Finite Group Databasebeta

← #27400428

Subgroups — #27400428

Order 13568.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811344C211yesmaximal, characteristic
2C2×#16810697C211yesmaximal, characteristic
3#20277640C211yesmaximal, characteristic
4#20275686C211yesmaximal, characteristic, complemented
5#20275661C211yesmaximal, characteristic, complemented
6#20275149C211yesmaximal, characteristic, complemented
7#20275135C211yesmaximal, characteristic, complemented
8#20275024C211yesmaximal, characteristic, complemented
9#20274811C211yesmaximal, characteristic, complemented
10#20274808C211yesmaximal, characteristic, complemented
11#20274728C211yesmaximal, characteristic, complemented
12#20274547C211yesmaximal, characteristic, complemented
13#20274434C211yesmaximal, characteristic, complemented
14#20274430C211yesmaximal, characteristic, complemented
15C53×#1872C211yesmaximal, characteristic, complemented
16C22×#11719917C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18#16811344—24no—
19#16811344C418yescomplemented
20C2×#13133216C2211yescharacteristic
21C2×#13133212—21no—
22C2×#13133210—21no—
23C2×#13133203—21no—
24C2×#13133193C2211yescharacteristic
25C2×Q8×Dic53C2211yescharacteristic
26C2×#13133182—21no—
27C2×C4×C22⋊D53C2211yescharacteristic
28C2×#13133176C2211yescharacteristic
29C2×#13133175C2211yescharacteristic
30C2×#13133175C2211yescharacteristic
31#16810697—24no—
32C2×#13133146C2211yescharacteristic
33C2×#13133141C2211yescharacteristic
34C2×#13133141C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×#13133127C2211yescharacteristic
37#16810513—21no—
38#16810504—21no—
39#16810502—21no—
40#16810488C2211yescharacteristic
41#16810483C2211yescharacteristic
42#16810480C2211yescharacteristic
43C4⋊C4×Dic53C2211yescharacteristic
44C4×C22⋊Dic53—21no—
45#16810386C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C2×C22⋊Q8×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic
57C2×#103×C53C2211yescharacteristic
58C2×#103×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×Dic106—21no—
63C22×C22⋊D53D411yescharacteristic
64C22×C4×D53C2311yescharacteristic
65C2×#11719917—22no—
66C2×#11719917—22no—
67C2×#11719917—41no—
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C2×C8×D53—22no—
71C2×C8×D53—22no—
72C2×C8×D53—41no—
73#13133216—22no—
74#13133216C2×C414yescomplemented
75#13133212—28no—
76#13133210—28no—
77#13133203—28no—
78#13133193—22no—
79#13133193C2×C414yescomplemented
80Q8×Dic53—22no—
81Q8×Dic53C2×C414yescomplemented
82#13133182—28no—
83C4×C22⋊D53C2×C414yes—
84C4×C22⋊D53D414yes—
85#13133176—22no—
86#13133176C2×C414yes—
87#13133175—22no—
88#13133175—22no—
89#13133175—41no—
90#13133175C2×C414yescomplemented
91C2×C4⋊Dic53—21no—
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×#11719919D411yescharacteristic
99C2×C22⋊Dic53—21no—
100C2×C22⋊Dic53—21no—
101C2×C22⋊Dic53D411yescharacteristic
102C2×#11719921—21no—
103C2×#11719921—21no—
104C2×#11719921—21no—
105C2×#11719921—21no—
106C2×#11719921D411yescharacteristic
107C2×C4×Dic53—21no—
108C2×C4×Dic53—21no—
109C2×C4×Dic53—21no—
110C2×C4×Dic53—21no—
111C2×C4×Dic53—21no—
112C2×C4×Dic53C2311yescharacteristic
113#13133146—22no—
114#13133141—22no—
115#13133141—41no—
116#13133129—22no—
117#13133127—22no—
118#13133124—21no—
119#13133124—21no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123C22×Q8×C53C2311yescharacteristic
124C23×C4×C53—21no—
125C23×C4×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128C22⋊Q8×C53—22no—
129C22⋊Q8×C53C2×C414yes—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53—22no—
