Finite Group Databasebeta

← #27399511

Subgroups — #27399511

Order 13568.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811269C211yesmaximal, characteristic
2C2×#16810620C211yesmaximal, characteristic, complemented
3C22×#13133139C211yesmaximal, characteristic, complemented
4#20277644C211yesmaximal, characteristic, complemented
5#20275645C211yesmaximal, characteristic, complemented
6#20275526C211yesmaximal, characteristic, complemented
7#20275143C211yesmaximal, characteristic, complemented
8#20275138C211yesmaximal, characteristic, complemented
9#20275035C211yesmaximal, characteristic, complemented
10#20275020C211yesmaximal, characteristic, complemented
11#20274726C211yesmaximal, characteristic, complemented
12#20274656C211yesmaximal, characteristic, complemented
13#20274647C211yesmaximal, characteristic, complemented
14C4×#13133139C211yesmaximal, characteristic, complemented
15C2×C8×D4×C53C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C23×D212C2211yescharacteristic
18#16811269—24no—
19#16811269C418yescomplemented
20C2×#13133205C2211yescharacteristic
21C2×#13133202—21no—
22C2×#13133196C2211yescharacteristic
23C2×#13133191C2211yescharacteristic
24C2×#13133190—21no—
25C2×#13133185—21no—
26C2×C4×D212C2211yescharacteristic
27C2×#13133176C2211yescharacteristic, complemented
28C22×C4⋊Dic53C2211yescharacteristic
29C2×C22⋊C4×D53—21no—
30#16810620—24no—
31C2×#13133142C2211yescharacteristic, complemented
32C2×#13133142C2211yescharacteristic, complemented
33C2×#13133142C2211yescharacteristic, complemented
34C2×#13133142C2211yescharacteristic, complemented
35C2×#13133139—24no—
36C2×#13133139C2211yescharacteristic
37C2×#13133139C2211yescharacteristic
38C2×#13133139C2211yescharacteristic
39C2×#13133139C2211yescharacteristic
40C2×#13133139C2211yescharacteristic
41C2×#13133139C2211yescharacteristic
42C2×#13133139C2211yescharacteristic
43C2×#13133139C2211yescharacteristic
44#16810516—21no—
45#16810509—21no—
46#16810503—21no—
47#16810489C2211yescharacteristic, complemented
48#16810483C2211yescharacteristic
49#16810483C2211yescharacteristic, complemented
50C4×C4⋊Dic53C2211yescharacteristic, complemented
51C22⋊C4×Dic53—21no—
52#16810386C2211yescharacteristic, complemented
53#16810386C2211yescharacteristic, complemented
54#16810386C2211yescharacteristic, complemented
55#16810386C2211yescharacteristic, complemented
56C23×C8×C53C2211yescharacteristic
57C23×C8×C53C2211yescharacteristic, complemented
58C2×C4×D4×C53C2211yescharacteristic
59C8×D4×C53—24no—
60C2×C4⋊C8×C53C2211yescharacteristic, complemented
61C2×C22⋊C8×C53C2211yescharacteristic
62C2×C22⋊C8×C53C2211yescharacteristic, complemented
63C2×C4×C8×C53C2211yescharacteristic, complemented
64C24×D53—21no—
65C2×#11719945—22no—
66C2×#11719945—22no—
67C2×#11719945—22no—
68C2×#11719945—41no—
69C2×#11719945—41no—
70C2×#11719945C2×C414yescomplemented
71C22×Dic106C2311yescharacteristic
72C22×D212—22no—
73C22×D212—22no—
74C22×D212—22no—
75C22×D212—21no—
76C22×D212—41no—
77C22×D212—41no—
78C22×D212C2×C414yes—
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C23×Dic53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86#13133205—22no—
87#13133205C2×C414yescomplemented
