×C414yes—
155C22×C4×C53C22×C414yes—
156C22×C4×C53C22×C412yes—
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2×D412yes—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—44no—
186C22×Dic53—48no—
187C22×Dic53—48no—
188C22×Dic53—44no—
189C22×Dic53—44no—
190C22×Dic53#4114yes—
191C22×Dic53#4114yes—
192C4⋊C4×C53—216no—
193C22⋊C4×C53—216no—
194C22⋊C4×C53—28no—
195C22⋊Dic53—48no—
196C22⋊Dic53—48no—
197C22⋊Dic53—48no—
198C22⋊Dic53—44no—
199C4⋊Dic53—44no—
200C4×Dic53—44no—
201C23×C53—24no—
202C23×C53—24no—
203C23×C53—22no—
204C23×C53—22no—
205C23×C53—22no—
206C23×C53—22no—
207C23×C53—24no—
208C23×C53—24no—
209C23×C53—22no—
210C23×C53—22no—
211C23×C53—22no—
212C23×C53—22no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53—22no—
216C23×C53—22no—
217C23×C53—24no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53—24no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—24no—
224C23×C53—24no—
225C23×C53—42no—
226C23×C53—42no—
227C23×C53—42no—
228C23×C53—42no—
229C23×C53—42no—
230C23×C53—42no—
231C23×C53—42no—
232C23×C53—42no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—42no—
236C23×C53—42no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—42no—
242C23×C53—42no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53C2×C22⋊C414yes—
246C23×C53C2×C22⋊C414yes—
247C23×C53C23×C411yescharacteristic
248C23×C53C22×D411yescharacteristic
249C23×C53C22×D411yescharacteristic
250C23×C53C2×#4112yes—
251C23×C53C2×#4112yes—
252C23×C53H(5,𝔽2)11yescharacteristic
253C23×C53H(5,𝔽2)11yescharacteristic
254C23×C53H(5,𝔽2)11yescharacteristic
255C23×C53H(5,𝔽2)11yescharacteristic
256C23×C53H(5,𝔽2)12yes—
257C23×C532−1+412yes—
258D4×C53—416no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—24no—
266C2×C4×C53—24no—
267C2×C4×C53—24no—
268C2×C4×C53—24no—
269C2×C4×C53—24no—
270C2×C4×C53—24no—
271C2×C4×C53—416no—
272C2×C4×C53—42no—
273C2×C4×C53—42no—
274C2×C4×C53—42no—
275C2×C4×C53—42no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53—42no—
280C2×C4×C53C2×C22⋊C414yes—
281C2×Dic53—24no—
282C2×Dic53—24no—
283C2×Dic53—24no—
284C2×Dic53—24no—
285C2×Dic53—24no—
286C2×Dic53—24no—
287C2×Dic53—416no—
288C2×Dic53—42no—
289C2×Dic53—42no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53—42no—
294C2×Dic53—42no—
295C2×Dic53—42no—
296C2×Dic53—42no—
297C2×Dic53—42no—
298C2×Dic53—42no—
299C2×Dic53—42no—
300C2×Dic53—42no—
301C2×Dic53—42no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310#14505—531nomaximal, Sylow
311C22×C53—24no—
312C22×C53—24no—
313C22×C53—28no—
314C22×C53—28no—
315C22×C53—44no—
316C22×C53—44no—
317C22×C53—42no—
318C22×C53—42no—
319C22×C53—42no—
320C22×C53—42no—
321C22×C53—42no—
322C22×C53—42no—
323C22×C53—44no—
324C22×C53—44no—
325C22×C53—44no—
326C22×C53—44no—
327C22×C53—42no—
328C22×C53—42no—
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53C22×C22⋊C411yescharacteristic
334C22×C53C4×#4112yes—
335C22×C53#51811yescharacteristic
336C22×C53#51811yescharacteristic
337C22×C53#52012yes—
338C22×C53#53411yescharacteristic
339C22×C53#53411yescharacteristic
340C22×C53#53411yescharacteristic
341C22×C53#53411yescharacteristic
342C22×C53#53812yes—
343C22×C53#53912yes—
344C22×C53#54012yes—
345C22×C53#54212yes—
346C22×C53#54612yes—
347C22×C53#54612yes—
348C22×C53#54712yes—
349C22×C53#54712yes—
350C22×C53#55111yescharacteristic
351C22×C53#55312yes—
