Finite Group Databasebeta

← #27420266

Subgroups — #27420266

Order 13568.

1068 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×#16810920C211yesmaximal, characteristic, complemented
2C2×#16810910C211yesmaximal, characteristic, complemented
3#20277408C211yesmaximal, characteristic
4#20276050C211yesmaximal, characteristic, complemented
5#20276045C211yesmaximal, characteristic, complemented
6#20275858C211yesmaximal, characteristic, complemented
7#20275848C211yesmaximal, characteristic, complemented
8#20275673C211yesmaximal, characteristic, complemented
9#20275668C211yesmaximal, characteristic, complemented
10#20275037C211yesmaximal, characteristic
11#20275032C211yesmaximal, characteristic
12#20274914C211yesmaximal, characteristic, complemented
13#20274908C211yesmaximal, characteristic, complemented
14#20274699C211yesmaximal, characteristic, complemented
15C2×C53×#544C211yesmaximal, characteristic, complemented
16C2×#13133191C2211yescharacteristic
17C2×C4×D212C2211yescharacteristic
18#16810920—24no—
19#16810910—24no—
20C2×#13133150C2211yescharacteristic
21C2×#13133148C2211yescharacteristic
22C2×#13133148C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×C4⋊#88322C2211yescharacteristic
25C2×C4⋊#88322C2211yescharacteristic
26C2×#13133137C2211yescharacteristic
27C2×#13133137C2211yescharacteristic
28C2×#13133137C2211yescharacteristic
29C2×#13133137C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32#16810525C2211yescharacteristic
33#16810523—21no—
34#16810521C2211yescharacteristic
35#16810513—21no—
36#16810499—21no—
37#16810494—21no—
38#16810483C2211yescharacteristic
39C4×C4⋊Dic53C2211yescharacteristic
40#16810385C2211yescharacteristic
41#16810385C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C53×#544—24no—
51C53×#544—24no—
52C2×C4⋊Q8×C53—21no—
53C2×C4⋊Q8×C53C2211yescharacteristic
54C2×C4⋊Q8×C53C2211yescharacteristic
55C2×#125×C53—21no—
56C2×#125×C53C2211yescharacteristic
57C2×#125×C53C2211yescharacteristic
58C2×C22⋊Q8×C53—21no—
59C2×C22⋊Q8×C53—21no—
60C2×#117×C53C2211yescharacteristic
61C2×#117×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×D212C2311yescharacteristic
64C22×C22⋊D53—21no—
65C22×C4×D53—21no—
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70#13133191—22no—
71#13133191Q814yescomplemented
72C4×D212—22no—
73C4×D212—22no—
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×C4⋊Dic53C2311yescharacteristic
77C2×#11719919—21no—
78C2×C22⋊Dic53—21no—
79C2×#11719921—21no—
80C2×#11719921—21no—
81C2×#11719921—21no—
82C2×#11719921—21no—
83C2×C4×Dic53—21no—
84#13133150—22no—
85#13133148—22no—
86#13133148—22no—
87#13133148—22no—
88C4⋊#88322—22no—
89C4⋊#88322—22no—
90#13133137—22no—
91#13133137—22no—
92#13133137—22no—
93#13133137—22no—
94C22⋊#88322—22no—
95C22⋊#88322—22no—
96#13133124—21no—
97#13133124—21no—
98#13133124—21no—
99C22×Q8×C53—21no—
100C22×Q8×C53—21no—
101C23×C4×C53—21no—
102C23×C4×C53C2311yescharacteristic
103C4⋊Q8×C53—28no—
104C4⋊Q8×C53—22no—
105C4⋊Q8×C53—22no—
106C4⋊Q8×C53—22no—
107C4⋊Q8×C53D414yescomplemented
108#125×C53—28no—
109#125×C53—22no—
110#125×C53—22no—
111#125×C53—22no—
112#125×C53D414yescomplemented
113C22⋊Q8×C53—28no—
114C22⋊Q8×C53—28no—
115#117×C53—22no—
116#117×C53—22no—
117#117×C53—22no—
118#117×C53—22no—
119C2×C4⋊C4×C53—22no—
120C2×C4⋊C4×C53—22no—
121C2×C4⋊C4×C53—21no—
122C2×C4⋊C4×C53—21no—
123C2×C4⋊C4×C53—21no—
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53—21no—
126C2×C4⋊C4×C53—21no—
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53D411yescharacteristic