88#13133202—28no—
89#13133196—22no—
90#13133196C2×C414yes—
91#13133191—22no—
92#13133191C2×C414yescomplemented
93#13133190—28no—
94#13133185—28no—
95C4×D212—22no—
96C4×D212C2×C414yescomplemented
97#13133176—22no—
98#13133176—41no—
99C2×C4⋊Dic53—21no—
100C2×C4⋊Dic53—22no—
101C2×C4⋊Dic53—41no—
102C2×C4⋊Dic53C2311yescharacteristic
103C2×C4⋊Dic53C2311yescharacteristic
104C2×C4⋊Dic53C2311yescharacteristic
105C2×C4⋊Dic53C2311yescharacteristic
106C2×C4⋊Dic53C2311yescharacteristic
107C2×#11719919—21no—
108C2×C22⋊Dic53—21no—
109C2×C22⋊Dic53—21no—
110C2×C22⋊Dic53—21no—
111C2×C22⋊Dic53—21no—
112C2×#11719921—21no—
113C2×#11719921—21no—
114C2×#11719921—21no—
115C2×#11719921—21no—
116C22⋊C4×D53—28no—
117C2×C4×Dic53—21no—
118C2×C4×Dic53—21no—
119#13133142—22no—
120#13133142—22no—
121#13133142—41no—
122#13133142—41no—
123#13133139—22no—
124#13133139—22no—
125#13133139—22no—
126#13133139—22no—
127#13133139—22no—
128#13133139—41no—
129#13133139—41no—
130#13133139D414yescomplemented
131#13133124—21no—
132#13133124—21no—
133#13133124—21no—
134#13133124—21no—
135#13133124—21no—
136C22×D4×C53D411yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C22×C8×C53—22no—
140C22×C8×C53—22no—
141C22×C8×C53—22no—
142C22×C8×C53—22no—
143C22×C8×C53—41no—
144C22×C8×C53—41no—
145C22×C8×C53C2311yescharacteristic
146C22×C8×C53C2311yescharacteristic
147C22×C8×C53C2311yescharacteristic
148C22×C8×C53C2311yescharacteristic
149C4×D4×C53C2×C414yes—
150C4×D4×C53D414yes—
151C2×C4⋊C4×C53D411yescharacteristic
152C2×C22⋊C4×C53D411yescharacteristic
153C2×C22⋊C4×C53D411yescharacteristic
154C2×C42×C53C2311yescharacteristic
155C4⋊C8×C53—22no—
156C22⋊C8×C53—22no—
157C22⋊C8×C53—22no—
158C4×C8×C53—22no—
159C24×C53C2×D411yescharacteristic
160C24×C53C2×D411yescharacteristic
161C23×D53—21no—
162C23×D53—21no—
163C23×D53—24no—
164C23×D53—42no—
165C23×D53—42no—
166C23×D53—42no—
167C23×D53—42no—
168C23×D53—81no—
169C23×D53—81no—
170C2×D4×C53—22no—
171C2×D4×C53—22no—
172C2×D4×C53C22⋊C414yes—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53C22×C412yes—
182C22×C4×C53C22×C412yes—
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D412yes—
188C22×C4×C53C2×D412yes—
189C22×C4×C53C2411yescharacteristic
190C2×C22⋊D53—24no—
191C2×C22⋊D53—24no—
192C2×C22⋊D53—42no—
193C2×C22⋊D53—42no—
194C2×C22⋊D53—81no—
195C2×C22⋊D53—81no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—42no—
203C22×Dic53—42no—
204C22×Dic53—81no—
205#11719945—28no—
206#11719945—44no—
207#11719945—44no—
208#11719945—44no—
209C2×D212—21no—
210C2×D212—21no—
211C2×D212—21no—
212C2×D212—21no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—21no—
216C2×D212—28no—
217C2×D212—24no—
218C2×D212—21no—
219C2×D212—44no—
220C2×D212—44no—
221C2×D212—44no—
222C2×D212—42no—
223C2×D212—42no—
224C2×D212C22×C412yes—
225C2×D212C22×C412yes—
226C2×D212C2×D412yes—
227C2×D212#4112yes—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—42no—
231C2×C4×D53—42no—
232C2×C4×D53—81no—
233C2×C4×D53—81no—
234C2×Dic106—21no—
235C2×Dic106—21no—
236C2×Dic106—21no—
237C2×Dic106—21no—
238C2×Dic106—21no—
239C2×Dic106C22×C412yes—
240C2×C8×C53—21no—
241C2×C8×C53—21no—
242C2×C8×C53—21no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—21no—
