Finite Group Databasebeta

← #27389243

Subgroups — #27389243

Order 13568.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811242C211yesmaximal, characteristic
2C2×#16810683C211yesmaximal, characteristic, complemented
3#20277069C211yesmaximal, characteristic, complemented
4#20275666C211yesmaximal, characteristic, complemented
5#20275663C211yesmaximal, characteristic, complemented
6#20275648C211yesmaximal, characteristic, complemented
7#20275034C211yesmaximal, characteristic
8#20275029C211yesmaximal, characteristic
9#20275024C211yesmaximal, characteristic, complemented
10#20275019C211yesmaximal, characteristic, complemented
11#20274547C211yesmaximal, characteristic, complemented
12#20274542C211yesmaximal, characteristic, complemented
13#103×Dic53C211yesmaximal, characteristic, complemented
14#102×Dic53C211yesmaximal, characteristic, complemented
15C53×#1983C211yesmaximal, characteristic, complemented
16#16811242—24no—
17#16811242C418yescomplemented
18C2×#13133217C2211yescharacteristic
19C2×#13133210—21no—
20C2×#13133203—21no—
21C2×#13133201—21no—
22C2×#13133194—21no—
23C2×#13133193C2211yescharacteristic
24C2×#13133188C2211yescharacteristic
25C2×Q8×Dic53C2211yescharacteristic
26C2×D4×Dic53C2211yescharacteristic
27C2×#13133175C2211yescharacteristic
28C2×#13133174C2211yescharacteristic
29C2×C4⋊C4×D53C2211yescharacteristic
30#16810683—24no—
31C2×C4⋊#88322C2211yescharacteristic
32C2×#13133141C2211yescharacteristic
33C2×#13133141C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×#13133127C2211yescharacteristic
39C2×C8×Dic53C2211yescharacteristic
40C4⋊C4×Dic53C2211yescharacteristic
41C4⋊C4×Dic53C2211yescharacteristic
42C4×#11719919—21no—
43C4×C4⋊Dic53C2211yescharacteristic
44#16810474—21no—
45C4×#11719921—21no—
46#16810470—21no—
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C2×#124×C53C2211yescharacteristic
56C2×C4⋊C8×C53C2211yescharacteristic
57C2×#103×C53C2211yescharacteristic
58C2×#103×C53C2211yescharacteristic
59C2×#102×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C4×C4⋊C4×C53C2211yescharacteristic
62C22×Dic106—21no—
63C22×C22⋊D53—21no—
64C23×Dic53—21no—
65C22×C4×D53—21no—
66C22×C4×D53C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69#13133217—22no—
70#13133217C2×C414yescomplemented
71#13133210—28no—
72#13133203—28no—
73#13133201—28no—
74#13133194—28no—
75#13133193—22no—
76#13133193C2×C414yes—
77#13133188—22no—
78#13133188C2×C414yes—
79Q8×Dic53—22no—
80Q8×Dic53C2×C414yescomplemented
81D4×Dic53—22no—
82D4×Dic53C2×C414yescomplemented
83#13133175—22no—
84#13133175—22no—
85#13133174C2×C414yes—
86#13133174D414yes—
87C2×C4⋊Dic53—21no—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53C2311yescharacteristic
90C2×C4⋊Dic53C2311yescharacteristic
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×#11719919—21no—
94C2×#11719919—21no—
95C2×#11719919D411yescharacteristic
96C2×#11719919D411yescharacteristic
97C4⋊C4×D53—22no—
98C4⋊C4×D53—22no—
99C2×C22⋊Dic53—21no—
100C2×C22⋊Dic53—21no—
101C2×#11719921—21no—
102C2×#11719921—21no—
103C2×#11719921D411yescharacteristic
104C2×#11719921D411yescharacteristic
105C2×C4×Dic53—21no—
106C2×C4×Dic53—21no—
107C2×C4×Dic53—21no—
108C2×C4×Dic53—21no—
109C2×C4×Dic53—21no—
110C2×C4×Dic53C2311yescharacteristic
111C4⋊#88322—22no—
112#13133141—22no—
113#13133141—22no—
114#13133138—22no—
115#13133138—22no—
116#13133129—22no—
117#13133129—22no—
118#13133127—22no—
119C8×Dic53—22no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123C22×Q8×C53C2311yescharacteristic
124C22×D4×C53C2311yescharacteristic
125C22×C8×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127#124×C53—22no—
128#124×C53C2×C414yescomplemented
