Finite Group Databasebeta

← #27417286

Subgroups — #27417286

Order 13568.

1284 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810961C211yesmaximal, characteristic, complemented
2C2×#16810632C211yesmaximal, characteristic, complemented
3#20279012C211yesmaximal, characteristic
4#20275958C211yesmaximal, characteristic, complemented
5#20275958C211yesmaximal, characteristic, complemented
6#20275915C211yesmaximal, characteristic, complemented
7#20275908C211yesmaximal, characteristic, complemented
8#20275149C211yesmaximal, characteristic, complemented
9#20275013C211yesmaximal, characteristic
10#20274983C211yesmaximal, characteristic, complemented
11#20274969C211yesmaximal, characteristic, complemented
12#20274650C211yesmaximal, characteristic, complemented
13#20274650C211yesmaximal, characteristic, complemented
14#20274650C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C53C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C2×#13133176C2211yescharacteristic
18#16810961—24no—
19C2×#13133150C2211yescharacteristic
20C2×#13133148C2211yescharacteristic
21#16810632—24no—
22C2×#13133141C2211yescharacteristic
23C2×#13133141C2211yescharacteristic
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133141C2211yescharacteristic
31C2×#13133141C2211yescharacteristic
32C2×#13133141C2211yescharacteristic
33C2×#13133141C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37#16810551—21no—
38#16810537—21no—
39#16810521C2211yescharacteristic
40#16810521C2211yescharacteristic
41#16810511—21no—
42#16810504—21no—
43#16810483C2211yescharacteristic
44#16810483C2211yescharacteristic
45#16810483C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C23×Q8×C53C2211yescharacteristic
51C23×Q8×C53C2211yescharacteristic
52D4×Q8×C53—24no—
53D4×Q8×C53—24no—
54C2×C4⋊Q8×C53—21no—
55C2×C4⋊Q8×C53C2211yescharacteristic
56C2×C22⋊Q8×C53—21no—
57C2×C22⋊Q8×C53—21no—
58C2×C22⋊Q8×C53C2211yescharacteristic
59C2×C22⋊Q8×C53C2211yescharacteristic
60C2×C4×Q8×C53C2211yescharacteristic
61C2×C4×D4×C53—21no—
62C2×C4×D4×C53C2211yescharacteristic
63C2×#11719917—22no—
64C2×#11719917—41no—
65C2×#11719917—41no—
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70#13133176—22no—
71#13133176—22no—
72C2×C4⋊Dic53C2311yescharacteristic
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×#11719919—21no—
77C2×#11719919—21no—
78C2×C22⋊Dic53—21no—
79C2×C22⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82C2×C4×Dic53—21no—
83#13133150—22no—
84#13133148—22no—
85#13133141—22no—
86#13133141—22no—
87#13133141—22no—
88#13133141—22no—
89#13133141—22no—
90#13133141—22no—
91#13133141—22no—
92#13133141—22no—
93#13133141—41no—
94#13133141—41no—
95#13133141—41no—
96#13133141—41no—
97C22⋊#88322—22no—
98C22⋊#88322—41no—
99C22⋊#88322—41no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105C22×Q8×C53—22no—
106C22×Q8×C53—22no—
107C22×Q8×C53—21no—
108C22×Q8×C53—21no—
109C22×Q8×C53—22no—
110C22×Q8×C53—22no—
111C22×Q8×C53—22no—
112C22×Q8×C53—22no—
113C22×Q8×C53—22no—
114C22×Q8×C53—41no—
115C22×Q8×C53—41no—
116C22×Q8×C53—41no—
117C22×Q8×C53—41no—
118C22×Q8×C53D414yes—
119C22×Q8×C53C2311yescharacteristic
120C22×Q8×C53C2311yescharacteristic
121C22×Q8×C53C2311yescharacteristic
122C22×D4×C53D411yescharacteristic
123C23×C4×C53—21no—
124C23×C4×C53—21no—
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C4⋊Q8×C53—28no—
128C4⋊Q8×C53—22no—
129C4⋊Q8×C53—22no—
130C22⋊Q8×C53—28no—
131C22⋊Q8×C53—28no—
132C22⋊Q8×C53—22no—
133C22⋊Q8×C53—22no—
134C22⋊Q8×C53—22no—
135C22⋊Q8×C53D414yes—
136C4×Q8×C53—22no—