250C2×C8×C53—21no—
251C2×C8×C53—44no—
252C2×C8×C53—44no—
253C2×C8×C53C2×D412yes—
254C4⋊C4×C53C22⋊C414yes—
255C22⋊C4×C53C22⋊C414yes—
256C22⋊C4×C53C22⋊C414yes—
257C42×C53C22×C412yes—
258C42×C53C2×D412yes—
259C22⋊Dic53—24no—
260C22⋊Dic53—42no—
261C22⋊Dic53—42no—
262C22⋊Dic53—81no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267C4⋊Dic53—21no—
268C4⋊Dic53—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—21no—
273C4⋊Dic53—21no—
274C4⋊Dic53—21no—
275C4⋊Dic53—42no—
276C4⋊Dic53C22×C412yes—
277C4⋊Dic53C2×D412yes—
278#11719919—24no—
279C4×Dic53—42no—
280C4×Dic53—81no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53C2×C22⋊C412yes—
292C23×C53C2×C22⋊C412yes—
293C23×C53#13512yes—
294C23×C53#13512yes—
295C23×C53C22×D411yescharacteristic
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—48no—
301C22×D53—41no—
302C22×D53—41no—
303C22×D53—41no—
304C22×D53—41no—
305C22×D53—41no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—48no—
312C22×D53—84no—
313C22×D53—84no—
314C22×D53—84no—
315C22×D53—84no—
316C22×D53—84no—
317D4×C53—28no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53C2×C22⋊C412yes—
335C2×C4×C53C2×C22⋊C412yes—
336C2×C4×C53C2×C22⋊C412yes—
337C2×C4×C53C2×C22⋊C412yes—
338C2×C4×C53C23×C411yescharacteristic
339C2×C4×C53C22×D411yescharacteristic
340C2×C4×C53C22×D411yescharacteristic
341C2×C4×C53C2×#4111yescharacteristic
342C2×C4×C53H(5,𝔽2)11yescharacteristic
343C2×C4×C53H(5,𝔽2)11yescharacteristic
344C22⋊D53—48no—
345C22⋊D53—84no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—41no—
350C2×Dic53—41no—
351C2×Dic53—41no—
352C2×Dic53—41no—
353C2×Dic53—41no—
354C2×Dic53—41no—
355C2×Dic53—41no—
356C2×Dic53—41no—
357C2×Dic53—41no—
358C2×Dic53—41no—
359C2×Dic53—41no—
360C2×Dic53—41no—
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—84no—
365D212—22no—
366D212—22no—
367D212—22no—
368D212—22no—
369D212—22no—
370D212—48no—
371D212—41no—
372D212—41no—
373D212C4×D414yes—
374C4×D53—48no—
375C4×D53—84no—
376Dic106—22no—
377Dic106—22no—
378Dic106—41no—
379Dic106—41no—
380C8×C53—22no—
381C8×C53—41no—
382C8×C53—41no—
383C8×C53—41no—
384#22414—531nomaximal, Sylow
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—22no—
389C22×C53—22no—
390C22×C53—22no—
391C22×C53—22no—
392C22×C53—22no—
393C22×C53—22no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53#41614yescomplemented
399C22×C53C22×C22⋊C411yescharacteristic
400C22×C53D4211yescharacteristic
401C22×C53#54611yescharacteristic
402C22×C53C2×#13511yescharacteristic
403C22×C53C2×#13511yescharacteristic
404C22×C53#57611yescharacteristic
405C22×C53#57711yescharacteristic
406C2×D53—24no—
407C2×D53—42no—
408C2×D53—42no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—42no—
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—42no—
415C2×D53—42no—
416C2×D53—816no—
417C2×D53—81no—
418C2×D53—81no—
419C2×D53—81no—
420C2×D53—81no—
421C4×C53—22no—
422C4×C53—22no—
423C4×C53—22no—
424C4×C53—22no—
425C4×C53C2×C4×D411yescharacteristic
426C4×C53#51811yescharacteristic
427C4×C53D4211yescharacteristic
428C4×C53#54611yescharacteristic
429Dic53—42no—
430Dic53—42no—
431Dic53—42no—
432Dic53—81no—
433Dic53—81no—