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53—21no—
133C2×C42×C53—21no—
134C2×C42×C53C2311yescharacteristic
135C4⋊C8×C53—22no—
136#103×C53—22no—
137#103×C53—22no—
138#102×C53—22no—
139#102×C53—22no—
140#95×C53—21no—
141C24×C53—21no—
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—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53C22×C412yes—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2411yescharacteristic
161C2×C22⋊D53—24no—
162C2×C22⋊D53—81no—
163C2×C22⋊D53—81no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—24no—
169C22×Dic53—81no—
170C22×Dic53—81no—
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×D53—24no—
179C2×C4×D53—81no—
180C2×C4×D53—81no—
181C2×C4×D53C22×C412yes—
182C2×C4×D53C2×D412yes—
183C2×Dic106—24no—
184C2×Dic106—81no—
185C2×Dic106—81no—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53#4112yes—
195C4⋊C4×C53#4112yes—
196C22⋊C4×C53—24no—
197C22⋊C4×C53—24no—
198C42×C53—81no—
199C42×C53C22×C412yes—
200C42×C53C2×D412yes—
201C22⋊Dic53—24no—
202C22⋊Dic53—24no—
203#11719921—24no—
204#11719921—24no—
205#11719921C22⋊C414yes—
206#11719921C22⋊C414yes—
207C4⋊Dic53—24no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—24no—
213C4⋊Dic53C22×C412yes—
214C4⋊Dic53C22×C412yes—
215C4⋊Dic53#4112yes—
216C4⋊Dic53#4112yes—
217#11719919—24no—
218#11719919—24no—
219#11719919C22⋊C414yes—
220#11719919C22⋊C414yes—
221C4×Dic53—24no—
222C4×Dic53—24no—
223C4×Dic53—81no—
224C4×Dic53—81no—
225C4×Dic53—81no—
226C4×Dic53C22×C412yes—
227C4×Dic53C2×D412yes—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C23×C53—22no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53C22×D411yescharacteristic
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53—21no—
247C22×D53—21no—
248C22×D53C2×C22⋊C412yes—
249Q8×C53—22no—
250Q8×C53—22no—
251Q8×C53—41no—
252Q8×C53—41no—
253D4×C53—22no—
254D4×C53—22no—
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—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
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×C53C2×C22⋊C412yes—
271C2×C4×C53C2×C22⋊C412yes—
272C2×C4×C53C23×C411yescharacteristic
273C2×C4×C53C22×D411yescharacteristic
274C2×C4×C53C2×#4111yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×C4×C53C2×#4111yescharacteristic
277C2×C4×C53C2×#4111yescharacteristic
278C22⋊D53—84no—
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—22no—
288C2×Dic53—22no—
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×Dic53—84no—
298C2×Dic53C2×C22⋊C412yes—
299C2×Dic53C2×C22⋊C412yes—
300C2×Dic53C2×C22⋊C412yes—
301C4×D53—22no—
302C4×D53—22no—
303C4×D53—22no—
304C4×D53—22no—
305C4×D53—84no—
306Dic106—84no—
307C8×C53—41no—
308C8×C53—41no—
309#88322—41no—
310#88322—41no—
311#21397—531nomaximal, Sylow
312C22×C53—42no—
313C22×C53—42no—
314C22×C53—42no—
315C22×C53—81no—
316C22×C53—81no—
317C22×C53—81no—
318C22×C53—81no—
319C22×C53C22×C22⋊C411yescharacteristic
320C22×C53#52511yescharacteristic
321C22×C53#52511yescharacteristic
322C22×C53#57611yescharacteristic
323C22×C53#57711yescharacteristic
324C22×C53#57711yescharacteristic
325C22×C53#57811yescharacteristic
326C2×D53—22no—
327C2×D53—22no—
328C2×D53—22no—
329C2×D53—41no—
330C2×D53—41no—
331C2×D53—41no—
332C2×D53—41no—
333C4×C53—22no—
334C4×C53—22no—
335C4×C53—42no—
336C4×C53—42no—
337C4×C53—42no—
338C4×C53C4×#4111yescharacteristic
339C4×C53C4×#4111yescharacteristic
340C4×C53#53211yescharacteristic
341C4×C53#53211yescharacteristic
342Dic53—22no—
343Dic53—22no—
344Dic53—22no—
345Dic53—42no—
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349C2×#542—531no—
350C2×#433—531no—
351#2274—531no—
352#1988—531no—
353#1987—531no—
354#1983—531no—