133C2×C4⋊C4×C53—41no—
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C22⋊C4×C53—21no—
138#103×C53—22no—
139#103×C53—41no—
140C22⋊C8×C53—22no—
141C24×C53C2×D411yescharacteristic
142C23×D53C2×D411yescharacteristic
143C2×Q8×C53—21no—
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53C22×C412yes—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
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—42no—
158C22×C4×C53—42no—
159C22×C4×C53—81no—
160C22×C4×C53C22×C412yes—
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53C2×D412yes—
163C22×C4×C53C2411yescharacteristic
164C2×C22⋊D53—41no—
165C2×C22⋊D53—41no—
166C2×C22⋊D53C22⋊C414yes—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53C2×D411yescharacteristic
172C22×Dic53C2×D411yescharacteristic
173C22×Dic53C2×D411yescharacteristic
174C2×C4×D53—21no—
175C2×C4×D53—21no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53C22×C412yes—
179C2×C4×D53C2×D412yes—
180C2×Dic106—24no—
181C2×Dic106—42no—
182C2×Dic106—42no—
183C2×C8×C53—21no—
184C2×C8×C53—21no—
185C2×C8×C53—21no—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C4⋊C4×C53—24no—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—42no—
195C4⋊C4×C53C22×C412yes—
196C4⋊C4×C53#4112yes—
197C22⋊C4×C53—24no—
198C22⋊Dic53—24no—
199C22⋊Dic53—42no—
200C22⋊Dic53C22⋊C414yes—
201#11719921—24no—
202#11719921—24no—
203#11719921—42no—
204#11719921—81no—
205#11719921C22⋊C414yes—
206C4⋊Dic53—21no—
207C4⋊Dic53—21no—
208C4⋊Dic53—24no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53C22×C412yes—
214C4⋊Dic53C22×C412yes—
215#11719919—24no—
216#11719919—24no—
217#11719919C22⋊C414yes—
218C4×Dic53—24no—
219C4×Dic53—24no—
220C4×Dic53—24no—
221C4×Dic53—42no—
222C4×Dic53—81no—
223C4×Dic53C22×C412yes—
224C4×Dic53C2×D412yes—
225#11719917—44no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322#4112yes—
232C8×D53—44no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53C2×C22⋊C412yes—
240C23×C53C22×D411yescharacteristic
241C22×D53—21no—
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53—21no—
247C22×D53C2×C22⋊C412yes—
248Q8×C53—22no—
249Q8×C53—22no—
250Q8×C53—41no—
251Q8×C53—41no—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—84no—
271C2×C4×C53C2×C22⋊C412yes—
272C2×C4×C53C23×C411yescharacteristic
273C2×C4×C53C22×D411yescharacteristic
274C2×C4×C53C2×#4111yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×C4×C53H(5,𝔽2)11yescharacteristic
277C2×C4×C532−1+411yescharacteristic
278C22⋊D53—44no—
279C2×Dic53—21no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53C2×C22⋊C412yes—
298C2×Dic53C2×C22⋊C412yes—
299C2×Dic53C2×C22⋊C412yes—
300C4×D53—22no—
301C4×D53—22no—
302C4×D53—22no—
303C4×D53—22no—
304Dic106—48no—
305C8×C53—41no—
306C8×C53—41no—
307#88322—22no—
308#88322—41no—
309#22494—531nomaximal, Sylow
310C22×C53—22no—
311C22×C53—22no—
312C22×C53—22no—
313C22×C53—41no—
314C22×C53—41no—
315C22×C53—41no—
316C22×C53—41no—
317C22×C53C22×C22⋊C411yescharacteristic
318C22×C53#54611yescharacteristic
319C22×C53#54711yescharacteristic
320C22×C53#57511yescharacteristic
321C22×C53#57511yescharacteristic
322C22×C53#57711yescharacteristic
323C22×C53#57811yescharacteristic
324C2×D53—22no—
325C2×D53—22no—
326C2×D53—22no—
327C2×D53—41no—
328C2×D53—41no—
329C2×D53—41no—
330C2×D53—41no—
331C4×C53—22no—
332C4×C53—42no—
333C4×C53—42no—
334C4×C53—42no—
335C4×C53—81no—
336C4×C53C4×#4111yescharacteristic
337C4×C53#52011yescharacteristic
338C4×C53#54611yescharacteristic
339C4×C53#54711yescharacteristic
340Dic53—22no—
341Dic53—22no—
342Dic53—22no—
343Dic53—42no—
344Dic53—42no—