129C2×C4⋊C4×C53D411yescharacteristic
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C4⋊C4×C53C2311yescharacteristic
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53D411yescharacteristic
136C2×C22⋊C4×C53D411yescharacteristic
137C2×C42×C53—21no—
138C2×C42×C53C2311yescharacteristic
139C2×C42×C53C2311yescharacteristic
140C24×C53C2×D411yescharacteristic
141C23×D53—21no—
142C2×Q8×C53—24no—
143C2×Q8×C53—24no—
144C2×Q8×C53—81no—
145C2×Q8×C53—81no—
146C2×Q8×C53—81no—
147C2×Q8×C53—81no—
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—21no—
155C22×C4×C53—21no—
156C22×C4×C53—24no—
157C22×C4×C53—81no—
158C22×C4×C53—81no—
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D411yescharacteristic
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53C2×D411yescharacteristic
163C22×C4×C53C2×D411yescharacteristic
164C22×C4×C53C2×Q812yes—
165C22×C4×C53#4112yes—
166C22×C4×C53C2411yescharacteristic
167C2×C22⋊D53—24no—
168C2×C22⋊D53—81no—
169C2×C22⋊D53—81no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C2×D212—21no—
174C2×D212—21no—
175C2×D212—21no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212C2×Q812yes—
179C2×C4×D53—42no—
180C2×C4×D53—81no—
181C2×C4×D53—81no—
182C4⋊C4×C53—24no—
183C4⋊C4×C53—24no—
184C4⋊C4×C53—24no—
185C4⋊C4×C53—24no—
186C4⋊C4×C53—24no—
187C4⋊C4×C53—24no—
188C4⋊C4×C53—24no—
189C4⋊C4×C53—22no—
190C4⋊C4×C53—22no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53C2×D412yes—
196C4⋊C4×C53C2×D412yes—
197C4⋊C4×C53C2×D412yes—
198C4⋊C4×C53C2×D412yes—
199C22⋊C4×C53—24no—
200C22⋊C4×C53—22no—
201C22⋊C4×C53—22no—
202C42×C53—24no—
203C42×C53—21no—
204C42×C53—21no—
205C42×C53C2×D412yes—
206C42×C53C2×D412yes—
207C22⋊Dic53—81no—
208#11719921—24no—
209#11719921—42no—
210#11719921—81no—
211#11719921—81no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53C2×Q812yes—
218#11719919—81no—
219C4×Dic53—81no—
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—21no—
231C2×#88322—21no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53C22⋊Q812yes—
239C23×C53C22×D411yescharacteristic
240C22×D53—22no—
241C22×D53—41no—
242C22×D53—41no—
243C22×D53—41no—
244C22×D53—41no—
245C22×D53—41no—
246C22×D53—41no—
247Q8×C53—84no—
248Q8×C53—84no—
249C2×C4×C53—21no—
250C2×C4×C53—21no—
251C2×C4×C53—21no—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
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—22no—
262C2×C4×C53—22no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—84no—
278C2×C4×C53#12012yes—
279C2×C4×C53#12012yes—
280C2×C4×C53C22⋊Q812yes—
281C2×C4×C53C22×D411yescharacteristic
282C2×C4×C53C22×D411yescharacteristic
283C2×C4×C53C22×Q811yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C532−1+411yescharacteristic
286C2×C4×C532−1+411yescharacteristic
287C22⋊D53—84no—
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—
297D212—22no—
298D212—22no—
299D212—41no—
300D212—41no—
301C4×D53—84no—
302#88322—41no—
303#88322—41no—
304#88322—41no—
305#88322—41no—
306#24309—531nomaximal, Sylow
307C22×C53—22no—
308C22×C53—22no—
309C22×C53—22no—
310C22×C53—41no—
311C22×C53—41no—
312C22×C53—41no—
313C22×C53—41no—
314C22×C53C2×#12011yescharacteristic
315C22×C53C2×C22⋊Q811yescharacteristic
316C22×C53#53611yescharacteristic
317C22×C53#57611yescharacteristic
318C22×C53#57711yescharacteristic
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—22no—
330C4×C53—22no—
331C4×C53—41no—
332C4×C53—42no—
333C4×C53—41no—
334C4×C53—42no—
335C4×C53—42no—
336C4×C53—42no—
337C4×C53#54811yescharacteristic
338C4×C53#54811yescharacteristic
