Finite Group Databasebeta

← #27400442

Subgroups — #27400442

Order 13568.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811277C211yesmaximal, characteristic
2#20277644C211yesmaximal, characteristic, complemented
3#20275688C211yesmaximal, characteristic, complemented
4#20275662C211yesmaximal, characteristic, complemented
5#20275153C211yesmaximal, characteristic, complemented
6#20275143C211yesmaximal, characteristic, complemented
7#20275035C211yesmaximal, characteristic, complemented
8#20275030C211yesmaximal, characteristic, complemented
9#20274806C211yesmaximal, characteristic, complemented
10#20274802C211yesmaximal, characteristic, complemented
11#20274726C211yesmaximal, characteristic, complemented
12#20274541C211yesmaximal, characteristic, complemented
13#20274435C211yesmaximal, characteristic, complemented
14C2×#16810386C211yesmaximal, characteristic, complemented
15C2×C53×#435C211yesmaximal, characteristic, complemented
16C22×#11719947—21no—
17#16811277—24no—
18#16811277C418yescomplemented
19C2×#13133217C2211yescharacteristic
20C2×#13133201—21no—
21C2×#13133201—21no—
22C2×#13133197—21no—
23C2×#13133191C2211yescharacteristic
24C2×#13133191C2211yescharacteristic
25C2×C4×D212C2211yescharacteristic
26C2×#13133176C2211yescharacteristic
27C22×C4⋊Dic53C2211yescharacteristic
28C22×C4⋊Dic53C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic
30C2×#13133139C2211yescharacteristic
31C2×#13133139C2211yescharacteristic
32C2×#13133139C2211yescharacteristic
33C2×#13133139C2211yescharacteristic
34#16810516—21no—
35#16810509—21no—
36#16810503—21no—
37#16810489C2211yescharacteristic
38#16810483C2211yescharacteristic
39#16810483C2211yescharacteristic
40C4×C4⋊Dic53C2211yescharacteristic
41C22⋊C4×Dic53—21no—
42#16810386C2211yescharacteristic
43#16810386C2211yescharacteristic
44#16810386C2211yescharacteristic
45#16810386C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810386C2211yescharacteristic
52#16810386C2211yescharacteristic
53#16810386C2211yescharacteristic
54C22×M16×C53C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C2×C4×D4×C53C2211yescharacteristic
57C53×#435—24no—
58C2×C4⋊C8×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C2×C22⋊C8×C53C2211yescharacteristic
61C2×#97×C53C2211yescharacteristic
62C2×#11719947—28no—
63C2×#11719947—44no—
64C2×#11719947—44no—
65C22×Dic106—21no—
66C22×D212C2311yescharacteristic
67C22×C22⋊D53—21no—
68C22×C22⋊D53—21no—
69C23×Dic53—21no—
70C23×Dic53—21no—
71C23×Dic53—21no—
72C22×C4×D53—21no—
73#13133217—22no—
74#13133217C2×C414yescomplemented
75#13133201—28no—
76#13133201—28no—
77#13133197—28no—
78#13133191—22no—
79#13133191—22no—
80#13133191C2×C414yes—
81#13133191C2×C414yescomplemented
82C4×D212—22no—
83C4×D212C2×C414yescomplemented
84#13133176—22no—
85#13133176—41no—
86C2×C4⋊Dic53—22no—
87C2×C4⋊Dic53—22no—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53—21no—
90C2×C4⋊Dic53—21no—
91C2×C4⋊Dic53—21no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53—41no—
94C2×C4⋊Dic53C2×C414yes—
95C2×C4⋊Dic53C2×C414yescomplemented
96C2×C4⋊Dic53C2311yescharacteristic
97C2×C4⋊Dic53C2311yescharacteristic
98C2×C4⋊Dic53C2311yescharacteristic
