Finite Group Databasebeta

← #27399647

Subgroups — #27399647

Order 13568.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810695C211yesmaximal, characteristic, complemented
2C2×#16810628C211yesmaximal, characteristic, complemented
3C2×#16810619C211yesmaximal, characteristic, complemented
4#20277664C211yesmaximal, characteristic, complemented
5#20275648C211yesmaximal, characteristic, complemented
6#20275532C211yesmaximal, characteristic, complemented
7#20275149C211yesmaximal, characteristic, complemented
8#20275144C211yesmaximal, characteristic, complemented
9#20275038C211yesmaximal, characteristic, complemented
10#20275028C211yesmaximal, characteristic, complemented
11#20274715C211yesmaximal, characteristic, complemented
12#20274655C211yesmaximal, characteristic, complemented
13#20274646C211yesmaximal, characteristic, complemented
14#20274540C211yesmaximal, characteristic, complemented
15C2×C53×#546C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C23×#88322C2211yescharacteristic, complemented
18C2×#13133176C2211yescharacteristic
19C2×#13133176C2211yescharacteristic, complemented
20#16810695—24no—
21C2×C4⋊#88322C2211yescharacteristic, complemented
22#16810628—24no—
23#16810619—24no—
24C2×#13133141C2211yescharacteristic, complemented
25C2×#13133141C2211yescharacteristic, complemented
26C2×#13133141C2211yescharacteristic, complemented
27C2×#13133141C2211yescharacteristic, complemented
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic, complemented
38C2×#13133128C2211yescharacteristic, complemented
39#16810526—21no—
40#16810516—21no—
41#16810516—21no—
42#16810493C2211yescharacteristic, complemented
43#16810483C2211yescharacteristic
44#16810483C2211yescharacteristic, complemented
45C4⋊C4×Dic53—21no—
46C4×C4⋊Dic53C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810385C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51C22×#41×C53C2211yescharacteristic
52C23×D4×C53C2211yescharacteristic
53C53×#546—24no—
54C53×#546C418yescomplemented
55C2×#124×C53C2211yescharacteristic
56C2×#123×C53—21no—
57C2×C22⋊Q8×C53C2211yescharacteristic
58C2×#121×C53—21no—
59C2×#121×C53C2211yescharacteristic
60C2×#120×C53—21no—
61C2×C4×D4×C53C2211yescharacteristic
62C2×C4×D4×C53C2211yescharacteristic
63C22×C22⋊C4×C53—21no—
64C2×#11719917—22no—
65C2×#11719917—22no—
66C2×#11719917—41no—
67C22×#88322—22no—
68C22×#88322—22no—
69C22×#88322—41no—
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74#13133176—22no—
75#13133176—22no—
76#13133176—41no—
77#13133176—41no—
78C2×C4⋊Dic53—21no—
79C2×C4⋊Dic53—21no—
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C4×Dic53—21no—
89C2×C4×Dic53—21no—
90C2×C4×Dic53—21no—
91C4⋊#88322—22no—
92#13133141—22no—
93#13133141—22no—
94#13133141—41no—
95#13133141—41no—
96#13133138—22no—
97#13133138—22no—
98#13133138—22no—
99#13133138—22no—
100#13133138—22no—
101#13133138—41no—
102#13133138—41no—
103#13133138D414yescomplemented
104C22⋊#88322—22no—
105C22⋊#88322—22no—
106#13133128—22no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110C25×C53—21no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53—22no—
114C2×#41×C53—41no—
115C2×#41×C53—41no—
116C2×#41×C53C2×C414yes—
117C22×Q8×C53C2311yescharacteristic
118C22×D4×C53—22no—