339C4×C53D4×Q811yescharacteristic
340C4×C53D4×Q811yescharacteristic
341Dic53—42no—
342Dic53—81no—
343Dic53—81no—
344C2×#544D5311yescharacteristic, complemented
345C2×#478—531no—
346C2×#476—531no—
347#2324—531no—
348#2059—531no—
349#2058—531no—
350#2025—531no—
351#2023—531no—
352#1989—531no—
353#1988—531no—
354#1875—531no—
355#1874—531no—
356#1854—531no—
357#1853—531no—
358#1798—531no—
359C2×C53—42no—
360C2×C53#240911yescharacteristic
361C2×C53#301011yescharacteristic
362C2×C53#301211yescharacteristic
363C2×C53#308111yescharacteristic
364C2×C53#308411yescharacteristic
365C2×C53#324111yescharacteristic
366C2×C53#324411yescharacteristic
367D53—82no—
368#544—24no—
369#544—24no—
370C2×C4⋊Q8—21no—
371C2×C4⋊Q8C2×D5311yescharacteristic
372C2×C4⋊Q8C2×D5311yescharacteristic
373C2×#125—21no—
374C2×#125C2×D5311yescharacteristic
375C2×#125C2×D5311yescharacteristic
376C2×C22⋊Q8—21no—
377C2×C22⋊Q8—21no—
378C2×#121—531no—
379C2×C4×D4—531no—
380C2×#117C2×D5311yescharacteristic
381C2×#117C2×D5311yescharacteristic
382C22×C4⋊C4C2×D5311yescharacteristic
383#478—1064no—
384#476—1064no—
385C2×#107—531no—
386C2×#106—531no—
387C2×#106—531no—
388C2×#106—531no—
389C2×C4⋊C8—531no—
390C2×C4⋊C8—531no—
391C2×#102—531no—
392C2×#102—531no—
393C2×#102—531no—
394C2×#102—531no—
395C2×C22⋊C8—531no—
396C2×C22⋊C8—531no—
397#390—531no—
398#390—1061no—
399#389—531no—
400#388—1061no—
401#386—1061no—
402#385—1061no—
403#380—531no—
404C4×C4⋊C4—531no—
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#336—531no—
414#336—531no—
415C53#2430911yescharacteristic, complemented, Sylow
416C22×Q8—21no—
417C22×Q8—21no—
418C22×D4—531no—
419C22×D4—1061no—
420C23×C4—21no—
421C23×C4—1061no—
422C23×C4C22×D5311yescharacteristic
423C22×C8—531no—
424C22×C8—531no—
425C22×C8—531no—
426C22×C8—531no—
427C4⋊Q8—28no—
428C4⋊Q8—22no—
429C4⋊Q8—22no—
430C4⋊Q8—22no—
431C4⋊Q8C22⋊D5314yescomplemented
432#125—28no—
433#125—22no—
434#125—22no—
435#125—22no—
436#125C22⋊D5314yescomplemented
437C22⋊Q8—28no—
438C22⋊Q8—28no—
439#121—534no—
440#121—1062no—
441C4×D4—1062no—
442C4×D4—1062no—
443#117—22no—
444#117—22no—
445#117—22no—
446#117—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—531no—
457C2×C4⋊C4—531no—
458C2×C4⋊C4—531no—
459C2×C4⋊C4—1061no—
460C2×C4⋊C4C22⋊D5311yescharacteristic
461C2×C4⋊C4C22⋊D5311yescharacteristic
462C2×C4⋊C4C22×D5311yescharacteristic
463C2×C4⋊C4C22×D5311yescharacteristic
464C2×C4⋊C4C22×D5311yescharacteristic
465C2×C4⋊C4C22×D5311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—1061no—
468C2×C22⋊C4—1061no—
469C2×C22⋊C4—1061no—
470C2×C22⋊C4—1061no—
471C2×C22⋊C4—1061no—
472C2×C22⋊C4C22⋊D5311yescharacteristic
473C2×C22⋊C4C22⋊D5311yescharacteristic
474C2×C42—21no—
475C2×C42—1061no—
476C2×C42C22×D5311yescharacteristic
477C2×C42C22×D5311yescharacteristic
478#107—1062no—
479#106—1062no—
480#106—1062no—
481#106—1062no—
482C4⋊C8—1062no—
483C4⋊C8—1062no—
484#102—1062no—
485#102—1062no—
486#102—1062no—
487#102—1062no—
488C22⋊C8—1062no—
489C22⋊C8—1062no—
490#95—1061no—
491#95—1061no—
492#95—1061no—
493C24—1061no—
494C24C2×C22⋊D5311yescharacteristic
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×D4—532no—
502C2×D4—1064no—
503C2×D4—1061no—
504C2×D4—1061no—
505C2×D4—1061no—
506C2×D4—1061no—
507C2×D4—1061no—
508C2×D4—4241no—
509C2×D4—4241no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—1061no—
522C22×C4—1061no—
523C22×C4—1061no—
524C22×C4—4241no—
525C22×C4—4241no—
526C22×C4—2122no—
527C22×C4Q8×D5312yes—
528C22×C4#1171994912yes—
529C22×C4C2×C22⋊D5311yescharacteristic
