Finite Group Databasebeta

← #27406681

Subgroups — #27406681

Order 13568.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810852C211yesmaximal, characteristic
2C2×#16810710C211yesmaximal, characteristic, complemented
3#20277731C211yesmaximal, characteristic
4#20277720C211yesmaximal, characteristic, complemented
5#20275567C211yesmaximal, characteristic, complemented
6#20275441C211yesmaximal, characteristic, complemented
7#20275348C211yesmaximal, characteristic, complemented
8#20275341C211yesmaximal, characteristic, complemented
9#20275032C211yesmaximal, characteristic
10#20275022C211yesmaximal, characteristic, complemented
11#20274980C211yesmaximal, characteristic, complemented
12#20274973C211yesmaximal, characteristic, complemented
13#106×Dic53C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic53C211yesmaximal, characteristic, complemented
15C22×#106×C53C211yesmaximal, characteristic, complemented
16C22×#11719913C2211yescharacteristic
17C2×#13133196C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×#13133182C2211yescharacteristic
20C2×#13133179C2211yescharacteristic
21C2×C4×C22⋊D53—21no—
22#16810852C418yescomplemented
23#16810710—24no—
24C2×#13133149C2211yescharacteristic
25C2×#13133142C2211yescharacteristic
26C2×#13133140C2211yescharacteristic
27C2×#13133140C2211yescharacteristic
28C2×#13133139C2211yescharacteristic
29C2×#13133137C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C8×Dic53C2211yescharacteristic
33C2×C8×Dic53C2211yescharacteristic
34#16810528C2211yescharacteristic
35#16810524C2211yescharacteristic
36#16810519C2211yescharacteristic
37#16810519C2211yescharacteristic
38#16810518—21no—
39#16810513—21no—
40#16810504—21no—
41#16810502—21no—
42#16810496—21no—
43#16810494—21no—
44C4⋊C4×Dic53C2211yescharacteristic
45C4⋊C4×Dic53C2211yescharacteristic
46C4×C22⋊Dic53—21no—
47C4×C22⋊Dic53C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C23×C8×C53C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic
57C2×#106×C53—24no—
58C2×#106×C53C2211yescharacteristic
59C2×#106×C53C2211yescharacteristic
60C2×#106×C53C2211yescharacteristic
61C2×#106×C53C2211yescharacteristic
62C22×Dic106C2311yescharacteristic
63C22×D212C2311yescharacteristic
64C22×C22⋊D53—21no—
65C22×C4×D53—21no—
66C2×#11719913—22no—
67C2×#11719913—22no—
68C2×#11719913C2×C414yescomplemented
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71#13133196—22no—
72#13133196C2×C414yescomplemented
73#13133191—22no—
74#13133191C2×C414yes—
75#13133182—22no—
76#13133182—41no—
77#13133179—22no—
78#13133179—41no—
79C4×C22⋊D53—44no—
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×#11719919—21no—
83C2×#11719919—21no—
84C2×#11719919—21no—
85C2×#11719919—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53D411yescharacteristic
88C2×C22⋊Dic53D411yescharacteristic
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×C4×Dic53—21no—
94C2×C4×Dic53—21no—
95C2×C4×Dic53—21no—
96C2×C4×Dic53C2311yescharacteristic
97C2×C4×Dic53C2311yescharacteristic
98#13133149C2×C414yescomplemented
99#13133142C2×C414yescomplemented
100#13133140—22no—
101#13133140—41no—