434Dic53—81no—
435C2×#546—531no—
436C2×C8×D4D5311yescharacteristic, complemented
437C2×#416—531no—
438C22×#102—531no—
439#2352—531no—
440#1983—531no—
441#1958—531no—
442#1893—531no—
443#1892—531no—
444#1875—531no—
445#1872—531no—
446#1804—531no—
447#1788—531no—
448#1786—531no—
449C4×#102—531no—
450C2×C53—24no—
451C2×C53—42no—
452C2×C53D4×C22⋊C411yescharacteristic
453C2×C53C2×#41611yescharacteristic
454C2×C53#289711yescharacteristic
455C2×C53#328011yescharacteristic
456C2×C53#328211yescharacteristic
457C2×C53#329611yescharacteristic
458C2×C53#329711yescharacteristic
459D53—44no—
460D53—82no—
461C22×#41—531no—
462C23×D4—531no—
463C23×C8C2×D5311yescharacteristic
464C23×C8C2×D5311yescharacteristic, complemented
465#546—538no—
466#546—1064no—
467C2×#124—531no—
468C2×#123—1061no—
469C2×C22⋊Q8—531no—
470C2×#121—531no—
471C2×#121—1061no—
472C2×#120—1061no—
473C2×C4×D4—531no—
474C2×C4×D4C2×D5311yescharacteristic
475C2×#117—531no—
476C22×C4⋊C4—531no—
477C22×C22⋊C4—1061no—
478C8×D4—24no—
479C2×C4⋊C8C2×D5311yescharacteristic, complemented
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×#102—1064no—
494C2×C22⋊C8C2×D5311yescharacteristic
495C2×C22⋊C8C2×D5311yescharacteristic, complemented
496C2×C4×C8C2×D5311yescharacteristic, complemented
497#388—1061no—
498#387—1061no—
499#386—1061no—
500#382—531no—
501#380—531no—
502#380—531no—
503C4×C4⋊C4—531no—
504C4×C22⋊C4—1061no—
505#340—531no—
506#340—531no—
507#340—531no—
508#340—531no—
509C53#2241411yescharacteristic, complemented, Sylow
510C25—1061no—
511C2×#41—534no—
512C2×#41—1062no—
513C2×#41—1062no—
514C2×#41—1062no—
515C2×#41—2121no—
516C2×#41—2121no—
517C22×Q8—531no—
518C22×D4—534no—
519C22×D4—531no—
520C22×D4—531no—
521C22×D4—1062no—
522C22×D4—1062no—
523C22×D4—1061no—
524C22×D4—1061no—
525C22×D4—1061no—
526C22×D4—1062no—
527C22×D4—2121no—
528C22×D4—2121no—
529C22×D4D21211yescharacteristic
530C23×C4—1061no—
531C23×C4—1061no—
532C23×C4—1061no—
533C23×C4C22×D5311yescharacteristic
534C23×C4C22×D5311yescharacteristic
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8C22×D5311yescharacteristic
542C22×C8C22×D5311yescharacteristic
543C22×C8C22×D5311yescharacteristic
544C22×C8C22×D5311yescharacteristic
545#124—534no—
546#124—1062no—
547#123—1068no—
548C22⋊Q8—534no—
549C22⋊Q8—1062no—
550#121—534no—
551#121—1062no—
552#121—1068no—
553#120—1068no—
554C4×D4—534no—
555C4×D4—1062no—
556C4×D4C4×D5314yes—
557C4×D4C22⋊D5314yes—
558#117—1062no—
559#117—2121no—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—531no—
563C2×C4⋊C4—531no—
564C2×C4⋊C4—531no—
565C2×C4⋊C4—1062no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4—2121no—
569C2×C4⋊C4D21211yescharacteristic
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1068no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1061no—
579C2×C22⋊C4D21211yescharacteristic
580C2×C22⋊C4D21211yescharacteristic
581C2×C42—1061no—
582C2×C42—1061no—
583C2×C42C22×D5311yescharacteristic
584C4⋊C8—22no—
585#103—1062no—
586#103—1062no—
587#103—2121no—
588#103—2121no—
589#102—534no—
590#102—1062no—
591#102—1062no—
592#102—1062no—
593#102—1062no—
594#102—1062no—
595#102—2121no—
596#102—2121no—
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—1061no—