345Dic53—81no—
346Dic53—81no—
347C2×#556—531no—
348C2×#435—531no—
349#2352—531no—
350#1993—531no—
351#1987—531no—
352#1894—531no—
353#1892—531no—
354#1873—531no—
355#1872D5311yescharacteristic, complemented
356#1825—531no—
357#1825—531no—
358#1805—531no—
359#1763—531no—
360#1736—531no—
361#1735—531no—
362C2×C53—42no—
363C2×C53#233911yescharacteristic
364C2×C53#289611yescharacteristic
365C2×C53#289811yescharacteristic
366C2×C53#331111yescharacteristic
367C2×C53#331311yescharacteristic
368C2×C53#334911yescharacteristic
369C2×C53#335011yescharacteristic
370D53—42no—
371C22×M16—531no—
372C23×C8—531no—
373#556—538no—
374#556—1064no—
375C2×C4⋊Q8—531no—
376C2×#126—1061no—
377C2×#126—1061no—
378C2×#124—1061no—
379C2×C22⋊Q8—531no—
380C2×C22⋊Q8C2×D5311yescharacteristic
381C2×C4×Q8—531no—
382C2×C4×Q8—1061no—
383C2×C4×D4—531no—
384C2×#117—531no—
385C2×#117—531no—
386C2×#117—531no—
387C22×C4⋊C4C2×D5311yescharacteristic
388#435—1064no—
389C2×C4⋊C8—531no—
390C2×#103—531no—
391C2×#103—531no—
392C2×#103C2×D5311yescharacteristic
393C2×#103C2×D5311yescharacteristic
394C2×C22⋊C8—531no—
395C2×C22⋊C8C2×D5311yescharacteristic
396C2×#97—531no—
397#388—1061no—
398#387—1061no—
399#386—1061no—
400#382—531no—
401#380—531no—
402#380—531no—
403C4×C4⋊C4—531no—
404C4×C22⋊C4—1061no—
405#340—531no—
406#340—531no—
407#340—531no—
408#340—531no—
409#340—531no—
410#340—531no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415#340C2×D5311yescharacteristic
416#340C2×D5311yescharacteristic
417C53#2249411yescharacteristic, complemented, Sylow
418C22×Q8—1061no—
419C22×Q8C22×D5311yescharacteristic
420C22×D4—531no—
421C23×C4—21no—
422C23×C4—531no—
423C23×C4C22×D5311yescharacteristic
424C2×M16—1062no—
425C2×M16—1062no—
426C2×M16—2121no—
427C22×C8—531no—
428C22×C8—531no—
429C22×C8—1062no—
430C22×C8—1062no—
431C22×C8—2121no—
432C22×C8C22×D5311yescharacteristic
433C22×C8C22×D5311yescharacteristic
434C4⋊Q8—534no—
435C4⋊Q8—1062no—
436#126—1068no—
437#126—1068no—
438#124—1068no—
439C22⋊Q8—22no—
440C22⋊Q8—534no—
441C22⋊Q8—1062no—
442C22⋊Q8C4×D5314yes—
443C4×Q8—534no—
444C4×Q8—1062no—
445C4×Q8—1068no—
446C4×D4—534no—
447C4×D4—534no—
448#117—534no—
449#117—534no—
450#117—1062no—
451#117—1062no—
452#117—1062no—
453#117—2121no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—531no—
459C2×C4⋊C4—531no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—1061no—
464C2×C4⋊C4—1061no—
465C2×C4⋊C4—1061no—
466C2×C4⋊C4C22×D5311yescharacteristic
467C2×C4⋊C4C22×D5311yescharacteristic
468C2×C4⋊C4C22×D5311yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—531no—
471C2×C22⋊C4—531no—
472C2×C22⋊C4—1061no—
473C2×C22⋊C4—1061no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4—1061no—
477C2×C22⋊C4—1061no—
478C2×C42—531no—
479C2×C42—1061no—
480C2×C42—1061no—
481C2×C42—1061no—
482C2×C42—1061no—
483C2×C42—1061no—
484C4⋊C8—1062no—
485#103—22no—
486#103—41no—
487#103—1062no—
488#103—2121no—
489C22⋊C8—22no—
490C22⋊C8—1062no—
491#97—1062no—
492#95—1061no—
493#95—1061no—
494#95—1061no—
495#95—1061no—
496#95—1061no—
497C24—531no—
498C24D4×D5311yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—1064no—
505C2×Q8—2122no—
506C2×Q8—2122no—
507C2×Q8C2×C4×D5312yes—
508C2×D4—534no—
509C2×D4—2121no—
510C2×D4—2121no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—81no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—531no—
525C22×C4—532no—
526C22×C4—532no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4C2×C4×D5312yes—
536C22×C4D4×D5311yescharacteristic
537C22×C4D4×D5312yes—
538C22×C4C23×D5311yescharacteristic