102#13133139C2×C414yescomplemented
103#13133137—22no—
104#13133137—41no—
105C22⋊#88322—22no—
106C8×Dic53—22no—
107C8×Dic53—22no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114#13133124D411yescharacteristic
115#13133124D411yescharacteristic
116C23×C4×C53—21no—
117C23×C4×C53—21no—
118C23×C4×C53C2311yescharacteristic
119C22×C8×C53—22no—
120C22×C8×C53—22no—
121C22×C8×C53C2×C414yescomplemented
122C22×C8×C53C2311yescharacteristic
123C22×C8×C53C2311yescharacteristic
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53—21no—
126C2×C4⋊C4×C53—22no—
127C2×C4⋊C4×C53—22no—
128C2×C4⋊C4×C53—41no—
129C2×C4⋊C4×C53—41no—
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C4⋊C4×C53C2311yescharacteristic
134#106×C53—22no—
135#106×C53—22no—
136#106×C53—22no—
137#106×C53D414yescomplemented
138C24×C53C2×D411yescharacteristic
139C23×D53—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—42no—
149C22×C4×C53—42no—
150C22×C4×C53—42no—
151C22×C4×C53—42no—
152C22×C4×C53—81no—
153C22×C4×C53—81no—
154C22×C4×C53C22×C412yes—
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53#4112yes—
157C22×C4×C53C2411yescharacteristic
158C2×C22⋊D53—24no—
159C2×C22⋊D53—42no—
160C2×C22⋊D53—42no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53C2×D411yescharacteristic
165C22×Dic53C2×D411yescharacteristic
166C22×Dic53C2×D411yescharacteristic
167C22×Dic53C2×D411yescharacteristic
168C2×D212—21no—
169C2×D212—21no—
170C2×D212—21no—
171C2×D212—21no—
172C2×D212—21no—
173C2×D212C22×C412yes—
174C2×C4×D53—42no—
175C2×C4×D53—42no—
176C2×C4×D53—81no—
177C2×Dic106—21no—
178C2×Dic106—21no—
179C2×Dic106—21no—
180C2×Dic106—21no—
181C2×Dic106—21no—
182C2×Dic106C22×C412yes—
183C2×C8×C53—21no—
184C2×C8×C53—21no—
185C2×C8×C53—28no—
186C2×C8×C53C22×C412yes—
187C2×C8×C53C22×C412yes—
188C2×C8×C53C2×D412yes—
189C2×C8×C53#4112yes—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—42no—
197C4⋊C4×C53—42no—
198C4⋊C4×C53C2×D412yes—
199C4⋊C4×C53C2×D412yes—
200C22⋊Dic53—24no—
201C22⋊Dic53—22no—
202C22⋊Dic53SD1614yescomplemented
203#11719921—24no—
204#11719921—42no—
205#11719921—42no—
206#11719921—81no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53C22×C412yes—
210C4⋊Dic53C22×C412yes—
211#11719919—24no—
212#11719919—42no—
213#11719919—42no—
214#11719919—81no—
215C4×Dic53—21no—
216C4×Dic53—21no—
217C4×Dic53—21no—
218C4×Dic53—21no—
219C4×Dic53—42no—
220C4×Dic53—42no—
221C4×Dic53—81no—
222C2×#88322—21no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228#11719913—28no—
229C23×C53—21no—
230C23×C53—21no—
231C23×C53—21no—
232C23×C53—21no—
233C23×C53C4×D412yes—
234C23×C53C2×SD1612yes—
235C23×C53#13512yes—
236C23×C53C22×D411yescharacteristic
237C22×D53—22no—
238C22×D53—41no—
239C22×D53—41no—
240C22×D53—41no—
241C22×D53—41no—
242C22×D53—41no—
243C22×D53—41no—
244C2×C4×C53—21no—
245C2×C4×C53—21no—
246C2×C4×C53—22no—
247C2×C4×C53—22no—
248C2×C4×C53—22no—
249C2×C4×C53—22no—
250C2×C4×C53—22no—
251C2×C4×C53—22no—
252C2×C4×C53—41no—
253C2×C4×C53—41no—
254C2×C4×C53—41no—
255C2×C4×C53—41no—
256C2×C4×C53—41no—
257C2×C4×C53—41no—
258C2×C4×C53—41no—
259C2×C4×C53—41no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—84no—