119C22×D4×C53—22no—
120C22×D4×C53—21no—
121C22×D4×C53—21no—
122C22×D4×C53—21no—
123C22×D4×C53—22no—
124C22×D4×C53—41no—
125C22×D4×C53—41no—
126C22×D4×C53C2×C414yes—
127C22×D4×C53D411yescharacteristic
128C22×D4×C53C2311yescharacteristic
129C22×D4×C53C2311yescharacteristic
130C23×C4×C53—21no—
131C23×C4×C53—21no—
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134#124×C53—22no—
135#124×C53C2×C414yes—
136#123×C53—28no—
137C22⋊Q8×C53—22no—
138C22⋊Q8×C53C2×C414yes—
139#121×C53—28no—
140#121×C53—22no—
141#121×C53C2×C414yes—
142#120×C53—28no—
143C4×D4×C53—22no—
144C4×D4×C53C2×C414yes—
145C4×D4×C53C2×C414yes—
146C4×D4×C53D414yes—
147C2×C4⋊C4×C53—21no—
148C2×C4⋊C4×C53D411yescharacteristic
149C2×C4⋊C4×C53C2311yescharacteristic
150C2×C22⋊C4×C53—28no—
151C2×C22⋊C4×C53—21no—
152C2×C22⋊C4×C53—21no—
153C2×C22⋊C4×C53—21no—
154C2×C22⋊C4×C53—21no—
155C2×C22⋊C4×C53—21no—
156C2×C22⋊C4×C53D411yescharacteristic
157C2×C22⋊C4×C53D411yescharacteristic
158C2×C42×C53C2311yescharacteristic
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—24no—
162C24×C53—42no—
163C24×C53—42no—
164C24×C53—42no—
165C24×C53—42no—
166C24×C53—81no—
167C24×C53—81no—
168C24×C53C2×D411yescharacteristic
169C24×C53C2×D411yescharacteristic
170#41×C53—28no—
171#41×C53—44no—
172#41×C53—44no—
173#41×C53—44no—
174C2×Q8×C53—21no—
175C2×Q8×C53—21no—
176C2×Q8×C53—21no—
177C2×Q8×C53—21no—
178C2×Q8×C53—21no—
179C2×Q8×C53C22×C412yes—
180C2×D4×C53—28no—
181C2×D4×C53—24no—
182C2×D4×C53—24no—
183C2×D4×C53—24no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—44no—
193C2×D4×C53—44no—
194C2×D4×C53—44no—
195C2×D4×C53—41no—
196C2×D4×C53—41no—
197C2×D4×C53—42no—
198C2×D4×C53—42no—
199C2×D4×C53—42no—
200C2×D4×C53—42no—
201C2×D4×C53—81no—
202C2×D4×C53—81no—
203C2×D4×C53C22⋊C414yes—
204C2×D4×C53C22×C412yes—
205C2×D4×C53C22×C412yes—
206C2×D4×C53C2×D412yes—
207C2×D4×C53#4112yes—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—24no—
219C22×C4×C53—24no—
220C22×C4×C53—42no—
221C22×C4×C53—42no—
222C22×C4×C53—81no—
223C22×C4×C53—81no—
224C22×C4×C53C22×C412yes—
225C22×C4×C53C22×C412yes—
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D412yes—
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2411yescharacteristic
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53C22⋊C414yes—
240C4⋊C4×C53C22×C412yes—
241C22⋊C4×C53—24no—
242C22⋊C4×C53—24no—
243C22⋊C4×C53—24no—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C22⋊C4×C53C22⋊C414yes—
247C22⋊C4×C53C22⋊C414yes—
248C42×C53C22×C412yes—
249C42×C53C2×D412yes—
250C22⋊Dic53—42no—
251C22⋊Dic53—42no—
252C22⋊Dic53—81no—
253C22⋊Dic53—81no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4⋊Dic53—42no—
262C4⋊Dic53—81no—
263C4⋊Dic53C2×D412yes—
264C4×Dic53—42no—
265C4×Dic53—42no—
266C4×Dic53—42no—
267#11719917—44no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—44no—
280C2×#88322C2×D412yes—
281C23×C53—22no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—22no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—22no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53—21no—
295C23×C53—21no—
296C23×C53—22no—
297C23×C53—48no—
298C23×C53—48no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—84no—
310C23×C53—84no—
311C23×C53—84no—
312C23×C53—84no—
313C23×C53—84no—
