Finite Group Databasebeta

← #27432241

Subgroups — #27432241

Order 13568.

1024 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810936C211yesmaximal, characteristic, complemented
2C2×#16810857C211yesmaximal, characteristic
3#20277729C211yesmaximal, characteristic, complemented
4#20276187C211yesmaximal, characteristic, complemented
5#20276119C211yesmaximal, characteristic, complemented
6#20276103C211yesmaximal, characteristic, complemented
7#20276025C211yesmaximal, characteristic, complemented
8#20275471C211yesmaximal, characteristic, complemented
9#20275332C211yesmaximal, characteristic, complemented
10#20275066C211yesmaximal, characteristic, complemented
11#20275033C211yesmaximal, characteristic, complemented
12#20274895C211yesmaximal, characteristic, complemented
13#20274712C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C53×#2501C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20C2×#13133177—21no—
21C22×C4⋊Dic53C2211yescharacteristic
22#16810936—24no—
23#16810857—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133150C2211yescharacteristic
26C2×#13133150C2211yescharacteristic
27C2×C4⋊#88322C2211yescharacteristic
28C2×C4⋊#88322C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36#16810525C2211yescharacteristic
37#16810521C2211yescharacteristic
38#16810515—21no—
39#16810500—21no—
40#16810497—21no—
41C4×C4⋊Dic53C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C2×#123×C53—21no—
51C2×#123×C53—21no—
52C2×#121×C53C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C53×#399—21no—
55C53×#399—21no—
56C53×#390C2211yescharacteristic
57C53×#390C2211yescharacteristic
58C53×#384C2211yescharacteristic
59C53×#384C2211yescharacteristic
60C4×C22⋊C4×C53C2211yescharacteristic
61C22×D212C2311yescharacteristic
62C22×C22⋊D53—21no—
63C23×Dic53—21no—
64C22×C4×D53—21no—
65C2×#11719922—22no—
66C2×#11719922—22no—
67C2×#11719922—41no—
68C22×#88322—22no—
69C22×#88322—22no—
70C22×#88322—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133191—22no—
76#13133191D414yes—
77C4×D212—22no—
78C4×D212—41no—
79#13133177—44no—
80C2×C4⋊Dic53—21no—
81C2×C4⋊Dic53—22no—
82C2×C4⋊Dic53—41no—
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×#11719919—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×C4×Dic53—21no—
92#13133150—22no—
93#13133150—22no—
94#13133150—22no—
95C4⋊#88322—22no—
96C4⋊#88322—41no—
97#13133138—22no—
98#13133138—22no—
99#13133138—41no—
100#13133137—22no—
101#13133137—22no—
102#13133137—22no—
103C22⋊#88322—22no—
104#13133124—21no—
105#13133124—21no—
106C22×D4×C53—21no—
107C22×D4×C53C2311yescharacteristic
108C23×C4×C53—21no—
109C23×C4×C53C2311yescharacteristic
110#123×C53—44no—
111#123×C53—44no—
112#121×C53—22no—
113#121×C53—22no—
114C2×C4⋊C4×C53—21no—
115C2×C4⋊C4×C53—21no—
116C2×C4⋊C4×C53—21no—
117C2×C4⋊C4×C53—21no—
118C2×C4⋊C4×C53—21no—
119C2×C4⋊C4×C53—22no—
120C2×C4⋊C4×C53—22no—
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53D411yescharacteristic
130C2×C22⋊C4×C53D411yescharacteristic
131C2×C42×C53C2311yescharacteristic
132C2×C42×C53C2311yescharacteristic
133#95×C53D411yescharacteristic
134#95×C53D411yescharacteristic
135C24×C53—21no—
136C24×C53C2×D411yescharacteristic
137C23×D53—21no—
138C2×D4×C53—21no—
139C2×D4×C53—21no—
140C2×D4×C53—21no—
141C2×D4×C53—21no—
142C2×D4×C53—21no—
143C2×D4×C53—21no—
144C2×D4×C53—42no—
145C2×D4×C53—42no—
146C2×D4×C53—42no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—42no—