355#1983D5311yescharacteristic, complemented
356#1875—531no—
357#1874—531no—
358#1873—531no—
359#1872—531no—
360#1763—531no—
361#1762—531no—
362C4×#103—531no—
363C4×#102—531no—
364C2×C53—82no—
365C2×C53#229711yescharacteristic
366C2×C53#289711yescharacteristic
367C2×C53#289811yescharacteristic
368C2×C53#311811yescharacteristic
369C2×C53#312111yescharacteristic
370C2×C53#312411yescharacteristic
371C2×C53#312511yescharacteristic
372D53—42no—
373#542—538no—
374#542—1064no—
375C2×C4⋊Q8—531no—
376C2×#126—1061no—
377C2×#124—1061no—
378C2×#124C2×D5311yescharacteristic
379C2×#123—1061no—
380C2×C22⋊Q8—531no—
381C2×C22⋊Q8—1061no—
382C2×#121—531no—
383C2×C4×Q8—531no—
384C2×C4×D4—531no—
385C2×#117—531no—
386C2×#117—531no—
387C22×C4⋊C4—531no—
388#433—1064no—
389C2×C4⋊C8—531no—
390C2×C4⋊C8C2×D5311yescharacteristic
391C2×#103—531no—
392C2×#103—531no—
393C2×#103C2×D5311yescharacteristic
394C2×#103C2×D5311yescharacteristic
395C2×#102—531no—
396C2×#102—531no—
397C2×#102C2×D5311yescharacteristic
398C2×#102C2×D5311yescharacteristic
399C2×C22⋊C8—531no—
400C2×C22⋊C8—531no—
401C2×#97—531no—
402C2×C4×C8—531no—
403C4×C4⋊C4—531no—
404C4×C4⋊C4—531no—
405C4×C4⋊C4—531no—
406C4×C4⋊C4—1061no—
407C4×C4⋊C4—1061no—
408C4×C4⋊C4C2×D5311yescharacteristic
409C4×C22⋊C4—1061no—
410C4×C22⋊C4—1061no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417#340—531no—
418#340—531no—
419C53#2139711yescharacteristic, complemented, Sylow
420C22×Q8—1061no—
421C22×Q8C22×D5311yescharacteristic
422C22×D4—1061no—
423C22×D4C22×D5311yescharacteristic
424C23×C4—531no—
425C23×C4—1061no—
426C23×C4—1061no—
427C22×C8—531no—
428C22×C8—531no—
429C22×C8C22×D5311yescharacteristic
430C22×C8C22×D5311yescharacteristic
431C4⋊Q8—534no—
432C4⋊Q8—1062no—
433#126—1068no—
434#124—22no—
435#124—1068no—
436#124C4×D5314yescomplemented
437#123—1068no—
438C22⋊Q8—534no—
439C22⋊Q8—1068no—
440C22⋊Q8—1062no—
441#121—534no—
442#121—1062no—
443C4×Q8—534no—
444C4×Q8—1062no—
445C4×D4—534no—
446C4×D4—1062no—
447#117—534no—
448#117—534no—
449#117—1062no—
450#117—1062no—
451C2×C4⋊C4—531no—
452C2×C4⋊C4—531no—
453C2×C4⋊C4—531no—
454C2×C4⋊C4—531no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4—531no—
457C2×C4⋊C4—1062no—
458C2×C4⋊C4—1061no—
459C2×C4⋊C4—1061no—
460C2×C4⋊C4—1061no—
461C2×C4⋊C4—1061no—
462C2×C4⋊C4—1062no—
463C2×C4⋊C4C22×D5311yescharacteristic
464C2×C4⋊C4C22×D5311yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—531no—
468C2×C22⋊C4—531no—
469C2×C22⋊C4—1061no—
470C2×C22⋊C4—1061no—
471C2×C22⋊C4—1061no—
472C2×C22⋊C4—1061no—
473C2×C42—21no—
474C2×C42—531no—
475C2×C42—1061no—
476C2×C42—1061no—
477C2×C42—1061no—
478C2×C42—1061no—
479C2×C42—1061no—
480C2×C42C22×D5311yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—1062no—
483#103—22no—
484#103—22no—
485#103—1062no—
486#103—1062no—
487#102—22no—
488#102—22no—
489#102—1062no—
490#102—1062no—
491C22⋊C8—1062no—
492C22⋊C8—1062no—
493#97—1062no—
494C4×C8—1062no—
495#95—21no—
496#95—1061no—
497#95—1061no—
498#95—1061no—
499C24—21no—
500C24—531no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—1064no—
507C2×Q8—4241no—
508C2×Q8—4241no—
509C2×Q8C2×C4×D5312yes—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—1064no—
516C2×D4—4241no—
517C2×D4—4241no—
518C2×D4C2×C4×D5312yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—531no—
525C22×C4—532no—
526C22×C4—532no—
527C22×C4—1064no—
528C22×C4—1064no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—4241no—
538C22×C4—4241no—
539C22×C4—4241no—
540C22×C4—4241no—
541C22×C4D4×D5311yescharacteristic
542C22×C4D4×D5311yescharacteristic
543C22×C4C23×D5311yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—1061no—
551C2×C8—1061no—
552C2×C8—1061no—