99C2×C4⋊Dic53C2311yescharacteristic
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×C4⋊Dic53C2311yescharacteristic
103C2×C22⋊Dic53—21no—
104C2×C22⋊Dic53—21no—
105C2×C22⋊Dic53—21no—
106C2×#11719921—21no—
107C2×#11719921—21no—
108C2×#11719921—21no—
109C2×C4×Dic53—21no—
110C2×C4×Dic53—21no—
111#13133139—22no—
112#13133139—22no—
113#13133139—41no—
114#13133139—41no—
115#13133124—21no—
116#13133124—21no—
117#13133124—21no—
118#13133124—21no—
119#13133124—21no—
120C22×D4×C53D411yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C2×M16×C53—22no—
124C2×M16×C53—22no—
125C2×M16×C53—41no—
126C22×C8×C53—22no—
127C22×C8×C53—22no—
128C22×C8×C53—41no—
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133C4×D4×C53C2×C414yes—
134C4×D4×C53D414yes—
135C2×C4⋊C4×C53D411yescharacteristic
136C2×C22⋊C4×C53D411yescharacteristic
137C2×C22⋊C4×C53D411yescharacteristic
138C2×C42×C53C2311yescharacteristic
139C4⋊C8×C53—22no—
140C22⋊C8×C53—22no—
141C22⋊C8×C53—22no—
142#97×C53—22no—
143C24×C53C2×D411yescharacteristic
144C24×C53C2×D411yescharacteristic
145C23×D53—21no—
146C2×D4×C53—22no—
147C2×D4×C53—22no—
148C2×D4×C53C22⋊C414yes—
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—21no—
157C22×C4×C53C22×C412yes—
158C22×C4×C53C22×C412yes—
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D411yescharacteristic
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53C2×D411yescharacteristic
163C22×C4×C53C2×D412yes—
164C22×C4×C53C2×D412yes—
165C22×C4×C53C2411yescharacteristic
166C2×C22⋊D53—24no—
167C2×C22⋊D53—24no—
168C2×C22⋊D53—42no—
169C2×C22⋊D53—42no—
170C2×C22⋊D53—42no—
171C2×C22⋊D53—42no—
172C22×Dic53—24no—
173C22×Dic53—24no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—42no—
182C22×Dic53—42no—
183C22×Dic53—42no—
184C22×Dic53—42no—
185C22×Dic53—42no—
186C22×Dic53—42no—
187C22×Dic53—81no—
188#11719947—432no—
189C2×D212—21no—
190C2×D212—21no—
191C2×D212—21no—
192C2×D212—21no—
193C2×D212—21no—
194C2×D212C22×C412yes—
195C2×C4×D53—24no—
196C2×C4×D53—42no—
197C2×C4×D53—42no—
198C2×Dic106—24no—
199C2×Dic106—42no—
200C2×Dic106—42no—
201M16×C53—44no—
202C2×C8×C53—21no—
203C2×C8×C53—21no—
204C2×C8×C53—21no—
205C2×C8×C53—21no—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53—21no—
211C2×C8×C53—21no—
212C2×C8×C53—21no—
213C2×C8×C53—44no—
214C2×C8×C53#4112yescomplemented
215C4⋊C4×C53C22⋊C414yes—
216C22⋊C4×C53C22⋊C414yes—
217C22⋊C4×C53C22⋊C414yes—
218C42×C53C22×C412yes—
219C42×C53C2×D412yes—
220C22⋊Dic53—42no—
221C22⋊Dic53—42no—
222C22⋊Dic53—81no—
223#11719921—24no—
224#11719921—24no—
225#11719921—24no—
226C4⋊Dic53—24no—
227C4⋊Dic53—24no—
228C4⋊Dic53—24no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53—21no—
235C4⋊Dic53—21no—
236C4⋊Dic53—21no—
237C4⋊Dic53—21no—
238C4⋊Dic53—21no—
239C4⋊Dic53—42no—
240C4⋊Dic53C22×C412yes—
241C4⋊Dic53C22×C412yes—
242C4⋊Dic53C22×C412yes—
243C4⋊Dic53#4112yescomplemented
244C4×Dic53—42no—
245C4×Dic53—81no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53C2×C22⋊C412yes—
257C23×C53C2×C22⋊C412yes—
258C23×C53AGL(1,ℤ/8)12yes—
259C23×C53AGL(1,ℤ/8)12yes—
260C23×C53C22×D411yescharacteristic
261C22×D53—22no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268D4×C53—28no—
