Finite Group Databasebeta

← #27413652

Subgroups — #27413652

Order 13568.

1042 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810733C211yesmaximal, characteristic, complemented
2C2×#16810680C211yesmaximal, characteristic, complemented
3C4×#13133191C211yesmaximal, characteristic, complemented
4#20276216C211yesmaximal, characteristic, complemented
5#20276152C211yesmaximal, characteristic, complemented
6#20276100C211yesmaximal, characteristic, complemented
7#20276089C211yesmaximal, characteristic, complemented
8#20276025C211yesmaximal, characteristic, complemented
9#20275904C211yesmaximal, characteristic, complemented
10#20275894C211yesmaximal, characteristic, complemented
11#20275711C211yesmaximal, characteristic
12#20274613C211yesmaximal, characteristic, complemented
13#20274543C211yesmaximal, characteristic, complemented
14#20274540C211yesmaximal, characteristic, complemented
15C4×#121×C53C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C2×#13133191C2211yescharacteristic
18C2×C4×D212C2211yescharacteristic
19C2×C4×C22⋊D53—21no—
20#16810733—24no—
21#16810680—24no—
22C2×#13133150C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×C4⋊#88322C2211yescharacteristic
26C2×C4⋊#88322C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×#13133128C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37#16810525C2211yescharacteristic
38#16810521C2211yescharacteristic
39#16810514—21no—
40#16810502—21no—
41#16810483C2211yescharacteristic
42C4×C4⋊Dic53C2211yescharacteristic
43C4×#11719921—21no—
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50C2×#121×C53C2211yescharacteristic
51C2×C4×D4×C53—21no—
52C2×C4×D4×C53C2211yescharacteristic
53C22×C42×C53C2211yescharacteristic
54C53×#390C2211yescharacteristic
55C53×#389C2211yescharacteristic
56C53×#388—21no—
57C53×#386—21no—
58C53×#380C2211yescharacteristic
59C4×C4⋊C4×C53C2211yescharacteristic
60C4×C22⋊C4×C53—21no—
61C22×D212C2311yescharacteristic
62C22×C22⋊D53—21no—
63C22×C4×D53—21no—
64C2×#11719922—22no—
65C2×#11719922—22no—
66C2×#11719922—22no—
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71#13133191—22no—
72#13133191—22no—
73C4×D212—22no—
74C4×D212—22no—
75C4×C22⋊D53—44no—
76C2×C4⋊Dic53C2311yescharacteristic
77C2×C4⋊Dic53C2311yescharacteristic
78C2×C4⋊Dic53C2311yescharacteristic
79C2×#11719919—21no—
80C2×C22⋊Dic53—21no—
81C2×#11719921—21no—
82C2×#11719921—21no—
83C2×#11719921—21no—
84C2×#11719921—21no—
85C2×C4×Dic53—21no—
86#13133150—22no—
87#13133148—22no—
88#13133148—22no—
89C4⋊#88322—22no—
90C4⋊#88322—22no—
91#13133138—22no—
92#13133138—22no—
93#13133138—22no—
94#13133137—22no—
95#13133137—22no—
96#13133137—22no—
97C22⋊#88322—22no—
98C22⋊#88322—22no—
99#13133128—22no—
100#13133128D414yescomplemented
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104C22×D4×C53—21no—
105C22×D4×C53C2311yescharacteristic
106C23×C4×C53—21no—
107C23×C4×C53D411yescharacteristic
108C23×C4×C53D411yescharacteristic
109C23×C4×C53C2311yescharacteristic
110#121×C53—22no—
111#121×C53—22no—
112C4×D4×C53—22no—
113C4×D4×C53—22no—
114C4×D4×C53—44no—
115C2×C4⋊C4×C53—21no—
116C2×C4⋊C4×C53C2311yescharacteristic
117C2×C4⋊C4×C53C2311yescharacteristic
118C2×C4⋊C4×C53C2311yescharacteristic
119C2×C22⋊C4×C53—21no—
120C2×C22⋊C4×C53—21no—
121C2×C22⋊C4×C53—21no—
122C2×C22⋊C4×C53—21no—
123C2×C22⋊C4×C53—21no—
124C2×C42×C53—22no—
125C2×C42×C53—22no—
126C2×C42×C53—21no—
127C2×C42×C53D411yescharacteristic
128C2×C42×C53D411yescharacteristic
129C2×C42×C53C2311yescharacteristic
130C2×C42×C53C2311yescharacteristic
131#95×C53—21no—
132#95×C53—21no—
133#95×C53—21no—
134C24×C53—21no—