601#95—1061no—
602#95—1061no—
603#95—1061no—
604#95—1061no—
605C24—1061no—
606C24—1064no—
607C24—1061no—
608C24—4241no—
609C24—4241no—
610C24—2122no—
611C24—2122no—
612C24—2122no—
613C24—2122no—
614C24C2×D21211yescharacteristic
615C24C2×D21211yescharacteristic
616#41—1068no—
617#41—2124no—
618#41—2124no—
619#41—2124no—
620C2×Q8—532no—
621C2×Q8—1061no—
622C2×Q8—1061no—
623C2×Q8—1061no—
624C2×Q8—1061no—
625C2×Q8—1061no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—532no—
629C2×D4—532no—
630C2×D4—532no—
631C2×D4—532no—
632C2×D4—1068no—
633C2×D4—1064no—
634C2×D4—1064no—
635C2×D4—1064no—
636C2×D4—1061no—
637C2×D4—1061no—
638C2×D4—1061no—
639C2×D4—1061no—
640C2×D4—1061no—
641C2×D4—1061no—
642C2×D4—1061no—
643C2×D4—1061no—
644C2×D4—4241no—
645C2×D4—4241no—
646C2×D4—2124no—
647C2×D4—2124no—
648C2×D4—2124no—
649C2×D4—2122no—
650C2×D4—2122no—
651C2×D4—2122no—
652C2×D4—2122no—
653C2×D4#1171992114yes—
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—1061no—
663C22×C4—1061no—
664C22×C4—1061no—
665C22×C4—1064no—
666C22×C4—1064no—
667C22×C4—1061no—
668C22×C4—1061no—
669C22×C4—1061no—
670C22×C4—4241no—
671C22×C4—4241no—
672C22×C4—4241no—
673C22×C4—2122no—
674C22×C4—2122no—
675C22×C4—2122no—
676C22×C4—2122no—
677C22×C4C2×C4×D5312yes—
678C22×C4C2×C4×D5312yes—
679C22×C4C2×D21211yescharacteristic
680C22×C4C2×D21211yescharacteristic
681C22×C4C2×D21211yescharacteristic
682C22×C4C2×D21211yescharacteristic
683C22×C4C2×C22⋊D5312yes—
684C22×C4C2×C22⋊D5312yes—
685C22×C4C23×D5311yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—44no—
698C2×C8—44no—
699C2×C8D4×D5312yes—
700C4⋊C4—532no—
701C4⋊C4—532no—
702C4⋊C4—1064no—
703C4⋊C4—1061no—
704C4⋊C4—1061no—
705C4⋊C4—1061no—
706C4⋊C4—1061no—
707C4⋊C4—1061no—
708C4⋊C4—1061no—
709C4⋊C4—1061no—
710C4⋊C4—1061no—
711C4⋊C4—2122no—
712C4⋊C4#1171992114yes—
713C22⋊C4—1064no—
714C22⋊C4—1064no—
715C22⋊C4—1064no—
716C22⋊C4—1064no—
717C22⋊C4—1064no—
718C22⋊C4—4241no—
719C22⋊C4—2122no—
720C22⋊C4—2122no—
721C22⋊C4#1171992114yes—
722C22⋊C4#1171992114yes—
723C42—4241no—
724C42—2122no—
725C42C2×C4×D5312yes—
726C42C2×C22⋊D5312yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—1062no—
738C23—1062no—
739C23—1062no—
740C23—1062no—
741C23—4244no—
742C23—4244no—
743C23—4244no—
744C23—4244no—
745C23—4244no—
746C23—2128no—
747C23—2121no—
748C23—2128no—
749C23—2121no—
750C23—2121no—
751C23—2121no—
752C23—2121no—
753C23—2121no—
754C23—2121no—
755C23—2121no—
756C23—2121no—
757C23—2121no—
758C23C2×#1171992112yes—
759C23C2×#1171992112yes—
760C23#1313323912yes—
761C23#1313323912yes—
762C23C22×D21211yescharacteristic
763Q8—1062no—
764Q8—1062no—
765Q8—2121no—
766Q8—2121no—
767D4—28no—
768D4—534no—
769D4—1062no—
770D4—1062no—
771D4—1062no—
772D4—1062no—
773D4—1062no—
774D4—4244no—
775D4—2128no—
776D4—2128no—
777D4—2121no—
778D4—2121no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
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—1062no—
796C2×C4—1062no—
797C2×C4—1062no—
798C2×C4—4244no—
799C2×C4—4244no—
800C2×C4—2128no—
801C2×C4—2121no—
802C2×C4—2121no—
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×C4—2121no—
815C2×C4—2121no—
816C2×C4C2×#1171992112yes—