352C22×C53#55911yescharacteristic
353C22×C53#56011yescharacteristic
354C22×C53#56212yes—
355C22×C53#56311yescharacteristic
356C4×C53—24no—
357C4×C53—44no—
358C4×C53—44no—
359Dic53—44no—
360Dic53—44no—
361Dic53—82no—
362Dic53—82no—
363C22×#123D5311yescharacteristic
364C2×#390—531no—
365C2×#386—531no—
366#1441—532no—
367#1440—532no—
368#1440—532no—
369#1436—532no—
370C22⋊#95—532no—
371C22⋊#95—532no—
372C2×C53—44no—
373C2×C53—44no—
374C2×C53#230811yescharacteristic
375C2×C53#233512yes—
376C2×C53#233912yes—
377C2×C53#237411yescharacteristic
378C2×C53#237611yescharacteristic
379C2×C53#269711yescharacteristic
380C2×C53#270112yes—
381C2×C53#270812yes—
382C2×C53#270911yescharacteristic
383C2×C53#271711yescharacteristic
384C2×C53#272411yescharacteristic
385C23×D4C2×D5311yescharacteristic
386C24×C4—531no—
387C24×C4C2×D5311yescharacteristic
388C2×#123—24no—
389C2×#123—24no—
390C2×#123Dic5318yescomplemented
391C22×C4⋊C4—531no—
392C22×C4⋊C4C2×D5312yes—
393C22×C22⋊C4—532no—
394C22×C22⋊C4—532no—
395C22×C22⋊C4—532no—
396C22×C22⋊C4—531no—
397C22×C22⋊C4C2×D5312yes—
398C22×C22⋊C4C2×D5311yescharacteristic
399C22×C42—531no—
400#390—1064no—
401#386—1064no—
402C2×#95—532no—
403C2×#95—532no—
404C2×#95—532no—
405C2×#95—532no—
406C2×#95—532no—
407C2×#95—532no—
408C2×#95—532no—
409C2×#95—532no—
410C2×#95—532no—
411C53#1450511yescharacteristic, complemented, Sylow
412C25C22×D5311yescharacteristic
413C25C22×D5311yescharacteristic
414C22×D4—41no—
415C22×D4—41no—
416C22×D4—41no—
417C22×D4—41no—
418C22×D4C2×Dic5314yes—
419C22×D4C22⋊D5314yes—
420C22×D4C22⋊D5314yes—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—41no—
424C23×C4—41no—
425C23×C4—41no—
426C23×C4—41no—
427C23×C4—532no—
428C23×C4—532no—
429C23×C4—532no—
430C23×C4—532no—
431C23×C4—1064no—
432C23×C4—1062no—
433C23×C4—2121no—
434C23×C4—2121no—
435C23×C4—2122no—
436C23×C4C2×Dic5314yescomplemented
437C23×C4C22×D5312yes—
438C23×C4C22×D5312yes—
439C23×C4C22×D5311yescharacteristic
440#123—232no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—1062no—
444C2×C4⋊C4—2121no—
445C2×C4⋊C4—2121no—
446C2×C4⋊C4C2×Dic5318yescomplemented
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—1064no—
452C2×C22⋊C4—1064no—
453C2×C22⋊C4—1064no—
454C2×C22⋊C4—1064no—
455C2×C22⋊C4—1062no—
456C2×C22⋊C4—1064no—
457C2×C22⋊C4—1064no—
458C2×C22⋊C4—2122no—
459C2×C22⋊C4—2122no—
460C2×C22⋊C4—2122no—
461C2×C22⋊C4—2121no—
462C2×C22⋊C4—2121no—
463C2×C22⋊C4C2×Dic5318yes—
464C2×C22⋊C4C2×Dic5314yescomplemented
465C2×C42—1062no—
466C2×C42—2121no—
467C2×C42—2121no—
468#95—1064no—
469#95—1064no—
470#95—1064no—
471#95—2122no—
472#95—2122no—
473#95—2122no—
474#95—2122no—
475#95—2122no—
476#95—2122no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24C22×Dic5312yes—
494C24C22×Dic5312yes—
495C24C2×C22⋊D5312yes—
496C24C2×C22⋊D5312yes—
497C24C2×C22⋊D5312yes—
498C24C2×C22⋊D5312yes—
499C24C23×D5311yescharacteristic
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4C22⋊Dic53116yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—534no—
531C22×C4—534no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1062no—
553C22×C4—1062no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—2124no—
559C22×C4—2128no—
560C22×C4—2128no—
561C22×C4—2124no—
562C22×C4—2124no—
563C22×C4C22×Dic5314yes—
564C22×C4C22×Dic5314yes—
565C22×C4C22×Dic5312yes—