135C24×C53C2×D411yescharacteristic
136C23×D53—21no—
137C2×D4×C53—24no—
138C2×D4×C53—21no—
139C2×D4×C53—21no—
140C2×D4×C53—21no—
141C2×D4×C53—21no—
142C2×D4×C53—21no—
143C2×D4×C53—42no—
144C2×D4×C53—42no—
145C2×D4×C53#4112yes—
146C22×C4×C53—22no—
147C22×C4×C53—21no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—41no—
160C22×C4×C53—41no—
161C22×C4×C53—42no—
162C22×C4×C53—42no—
163C22×C4×C53—42no—
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53C2×D411yescharacteristic
166C22×C4×C53C2×D411yescharacteristic
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53C2411yescharacteristic
170C2×C22⋊D53—24no—
171C2×C22⋊D53—42no—
172C2×C22⋊D53—42no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212—21no—
180C2×D212—21no—
181C2×D212#4112yes—
182C2×C4×D53—42no—
183C2×C4×D53—42no—
184C2×C4×D53—42no—
185C4⋊C4×C53—21no—
186C4⋊C4×C53—21no—
187C4⋊C4×C53—21no—
188C4⋊C4×C53—21no—
189C4⋊C4×C53—21no—
190C4⋊C4×C53—42no—
191C4⋊C4×C53#4112yes—
192C22⋊C4×C53—24no—
193C22⋊C4×C53—42no—
194C22⋊C4×C53—42no—
195C22⋊C4×C53—42no—
196C22⋊C4×C53—42no—
197C42×C53—22no—
198C42×C53—22no—
199C42×C53—21no—
200C42×C53—21no—
201C42×C53—42no—
202C42×C53C2×D412yes—
203C42×C53#4112yes—
204C22⋊Dic53—42no—
205#11719922—28no—
206#11719921—24no—
207#11719921—42no—
208#11719921—42no—
209#11719921—42no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53#4112yes—
216#11719919—42no—
217C4×Dic53—42no—
218C2×#88322—21no—
219C2×#88322—21no—
220C2×#88322—21no—
221C2×#88322—21no—
222C2×#88322—21no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322C2×D412yes—
229C2×#88322C2×D412yes—
230C23×C53—21no—
231C23×C53—21no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—22no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53AGL(1,ℤ/8)12yes—
244C23×C53C22×D411yescharacteristic
245C22×D53—22no—
246C22×D53—41no—
247C22×D53—41no—
248C22×D53—41no—
249C22×D53—41no—
250C22×D53—41no—
251C22×D53—41no—
252D4×C53—22no—
253D4×C53—22no—
254D4×C53—48no—
255D4×C53—41no—
256D4×C53—41no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—22no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—44no—
271C2×C4×C53—44no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—84no—
285C2×C4×C53#12112yes—
286C2×C4×C53#12112yes—
287C2×C4×C53AGL(1,ℤ/8)12yes—
288C2×C4×C53C22×D411yescharacteristic
289C2×C4×C53C2×#4111yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53C2×#4111yescharacteristic
292C2×C4×C53C2×#4111yescharacteristic
293C2×C4×C53C2×#4111yescharacteristic
294C22⋊D53—48no—
295C2×Dic53—22no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304D212—22no—
305D212—22no—
306D212—41no—
307D212—41no—
308C4×D53—84no—
309#88322—22no—
310#88322—22no—
311#88322—41no—
312#88322—41no—
313#23708—531nomaximal, Sylow
314C22×C53—22no—
315C22×C53—22no—
316C22×C53—22no—
317C22×C53—41no—
318C22×C53—41no—
319C22×C53—41no—
320C22×C53—41no—
321C22×C53—42no—
322C22×C53—42no—
323C22×C53—42no—
324C22×C53—81no—
325C22×C53—81no—
326C22×C53—81no—
327C22×C53—81no—
328C22×C53C2×#12111yescharacteristic
329C22×C53#52511yescharacteristic
330C22×C53#52511yescharacteristic
331C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C53#57511yescharacteristic
334C22×C53#57511yescharacteristic
335C2×D53—42no—
336C2×D53—42no—
337C2×D53—42no—
338C2×D53—81no—
339C2×D53—81no—
340C2×D53—81no—
341C2×D53—81no—
342C4×C53—22no—
343C4×C53—22no—
344C4×C53—22no—
345C4×C53—42no—
346C4×C53—41no—
347C4×C53—41no—
348C4×C53—81no—
349C4×C53—81no—
350C4×C53#52511yescharacteristic
351C4×C53#52911yescharacteristic
352C4×C53#52911yescharacteristic
353C4×C53#53211yescharacteristic