263C2×C4×C53—84no—
264C2×C4×C53C4×D412yes—
265C2×C4×C53C23×C411yescharacteristic
266C2×C4×C53C22×D411yescharacteristic
267C2×C4×C53C2×#4111yescharacteristic
268C2×C4×C53C2×#4111yescharacteristic
269C2×C4×C53H(5,𝔽2)11yescharacteristic
270C2×C4×C532−1+411yescharacteristic
271C22⋊D53—48no—
272C2×Dic53—21no—
273C2×Dic53—21no—
274C2×Dic53—21no—
275C2×Dic53—21no—
276C2×Dic53—22no—
277C2×Dic53—22no—
278C2×Dic53—22no—
279C2×Dic53—21no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53C2×SD1612yes—
292C2×Dic53C2×SD1612yes—
293D212—22no—
294D212—22no—
295D212—41no—
296D212—41no—
297C4×D53—84no—
298Dic106—22no—
299Dic106—22no—
300Dic106—41no—
301Dic106—41no—
302C8×C53—22no—
303C8×C53C4×D414yescomplemented
304#88322—41no—
305#88322—41no—
306#23022—531nomaximal, Sylow
307C22×C53—22no—
308C22×C53—22no—
309C22×C53—22no—
310C22×C53—22no—
311C22×C53—22no—
312C22×C53—22no—
313C22×C53C4×SD1614yescomplemented
314C22×C53C2×C4×D411yescharacteristic
315C22×C53D4211yescharacteristic
316C22×C53#54711yescharacteristic
317C22×C53C22×SD1611yescharacteristic
318C22×C53C2×#13511yescharacteristic
319C22×C53#57711yescharacteristic
320C22×C53#57711yescharacteristic
321C2×D53—42no—
322C2×D53—42no—
323C2×D53—42no—
324C2×D53—81no—
325C2×D53—81no—
326C2×D53—81no—
327C2×D53—81no—
328C4×C53—22no—
329C4×C53—42no—
330C4×C53—42no—
331C4×C53—81no—
332C4×C53—81no—
333C4×C53C2×C4×D411yescharacteristic
334C4×C53#52011yescharacteristic
335C4×C53#54811yescharacteristic
336C4×C53#55311yescharacteristic
337Dic53—22no—
338Dic53—22no—
339Dic53—41no—
340Dic53—42no—
341Dic53—42no—
342Dic53—42no—
343Dic53—41no—
344C2×#465—531no—
345C2×C4×SD16—531no—
346C22×#106D5311yescharacteristic, complemented
347#2361—531no—
348#2360—531no—
349#1968—531no—
350#1941—531no—
351#1927—531no—
352#1926—531no—
353#1874—531no—
354#1872—531no—
355#1865—531no—
356#1864—531no—
357C4×#106—531no—
358C8×C22⋊C4—531no—
359C2×C53—24no—
360C2×C53#236111yescharacteristic
361C2×C53C2×C4×SD1611yescharacteristic
362C2×C53#295211yescharacteristic
363C2×C53D4×SD1611yescharacteristic
364C2×C53#328211yescharacteristic
365C2×C53#333511yescharacteristic
366C2×C53#333711yescharacteristic
367D53—82no—
368C22×SD16—531no—
369C23×C8C2×D5311yescharacteristic
370C2×C22⋊Q8—531no—
371C2×#121—531no—
372C2×C4×Q8—531no—
373C2×C4×D4—531no—
374C2×C4×D4—1061no—
375C22×C4⋊C4C2×D5311yescharacteristic
376C22×C4⋊C4C2×D5311yescharacteristic
377#465—538no—
378C4×SD16—1064no—
379C2×#106—24no—
380C2×#106—531no—
381C2×#106C2×D5311yescharacteristic
382C2×#106C2×D5311yescharacteristic
383C2×#106C2×D5311yescharacteristic
384C2×#106C2×D5311yescharacteristic
385C2×#103—531no—
386C2×#103—531no—
387C2×#103—531no—
388C2×#102—531no—
389C2×#102—531no—
390C2×#102—531no—
391C2×C22⋊C8—531no—
392C2×C4×C8—531no—
393C2×C4×C8—531no—
394#391—531no—
395#390—531no—
396#389—531no—
397#389—531no—
398#389—1061no—
399#388—1061no—
400#387—1061no—
401#386—1061no—
402#385—1061no—
403#385—1061no—
404C4×C4⋊C4—531no—
405C4×C4⋊C4—531no—
406C4×C22⋊C4—531no—
407C4×C22⋊C4—1061no—
408#340—531no—
409#340—531no—
410#340—531no—
411#340—531no—
412#336—531no—
413#336—531no—