155C22×C4×C53—42no—
156C22×C4×C53—42no—
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53C2×D411yescharacteristic
163C22×C4×C53#4112yes—
164C22×C4×C53C2411yescharacteristic
165C2×C22⋊D53—24no—
166C2×C22⋊D53—42no—
167C2×C22⋊D53—42no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—42no—
172C22×Dic53—42no—
173C22×Dic53—81no—
174C2×D212—21no—
175C2×D212—21no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212C2×D412yes—
180C2×C4×D53—42no—
181C2×C4×D53—42no—
182C2×C4×D53—81no—
183C4⋊C4×C53—21no—
184C4⋊C4×C53—21no—
185C4⋊C4×C53—21no—
186C4⋊C4×C53—21no—
187C4⋊C4×C53—21no—
188C4⋊C4×C53—21no—
189C4⋊C4×C53—42no—
190C4⋊C4×C53—42no—
191C4⋊C4×C53—42no—
192C4⋊C4×C53—42no—
193C4⋊C4×C53—42no—
194C22⋊C4×C53—22no—
195C22⋊C4×C53—42no—
196C22⋊C4×C53—42no—
197C22⋊C4×C53—42no—
198C22⋊C4×C53—42no—
199C22⋊C4×C53—42no—
200C22⋊C4×C53D814yescomplemented
201C42×C53—21no—
202C42×C53—21no—
203C42×C53—21no—
204C42×C53—21no—
205#11719922—44no—
206#11719921—24no—
207#11719921—42no—
208#11719921—42no—
209#11719921—81no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—42no—
215C4⋊Dic53C2×D412yes—
216C4⋊Dic53#4112yes—
217#11719919—42no—
218C4×Dic53—42no—
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×#88322—21no—
229C2×#88322—21no—
230C2×#88322—44no—
231C2×#88322#4112yes—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53#12112yes—
244C23×C53C2×D812yes—
245C23×C53AGL(1,ℤ/8)12yes—
246C23×C53C22×D411yescharacteristic
247C22×D53—22no—
248C22×D53—41no—
249C22×D53—41no—
250C22×D53—41no—
251C22×D53—41no—
252C22×D53—41no—
253C22×D53—41no—
254D4×C53—41no—
255D4×C53—41no—
256D4×C53—41no—
257D4×C53—41no—
258D4×C53—84no—
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—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
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—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×C53C2×D812yes—
287C2×C4×C53C2×D812yes—
288C2×C4×C53C22×D411yescharacteristic
289C2×C4×C53C2×#4111yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53C2×#4111yescharacteristic
292C2×C4×C53H(5,𝔽2)11yescharacteristic
293C2×C4×C532−1+411yescharacteristic
294C22⋊D53—48no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—84no—
305D212—22no—
306D212—22no—
307D212—41no—
308D212—41no—
309C4×D53—84no—
310#88322—22no—
311#88322—41no—
312#88322—41no—
313#88322—41no—
314#25200—531nomaximal, Sylow
315C22×C53—22no—
316C22×C53—22no—
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—81no—
322C22×C53—81no—
323C22×C53—81no—
324C22×C53—81no—
325C22×C53—81no—
326C22×C53—81no—
327C22×C53—81no—
328C22×C53#45914yes—
329C22×C53C2×#12111yescharacteristic
330C22×C53#54611yescharacteristic
331C22×C53#54711yescharacteristic
332C22×C53C22×D811yescharacteristic
333C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C53#57711yescharacteristic
335C22×C53#57811yescharacteristic
336C2×D53—42no—
337C2×D53—42no—
338C2×D53—42no—
339C2×D53—81no—
340C2×D53—81no—
341C2×D53—81no—
342C2×D53—81no—
343C4×C53—22no—
344C4×C53—22no—
345C4×C53—22no—
346C4×C53—41no—
347C4×C53—41no—
348C4×C53—81no—
349C4×C53—81no—
350C4×C53—81no—
351C4×C53#52911yescharacteristic
352C4×C53#53911yescharacteristic
353C4×C53#54611yescharacteristic
354C4×C53#54711yescharacteristic
355Dic53—42no—
356Dic53—42no—
357Dic53—81no—
358C2×#480—531no—
359C2×#466—531no—
360#2501D5311yescharacteristic, complemented
361#2361—531no—
362#2083—531no—
363#2071—531no—