530C22×C4C2×C22⋊D5311yescharacteristic
531C22×C4C2×C22⋊D5311yescharacteristic
532C22×C4C2×C22⋊D5311yescharacteristic
533C22×C4C2×C22⋊D5311yescharacteristic
534C22×C4C23×D5311yescharacteristic
535C2×C8—1061no—
536C2×C8—1061no—
537C2×C8—1061no—
538C2×C8—1061no—
539C2×C8—1061no—
540C2×C8—1061no—
541C2×C8—1061no—
542C2×C8—1061no—
543C2×C8—1061no—
544C2×C8—1061no—
545C2×C8—1061no—
546C2×C8—1061no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—532no—
561C4⋊C4—1061no—
562C4⋊C4—1061no—
563C4⋊C4—1061no—
564C4⋊C4—1061no—
565C4⋊C4—1061no—
566C4⋊C4—4241no—
567C4⋊C4C2×C22⋊D5312yes—
568C4⋊C4C2×C22⋊D5312yes—
569C4⋊C4C2×C22⋊D5312yes—
570C4⋊C4C2×C22⋊D5312yes—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—1064no—
575C22⋊C4—4241no—
576C22⋊C4—4241no—
577C22⋊C4—4241no—
578C22⋊C4—2122no—
579C42—24no—
580C42—21no—
581C42—21no—
582C42—4241no—
583C42C2×C22⋊D5312yes—
584C42C2×C22⋊D5312yes—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—1062no—
592C23—2121no—
593C23—2121no—
594C23—2121no—
595C23—2121no—
596C23—2121no—
597C23—2121no—
598C23#1313319312yes—
599C23C22×C22⋊D5311yescharacteristic
600Q8—84no—
601Q8—84no—
602D4—1062no—
603D4—1062no—
604D4—4244no—
605D4—2121no—
606D4—2121no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—1062no—
637C2×C4—4244no—
638C2×C4—2121no—
639C2×C4—2121no—
640C2×C4—2121no—
641C2×C4—2121no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4#1313318612yes—
647C2×C4#1313318612yes—
648C2×C4#1313319312yes—
649C2×C4C22×C22⋊D5311yescharacteristic
650C2×C4C22×C22⋊D5311yescharacteristic
651C2×C4C2×Q8×D5311yescharacteristic
652C2×C4C2×#1171994911yescharacteristic
653C2×C4#1313326511yescharacteristic
654C2×C4#1313326511yescharacteristic
655C8—2121no—
656C8—2121no—
657C8—2121no—
658C8—2121no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—4241no—
667C22—4241no—
668C22—4241no—
669C22—4241no—
670C22—2122no—
671C22—2122no—
672C22—2122no—
673C22C2×#1313318611yescharacteristic
674C22C2×#1313319311yescharacteristic
675C22#1681119711yescharacteristic
676C22#1681142611yescharacteristic
677C22#1681143111yescharacteristic
678C22#1681143111yescharacteristic
679C22#1681143411yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—4241no—
690C4—4241no—
691C4—2122no—
692C4#1681128411yescharacteristic
693C4#1681128411yescharacteristic
694C4Q8×C22⋊D5311yescharacteristic
695C4Q8×C22⋊D5311yescharacteristic
696C2—42no—
697C2—4242no—
698C2#2027807411yescharacteristic
699C2#2028400111yescharacteristic
700C2#2028401911yescharacteristic
701C2#2028454011yescharacteristic
702C2#2028457311yescharacteristic
703C2#2028596811yescharacteristic
704C2#2028601311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C53×#544C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
hypercenterC2×#544D53
hypocenterC53#24309
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×#16810920C2semidirect
2. C2×#16810910C2semidirect
4. #20276050C2semidirect
5. #20276045C2semidirect
6. #20275858C2semidirect
7. #20275848C2semidirect
8. #20275673C2semidirect
9. #20275668C2semidirect
12. #20274914C2semidirect
13. #20274908C2semidirect
14. #20274699C2semidirect
15. C2×C53×#544C2semidirect
71. #13133191Q8semidirect
107. C4⋊Q8×C53D4semidirect
112. #125×C53D4semidirect
344. C2×#544D53semidirect
415. C53#24309semidirect
431. C4⋊Q8C22⋊D53semidirect
436. #125C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168109202
C2×#168109102
#202774082
#202760502
#202760452
#202758582
#202758482
#202756732
#202756682
#202750372
#202750322
#202749142
#202749082
#202746992
C2×C53×#5442
#2430953