314C23×C53C2×C22⋊C412yes—
315C23×C53C2×C22⋊C412yes—
316C23×C53C22×D411yescharacteristic
317Q8×C53—22no—
318Q8×C53—22no—
319Q8×C53—41no—
320Q8×C53—41no—
321D4×C53—22no—
322D4×C53—22no—
323D4×C53—22no—
324D4×C53—22no—
325D4×C53—22no—
326D4×C53—44no—
327D4×C53—48no—
328D4×C53—48no—
329D4×C53—41no—
330D4×C53—41no—
331D4×C53—84no—
332D4×C53C4×D414yes—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—48no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—84no—
357C2×C4×C53C2×C22⋊C412yes—
358C2×C4×C53C2×C22⋊C412yes—
359C2×C4×C53C2×C22⋊C412yes—
360C2×C4×C53C2×C22⋊C412yes—
361C2×C4×C53C23×C411yescharacteristic
362C2×C4×C53C22×D411yescharacteristic
363C2×C4×C53C22×D411yescharacteristic
364C2×C4×C53C2×#4111yescharacteristic
365C2×C4×C53H(5,𝔽2)11yescharacteristic
366C2×C4×C53H(5,𝔽2)11yescharacteristic
367C2×Dic53—22no—
368C2×Dic53—41no—
369C2×Dic53—41no—
370C2×Dic53—41no—
371C2×Dic53—41no—
372C2×Dic53—41no—
373C2×Dic53—41no—
374C2×Dic53—41no—
375C2×Dic53—41no—
376C2×Dic53—41no—
377C2×Dic53—41no—
378C2×Dic53—41no—
379#88322—22no—
380#88322—41no—
381#88322—41no—
382#88322—41no—
383#22424—531nomaximal, Sylow
384C22×C53—22no—
385C22×C53—22no—
386C22×C53—24no—
387C22×C53—22no—
388C22×C53—22no—
389C22×C53—22no—
390C22×C53—22no—
391C22×C53—42no—
392C22×C53—42no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—42no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53—42no—
399C22×C53—41no—
400C22×C53—41no—
401C22×C53—42no—
402C22×C53—41no—
403C22×C53—41no—
404C22×C53—42no—
405C22×C53—42no—
406C22×C53—42no—
407C22×C53—42no—
408C22×C53—816no—
409C22×C53—81no—
410C22×C53—81no—
411C22×C53—81no—
412C22×C53—81no—
413C22×C53C22×C22⋊C411yescharacteristic
414C22×C53D4211yescharacteristic
415C22×C53#54611yescharacteristic
416C22×C53#57511yescharacteristic
417C22×C53#57511yescharacteristic
418C22×C53#57611yescharacteristic
419C22×C53#57711yescharacteristic
420C4×C53—22no—
421C4×C53—22no—
422C4×C53—22no—
423C4×C53—22no—
424C4×C53—42no—
425C4×C53—42no—
426C4×C53C2×C4×D411yescharacteristic
427C4×C53#51811yescharacteristic
428C4×C53D4211yescharacteristic
429C4×C53#54611yescharacteristic
430Dic53—42no—
431Dic53—81no—
432Dic53—81no—
433Dic53—81no—
434C2×#546D5311yescharacteristic
435C2×#435—531no—
436C2×#418—531no—
437C2×#416—531no—
438#2354—531no—
439#1983—531no—
440#1959—531no—
441#1894—531no—
442#1893—531no—
443#1875—531no—
444#1873—531no—
445#1802—531no—
446#1788—531no—
447#1786—531no—
448#1762—531no—
449C2×C53—42no—
450C2×C53—42no—
451C2×C53—44no—
452C2×C53—82no—
453C2×C53D4×C22⋊C411yescharacteristic
454C2×C53#289611yescharacteristic
455C2×C53#289711yescharacteristic
456C2×C53#326711yescharacteristic
457C2×C53#326811yescharacteristic
458C2×C53#331111yescharacteristic
459C2×C53#331911yescharacteristic
460C22×#41C2×D5311yescharacteristic
461C23×D4C2×D5311yescharacteristic
462C22×M16—531no—
463C23×C8—531no—
464#546—24no—
465#546Dic5318yescomplemented
466C2×#124C2×D5311yescharacteristic
467C2×#123—21no—
468C2×C22⋊Q8C2×D5311yescharacteristic
469C2×#121—21no—
470C2×#121C2×D5311yescharacteristic
471C2×#120—21no—
472C2×C4×D4C2×D5311yescharacteristic
473C2×C4×D4C2×D5311yescharacteristic
474C2×#117—531no—
475C2×#117—531no—
476C22×C22⋊C4—21no—
477#435—1064no—
478C2×C4⋊C8—531no—
479#418—1064no—