137C4×Q8×C53—22no—
138C4×D4×C53—28no—
139C4×D4×C53—22no—
140C4×D4×C53—22no—
141C2×C4⋊C4×C53—21no—
142C2×C4⋊C4×C53—21no—
143C2×C4⋊C4×C53—21no—
144C2×C4⋊C4×C53—21no—
145C2×C4⋊C4×C53—21no—
146C2×C4⋊C4×C53D411yescharacteristic
147C2×C4⋊C4×C53C2311yescharacteristic
148C2×C22⋊C4×C53—21no—
149C2×C22⋊C4×C53—21no—
150C2×C22⋊C4×C53D411yescharacteristic
151C2×C22⋊C4×C53D411yescharacteristic
152C2×C42×C53—21no—
153C2×C42×C53C2311yescharacteristic
154C24×C53C2×D411yescharacteristic
155C24×C53C2×D411yescharacteristic
156C2×Q8×C53—24no—
157C2×Q8×C53—24no—
158C2×Q8×C53—21no—
159C2×Q8×C53—21no—
160C2×Q8×C53—21no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—28no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53—21no—
172C2×Q8×C53—42no—
173C2×Q8×C53—42no—
174C2×Q8×C53—42no—
175C2×Q8×C53—42no—
176C2×Q8×C53—44no—
177C2×Q8×C53—44no—
178C2×Q8×C53—44no—
179C2×Q8×C53—44no—
180C2×Q8×C53—44no—
181C2×Q8×C53—44no—
182C2×Q8×C53—44no—
183C2×Q8×C53C2×D412yes—
184C2×Q8×C53C2×D412yes—
185C2×Q8×C53C2×D412yes—
186C2×Q8×C53#4112yes—
187C2×Q8×C53#4112yes—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—24no—
197C22×C4×C53—24no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—42no—
208C22×C4×C53—42no—
209C22×C4×C53—42no—
210C22×C4×C53—42no—
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D412yes—
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2411yescharacteristic
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—24no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—22no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53C2×D412yes—
230C22⋊C4×C53—24no—
231C22⋊C4×C53—24no—
232C22⋊C4×C53—22no—
233C22⋊C4×C53—22no—
234C42×C53—24no—
235C42×C53—21no—
236C42×C53—21no—
237C22⋊Dic53—42no—
238C22⋊Dic53—42no—
239C22⋊Dic53—81no—
240C22⋊Dic53—81no—
241C4⋊Dic53—21no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—21no—
249#11719919—42no—
250#11719919—81no—
251C4×Dic53—42no—
252#11719917—44no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53#12012yes—
278C23×C53#13712yes—
279C23×C53C22×D411yescharacteristic
280Q8×C53—22no—
281Q8×C53—22no—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—22no—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—48no—
288Q8×C53—48no—
289Q8×C53—41no—
290Q8×C53—41no—
291Q8×C53—41no—
292Q8×C53—41no—
293Q8×C53#12314yes—
294D4×C53—28no—
295C2×C4×C53—22no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—21no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—21no—
309C2×C4×C53—22no—
310C2×C4×C53—21no—
311C2×C4×C53—21no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—48no—
316C2×C4×C53—48no—
317C2×C4×C53—41no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53—41no—
327C2×C4×C53#12012yes—
328C2×C4×C53#13712yes—
329C2×C4×C53C22×D411yescharacteristic
330C2×C4×C53C22×D411yescharacteristic
331C2×C4×C53C2×#4111yescharacteristic
332C2×C4×C53C2×#4111yescharacteristic
333C2×C4×C53H(5,𝔽2)11yescharacteristic
334C2×C4×C53H(5,𝔽2)11yescharacteristic
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347#88322—41no—
348#88322—41no—
349#88322—41no—
350#88322—41no—
351#24053—531nomaximal, Sylow
352C22×C53—22no—
353C22×C53—22no—
354C22×C53—22no—
355C22×C53—22no—
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53—41no—
364C22×C53—41no—
365C22×C53—41no—
366C22×C53C2×#12011yescharacteristic
367C22×C53#54611yescharacteristic
368C22×C53#54611yescharacteristic
369C22×C53C2×#13711yescharacteristic
370C22×C53C2×#13711yescharacteristic
371C22×C53#57711yescharacteristic
372C22×C53#57811yescharacteristic