354Dic53—42no—
355Dic53—81no—
356Dic53—81no—
357C2×#442—531no—
358C2×#432—531no—
359C4×#121—531no—
360C4×#121D5311yescharacteristic, complemented
361#2088—531no—
362#2077—531no—
363#2067—531no—
364#2065—531no—
365#2054—531no—
366#2034—531no—
367#2033—531no—
368#1999—531no—
369#1776—531no—
370#1762—531no—
371#1762—531no—
372C2×C53—42no—
373C2×C53—82no—
374C2×C53#239211yescharacteristic
375C2×C53#305511yescharacteristic
376C2×C53#305511yescharacteristic
377C2×C53#310911yescharacteristic
378C2×C53#311111yescharacteristic
379C2×C53#311411yescharacteristic
380C2×C53#311511yescharacteristic
381D53—82no—
382C22×D8—531no—
383C2×#121—531no—
384C2×#121C2×D5311yescharacteristic
385C2×C4×D4—21no—
386C2×C4×D4—531no—
387C2×C4×D4—1061no—
388C2×C4×D4C2×D5311yescharacteristic
389C22×C42C2×D5311yescharacteristic
390#442—1064no—
391#432—1064no—
392C2×#107—531no—
393C2×#106—531no—
394C2×#106—531no—
395C2×C4⋊C8—531no—
396C2×C4⋊C8—531no—
397C2×#102—531no—
398C2×#102—531no—
399C2×#102—531no—
400C2×#102—531no—
401C2×#102—531no—
402C2×#102—531no—
403C2×C22⋊C8—531no—
404C2×C22⋊C8—531no—
405C2×#97—531no—
406C2×#97—531no—
407#390—531no—
408#390C2×D5311yescharacteristic
409#389—531no—
410#389C2×D5311yescharacteristic
411#388—21no—
412#388—1061no—
413#386—21no—
414#386—1061no—
415#380—531no—
416#380C2×D5311yescharacteristic
417C4×C4⋊C4—531no—
418C4×C4⋊C4C2×D5311yescharacteristic
419C4×C22⋊C4—21no—
420C4×C22⋊C4—1061no—
421#340—531no—
422#340—531no—
423#340—531no—
424#340—531no—
425#340—531no—
426#340—531no—
427C53#2370811yescharacteristic, complemented, Sylow
428C22×D4—21no—
429C22×D4—531no—
430C22×D4—1061no—
431C22×D4C22×D5311yescharacteristic
432C23×C4—21no—
433C23×C4—1061no—
434C23×C4C22⋊D5311yescharacteristic
435C23×C4C22⋊D5311yescharacteristic
436C23×C4C22×D5311yescharacteristic
437C2×D8—1062no—
438C2×D8—1062no—
439C2×D8—1062no—
440C22×C8—531no—
441C22×C8—531no—
442C22×C8—531no—
443C22×C8—531no—
444#121—22no—
445#121—22no—
446#121—1062no—
447#121—1062no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—44no—
451C4×D4—1062no—
452C4×D4—1062no—
453C4×D4—2124no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4—531no—
457C2×C4⋊C4—531no—
458C2×C4⋊C4—1061no—
459C2×C4⋊C4C22×D5311yescharacteristic
460C2×C4⋊C4C22×D5311yescharacteristic
461C2×C4⋊C4C22×D5311yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—1061no—
468C2×C22⋊C4—1061no—
469C2×C22⋊C4—1061no—
470C2×C22⋊C4—1061no—
471C2×C22⋊C4—1061no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—21no—
475C2×C42—1061no—
476C2×C42C22⋊D5311yescharacteristic
477C2×C42C22⋊D5311yescharacteristic
478C2×C42C22×D5311yescharacteristic
479C2×C42C22×D5311yescharacteristic
480#107—1062no—
481#106—1062no—
482#106—1062no—
483C4⋊C8—1062no—
484C4⋊C8—1062no—
485#102—1062no—
486#102—1062no—
487#102—1062no—
488#102—1062no—
489#102—1062no—
490#102—1062no—
491C22⋊C8—1062no—
492C22⋊C8—1062no—
493#97—534no—
494#97—1062no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—1061no—
499#95—1061no—
500#95—1061no—
501C24—21no—
502C24—1061no—
503C24C2×C22⋊D5311yescharacteristic
504C2×D4—24no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—532no—
513C2×D4—1064no—
514C2×D4—1061no—
515C2×D4—1061no—
516C2×D4—1061no—
517C2×D4—1061no—
518C2×D4—1061no—
519C2×D4—2122no—
520C2×D4—2122no—
521C2×D4#1171994512yes—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—1061no—
541C22×C4—1061no—
542C22×C4—1061no—
543C22×C4—2122no—
544C22×C4—2122no—
545C22×C4—2122no—
546C22×C4C2×C22⋊D5311yescharacteristic
547C22×C4C2×C22⋊D5311yescharacteristic
548C22×C4C2×C22⋊D5311yescharacteristic
549C22×C4C2×C22⋊D5311yescharacteristic
