Finite Group Databasebeta

← #27427907

Subgroups — #27427907

Order 13568.

1016 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810762C211yesmaximal, characteristic
2C2×C4×#11719924C211yesmaximal, characteristic, complemented
3#20278229C211yesmaximal, characteristic
4#20276258C211yesmaximal, characteristic, complemented
5#20276152C211yesmaximal, characteristic, complemented
6#20276030C211yesmaximal, characteristic, complemented
7#20275904C211yesmaximal, characteristic
8#20275394C211yesmaximal, characteristic, complemented
9#20275323C211yesmaximal, characteristic, complemented
10#20275070C211yesmaximal, characteristic, complemented
11#20275052C211yesmaximal, characteristic, complemented
12#20274983C211yesmaximal, characteristic, complemented
13#20274720C211yesmaximal, characteristic, complemented
14#20274650C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C53C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719924C2211yescharacteristic
18C2×#13133199—21no—
19C2×#13133191C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21#16810762—24no—
22C4×#11719924—24no—
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×C4⋊#88322C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133141C2211yescharacteristic
31C2×#13133141C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×C4×#88322C2211yescharacteristic
37#16810550—21no—
38#16810539—21no—
39#16810525C2211yescharacteristic
40#16810521C2211yescharacteristic
41#16810497—21no—
42#16810493C2211yescharacteristic
43#16810483C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C23×Q8×C53C2211yescharacteristic
51C2×C4×Q8×C53C2211yescharacteristic
52C2×C4×Q8×C53C2211yescharacteristic
53C53×#391—21no—
54C53×#391—21no—
55C53×#391C2211yescharacteristic
56C53×#391C2211yescharacteristic
57C53×#380—21no—
58C53×#380C2211yescharacteristic
59C4×C22⋊C4×C53—21no—
60C4×C22⋊C4×C53C2211yescharacteristic
61C22×D212C2311yescharacteristic
62C22×C22⋊D53—21no—
63C22×C4×D53—21no—
64C2×#11719924—22no—
65C2×#11719924—22no—
66C2×#11719924—22no—
67C2×#11719924—22no—
68C2×#11719924—41no—
69C2×#11719924D414yes—
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74#13133199—44no—
75#13133191—22no—
76#13133191—41no—
77C4×D212—22no—
78C4×D212—41no—
79C2×C4⋊Dic53—21no—
80C2×C4⋊Dic53—21no—
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×#11719919—21no—
85C2×C22⋊Dic53—21no—
86C2×#11719921—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90#13133148—22no—
91#13133148—41no—
92C4⋊#88322—41no—
93#13133141—22no—
94#13133141—22no—
95#13133141—22no—
96#13133141—22no—
97#13133141—22no—
98#13133141—41no—
99#13133137—22no—
100#13133137—41no—
101C22⋊#88322—22no—
102C22⋊#88322—41no—
103C4×#88322—22no—
104#13133124—21no—
105#13133124—21no—
106C22×Q8×C53—22no—
107C22×Q8×C53—22no—
108C22×Q8×C53—21no—
109C22×Q8×C53—22no—
110C22×Q8×C53—22no—
111C22×Q8×C53—41no—
112C22×Q8×C53—41no—
113C22×Q8×C53C2311yescharacteristic
114C22×Q8×C53C2311yescharacteristic
115C23×C4×C53—21no—
116C23×C4×C53C2311yescharacteristic
117C4×Q8×C53—22no—
118C4×Q8×C53—22no—
119C4×Q8×C53—41no—
120C4×Q8×C53—41no—
121C2×C4⋊C4×C53—21no—
122C2×C4⋊C4×C53—21no—
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53D411yescharacteristic
127C2×C22⋊C4×C53D411yescharacteristic
128C2×C42×C53—21no—
129C2×C42×C53—21no—
130C2×C42×C53C2311yescharacteristic
131C2×C42×C53C2311yescharacteristic
132#95×C53—21no—
133#95×C53—21no—
134#95×C53—21no—
135#95×C53—21no—
136#95×C53—21no—
137#95×C53D411yescharacteristic
138#95×C53D411yescharacteristic
