Finite Group Databasebeta

← #27436748

Subgroups — #27436748

Order 13568.

1374 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810953C211yesmaximal, characteristic, complemented
2C2×#16810850C211yesmaximal, characteristic, complemented
3#20278166C211yesmaximal, characteristic, complemented
4#20276045C211yesmaximal, characteristic, complemented
5#20275901C211yesmaximal, characteristic, complemented
6#20275853C211yesmaximal, characteristic, complemented
7#20275718C211yesmaximal, characteristic, complemented
8#20275049C211yesmaximal, characteristic, complemented
9#20275033C211yesmaximal, characteristic, complemented
10#20275022C211yesmaximal, characteristic, complemented
11#20275008C211yesmaximal, characteristic, complemented
12#20274976C211yesmaximal, characteristic, complemented
13#20274908C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C2×C53×#547C211yesmaximal, characteristic
16C22×#11719923C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19C2×#13133196C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21#16810953—24no—
22#16810850—24no—
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×#13133140C2211yescharacteristic
27C2×#13133140C2211yescharacteristic
28C2×#13133140C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35#16810556—21no—
36#16810546—21no—
37#16810529C2211yescharacteristic
38#16810521C2211yescharacteristic
39#16810503—21no—
40#16810483C2211yescharacteristic
41#16810481—21no—
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C22×#41×C53—21no—
51C53×#547—24no—
52C53×#547—24no—
53C2×C4⋊Q8×C53C2211yescharacteristic
54C2×#123×C53—21no—
55C2×#123×C53—21no—
56C2×C22⋊Q8×C53—21no—
57C2×#121×C53C2211yescharacteristic
58C2×#121×C53C2211yescharacteristic
59C2×C4×D4×C53C2211yescharacteristic
60C2×C4×D4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×Dic106C2311yescharacteristic
64C23×Dic53—21no—
65C2×#11719923—22no—
66C2×#11719923—22no—
67C2×#11719923—41no—
68C22×#88322—22no—
69C22×#88322—22no—
70C22×#88322—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133196—22no—
76#13133196—22no—
77#13133196—22no—
78#13133196—41no—
79C2×C4⋊Dic53—21no—
80C2×C4⋊Dic53—22no—
81C2×C4⋊Dic53—41no—
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×#11719919—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91#13133148—22no—
92#13133148—22no—
93#13133148—22no—
94#13133140—22no—
95#13133140—22no—
96#13133140—22no—
97#13133138—22no—
98#13133138—22no—
99#13133138—41no—
100C22⋊#88322—22no—
101C22⋊#88322—22no—
102C22⋊#88322—41no—
103#13133124—21no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107C2×#41×C53—28no—
108C2×#41×C53—44no—
109C2×#41×C53—44no—
110C22×Q8×C53—21no—
111C22×D4×C53—21no—
112C22×D4×C53—21no—
113C22×D4×C53D411yescharacteristic
114C22×D4×C53C2311yescharacteristic
115C23×C4×C53—21no—
116C23×C4×C53—21no—
117C23×C4×C53—21no—
118C23×C4×C53C2311yescharacteristic
119C23×C4×C53C2311yescharacteristic
120C4⋊Q8×C53—22no—
121C4⋊Q8×C53—22no—
122#123×C53—28no—
123#123×C53—28no—
124C22⋊Q8×C53—28no—
125#121×C53—22no—
126#121×C53—22no—
127#121×C53—22no—
128#121×C53D414yes—
129C4×D4×C53—22no—
130C4×D4×C53—22no—
131C4×D4×C53—22no—
132C4×D4×C53—22no—
133C2×C4⋊C4×C53—22no—
134C2×C4⋊C4×C53—22no—
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53—21no—
137C2×C4⋊C4×C53—22no—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53D414yes—
140C2×C4⋊C4×C53D411yescharacteristic
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C22⋊C4×C53—21no—
145C2×C22⋊C4×C53—21no—
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53D411yescharacteristic
148C2×C22⋊C4×C53D411yescharacteristic