539M16—2124no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—532no—
547C2×C8—1061no—
548C2×C8—1061no—
549C2×C8—1061no—
550C2×C8—1061no—
551C2×C8—1061no—
552C2×C8—2124no—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—534no—
560C4⋊C4—532no—
561C4⋊C4—532no—
562C4⋊C4—1064no—
563C4⋊C4—1064no—
564C4⋊C4—1064no—
565C4⋊C4—1061no—
566C4⋊C4—1061no—
567C4⋊C4—1061no—
568C4⋊C4—1061no—
569C4⋊C4—1061no—
570C4⋊C4—1061no—
571C4⋊C4C2×C4×D5312yes—
572C4⋊C4#1171994712yes—
573C22⋊C4—24no—
574C22⋊C4—534no—
575C22⋊C4—534no—
576C22⋊C4—1064no—
577C22⋊C4—1064no—
578C22⋊C4—1064no—
579C22⋊C4—4241no—
580C22⋊C4—2122no—
581C22⋊C4—2122no—
582C42—532no—
583C42—532no—
584C42—1064no—
585C42—1064no—
586C42—1064no—
587C42—4241no—
588C42—2122no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—532no—
596C23—1061no—
597C23—1061no—
598C23—1061no—
599C23—1061no—
600C23—1061no—
601C23—1061no—
602C23C22⋊C4×D5312yes—
603C23C2×D4×D5311yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608Q8—2128no—
609D4—2124no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—84no—
629C2×C4—532no—
630C2×C4—532no—
631C2×C4—532no—
632C2×C4—1061no—
633C2×C4—1061no—
634C2×C4—1061no—
635C2×C4—1061no—
636C2×C4—1061no—
637C2×C4—1061no—
638C2×C4—1062no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4—2121no—
653C2×C4—2121no—
654C2×C4C22⋊C4×D5312yes—
655C2×C4C22×C4×D5311yescharacteristic
656C2×C4C2×D4×D5311yescharacteristic
657C2×C4#41×D5311yescharacteristic
658C2×C4C2×#1171994711yescharacteristic
659C2×C4#1313326211yescharacteristic
660C2×C4#1313326411yescharacteristic
661C8—41no—
662C8—41no—
663C8—1062no—
664C8—2121no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—1062no—
673C22—1062no—
674C22—1062no—
675C22—2121no—
676C22—2121no—
677C22—2121no—
678C22—2121no—
679C22C2×C22⋊C4×D5311yescharacteristic
680C22#1681126011yescharacteristic
681C22#1681127111yescharacteristic
682C22#1681141911yescharacteristic
683C22#1681142211yescharacteristic
684C22#1681142911yescharacteristic
685C22#1681143611yescharacteristic
686C4—22no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—1062no—
692C4—1062no—
693C4—1062no—
694C4—4241no—
695C4—4241no—
696C4—2122no—
697C4—2122no—
698C4C4×#1171994711yescharacteristic
699C4#1681110211yescharacteristic
700C4#1681126211yescharacteristic
701C4#1681127311yescharacteristic
702C2—42no—
703C2—2122no—
704C2#2027754111yescharacteristic
705C2#2028323111yescharacteristic
706C2#2028324311yescharacteristic
707C2#2028674411yescharacteristic
708C2#2028677411yescharacteristic
709C2#2028723811yescharacteristic
710C2#2028726311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1872C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
cosocleC22×C4×C53C24
hypercenter#1872D53
hypocenterC53#22494
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #20275686C2semidirect
5. #20275661C2semidirect
6. #20275149C2semidirect
7. #20275135C2semidirect
8. #20275024C2semidirect
9. #20274811C2semidirect
10. #20274808C2semidirect
11. #20274728C2semidirect
12. #20274547C2semidirect
13. #20274434C2semidirect
14. #20274430C2semidirect
15. C53×#1872C2semidirect
19. #16811344C4semidirect
74. #13133216C2×C4semidirect
79. #13133193C2×C4semidirect
81. Q8×Dic53C2×C4semidirect
90. #13133175C2×C4semidirect
355. #1872D53semidirect
417. C53#22494semidirect

Maximal subgroups

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

subgroupindex
C2×#168113442
C2×#168106972
#202776402
#202756862
#202756612
#202751492
#202751352
#202750242
#202748112
#202748082
#202747282
#202745472
#202744342
#202744302
C53×#18722
#2249453