139C24×C53C2×D411yescharacteristic
140C23×D53—21no—
141C2×Q8×C53—24no—
142C2×Q8×C53—21no—
143C2×Q8×C53—21no—
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53—42no—
151C2×Q8×C53—42no—
152C2×Q8×C53—44no—
153C2×Q8×C53—44no—
154C2×Q8×C53—44no—
155C2×Q8×C53—44no—
156C2×Q8×C53C2×D412yes—
157C2×Q8×C53#4112yes—
158C2×Q8×C53#4112yes—
159C2×Q8×C53#4112yes—
160C22×C4×C53—21no—
161C22×C4×C53—24no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—42no—
172C22×C4×C53—42no—
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2411yescharacteristic
179C2×C22⋊D53—42no—
180C2×C22⋊D53—42no—
181C2×C22⋊D53—81no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C2×D212—21no—
186C2×D212—21no—
187C2×D212—21no—
188C2×D212—21no—
189C2×D212—21no—
190C2×D212C2×D412yes—
191C2×C4×D53—42no—
192C2×C4×D53—42no—
193C2×C4×D53—81no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—42no—
199C4⋊C4×C53—42no—
200C22⋊C4×C53—41no—
201C22⋊C4×C53—42no—
202C22⋊C4×C53SD1614yescomplemented
203C42×C53—21no—
204C42×C53—21no—
205C42×C53—21no—
206C42×C53—21no—
207C42×C53—42no—
208C42×C53—42no—
209C22⋊Dic53—42no—
210#11719924—28no—
211#11719924—44no—
212#11719921—42no—
213#11719921—42no—
214#11719921—42no—
215#11719921—42no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—42no—
223C4⋊Dic53—81no—
224#11719919—42no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322C2×D412yes—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53C2×SD1612yes—
244C23×C53C22×D411yescharacteristic
245C22×D53—22no—
246C22×D53—41no—
247C22×D53—41no—
248C22×D53—41no—
249C22×D53—41no—
250C22×D53—41no—
251C22×D53—41no—
252Q8×C53—22no—
253Q8×C53—22no—
254Q8×C53—22no—
255Q8×C53—22no—
256Q8×C53—22no—
257Q8×C53—48no—
258Q8×C53—41no—
259Q8×C53—41no—
260Q8×C53#12314yescomplemented
261C2×C4×C53—22no—
262C2×C4×C53—21no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—22no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—48no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53C2×SD1612yes—
292C2×C4×C53C2×SD1612yes—
293C2×C4×C53C22×D411yescharacteristic
294C2×C4×C53C2×#4111yescharacteristic
295C2×C4×C53C2×#4111yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53H(5,𝔽2)11yescharacteristic
298C2×C4×C53H(5,𝔽2)11yescharacteristic
299C22⋊D53—84no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309D212—22no—
310D212—22no—
311D212—41no—
312D212—41no—
313C4×D53—84no—
314#88322—22no—
315#88322—41no—
316#88322—41no—
317#88322—41no—
318#24898—531nomaximal, Sylow
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53—41no—
326C22×C53#52511yescharacteristic
327C22×C53D4211yescharacteristic
328C22×C53#54611yescharacteristic
329C22×C53C22×SD1611yescharacteristic
330C22×C53#57511yescharacteristic
331C22×C53#57711yescharacteristic
332C22×C53#57811yescharacteristic
333C2×D53—42no—
334C2×D53—42no—
335C2×D53—42no—
336C2×D53—81no—
337C2×D53—81no—
338C2×D53—81no—
339C2×D53—81no—
340C4×C53—24no—
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—41no—
344C4×C53—42no—
345C4×C53—41no—
346C4×C53—41no—
347C4×C53—81no—
348C4×C53—81no—
349C4×C53C2×#12311yescharacteristic
350C4×C53#53811yescharacteristic
351C4×C53#54611yescharacteristic
352C4×C53#55111yescharacteristic
353Dic53—81no—
354Dic53—81no—
355Dic53—81no—
356C2×#448—531no—
357C2×C4×SD16—531no—
358#2422—531no—
359Q8×C22⋊C4D5311yescharacteristic, complemented
360#2096—531no—
361#2077—531no—
362#2055—531no—
363#2034—531no—
364#1933—531no—
365#1923—531no—
366#1880—531no—
367#1877—531no—
368#1865—531no—
369#1803—531no—
370#1787—531no—
371C2×C53—42no—