149C2×C42×C53C2311yescharacteristic
150C24×C53—21no—
151C24×C53C2×D411yescharacteristic
152C24×C53C2×D411yescharacteristic
153#41×C53—432no—
154C2×Q8×C53—24no—
155C2×Q8×C53—42no—
156C2×Q8×C53—42no—
157C2×D4×C53—22no—
158C2×D4×C53—22no—
159C2×D4×C53—24no—
160C2×D4×C53—24no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—21no—
166C2×D4×C53—42no—
167C2×D4×C53—42no—
168C2×D4×C53—42no—
169C2×D4×C53—42no—
170C2×D4×C53SD1614yescomplemented
171C2×D4×C53C2×D412yes—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—24no—
177C22×C4×C53—24no—
178C22×C4×C53—24no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—42no—
189C22×C4×C53—42no—
190C22×C4×C53—42no—
191C22×C4×C53—42no—
192C22×C4×C53—42no—
193C22×C4×C53—42no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D412yes—
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—42no—
206C22×Dic53—42no—
207C22×Dic53—81no—
208C2×Dic106—21no—
209C2×Dic106—21no—
210C2×Dic106—21no—
211C2×Dic106—21no—
212C2×Dic106—21no—
213C2×Dic106—21no—
214C4⋊C4×C53—24no—
215C4⋊C4×C53—24no—
216C4⋊C4×C53—24no—
217C4⋊C4×C53—22no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53—21no—
220C4⋊C4×C53—21no—
221C4⋊C4×C53C2×D412yes—
222C4⋊C4×C53C2×D412yes—
223C4⋊C4×C53C2×D412yes—
224C22⋊C4×C53—24no—
225C22⋊C4×C53—24no—
226C22⋊C4×C53—22no—
227C22⋊C4×C53—24no—
228C22⋊C4×C53—22no—
229C42×C53—21no—
230C42×C53—21no—
231C22⋊Dic53—42no—
232C22⋊Dic53—42no—
233C22⋊Dic53—81no—
234#11719923—44no—
235C4⋊Dic53—21no—
236C4⋊Dic53—21no—
237C4⋊Dic53—21no—
238C4⋊Dic53—21no—
239C4⋊Dic53—21no—
240C4⋊Dic53—42no—
241C4⋊Dic53#4112yescomplemented
242#11719919—42no—
243#11719919—42no—
244#11719919—81no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—44no—
257C2×#88322#4112yescomplemented
258C23×C53—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—22no—
269C23×C53—41no—
270C23×C53—41no—
271C23×C53—41no—
272C23×C53—41no—
273C23×C53—41no—
274C23×C53—41no—
275C23×C53#12012yes—
276C23×C53C2×SD1612yes—
277C23×C53C2×SD1612yes—
278C23×C53AGL(1,ℤ/8)12yes—
279C23×C53C22×D411yescharacteristic
280Q8×C53—48no—
281D4×C53—28no—
282D4×C53—22no—
283D4×C53—22no—
284D4×C53—48no—
285D4×C53—48no—
286D4×C53—41no—
287D4×C53—41no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—48no—
306C2×C4×C53—48no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—48no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53#12012yes—
319C2×C4×C53C2×SD1612yes—
320C2×C4×C53C22×D411yescharacteristic
321C2×C4×C53C22×D411yescharacteristic
322C2×C4×C53C2×#4111yescharacteristic
323C2×C4×C53C2×#4111yescharacteristic
324C2×C4×C53H(5,𝔽2)11yescharacteristic
325C2×C4×C532−1+411yescharacteristic
326C2×Dic53—22no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53—41no—
330C2×Dic53—41no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—41no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—84no—
339Dic106—41no—
340Dic106—41no—
341Dic106—41no—
342Dic106—41no—
343#88322—22no—
344#88322—41no—
345#88322—41no—
346#88322—41no—
347#25531—531nomaximal, Sylow
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—22no—
353C22×C53—22no—
354C22×C53—22no—
355C22×C53—22no—
356C22×C53—22no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—81no—
365C22×C53—81no—
366C22×C53—81no—
367C22×C53—81no—
368C22×C53#45014yes—
369C22×C53C2×#12011yescharacteristic
370C22×C53#54611yescharacteristic
371C22×C53#54711yescharacteristic
372C22×C53C22×SD1611yescharacteristic
373C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C53#57711yescharacteristic
375C22×C53#57811yescharacteristic
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—41no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53—41no—