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—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53C2×C22⋊C412yes—
286C2×C4×C53C2×C22⋊C412yes—
287C2×C4×C53C2×C22⋊C412yes—
288C2×C4×C53C2×C22⋊C412yes—
289C2×C4×C53C23×C411yescharacteristic
290C2×C4×C53C22×D411yescharacteristic
291C2×C4×C53C2×#4111yescharacteristic
292C2×C4×C53C2×#4111yescharacteristic
293C2×C4×C53H(5,𝔽2)11yescharacteristic
294C2×C4×C532−1+411yescharacteristic
295C22⋊D53—48no—
296C22⋊D53—48no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—48no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—48no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—84no—
321D212—22no—
322D212—22no—
323D212—41no—
324D212—41no—
325C4×D53—48no—
326Dic106—48no—
327C8×C53—22no—
328C8×C53—41no—
329C8×C53—41no—
330C8×C53—41no—
331#22495—531nomaximal, Sylow
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—41no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53#41814yes—
346C22×C53C22×C22⋊C411yescharacteristic
347C22×C53#54611yescharacteristic
348C22×C53#54711yescharacteristic
349C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C53#57711yescharacteristic
352C22×C53#57811yescharacteristic
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—81no—
357C2×D53—81no—
358C2×D53—81no—
359C2×D53—81no—
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—22no—
364C4×C53C4×#4111yescharacteristic
365C4×C53#52011yescharacteristic
366C4×C53#54611yescharacteristic
367C4×C53#54711yescharacteristic
368Dic53—42no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372Dic53—81no—
373Dic53—81no—
374Dic53—81no—
375C2×#547—531no—
376C2×#435D5311yescharacteristic, complemented
377#2352—531no—
378#1993—531no—
379#1987—531no—
380#1895—531no—
381#1893—531no—
382#1875—531no—
383#1874—531no—
384#1824—531no—
385#1823—531no—
386#1804—531no—
387#1762—531no—
388#1736—531no—
389C2×#340—531no—
390C2×C53—24no—
391C2×C53—42no—
392C2×C53#233911yescharacteristic
393C2×C53C2×#41811yescharacteristic
394C2×C53#289811yescharacteristic
395C2×C53#330611yescharacteristic
396C2×C53#330811yescharacteristic
397C2×C53#334311yescharacteristic
398C2×C53#334511yescharacteristic
399D53—82no—
400C22×#41—1061no—
401C22×M16C2×D5311yescharacteristic
402C23×C8C2×D5311yescharacteristic
403#547—538no—
404#547—1064no—
405C2×C4⋊Q8—531no—
406C2×#123—1061no—
407C2×#123—1061no—
408C2×C22⋊Q8—1061no—
409C2×#121—531no—
410C2×#121—531no—
411C2×C4×D4—531no—
412C2×C4×D4C2×D5311yescharacteristic
413C2×#117—531no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417#435—24no—
418C2×C4⋊C8C2×D5311yescharacteristic
419C2×#102—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×C22⋊C8C2×D5311yescharacteristic
424C2×C22⋊C8C2×D5311yescharacteristic
425C2×#97C2×D5311yescharacteristic
426#388—1061no—
427#387—1061no—
428#386—1061no—
429#382—531no—
430#380—531no—
431#380—531no—
432C4×C4⋊C4—531no—
433C4×C22⋊C4—1061no—
434#340—531no—
435#340—531no—
436#340—531no—
437#340—531no—
438#340—531no—
439#340—531no—
440#340—531no—
441#340—531no—
442#340—531no—
443#340—531no—
444#340—531no—
445#340—531no—
446C53#2249511yescharacteristic, complemented, Sylow
447C2×#41—1068no—