372C2×C53#241811yescharacteristic
373C2×C53#310311yescharacteristic
374C2×C53#312111yescharacteristic
375C2×C53#326911yescharacteristic
376C2×C53D4×SD1611yescharacteristic
377C2×C53#329811yescharacteristic
378C2×C53#332611yescharacteristic
379D53—82no—
380C23×Q8C2×D5311yescharacteristic
381C22×SD16—531no—
382C22×SD16—531no—
383C2×#123—1061no—
384C2×#121—531no—
385C2×C4×Q8C2×D5311yescharacteristic
386C2×C4×Q8C2×D5311yescharacteristic
387C2×C4×D4—531no—
388#448—1064no—
389C4×SD16—1064no—
390C2×#106—531no—
391C2×#106—531no—
392C2×C4⋊C8—531no—
393C2×#103—531no—
394C2×#103—531no—
395C2×#103—531no—
396C2×#103—531no—
397C2×#103—531no—
398C2×#103—531no—
399C2×#102—531no—
400C2×#102—531no—
401C2×C22⋊C8—531no—
402C2×C22⋊C8—531no—
403C2×C4×C8—531no—
404#397—1061no—
405#394—1061no—
406#391—21no—
407#391—21no—
408#391C2×D5311yescharacteristic
409#391C2×D5311yescharacteristic
410#390—531no—
411#389—531no—
412#385—1061no—
413#384—531no—
414#380—21no—
415#380—531no—
416#380C2×D5311yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4C2×D5311yescharacteristic
419#340—531no—
420#340—531no—
421#340—531no—
422#340—531no—
423#336—531no—
424#336—531no—
425C53#2489811yescharacteristic, complemented, Sylow
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—21no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—41no—
432C22×Q8—41no—
433C22×Q8C22×D5311yescharacteristic
434C22×Q8C22×D5311yescharacteristic
435C22×D4—531no—
436C22×D4—1061no—
437C23×C4—21no—
438C23×C4—1061no—
439C23×C4C22×D5311yescharacteristic
440C2×SD16—534no—
441C2×SD16—1062no—
442C2×SD16—1062no—
443C2×SD16—1062no—
444C2×SD16—1062no—
445C2×SD16—2121no—
446C22×C8—531no—
447C22×C8—531no—
448C22×C8—531no—
449C22×C8—531no—
450#123—2124no—
451#121—1062no—
452#121—2121no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—41no—
456C4×Q8—41no—
457C4×D4—1062no—
458C4×D4—2121no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—1061no—
465C2×C4⋊C4—1061no—
466C2×C4⋊C4—1061no—
467C2×C4⋊C4C22×D5311yescharacteristic
468C2×C4⋊C4C22×D5311yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1061no—
471C2×C22⋊C4—1061no—
472C2×C22⋊C4—1061no—
473C2×C22⋊C4—1061no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4C22⋊D5311yescharacteristic
476C2×C22⋊C4C22⋊D5311yescharacteristic
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C22×D5311yescharacteristic
480C2×C42C22×D5311yescharacteristic
481#106—1062no—
482#106—2121no—
483C4⋊C8—2121no—
484#103—1062no—
485#103—1062no—
486#103—1062no—
487#103—1062no—
488#103—1062no—
489#103—2121no—
490#102—1062no—
491#102—2121no—
492C22⋊C8—1062no—
493C22⋊C8—2121no—
494C4×C8—1062no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—1061no—
501#95—1061no—
502#95C22⋊D5311yescharacteristic
503#95C22⋊D5311yescharacteristic
504C24—1061no—
505C24C2×C22⋊D5311yescharacteristic
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8#1171994512yes—
522C2×Q8#1171994512yes—
523C2×Q8D4×D5312yes—
524C2×Q8#1171994712yes—
525C2×D4—532no—
526C2×D4—1061no—
527C2×D4—1061no—
528C2×D4—1061no—
529C2×D4—1061no—
530C2×D4—1061no—
531C2×D4—4241no—
532C2×D4—2122no—
533C2×D4—2122no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1061no—
550C22×C4—4241no—
551C22×C4—2122no—
552C22×C4—2122no—
553C22×C4C2×C22⋊D5311yescharacteristic
554C22×C4C2×C22⋊D5311yescharacteristic
555C22×C4C2×C22⋊D5311yescharacteristic
556C22×C4C2×C22⋊D5311yescharacteristic
557C22×C4C2×C22⋊D5311yescharacteristic
558C22×C4C23×D5311yescharacteristic
559SD16—1068no—
560SD16—2124no—
561C2×C8—532no—