383C4×C53#53211yescharacteristic
384C4×C53#53711yescharacteristic
385C4×C53#54611yescharacteristic
386C4×C53#54711yescharacteristic
387Dic53—42no—
388Dic53—81no—
389Dic53—81no—
390Dic53—81no—
391C2×#547D5311yescharacteristic
392C2×#483—531no—
393C2×#465—531no—
394#2417—531no—
395#2058—531no—
396#2034—531no—
397#2024—531no—
398#2000—531no—
399#1877—531no—
400#1874—531no—
401#1872—531no—
402#1869—531no—
403#1864—531no—
404#1853—531no—
405C2×#340—531no—
406C2×C53—24no—
407C2×C53—42no—
408C2×C53—82no—
409C2×C53#243011yescharacteristic
410C2×C53C2×#45011yescharacteristic
411C2×C53#301311yescharacteristic
412C2×C53#329811yescharacteristic
413C2×C53#330611yescharacteristic
414C2×C53#333511yescharacteristic
415C2×C53#334311yescharacteristic
416C22×#41—21no—
417C22×SD16—531no—
418C23×C8—531no—
419#547—24no—
420#547—24no—
421C2×C4⋊Q8C2×D5311yescharacteristic
422C2×#123—21no—
423C2×#123—21no—
424C2×C22⋊Q8—21no—
425C2×C22⋊Q8—531no—
426C2×C22⋊Q8—531no—
427C2×#121C2×D5311yescharacteristic
428C2×#121C2×D5311yescharacteristic
429C2×C4×D4C2×D5311yescharacteristic
430C2×C4×D4C2×D5311yescharacteristic
431C22×C4⋊C4—531no—
432C22×C4⋊C4C2×D5311yescharacteristic
433C22×C4⋊C4C2×D5311yescharacteristic
434#483—1064no—
435#465—1064no—
436C2×#106—531no—
437C2×#106—531no—
438C2×#106—531no—
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8—531no—
447C2×C22⋊C8—531no—
448#398—1061no—
449#396—1061no—
450#391—531no—
451#389—531no—
452#386—1061no—
453#380—531no—
454#380—1061no—
455#340—531no—
456#340—531no—
457#340—531no—
458#340—531no—
459#340—531no—
460#340—531no—
461#336—531no—
462#336—531no—
463C53#2553111yescharacteristic, complemented, Sylow
464C2×#41—28no—
465C2×#41—44no—
466C2×#41—44no—
467C22×Q8—21no—
468C22×Q8—531no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4C22⋊D5311yescharacteristic
472C22×D4C22×D5311yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—1061no—
477C23×C4C22×D5311yescharacteristic
478C23×C4C22×D5311yescharacteristic
479C2×SD16—1062no—
480C2×SD16—1062no—
481C2×SD16—2121no—
482C22×C8—531no—
483C22×C8—531no—
484C22×C8—531no—
485C22×C8—531no—
486C22×C8—1062no—
487C22×C8—1062no—
488C22×C8—2121no—
489C4⋊Q8—22no—
490C4⋊Q8—22no—
491#123—28no—
492#123—28no—
493C22⋊Q8—28no—
494C22⋊Q8—1062no—
495C22⋊Q8—1062no—
496C22⋊Q8—1062no—
497C22⋊Q8—2121no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121C22⋊D5314yes—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—1062no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—2121no—
521C2×C4⋊C4C22⋊D5311yescharacteristic
522C2×C4⋊C4C22⋊D5314yes—
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C4⋊C4C22×D5311yescharacteristic
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4C22⋊D5311yescharacteristic
533C2×C22⋊C4C22⋊D5311yescharacteristic
534C2×C42C22×D5311yescharacteristic
535#106—1062no—
536#106—1062no—
537#106—1062no—
538#103—1062no—
539#103—1062no—
540#103—1062no—
541#102—1062no—
542#102—1062no—
543#102—2121no—
544C22⋊C8—1062no—
545C22⋊C8—1062no—
546C22⋊C8—2121no—
547#95—1061no—
548#95—1061no—
549#95—1061no—
550#95—1061no—
551C24—21no—
552C24C2×C22⋊D5311yescharacteristic
553C24C2×C22⋊D5311yescharacteristic
554#41—432no—
555C2×Q8—24no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8—1061no—
559C2×Q8—1061no—
560C2×Q8—1061no—
561C2×Q8—1061no—
562C2×Q8—1061no—
563C2×Q8—1061no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4#1171992314yescomplemented
578C2×D4C2×C22⋊D5312yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—4241no—
606C22×C4—2122no—
607C22×C4—2122no—
608C22×C4C2×C22⋊D5311yescharacteristic
609C22×C4C2×C22⋊D5311yescharacteristic