550C22×C4C2×C22⋊D5311yescharacteristic
551C22×C4C23×D5311yescharacteristic
552D8—1068no—
553C2×C8—532no—
554C2×C8—532no—
555C2×C8—1061no—
556C2×C8—1061no—
557C2×C8—1061no—
558C2×C8—1061no—
559C2×C8—1061no—
560C2×C8—1061no—
561C2×C8—1061no—
562C2×C8—1061no—
563C2×C8—1061no—
564C2×C8—1061no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—42no—
571C4⋊C4—532no—
572C4⋊C4—1061no—
573C4⋊C4—1061no—
574C4⋊C4—1061no—
575C4⋊C4—1061no—
576C4⋊C4—1061no—
577C4⋊C4—2122no—
578C4⋊C4#1171994512yes—
579C22⋊C4—24no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—1064no—
585C22⋊C4—2122no—
586C22⋊C4—2122no—
587C22⋊C4—2122no—
588C22⋊C4—2122no—
589C42—22no—
590C42—22no—
591C42—21no—
592C42—21no—
593C42—42no—
594C42—2122no—
595C42D4×D5312yes—
596C42#1171994712yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—1062no—
611C23—2121no—
612C23—2121no—
613C23—2121no—
614C23—2121no—
615C23—2121no—
616C23—2121no—
617C23#1313324212yes—
618C23C22×C22⋊D5311yescharacteristic
619D4—22no—
620D4—22no—
621D4—48no—
622D4—41no—
623D4—41no—
624D4—1062no—
625D4—1062no—
626D4—2128no—
627D4—2121no—
628D4—2121no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—84no—
657C2×C4—1062no—
658C2×C4—4244no—
659C2×C4—2121no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4—2121no—
663C2×C4—2121no—
664C2×C4—2121no—
665C2×C4—2121no—
666C2×C4—2121no—
667C2×C4#1313318912yes—
668C2×C4#1313318912yes—
669C2×C4#1313324312yes—
670C2×C4C2×D4×D5311yescharacteristic
671C2×C4#41×D5311yescharacteristic
672C2×C4#41×D5311yescharacteristic
673C2×C4C2×#1171994711yescharacteristic
674C2×C4C2×#1171994511yescharacteristic
675C2×C4C2×#1171994511yescharacteristic
676C8—1062no—
677C8—1062no—
678C8—2121no—
679C8—2121no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—4241no—
695C22—4241no—
696C22—4241no—
697C22—4241no—
698C22—2122no—
699C22—2122no—
700C22—2122no—
701C22C2×#1313318911yescharacteristic
702C22#1681113011yescharacteristic
703C22#1681113411yescharacteristic
704C22C2×#1313324211yescharacteristic
705C22C2×#1313324311yescharacteristic
706C22#1681142111yescharacteristic
707C22#1681142111yescharacteristic
708C4—22no—
709C4—22no—
710C4—22no—
711C4—42no—
712C4—41no—
713C4—41no—
714C4—81no—
715C4—81no—
716C4—4241no—
717C4—4241no—
718C4—2122no—
719C4#1681113211yescharacteristic
720C4#1681115311yescharacteristic
721C4#1681115511yescharacteristic
722C4#1681117011yescharacteristic
723C2—42no—
724C2—82no—
725C2—4242no—
726C2#2027795711yescharacteristic
727C2#2028433011yescharacteristic
728C2#2028433611yescharacteristic
729C2#2028480611yescharacteristic
730C2#2028482411yescharacteristic
731C2#2028484911yescharacteristic
732C2#2028486011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC4×#121×C53C2
socleC23×C53C22×D4
prime radical#20275711C2
hypercenterC4×#121D53
hypocenterC53#23708
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16810733C2semidirect
2. C2×#16810680C2semidirect
3. C4×#13133191C2semidirect
4. #20276216C2semidirect
5. #20276152C2semidirect
6. #20276100C2semidirect
7. #20276089C2semidirect
8. #20276025C2semidirect
9. #20275904C2semidirect
10. #20275894C2semidirect
12. #20274613C2semidirect
13. #20274543C2semidirect
14. #20274540C2semidirect
15. C4×#121×C53C2semidirect
100. #13133128D4semidirect
360. C4×#121D53semidirect
427. C53#23708semidirect

Maximal subgroups

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

subgroupindex
C2×#168107332
C2×#168106802
C4×#131331912
#202762162
#202761522
#202761002
#202760892
#202760252
#202759042
#202758942
#202757112
#202746132
#202745432
#202745402
C4×#121×C532
#2370853