817C2×C4C2×#1171992112yes—
818C2×C4C2×#1171992112yes—
819C2×C4C2×#1171992112yes—
820C2×C4C22×C4×D5311yescharacteristic
821C2×C4C2×D4×D5311yescharacteristic
822C2×C4C22×C22⋊D5311yescharacteristic
823C2×C4#41×D5311yescharacteristic
824C2×C4#1313326211yescharacteristic
825C2×C4#1313326311yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—1064no—
844C22—42416no—
845C22—4241no—
846C22—4241no—
847C22—4241no—
848C22—4241no—
849C22—2122no—
850C22—2122no—
851C22—2122no—
852C22—2122no—
853C22—2122no—
854C22—2122no—
855C22—2122no—
856C22—2122no—
857C22—2122no—
858C22#1681062014yescomplemented
859C22C22×#1171992111yescharacteristic
860C22D4×D21211yescharacteristic
861C22#1681126811yescharacteristic
862C22C2×#1313323911yescharacteristic
863C22C2×#1313323911yescharacteristic
864C22#1681142811yescharacteristic
865C22#1681143511yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—4241no—
871C4—4241no—
872C4—4241no—
873C4—2122no—
874C4—2122no—
875C4—2122no—
876C4C4×D4×D5311yescharacteristic
877C4#1681109511yescharacteristic
878C4D4×C22⋊D5311yescharacteristic
879C4#1681126111yescharacteristic
880C2—24no—
881C2—42no—
882C2—4242no—
883C2—2124no—
884C2D4×#1171992111yescharacteristic
885C2C2×#1681062011yescharacteristic
886C2#2028324211yescharacteristic
887C2#2028640211yescharacteristic
888C2#2028642711yescharacteristic
889C2#2028655211yescharacteristic
890C2#2028656711yescharacteristic
subgroupG/H
centerC23C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C8×D4×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811269C2
cosocleC22×C4×C53C24
hypercenterC2×C8×D4D53
hypocenterC53#22414
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×#16810620C2semidirect
3. C22×#13133139C2semidirect
4. #20277644C2semidirect
5. #20275645C2semidirect
6. #20275526C2semidirect
7. #20275143C2semidirect
8. #20275138C2semidirect
9. #20275035C2semidirect
10. #20275020C2semidirect
11. #20274726C2semidirect
12. #20274656C2semidirect
13. #20274647C2semidirect
14. C4×#13133139C2semidirect
15. C2×C8×D4×C53C2semidirect
19. #16811269C4semidirect
27. C2×#13133176C22semidirect
31. C2×#13133142C22semidirect
32. C2×#13133142C22semidirect
33. C2×#13133142C22semidirect
34. C2×#13133142C22semidirect
47. #16810489C22semidirect
49. #16810483C22semidirect
50. C4×C4⋊Dic53C22semidirect
52. #16810386C22semidirect
53. #16810386C22semidirect
54. #16810386C22semidirect
55. #16810386C22semidirect
57. C23×C8×C53C22semidirect
60. C2×C4⋊C8×C53C22semidirect
62. C2×C22⋊C8×C53C22semidirect
63. C2×C4×C8×C53C22semidirect
70. C2×#11719945C2×C4semidirect
87. #13133205C2×C4semidirect
92. #13133191C2×C4semidirect
96. C4×D212C2×C4semidirect
130. #13133139D4semidirect
398. C22×C53#416semidirect
436. C2×C8×D4D53semidirect
464. C23×C8C2×D53semidirect
479. C2×C4⋊C8C2×D53semidirect
495. C2×C22⋊C8C2×D53semidirect
496. C2×C4×C8C2×D53semidirect
509. C53#22414semidirect
858. C22#16810620semidirect

Maximal subgroups

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

subgroupindex
C2×#168112692
C2×#168106202
C22×#131331392
#202776442
#202756452
#202755262
#202751432
#202751382
#202750352
#202750202
#202747262
#202746562
#202746472
C4×#131331392
C2×C8×D4×C532
#2241453