562C2×C8—1061no—
563C2×C8—1061no—
564C2×C8—1061no—
565C2×C8—1061no—
566C2×C8—1061no—
567C2×C8—1061no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—1061no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—1061no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—1061no—
584C4⋊C4—1061no—
585C4⋊C4—4241no—
586C4⋊C4—2122no—
587C4⋊C4—2122no—
588C22⋊C4—41no—
589C22⋊C4—42no—
590C22⋊C4—2122no—
591C22⋊C4—2122no—
592C22⋊C4—2122no—
593C22⋊C4—2122no—
594C22⋊C4—2122no—
595C22⋊C4#1171992414yescomplemented
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—42no—
601C42—42no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—1062no—
609C23—2121no—
610C23—2121no—
611C23—2121no—
612C23—2121no—
613C23—2121no—
614C23—2121no—
615C23C2×#1171992412yes—
616C23C22×C22⋊D5311yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—48no—
623Q8—41no—
624Q8—41no—
625Q8#1313319914yescomplemented
626D4—1062no—
627D4—1062no—
628D4—4244no—
629D4—2121no—
630D4—2121no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—48no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—4244no—
662C2×C4—2121no—
663C2×C4—2121no—
664C2×C4—2121no—
665C2×C4—2121no—
666C2×C4—2121no—
667C2×C4—2121no—
668C2×C4—2121no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4C2×#1171992412yes—
672C2×C4C2×#1171992412yes—
673C2×C4C2×D4×D5311yescharacteristic
674C2×C4C2×#1171994711yescharacteristic
675C2×C4C2×#1171994511yescharacteristic
676C2×C4C2×#1171994511yescharacteristic
677C2×C4#1313326211yescharacteristic
678C2×C4#1313326211yescharacteristic
679C8—1062no—
680C8—2121no—
681C8—2121no—
682C8—2121no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—4241no—
691C22—4241no—
692C22—4241no—
693C22—4241no—
694C22—2122no—
695C22—2122no—
696C22—2122no—
697C22#1681113411yescharacteristic
698C22D4×C22⋊D5311yescharacteristic
699C22#1681126711yescharacteristic
700C22C22×#1171992411yescharacteristic
701C22#1681142111yescharacteristic
702C22#1681143111yescharacteristic
703C22#1681143811yescharacteristic
704C4—22no—
705C4—24no—
706C4—22no—
707C4—41no—
708C4—41no—
709C4—42no—
710C4—41no—
711C4—81no—
712C4—81no—
713C4—4241no—
714C4—4241no—
715C4—4241no—
716C4C2×#1313319911yescharacteristic
717C4#1681121111yescharacteristic
718C4#1681126311yescharacteristic
719C4#1681129911yescharacteristic
720C2—42no—
721C2—4242no—
722C2#2027817711yescharacteristic
723C2#2028474611yescharacteristic
724C2#2028494411yescharacteristic
725C2#2028627111yescharacteristic
726C2D4×#1171992411yescharacteristic
727C2#2028658011yescharacteristic
728C2#2028696811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingQ8×C22⋊C4×C53C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
hypercenterQ8×C22⋊C4D53
hypocenterC53#24898
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719924C2semidirect
4. #20276258C2semidirect
5. #20276152C2semidirect
6. #20276030C2semidirect
8. #20275394C2semidirect
9. #20275323C2semidirect
10. #20275070C2semidirect
11. #20275052C2semidirect
12. #20274983C2semidirect
13. #20274720C2semidirect
14. #20274650C2semidirect
15. Q8×C22⋊C4×C53C2semidirect
202. C22⋊C4×C53SD16semidirect
260. Q8×C53#123semidirect
359. Q8×C22⋊C4D53semidirect
425. C53#24898semidirect
595. C22⋊C4#11719924semidirect
625. Q8#13133199semidirect

Maximal subgroups

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

subgroupindex
C2×#168107622
C2×C4×#117199242
#202782292
#202762582
#202761522
#202760302
#202759042
#202753942
#202753232
#202750702
#202750522
#202749832
#202747202
#202746502
Q8×C22⋊C4×C532
#2489853