414C53#2302211yescharacteristic, complemented, Sylow
415C22×Q8—531no—
416C22×D4—531no—
417C22×D4—1061no—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—1061no—
421C23×C4C22×D5311yescharacteristic
422C2×SD16—534no—
423C2×SD16—1062no—
424C2×SD16—1062no—
425C22×C8—22no—
426C22×C8—22no—
427C22×C8—531no—
428C22×C8—531no—
429C22×C8C4×D5314yescomplemented
430C22×C8C22×D5311yescharacteristic
431C22×C8C22×D5311yescharacteristic
432C22⋊Q8—534no—
433C22⋊Q8—1062no—
434#121—534no—
435#121—1062no—
436C4×Q8—1062no—
437C4×Q8—2121no—
438C4×D4—1062no—
439C4×D4—2121no—
440C4×D4—2124no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—531no—
448C2×C4⋊C4—531no—
449C2×C4⋊C4—1061no—
450C2×C4⋊C4—1061no—
451C2×C4⋊C4—1061no—
452C2×C4⋊C4—1061no—
453C2×C4⋊C4C22×D5311yescharacteristic
454C2×C4⋊C4C22×D5311yescharacteristic
455C2×C4⋊C4C22×D5311yescharacteristic
456C2×C4⋊C4C22×D5311yescharacteristic
457C2×C22⋊C4—531no—
458C2×C22⋊C4—531no—
459C2×C22⋊C4—1061no—
460C2×C22⋊C4—1061no—
461C2×C22⋊C4—1061no—
462C2×C22⋊C4—1061no—
463C2×C22⋊C4—1061no—
464C2×C42—531no—
465C2×C42—531no—
466C2×C42—1061no—
467C2×C42—1061no—
468C2×C42—1061no—
469#106—22no—
470#106—22no—
471#106—22no—
472#106—534no—
473#106C22⋊D5314yescomplemented
474#103—534no—
475#103—1062no—
476#103—2121no—
477#102—534no—
478#102—1062no—
479#102—2121no—
480C22⋊C8—1062no—
481C4×C8—1062no—
482C4×C8—1062no—
483#95—531no—
484#95—531no—
485#95—1061no—
486#95—1061no—
487#95—1061no—
488#95—1061no—
489#95—1061no—
490#95—1061no—
491C24—1061no—
492C24D4×D5311yescharacteristic
493C2×Q8—532no—
494C2×Q8—1061no—
495C2×Q8—1061no—
496C2×Q8—1061no—
497C2×Q8—1061no—
498C2×Q8—1061no—
499C2×D4—532no—
500C2×D4—1064no—
501C2×D4—1061no—
502C2×D4—1061no—
503C2×D4—1061no—
504C2×D4—1061no—
505C2×D4—1061no—
506C2×D4—2122no—
507C2×D4—2122no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—531no—
525C22×C4—531no—
526C22×C4—1061no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—4241no—
530C22×C4—2122no—
531C22×C4—2122no—
532C22×C4C2×C4×D5312yes—
533C22×C4D4×D5311yescharacteristic
534C22×C4#1171994912yes—
535C22×C4C23×D5311yescharacteristic
536SD16—1068no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—28no—
540C2×C8—1061no—
541C2×C8—1061no—
542C2×C8—1061no—
543C2×C8—1061no—
544C2×C8—1061no—
545C2×C8—1061no—
546C2×C8C2×C4×D5312yes—
547C2×C8C2×C4×D5312yes—
548C2×C8#1171994512yes—
549C2×C8C2×C22⋊D5312yes—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—532no—
559C4⋊C4—532no—
560C4⋊C4—1064no—
561C4⋊C4—1061no—
562C4⋊C4—1061no—
563C4⋊C4—4241no—
564C4⋊C4—2122no—
565C4⋊C4—2122no—
566C4⋊C4C2×C22⋊D5312yes—
567C4⋊C4C2×C22⋊D5312yes—
568C22⋊C4—534no—
569C22⋊C4—1064no—
570C22⋊C4—1062no—
571C22⋊C4—1064no—
572C22⋊C4—4241no—
573C22⋊C4—2122no—
574C22⋊C4—2122no—
575C42—1061no—
576C42—1061no—
577C42—1061no—
578C42—1061no—
579C42—4241no—
580C42—2122no—
581C42—2122no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—1062no—
587C23—2121no—
588C23—2121no—
589C23—2121no—
590C23—2121no—
591C23—2121no—
592C23—2121no—
593C23#1313317912yes—
594C23SD16×D5312yes—
595C23#1313323812yes—
596C23C2×D4×D5311yescharacteristic
597Q8—1062no—
598Q8—1062no—