373C4×C53—22no—
374C4×C53—24no—
375C4×C53—22no—
376C4×C53—41no—
377C4×C53—42no—
378C4×C53—42no—
379C4×C53—41no—
380C4×C53—42no—
381C4×C53C2×#12311yescharacteristic
382C4×C53#53411yescharacteristic
383C4×C53#54611yescharacteristic
384C4×C53#54611yescharacteristic
385Dic53—81no—
386Dic53—81no—
387Dic53—81no—
388Dic53—81no—
389C2×D4×Q8D5311yescharacteristic
390C2×#485—531no—
391C2×#419—531no—
392#2485—531no—
393#2043—531no—
394#2043—531no—
395#2036—531no—
396#2035—531no—
397#1894—531no—
398#1870—531no—
399#1865—531no—
400#1863—531no—
401#1787—531no—
402#1787—531no—
403#1787—531no—
404C2×C53—42no—
405C2×C53—42no—
406C2×C53#240511yescharacteristic
407C2×C53#300411yescharacteristic
408C2×C53#301311yescharacteristic
409C2×C53#331211yescharacteristic
410C2×C53#332011yescharacteristic
411C2×C53#332811yescharacteristic
412C2×C53#332911yescharacteristic
413C23×Q8C2×D5311yescharacteristic
414C23×Q8C2×D5311yescharacteristic
415C22×M16—531no—
416D4×Q8—24no—
417D4×Q8—24no—
418C2×C4⋊Q8—21no—
419C2×C4⋊Q8C2×D5311yescharacteristic
420C2×C22⋊Q8—21no—
421C2×C22⋊Q8—21no—
422C2×C22⋊Q8C2×D5311yescharacteristic
423C2×C22⋊Q8C2×D5311yescharacteristic
424C2×C4×Q8C2×D5311yescharacteristic
425C2×C4×D4—21no—
426C2×C4×D4C2×D5311yescharacteristic
427C2×#117—531no—
428#485—1064no—
429C2×#107—531no—
430C2×#106—531no—
431#419—1064no—
432C2×#103—531no—
433C2×#103—531no—
434C2×#103—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×C22⋊C8—531no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8—531no—
447#397—1061no—
448#394—1061no—
449#389—531no—
450#389—531no—
451#388—1061no—
452#387—1061no—
453#380—531no—
454#380—531no—
455#380—531no—
456#340—531no—
457#340—531no—
458#336—531no—
459#336—531no—
460C53#2405311yescharacteristic, complemented, Sylow
461C22×Q8—22no—
462C22×Q8—22no—
463C22×Q8—21no—
464C22×Q8—21no—
465C22×Q8—22no—
466C22×Q8—22no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—22no—
470C22×Q8—41no—
471C22×Q8—41no—
472C22×Q8—41no—
473C22×Q8—41no—
474C22×Q8C22⋊D5314yes—
475C22×Q8C22×D5311yescharacteristic
476C22×Q8C22×D5311yescharacteristic
477C22×Q8C22×D5311yescharacteristic
478C22×D4C22⋊D5311yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C22×D5311yescharacteristic
482C23×C4C22×D5311yescharacteristic
483C2×M16—1062no—
484C2×M16—2121no—
485C2×M16—2121no—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8—531no—
489C22×C8—531no—
490C4⋊Q8—28no—
491C4⋊Q8—22no—
492C4⋊Q8—22no—
493C22⋊Q8—28no—
494C22⋊Q8—28no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8C22⋊D5314yes—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×D4—28no—
502C4×D4—22no—
503C4×D4—22no—
504#117—1062no—
505#117—1062no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4C22⋊D5311yescharacteristic
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4C22⋊D5311yescharacteristic
526C2×C22⋊C4C22⋊D5311yescharacteristic
527C2×C42—21no—
528C2×C42—1061no—
529C2×C42C22×D5311yescharacteristic
530#107—1062no—
531#106—1062no—
532#103—1062no—
533#103—1062no—
534#103—1062no—
535#103—1062no—
536#103—1062no—
537#103—1062no—
538#103—1062no—
539#103—1062no—
540#103—2121no—
541#103—2121no—
542#103—2121no—
543#103—2121no—
544C22⋊C8—1062no—
545C22⋊C8—2121no—
546C22⋊C8—2121no—
547#95—1061no—
548#95—1061no—
549#95—1061no—
550#95—1061no—
551#95—1061no—
552C24C2×C22⋊D5311yescharacteristic
553C24C2×C22⋊D5311yescharacteristic
554C2×Q8—24no—
555C2×Q8—24no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—28no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—44no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8#1171994712yes—