610C22×C4C2×C22⋊D5311yescharacteristic
611C22×C4C2×C22⋊D5312yes—
612C22×C4C2×C22⋊D5312yes—
613C22×C4C2×C22⋊D5311yescharacteristic
614C22×C4C23×D5311yescharacteristic
615SD16—2124no—
616C2×C8—532no—
617C2×C8—1061no—
618C2×C8—1061no—
619C2×C8—1061no—
620C2×C8—1061no—
621C2×C8—1061no—
622C2×C8—1061no—
623C2×C8—1061no—
624C2×C8—1061no—
625C2×C8—1061no—
626C2×C8—1061no—
627C2×C8—1061no—
628C2×C8—2124no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—532no—
637C4⋊C4—1061no—
638C4⋊C4—1061no—
639C4⋊C4—1061no—
640C4⋊C4—1061no—
641C4⋊C4—1061no—
642C4⋊C4—4241no—
643C4⋊C4—2122no—
644C4⋊C4—2122no—
645C4⋊C4—2122no—
646C4⋊C4C2×C22⋊D5312yes—
647C4⋊C4C2×C22⋊D5312yes—
648C4⋊C4C2×C22⋊D5312yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—24no—
653C22⋊C4—22no—
654C22⋊C4—4241no—
655C22⋊C4—2122no—
656C22⋊C4—2122no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23#1313318612yes—
677C23C2×#1171992312yes—
678C23C2×#1171992312yes—
679C23#1313324312yes—
680C23C22×C22⋊D5311yescharacteristic
681Q8—48no—
682Q8—2121no—
683Q8—2121no—
684Q8—2121no—
685Q8—2121no—
686D4—28no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—48no—
691D4—41no—
692D4—41no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—48no—
711C2×C4—48no—
712C2×C4—48no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—1062no—
724C2×C4—4244no—
725C2×C4—2121no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4—2121no—
730C2×C4—2121no—
731C2×C4—2121no—
732C2×C4—2121no—
733C2×C4—2121no—
734C2×C4—2121no—
735C2×C4—2121no—
736C2×C4#1313318612yes—
737C2×C4C2×#1171992312yes—
738C2×C4C22×C22⋊D5311yescharacteristic
739C2×C4C22×C22⋊D5311yescharacteristic
740C2×C4#41×D5311yescharacteristic
741C2×C4#41×D5311yescharacteristic
742C2×C4#1313326311yescharacteristic
743C2×C4#1313326411yescharacteristic
744C8—1062no—
745C8—2121no—
746C8—2121no—
747C8—2121no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22#1681077414yes—
769C22C2×#1313318611yescharacteristic
770C22#1681126111yescharacteristic
771C22#1681127211yescharacteristic
772C22C22×#1171992311yescharacteristic
773C22C2×#1313324311yescharacteristic
774C22#1681143111yescharacteristic
775C22#1681143811yescharacteristic
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—4241no—
784C4—4241no—
785C4—4241no—
786C4—2122no—
787C4#1681116911yescharacteristic
788C4#1681120111yescharacteristic
789C4#1681126111yescharacteristic
790C4#1681127211yescharacteristic
791C2—24no—
792C2—42no—
793C2—82no—
794C2#2027831911yescharacteristic
795C2C2×#1681077411yescharacteristic
796C2#2028403011yescharacteristic
797C2#2028657411yescharacteristic
798C2#2028667011yescharacteristic
799C2#2028707211yescharacteristic
800C2#2028714911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#547C2
socleC23×C53C22×D4
hypercenterC2×#547D53
hypocenterC53#25531
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16810953C2semidirect
2. C2×#16810850C2semidirect
3. #20278166C2semidirect
4. #20276045C2semidirect
5. #20275901C2semidirect
6. #20275853C2semidirect
7. #20275718C2semidirect
8. #20275049C2semidirect
9. #20275033C2semidirect
10. #20275022C2semidirect
11. #20275008C2semidirect
12. #20274976C2semidirect
13. #20274908C2semidirect
14. C2×#16810385C2semidirect
170. C2×D4×C53SD16semidirect
241. C4⋊Dic53#41semidirect
257. C2×#88322#41semidirect
463. C53#25531semidirect
577. C2×D4#11719923semidirect

Maximal subgroups

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

subgroupindex
C2×#168109532
C2×#168108502
#202781662
#202760452
#202759012
#202758532
#202757182
#202750492
#202750332
#202750222
#202750082
#202749762
#202749082
C2×#168103852
C2×C53×#5472
#2553153