448C2×#41—2124no—
449C2×#41—2124no—
450C22×Q8—1061no—
451C22×D4—531no—
452C22×D4—1061no—
453C22×D4—1061no—
454C22×D4D21211yescharacteristic
455C23×C4—1061no—
456C23×C4—1061no—
457C23×C4—1061no—
458C23×C4—1061no—
459C23×C4C22×D5311yescharacteristic
460C23×C4C22×D5311yescharacteristic
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—41no—
464C22×C8—22no—
465C22×C8—22no—
466C22×C8—41no—
467C22×C8C22×D5311yescharacteristic
468C22×C8C22×D5311yescharacteristic
469C22×C8C22×D5311yescharacteristic
470C22×C8C22×D5311yescharacteristic
471C4⋊Q8—534no—
472C4⋊Q8—1062no—
473#123—1068no—
474#123—1068no—
475C22⋊Q8—1068no—
476#121—534no—
477#121—534no—
478#121—1062no—
479#121—1062no—
480C4×D4—534no—
481C4×D4—1062no—
482C4×D4C4×D5314yes—
483C4×D4C22⋊D5314yes—
484#117—1062no—
485#117—2121no—
486C2×C4⋊C4—534no—
487C2×C4⋊C4—534no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—1062no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1062no—
500C2×C4⋊C4—1062no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—2121no—
503C2×C4⋊C4D21211yescharacteristic
504C2×C22⋊C4—1061no—
505C2×C22⋊C4—1061no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4D21211yescharacteristic
511C2×C22⋊C4D21211yescharacteristic
512C2×C42—1061no—
513C2×C42—1061no—
514C2×C42C22×D5311yescharacteristic
515C4⋊C8—22no—
516#102—1062no—
517#102—1062no—
518#102—2121no—
519#102—2121no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522#97—22no—
523#95—1061no—
524#95—1061no—
525#95—1061no—
526#95—1061no—
527#95—1061no—
528C24—1061no—
529C24C2×D21211yescharacteristic
530C24C2×D21211yescharacteristic
531#41—21232no—
532C2×Q8—1064no—
533C2×Q8—2122no—
534C2×Q8—2122no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—532no—
538C2×D4—1064no—
539C2×D4—1064no—
540C2×D4—1061no—
541C2×D4—1061no—
542C2×D4—1061no—
543C2×D4—1061no—
544C2×D4—1061no—
545C2×D4—2122no—
546C2×D4—2122no—
547C2×D4—2122no—
548C2×D4—2122no—
549C2×D4#1171992114yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—1064no—
559C22×C4—1064no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1064no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—4241no—
569C22×C4—2122no—
570C22×C4—2122no—
571C22×C4—2122no—
572C22×C4—2122no—
573C22×C4—2122no—
574C22×C4—2122no—
575C22×C4—2122no—
576C22×C4—2122no—
577C22×C4C2×C4×D5312yes—
578C22×C4C2×C4×D5312yes—
579C22×C4C2×D21211yescharacteristic
580C22×C4C2×D21211yescharacteristic
581C22×C4C2×D21211yescharacteristic
582C22×C4C2×D21211yescharacteristic
583C22×C4C2×C22⋊D5312yes—
584C22×C4C2×C22⋊D5312yes—
585C22×C4C23×D5311yescharacteristic
586M16—44no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—44no—
599C2×C8#1171994712yescomplemented
600C4⋊C4—532no—
601C4⋊C4—532no—
602C4⋊C4—532no—
603C4⋊C4—532no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1061no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—1061no—
611C4⋊C4—1061no—
612C4⋊C4—1061no—
613C4⋊C4—1061no—
614C4⋊C4—1061no—
615C4⋊C4—1061no—
616C4⋊C4—1061no—
617C4⋊C4—2122no—
618C4⋊C4#1171992114yes—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—4241no—
623C22⋊C4—2122no—
624C22⋊C4—2122no—
625C22⋊C4#1171992114yes—
626C22⋊C4#1171992114yes—