582C2×Q8#1171994712yes—
583C2×Q8C2×C22⋊D5312yes—
584C2×Q8C2×C22⋊D5312yes—
585C2×Q8C2×C22⋊D5312yes—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4C2×C22⋊D5311yescharacteristic
614C22×C4C2×C22⋊D5311yescharacteristic
615C22×C4C2×C22⋊D5311yescharacteristic
616C22×C4C2×C22⋊D5312yes—
617C22×C4C2×C22⋊D5312yes—
618C22×C4C2×C22⋊D5311yescharacteristic
619C22×C4C23×D5311yescharacteristic
620M16—2124no—
621C2×C8—1061no—
622C2×C8—1061no—
623C2×C8—1061no—
624C2×C8—1061no—
625C2×C8—1061no—
626C2×C8—1061no—
627C2×C8—1061no—
628C2×C8—1061no—
629C2×C8—1061no—
630C2×C8—1061no—
631C2×C8—1061no—
632C2×C8—1061no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—1061no—
641C4⋊C4—1061no—
642C4⋊C4—1061no—
643C4⋊C4—1061no—
644C4⋊C4—1061no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4—1061no—
648C4⋊C4—4241no—
649C4⋊C4—2122no—
650C4⋊C4C2×C22⋊D5312yes—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—4241no—
656C22⋊C4—4241no—
657C22⋊C4—2122no—
658C22⋊C4—2122no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—2122no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23#1313318612yes—
676C23#1313324812yes—
677C23C22×C22⋊D5311yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—48no—
686Q8—48no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8#1313319814yes—
692D4—28no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—48no—
714C2×C4—48no—
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—41no—
724C2×C4—41no—
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—2121no—
737C2×C4#1313318612yes—
738C2×C4#1313324812yes—
739C2×C4C22×C22⋊D5311yescharacteristic
740C2×C4C22×C22⋊D5311yescharacteristic
741C2×C4C2×#1171994711yescharacteristic
742C2×C4C2×#1171994711yescharacteristic
743C2×C4#1313326211yescharacteristic
744C2×C4#1313326211yescharacteristic
745C8—2121no—
746C8—2121no—
747C8—2121no—
748C8—2121no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22C2×#1313318611yescharacteristic
764C22#1681126711yescharacteristic
765C22#1681126711yescharacteristic
766C22C2×#1313324811yescharacteristic
767C22C2×#1313324811yescharacteristic
768C22#1681143111yescharacteristic
769C22#1681143811yescharacteristic
770C4—22no—
771C4—24no—
772C4—22no—
773C4—41no—
774C4—42no—
775C4—42no—
776C4—41no—
777C4—42no—
778C4—4241no—
779C4—4241no—
780C4—4241no—
781C4—4241no—
782C4C2×#1313319811yescharacteristic
783C4#1681118211yescharacteristic
784C4#1681126711yescharacteristic
785C4#1681126711yescharacteristic
786C2—42no—
787C2—42no—
788C2#2027803811yescharacteristic
789C2#2028394911yescharacteristic
790C2#2028403011yescharacteristic
791C2#2028676611yescharacteristic
792C2#2028688611yescharacteristic
793C2#2028699811yescharacteristic
794C2#2028700911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×D4×Q8×C53C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
hypercenterC2×D4×Q8D53
hypocenterC53#24053
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16810961C2semidirect
2. C2×#16810632C2semidirect
4. #20275958C2semidirect
5. #20275958C2semidirect
6. #20275915C2semidirect
7. #20275908C2semidirect
8. #20275149C2semidirect
10. #20274983C2semidirect
11. #20274969C2semidirect
12. #20274650C2semidirect
13. #20274650C2semidirect
14. #20274650C2semidirect
460. C53#24053semidirect

Maximal subgroups

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

subgroupindex
C2×#168109612
C2×#168106322
#202790122
#202759582
#202759152
#202759082
#202751492
#202750132
#202749832
#202749692
#202746502
C2×D4×Q8×C532
#2405353