480#416—1064no—
481C2×#103—531no—
482C2×#103—531no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#102—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102—531no—
491C2×#102—531no—
492C2×#102—531no—
493C2×C22⋊C8—531no—
494C2×C22⋊C8—531no—
495C2×#97—531no—
496#390—1061no—
497#388—1061no—
498#388—1061no—
499#384—531no—
500#380—531no—
501#380—531no—
502C4×C4⋊C4—531no—
503C4×C4⋊C4—1061no—
504#340—531no—
505#340—531no—
506#340—531no—
507#340—531no—
508C53#2242411yescharacteristic, complemented, Sylow
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic5314yes—
516C22×Q8C22×D5311yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×Dic5314yes—
526C22×D4C22⋊D5311yescharacteristic
527C22×D4C22×D5311yescharacteristic
528C22×D4C22×D5311yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D5311yescharacteristic
532C23×C4C22×D5311yescharacteristic
533C2×M16—1062no—
534C2×M16—1062no—
535C2×M16—2121no—
536C22×C8—531no—
537C22×C8—531no—
538C22×C8—531no—
539C22×C8—531no—
540C22×C8—1062no—
541C22×C8—1062no—
542C22×C8—2121no—
543#124—22no—
544#124C2×Dic5314yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×Dic5314yes—
548#121—22no—
549#121—28no—
550#121C2×Dic5314yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×Dic5314yes—
554C4×D4C2×Dic5314yes—
555C4×D4C22⋊D5314yes—
556#117—1062no—
557#117—1062no—
558#117—2121no—
559#117—2121no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—531no—
563C2×C4⋊C4—531no—
564C2×C4⋊C4—531no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4C22⋊D5311yescharacteristic
568C2×C4⋊C4C22×D5311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1061no—
579C2×C22⋊C4C22⋊D5311yescharacteristic
580C2×C22⋊C4C22⋊D5311yescharacteristic
581C2×C42—1061no—
582C2×C42—1061no—
583C2×C42—1061no—
584C2×C42C22×D5311yescharacteristic
585C4⋊C8—1062no—
586#103—1062no—
587#103—1062no—
588#103—2121no—
589#103—2121no—
590#102—534no—
591#102—1062no—
592#102—1062no—
593#102—1062no—
594#102—1062no—
595#102—1062no—
596#102—2121no—
597#102—2121no—
598C22⋊C8—1062no—
599C22⋊C8—1062no—
600#97—1062no—
601#95—1061no—
602#95—1061no—
603#95—1061no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×C22⋊D5311yescharacteristic
614C24C2×C22⋊D5311yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×Dic5312yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic5314yes—
649C2×D4D4×D5312yes—
650C2×D4#1171994712yes—
651C2×D4C22×Dic5312yes—
652C2×D4C22×Dic5312yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—81no—
669C22×C4—1061no—
670C22×C4—1061no—
671C22×C4—1061no—
672C22×C4—1061no—
673C22×C4C22×Dic5312yes—
674C22×C4C22×Dic5312yes—
675C22×C4C2×C22⋊D5311yescharacteristic
676C22×C4C2×C22⋊D5311yescharacteristic
677C22×C4C2×C22⋊D5311yescharacteristic
678C22×C4C2×C22⋊D5311yescharacteristic
679C22×C4C2×C22⋊D5312yes—
680C22×C4C2×C22⋊D5312yes—
681C22×C4C23×D5311yescharacteristic
682M16—2124no—
683C2×C8—532no—
684C2×C8—1061no—
685C2×C8—1061no—
686C2×C8—1061no—
687C2×C8—1061no—
688C2×C8—1061no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—1061no—
695C2×C8—2124no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—532no—
699C4⋊C4—1061no—
700C4⋊C4—1061no—
701C4⋊C4—1061no—
702C4⋊C4—1061no—
703C4⋊C4—1061no—
704C4⋊C4—1061no—
705C4⋊C4—1061no—
706C4⋊C4—4241no—