364#2067—531no—
365#2054—531no—
366#1947—531no—
367#1925—531no—
368#1879—531no—
369#1874—531no—
370#1850—531no—
371#1802—531no—
372C2×#340—531no—
373C2×C53—24no—
374C2×C53—161no—
375C2×C53#242511yescharacteristic
376C2×C53C2×#45911yescharacteristic
377C2×C53#304611yescharacteristic
378C2×C53#329411yescharacteristic
379C2×C53#330811yescharacteristic
380C2×C53#333411yescharacteristic
381C2×C53#334511yescharacteristic
382D53—82no—
383C22×D8—531no—
384C23×C8—531no—
385C2×#123—21no—
386C2×#123—21no—
387C2×#121—531no—
388C2×#121C2×D5311yescharacteristic
389C2×C4×D4—531no—
390C2×C4×D4—1061no—
391C22×C4⋊C4—531no—
392C22×C4⋊C4C2×D5311yescharacteristic
393#480—1064no—
394#466—1064no—
395C2×#107—531no—
396C2×#107—531no—
397C2×#107—531no—
398C2×C4⋊C8—531no—
399C2×C4⋊C8—531no—
400C2×#102—531no—
401C2×#102—531no—
402C2×#102—531no—
403C2×#102—531no—
404C2×#102—531no—
405C2×#102—531no—
406C2×C22⋊C8—531no—
407#399—21no—
408#399—21no—
409#390—531no—
410#390C2×D5311yescharacteristic
411#390C2×D5311yescharacteristic
412#389—531no—
413#388—1061no—
414#386—1061no—
415#385—1061no—
416#384C2×D5311yescharacteristic
417#384C2×D5311yescharacteristic
418C4×C4⋊C4—531no—
419C4×C22⋊C4C2×D5311yescharacteristic
420#340—531no—
421#340—531no—
422#340—531no—
423#340—531no—
424#340—531no—
425#340—531no—
426#336—531no—
427#336—531no—
428C53#2520011yescharacteristic, complemented, Sylow
429C22×D4—21no—
430C22×D4—531no—
431C22×D4—1061no—
432C22×D4C22×D5311yescharacteristic
433C23×C4—21no—
434C23×C4—1061no—
435C23×C4—1061no—
436C23×C4C22×D5311yescharacteristic
437C2×D8—1062no—
438C2×D8—1062no—
439C2×D8—2121no—
440C22×C8—531no—
441C22×C8—531no—
442C22×C8—531no—
443C22×C8—531no—
444C22×C8—1062no—
445C22×C8—1062no—
446C22×C8—2121no—
447#123—44no—
448#123—44no—
449#121—22no—
450#121—22no—
451#121—534no—
452#121—1062no—
453C4×D4—1062no—
454C4×D4—2121no—
455C4×D4—2124no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—1062no—
467C2×C4⋊C4—1061no—
468C2×C4⋊C4—1061no—
469C2×C4⋊C4—2121no—
470C2×C4⋊C4C22×D5311yescharacteristic
471C2×C4⋊C4C22×D5311yescharacteristic
472C2×C4⋊C4C22×D5311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1061no—
479C2×C22⋊C4—1061no—
480C2×C22⋊C4—1061no—
481C2×C22⋊C4—1061no—
482C2×C22⋊C4C22⋊D5311yescharacteristic
483C2×C22⋊C4C22⋊D5311yescharacteristic
484C2×C42—1061no—
485C2×C42C22×D5311yescharacteristic
486C2×C42C22×D5311yescharacteristic
487#107—1062no—
488#107—1062no—
489#107—1062no—
490C4⋊C8—1062no—
491C4⋊C8—2121no—
492#102—1062no—
493#102—1062no—
494#102—1062no—
495#102—1062no—
496#102—1062no—
497#102—2121no—
498C22⋊C8—1062no—
499#95—1061no—
500#95—1061no—
501#95C22⋊D5311yescharacteristic
502#95C22⋊D5311yescharacteristic
503C24—21no—
504C24—1061no—
505C24C2×C22⋊D5311yescharacteristic
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—532no—
516C2×D4—1064no—
517C2×D4—1061no—
518C2×D4—1061no—
519C2×D4—1061no—
520C2×D4—1061no—
521C2×D4—1061no—
522C2×D4—2122no—
523C2×D4—2122no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—4241no—
538C22×C4—4241no—
539C22×C4—2122no—
540C22×C4—2122no—
541C22×C4—2122no—
542C22×C4—2122no—
543C22×C4D4×D5312yes—
544C22×C4#1171994712yes—
545C22×C4C2×C22⋊D5311yescharacteristic
546C22×C4C2×C22⋊D5311yescharacteristic
547C22×C4C2×C22⋊D5311yescharacteristic
548C22×C4C2×C22⋊D5311yescharacteristic
549C22×C4C2×C22⋊D5311yescharacteristic
550C22×C4C23×D5311yescharacteristic
551D8—2124no—
552C2×C8—532no—