627C42—4241no—
628C42—2122no—
629C42C2×C4×D5312yes—
630C42C2×C22⋊D5312yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—1062no—
642C23—2121no—
643C23—2121no—
644C23—2121no—
645C23—2121no—
646C23—2121no—
647C23—2121no—
648C23C2×#1171992112yes—
649C23C2×#1171992112yes—
650C23#1313324512yes—
651C23#1313324512yes—
652C23C22×D21211yescharacteristic
653Q8—2128no—
654D4—28no—
655D4—1062no—
656D4—1062no—
657D4—2128no—
658D4—2128no—
659D4—2121no—
660D4—2121no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—4244no—
682C2×C4—2128no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2128no—
693C2×C4—2128no—
694C2×C4—2121no—
695C2×C4—2121no—
696C2×C4—2121no—
697C2×C4—2121no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4C2×#1171992112yes—
703C2×C4C2×#1171992112yes—
704C2×C4C2×#1171992112yes—
705C2×C4C2×#1171992112yes—
706C2×C4C22×C4×D5311yescharacteristic
707C2×C4C22×C22⋊D5311yescharacteristic
708C2×C4#41×D5311yescharacteristic
709C2×C4C2×#1171994711yescharacteristic
710C2×C4#1313326211yescharacteristic
711C2×C4#1313326411yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—4241no—
730C22—4241no—
731C22—4241no—
732C22—4241no—
733C22—2122no—
734C22—2122no—
735C22—2122no—
736C22#1681062914yes—
737C22C22×#1171992111yescharacteristic
738C22#1681126811yescharacteristic
739C22#1681127711yescharacteristic
740C22C2×#1313324511yescharacteristic
741C22C2×#1313324511yescharacteristic
742C22#1681143511yescharacteristic
743C22#1681144011yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—4241no—
749C4—4241no—
750C4—4241no—
751C4—2122no—
752C4—2122no—
753C4—2122no—
754C4—2122no—
755C4C4×#1171994711yescharacteristic
756C4#1681110211yescharacteristic
757C4#1681126711yescharacteristic
758C4#1681127211yescharacteristic
759C2—24no—
760C2—42no—
761C2—4242no—
762C2#2027754011yescharacteristic
763C2C2×#1681062911yescharacteristic
764C2#2028324911yescharacteristic
765C2#2028667811yescharacteristic
766C2#2028670811yescharacteristic
767C2#2028715711yescharacteristic
768C2#2028718711yescharacteristic
subgroupG/H
centerC23C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC2×#16811277C2
cosocleC22×C4×C53C24
hypercenterC2×#435D53
hypocenterC53#22495
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #20277644C2semidirect
3. #20275688C2semidirect
4. #20275662C2semidirect
5. #20275153C2semidirect
6. #20275143C2semidirect
7. #20275035C2semidirect
8. #20275030C2semidirect
9. #20274806C2semidirect
10. #20274802C2semidirect
11. #20274726C2semidirect
12. #20274541C2semidirect
13. #20274435C2semidirect
14. C2×#16810386C2semidirect
15. C2×C53×#435C2semidirect
18. #16811277C4semidirect
74. #13133217C2×C4semidirect
81. #13133191C2×C4semidirect
83. C4×D212C2×C4semidirect
95. C2×C4⋊Dic53C2×C4semidirect
214. C2×C8×C53#41semidirect
243. C4⋊Dic53#41semidirect
376. C2×#435D53semidirect
446. C53#22495semidirect
599. C2×C8#11719947semidirect

Maximal subgroups

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

subgroupindex
C2×#168112772
#202776442
#202756882
#202756622
#202751532
#202751432
#202750352
#202750302
#202748062
#202748022
#202747262
#202745412
#202744352
C2×#168103862
C2×C53×#4352
#2249553