566C22×C4C2×C22⋊D5312yes—
567C22×C4C2×C22⋊D5312yes—
568C4⋊C4—216no—
569C4⋊C4—2124no—
570C22⋊C4—216no—
571C22⋊C4—28no—
572C22⋊C4—2128no—
573C22⋊C4—2128no—
574C22⋊C4—2128no—
575C22⋊C4—2124no—
576C42—2124no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23C2×C22⋊Dic5314yes—
622C23C2×C22⋊Dic5314yes—
623C23C23×Dic5311yescharacteristic
624C23C22×C22⋊D5311yescharacteristic
625C23C22×C22⋊D5311yescharacteristic
626C23#41×D5312yes—
627C23#41×D5312yes—
628C23#1313326211yescharacteristic
629C23#1313326211yescharacteristic
630C23#1313326211yescharacteristic
631C23#1313326211yescharacteristic
632C23#1313326312yes—
633C23#1313326412yes—
634D4—416no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—416no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—1064no—
657C2×C4—1064no—
658C2×C4—1064no—
659C2×C4—1064no—
660C2×C4—1064no—
661C2×C4—1064no—
662C2×C4—2122no—
663C2×C4—2122no—
664C2×C4—2122no—
665C2×C4—2122no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4—2122no—
669C2×C4—2122no—
670C2×C4—2122no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4—2122no—
676C2×C4—21216no—
677C2×C4—2122no—
678C2×C4—2122no—
679C2×C4—2122no—
680C2×C4—2122no—
681C2×C4—2122no—
682C2×C4—2122no—
683C2×C4—2122no—
684C2×C4—2122no—
685C2×C4C2×C22⋊Dic5314yes—
686C22—28no—
687C22—28no—
688C22—24no—
689C22—24no—
690C22—44no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—44no—
695C22—44no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—44no—
707C22—44no—
708C22C22×C22⋊Dic5311yescharacteristic
709C22#41×Dic5312yes—
710C22#1681109811yescharacteristic
711C22#1681109811yescharacteristic
712C22#1681110612yes—
713C22#1681118211yescharacteristic
714C22#1681118211yescharacteristic
715C22#1681118211yescharacteristic
716C22#1681118211yescharacteristic
717C22#1681120912yes—
718C22#1681121612yes—
719C22#1681122512yes—
720C22#1681124112yes—
721C22#1681126112yes—
722C22#1681126112yes—
723C22#1681127212yes—
724C22#1681127212yes—
725C22#1681130111yescharacteristic
726C22#1681131812yes—
727C22#1681135711yescharacteristic
728C22#1681136311yescharacteristic
729C22#1681137012yes—
730C22#1681137611yescharacteristic
731C4—24no—
732C4—44no—
733C4—44no—
734C4—4242no—
735C4—4242no—
736C4—2124no—
737C4—2124no—
738C2—44no—
739C2—44no—
740C2#2027729311yescharacteristic
741C2#2027750912yes—
742C2#2027754512yes—
743C2#2027785111yescharacteristic
744C2#2027786311yescharacteristic
745C2#2028127411yescharacteristic
746C2#2028132212yes—
747C2#2028142912yes—
748C2#2028144411yescharacteristic
749C2#2028155211yescharacteristic
750C2#2028164311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×#123×C53C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC22×#123D53
hypocenterC53#14505
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
3. #20272968C2semidirect
4. #20272964C2semidirect
5. #20272964C2semidirect
6. #20272947C2semidirect
7. #20272938C2semidirect
8. #20272937C2semidirect
32. C2×#123×C53C4semidirect
87. C23×C4×C53C2×C4semidirect
94. C2×C4⋊C4×C53C2×C4semidirect
100. C2×C22⋊C4×C53C2×C4semidirect
390. C2×#123Dic53semidirect
411. C53#14505semidirect
436. C23×C4C2×Dic53semidirect
446. C2×C4⋊C4C2×Dic53semidirect
464. C2×C22⋊C4C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105262
C2×#168105032
#202729682
#202729642
#202729472
#202729382
#202729372
C22×#123×C532
#1450553