599Q8—2121no—
600Q8—2121no—
601D4—1062no—
602D4—1062no—
603D4—2128no—
604D4—2121no—
605D4—2121no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—84no—
625C2×C4—84no—
626C2×C4—532no—
627C2×C4—532no—
628C2×C4—1061no—
629C2×C4—1061no—
630C2×C4—1061no—
631C2×C4—1061no—
632C2×C4—1061no—
633C2×C4—1062no—
634C2×C4—1062no—
635C2×C4—1062no—
636C2×C4—1061no—
637C2×C4—1061no—
638C2×C4—1061no—
639C2×C4—1061no—
640C2×C4—1061no—
641C2×C4—4244no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4#1313317912yes—
649C2×C4C22×C4×D5311yescharacteristic
650C2×C4C22×C22⋊D5311yescharacteristic
651C2×C4C2×#1171994511yescharacteristic
652C2×C4C2×#1171994911yescharacteristic
653C2×C4#1313326211yescharacteristic
654C2×C4#1313326511yescharacteristic
655C8—22no—
656C8—2121no—
657C8—2121no—
658C8C4×C22⋊D5314yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—4241no—
666C22—4241no—
667C22—4241no—
668C22—4241no—
669C22—2122no—
670C22—2122no—
671C22—2122no—
672C22#1681071014yescomplemented
673C22C2×#1313317911yescharacteristic
674C22D4×C22⋊D5311yescharacteristic
675C22#1681127411yescharacteristic
676C22C2×SD16×D5311yescharacteristic
677C22C2×#1313323811yescharacteristic
678C22#1681142911yescharacteristic
679C22#1681142911yescharacteristic
680C4—22no—
681C4—42no—
682C4—42no—
683C4—81no—
684C4—81no—
685C4—1062no—
686C4—1062no—
687C4—2122no—
688C4—2121no—
689C4—2122no—
690C4—2121no—
691C4—2122no—
692C4C2×C4×C22⋊D5311yescharacteristic
693C4#1681110411yescharacteristic
694C4#1681128411yescharacteristic
695C4#1681132111yescharacteristic
696C2—24no—
697C2—4242no—
698C2#2027773111yescharacteristic
699C2C2×#1681071011yescharacteristic
700C2#2028359811yescharacteristic
701C2SD16×C22⋊D5311yescharacteristic
702C2#2028642211yescharacteristic
703C2#2028706811yescharacteristic
704C2#2028709011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC22×#106×C53C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
cosocleC22×C4×C53C24
hypercenterC22×#106D53
hypocenterC53#23022
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#16810710C2semidirect
4. #20277720C2semidirect
5. #20275567C2semidirect
6. #20275441C2semidirect
7. #20275348C2semidirect
8. #20275341C2semidirect
10. #20275022C2semidirect
11. #20274980C2semidirect
12. #20274973C2semidirect
13. #106×Dic53C2semidirect
14. C8×C22⋊Dic53C2semidirect
15. C22×#106×C53C2semidirect
22. #16810852C4semidirect
68. C2×#11719913C2×C4semidirect
72. #13133196C2×C4semidirect
98. #13133149C2×C4semidirect
99. #13133142C2×C4semidirect
102. #13133139C2×C4semidirect
121. C22×C8×C53C2×C4semidirect
137. #106×C53D4semidirect
202. C22⋊Dic53SD16semidirect
303. C8×C53C4×D4semidirect
313. C22×C53C4×SD16semidirect
346. C22×#106D53semidirect
414. C53#23022semidirect
429. C22×C8C4×D53semidirect
473. #106C22⋊D53semidirect
658. C8C4×C22⋊D53semidirect
672. C22#16810710semidirect

Maximal subgroups

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

subgroupindex
C2×#168108522
C2×#168107102
#202777312
#202777202
#202755672
#202754412
#202753482
#202753412
#202750322
#202750222
#202749802
#202749732
#106×Dic532
C8×C22⋊Dic532
C22×#106×C532
#2302253