553C2×C8—1061no—
554C2×C8—1061no—
555C2×C8—1061no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—534no—
559C4⋊C4—534no—
560C4⋊C4—532no—
561C4⋊C4—532no—
562C4⋊C4—532no—
563C4⋊C4—532no—
564C4⋊C4—1064no—
565C4⋊C4—1064no—
566C4⋊C4—1064no—
567C4⋊C4—1064no—
568C4⋊C4—1061no—
569C4⋊C4—1061no—
570C4⋊C4—1061no—
571C4⋊C4—1061no—
572C4⋊C4#1171994712yes—
573C4⋊C4#1171994712yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—534no—
577C22⋊C4—534no—
578C22⋊C4—1064no—
579C22⋊C4—1064no—
580C22⋊C4—1064no—
581C22⋊C4—1064no—
582C42—81no—
583C42—532no—
584C42—532no—
585C42—1064no—
586C42—1064no—
587C42—4241no—
588C42—4241no—
589C42—4241no—
590C42C2×C4×D5312yes—
591C42D4×D5312yes—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—532no—
600C23—1061no—
601C23—1061no—
602C23—1061no—
603C23—1061no—
604C23—1061no—
605C23—1061no—
606C23C2×D4×D5311yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—4244no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—4244no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—532no—
631C2×C4—532no—
632C2×C4—532no—
633C2×C4—1061no—
634C2×C4—1061no—
635C2×C4—1061no—
636C2×C4—1061no—
637C2×C4—1061no—
638C2×C4—1061no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—1062no—
645C2×C4—1062no—
646C2×C4—1062no—
647C2×C4—4244no—
648C2×C4—4244no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4—2121no—
653C2×C4—2121no—
654C2×C4—2121no—
655C2×C4—2121no—
656C2×C4—2121no—
657C2×C4C22⋊C4×D5312yes—
658C2×C4C22⋊C4×D5312yes—
659C2×C4C22×C4×D5311yescharacteristic
660C2×C4C2×D4×D5311yescharacteristic
661C2×C4#41×D5311yescharacteristic
662C2×C4#41×D5311yescharacteristic
663C2×C4C2×#1171994711yescharacteristic
664C2×C4C2×#1171994711yescharacteristic
665C8—41no—
666C8—41no—
667C8—2121no—
668C8—2121no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—1062no—
677C22—1062no—
678C22—1062no—
679C22—2121no—
680C22—2121no—
681C22—2121no—
682C22—2121no—
683C22C2×C22⋊C4×D5311yescharacteristic
684C22#1681113311yescharacteristic
685C22#1681113311yescharacteristic
686C22#1681142511yescharacteristic
687C22#1681143011yescharacteristic
688C22#1681143311yescharacteristic
689C22#1681143911yescharacteristic
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—1062no—
696C4—1062no—
697C4—1062no—
698C4—2122no—
699C4—2122no—
700C4—2122no—
701C4—2122no—
702C4C4×#1171994711yescharacteristic
703C4C4×#1171994711yescharacteristic
704C4#1681117111yescharacteristic
705C4#1681117211yescharacteristic
706C2—82no—
707C2—2122no—
708C2#2027720211yescharacteristic
709C2#2028323711yescharacteristic
710C2#2028324611yescharacteristic
711C2#2028489611yescharacteristic
712C2#2028494111yescharacteristic
713C2#2028497611yescharacteristic
714C2#2028498911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1983C2
socleC23×C53C22×D4
prime radicalC2×#13133188C22
cosocleC22×C4×C53C24
hypercenter#1983D53
hypocenterC53#21397
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#16810683C2semidirect
3. #20277069C2semidirect
4. #20275666C2semidirect
5. #20275663C2semidirect
6. #20275648C2semidirect
9. #20275024C2semidirect
10. #20275019C2semidirect
11. #20274547C2semidirect
12. #20274542C2semidirect
13. #103×Dic53C2semidirect
14. #102×Dic53C2semidirect
15. C53×#1983C2semidirect
17. #16811242C4semidirect
70. #13133217C2×C4semidirect
80. Q8×Dic53C2×C4semidirect
82. D4×Dic53C2×C4semidirect
128. #124×C53C2×C4semidirect
355. #1983D53semidirect
419. C53#21397semidirect
436. #124C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168112422
C2×#168106832
#202770692
#202756662
#202756632
#202756482
#202750342
#202750292
#202750242
#202750192
#202745472
#202745422
#103×Dic532
#102×Dic532
C53×#19832
#2139753