707C4⋊C4—2122no—
708C4⋊C4C22⋊Dic5314yes—
709C4⋊C4C22×Dic5312yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—4241no—
716C22⋊C4—4241no—
717C22⋊C4—2122no—
718C22⋊C4—2122no—
719C22⋊C4C22⋊Dic5314yes—
720C22⋊C4C22⋊Dic5314yes—
721C42—2122no—
722C42—2122no—
723C42—2122no—
724C42C22×Dic5312yes—
725C42C2×C22⋊D5312yes—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊Dic5312yes—
760C23C2×C22⋊Dic5312yes—
761C23C22×C22⋊D5311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4D4×Dic5314yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—1062no—
803C2×C4—2121no—
804C2×C4—2121no—
805C2×C4—2121no—
806C2×C4—2121no—
807C2×C4—2121no—
808C2×C4—2121no—
809C2×C4—2121no—
810C2×C4—2121no—
811C2×C4—2121no—
812C2×C4—2121no—
813C2×C4—2121no—
814C2×C4C2×C22⋊Dic5312yes—
815C2×C4C2×C22⋊Dic5312yes—
816C2×C4C2×C22⋊Dic5312yes—
817C2×C4C2×C22⋊Dic5312yes—
818C2×C4C23×Dic5311yescharacteristic
819C2×C4C2×D4×D5311yescharacteristic
820C2×C4C22×C22⋊D5311yescharacteristic
821C2×C4C2×#1171994711yescharacteristic
822C2×C4#1313326211yescharacteristic
823C2×C4#1313326211yescharacteristic
824C8—1062no—
825C8—2121no—
826C8—2121no—
827C8—2121no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊Dic5311yescharacteristic
858C22D4×C22⋊D5311yescharacteristic
859C22#1681126711yescharacteristic
860C22#1681142111yescharacteristic
861C22#1681142111yescharacteristic
862C22#1681142611yescharacteristic
863C22#1681143411yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—4241no—
871C4—4241no—
872C4—4241no—
873C4—2122no—
874C4C2×D4×Dic5311yescharacteristic
875C4#1681109811yescharacteristic
876C4D4×C22⋊D5311yescharacteristic
877C4#1681126711yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊Dic5311yescharacteristic
883C2#2028323411yescharacteristic
884C2#2028324111yescharacteristic
885C2#2028623611yescharacteristic
886C2#2028625111yescharacteristic
887C2#2028675111yescharacteristic
888C2#2028687111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#546C2
socleC23×C53C22×D4
cosocleC22×C4×C53C24
hypercenterC2×#546D53
hypocenterC53#22424
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16810695C2semidirect
2. C2×#16810628C2semidirect
3. C2×#16810619C2semidirect
4. #20277664C2semidirect
5. #20275648C2semidirect
6. #20275532C2semidirect
7. #20275149C2semidirect
8. #20275144C2semidirect
9. #20275038C2semidirect
10. #20275028C2semidirect
11. #20274715C2semidirect
12. #20274655C2semidirect
13. #20274646C2semidirect
14. #20274540C2semidirect
17. C23×#88322C22semidirect
19. C2×#13133176C22semidirect
21. C2×C4⋊#88322C22semidirect
24. C2×#13133141C22semidirect
25. C2×#13133141C22semidirect
26. C2×#13133141C22semidirect
27. C2×#13133141C22semidirect
37. C2×C22⋊#88322C22semidirect
38. C2×#13133128C22semidirect
42. #16810493C22semidirect
44. #16810483C22semidirect
46. C4×C4⋊Dic53C22semidirect
47. #16810385C22semidirect
48. #16810385C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
54. C53×#546C4semidirect
103. #13133138D4semidirect
465. #546Dic53semidirect
508. C53#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#168106952
C2×#168106282
C2×#168106192
#202776642
#202756482
#202755322
#202751492
#202751442
#202750382
#202750282
#202747152
#202746552
#202746462
#202745402
C2×C53×#5462
#2242453