553C2×C8—1061no—
554C2×C8—1061no—
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—2124no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—532no—
577C4⋊C4—532no—
578C4⋊C4—1061no—
579C4⋊C4—1061no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—2122no—
583C4⋊C4—2122no—
584C22⋊C4—22no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—1064no—
591C22⋊C4—4241no—
592C22⋊C4—2122no—
593C22⋊C4—2122no—
594C22⋊C4#1171992214yescomplemented
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—2122no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—1062no—
612C23—2121no—
613C23—2121no—
614C23—2121no—
615C23—2121no—
616C23—2121no—
617C23—2121no—
618C23#1313318812yes—
619C23C2×#1171992212yes—
620C23#1313324312yes—
621C23C22×C22⋊D5311yescharacteristic
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—84no—
627D4—1062no—
628D4—1062no—
629D4—2128no—
630D4—2121no—
631D4—2121no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
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—41no—
657C2×C4—84no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—4244no—
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#1313318812yes—
670C2×C4C2×#1171992212yes—
671C2×C4C2×#1171992212yes—
672C2×C4C2×D4×D5311yescharacteristic
673C2×C4#41×D5311yescharacteristic
674C2×C4#41×D5311yescharacteristic
675C2×C4C2×#1171994711yescharacteristic
676C2×C4#1313326311yescharacteristic
677C2×C4#1313326411yescharacteristic
678C8—1062no—
679C8—2121no—
680C8—2121no—
681C8—2121no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—4241no—
696C22—4241no—
697C22—4241no—
698C22—4241no—
699C22—2122no—
700C22—2122no—
701C22—2122no—
702C22#1681081514yes—
703C22C2×#1313318811yescharacteristic
704C22#1681126111yescharacteristic
705C22#1681127211yescharacteristic
706C22C22×#1171992211yescharacteristic
707C22C2×#1313324311yescharacteristic
708C22#1681143111yescharacteristic
709C22#1681143811yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—41no—
714C4—41no—
715C4—81no—
716C4—81no—
717C4—81no—
718C4—4241no—
719C4—2122no—
720C4—2122no—
721C4#1681115011yescharacteristic
722C4#1681121711yescharacteristic
723C4#1681126511yescharacteristic
724C4#1681127111yescharacteristic
725C2—24no—
726C2—161no—
727C2—4242no—
728C2#2027826211yescharacteristic
729C2C2×#1681081511yescharacteristic
730C2#2028426111yescharacteristic
731C2#2028652211yescharacteristic
732C2#2028670011yescharacteristic
733C2#2028705811yescharacteristic
734C2#2028718511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2501C2
socleC23×C53C22×D4
prime radicalC2×#16810857C2
hypercenter#2501D53
hypocenterC53#25200
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
1. C2×#16810936C2semidirect
3. #20277729C2semidirect
4. #20276187C2semidirect
5. #20276119C2semidirect
6. #20276103C2semidirect
7. #20276025C2semidirect
8. #20275471C2semidirect
9. #20275332C2semidirect
10. #20275066C2semidirect
11. #20275033C2semidirect
12. #20274895C2semidirect
13. #20274712C2semidirect
14. C2×#16810385C2semidirect
15. C53×#2501C2semidirect
200. C22⋊C4×C53D8semidirect
360. #2501D53semidirect
428. C53#25200semidirect
594. C22⋊C4#11719922semidirect

Maximal subgroups

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

subgroupindex
C2×#168109362
C2×#168108572
#202777292
#202761872
#202761192
#202761032
#202760252
#202754712
#202753322
#202750662
#202750332
#202748952
#202747122
C2×#168103852
C53×#25012
#2520053