Finite Group Databasebeta

← #27404818

Subgroups — #27404818

Order 13568.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic53C211yesmaximal, characteristic, complemented
2C2×#16810632C211yesmaximal, characteristic, complemented
3#20277757C211yesmaximal, characteristic
4Q8×C22⋊Dic53C211yesmaximal, characteristic, complemented
5#20275598C211yesmaximal, characteristic, complemented
6#20275393C211yesmaximal, characteristic, complemented
7#20275351C211yesmaximal, characteristic, complemented
8#20275154C211yesmaximal, characteristic
9#20275072C211yesmaximal, characteristic, complemented
10#20275051C211yesmaximal, characteristic, complemented
11#20274971C211yesmaximal, characteristic, complemented
12#20274916C211yesmaximal, characteristic, complemented
13#20274547C211yesmaximal, characteristic, complemented
14#20274501C211yesmaximal, characteristic, complemented
15C2×C53×#448C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C2×Q8×Dic53C2211yescharacteristic
18C2×Q8×Dic53C2211yescharacteristic
19C2×D4×Dic53C2211yescharacteristic
20C2×#13133176C2211yescharacteristic
21SD16×Dic53—24no—
22C2×#13133151C2211yescharacteristic
23C2×#13133149C2211yescharacteristic
24#16810632—24no—
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133127C2211yescharacteristic
32C2×C8×Dic53C2211yescharacteristic
33#16810530—21no—
34#16810530—21no—
35#16810530C2211yescharacteristic
36#16810530C2211yescharacteristic
37#16810526—21no—
38#16810526C2211yescharacteristic
39#16810522C2211yescharacteristic
40#16810516—21no—
41#16810503—21no—
42#16810483—21no—
43#16810483C2211yescharacteristic
44C4⋊C4×Dic53C2211yescharacteristic
45C22⋊C4×Dic53—21no—
46C4×C22⋊Dic53—21no—
47C4×C22⋊Dic53C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C23×Q8×C53C2211yescharacteristic
55C22×SD16×C53C2211yescharacteristic
56C22×SD16×C53C2211yescharacteristic
57C2×#121×C53C2211yescharacteristic
58C53×#448C418yescomplemented
59C2×#103×C53C2211yescharacteristic
60C2×#103×C53C2211yescharacteristic
61C2×C22⋊C8×C53C2211yescharacteristic
62C23×Dic53—21no—
63C2×#11719917—22no—
64C2×#11719917—22no—
65C2×#11719917—41no—
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68Q8×Dic53—22no—
69Q8×Dic53—22no—
70Q8×Dic53—41no—
71Q8×Dic53—41no—
72D4×Dic53—22no—
73D4×Dic53—41no—
74#13133176—22no—
75#13133176—41no—
76C2×C4⋊Dic53—21no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—21no—
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53D411yescharacteristic
89C2×C22⋊Dic53D411yescharacteristic
90C2×C4×Dic53—21no—
91C2×C4×Dic53—21no—
92C2×C4×Dic53—21no—
93C2×C4×Dic53—21no—
94C2×C4×Dic53C2311yescharacteristic
95C2×C4×Dic53C2311yescharacteristic
96#13133151—41no—
97#13133149—22no—
98#13133141—22no—
99#13133141—22no—
100#13133141—22no—
101#13133141D414yescomplemented
102#13133138—22no—
103#13133138—41no—
104#13133127—41no—
105C8×Dic53—22no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124D411yescharacteristic
114#13133124D411yescharacteristic
115C22×Q8×C53—21no—
116C22×Q8×C53—22no—
117C22×Q8×C53—22no—
118C22×Q8×C53—22no—
119C22×Q8×C53—41no—
120C22×Q8×C53—41no—
121C22×Q8×C53C2×C414yescomplemented
122C22×Q8×C53C2311yescharacteristic
123C22×Q8×C53C2311yescharacteristic
124C22×D4×C53—21no—
125C22×D4×C53C2311yescharacteristic
126C23×C4×C53—21no—
127C23×C4×C53C2311yescharacteristic
128C2×SD16×C53—22no—
129C2×SD16×C53—22no—
130C2×SD16×C53—41no—
131C2×SD16×C53—41no—
132C2×SD16×C53C2×C414yes—
133C2×SD16×C53C2×C414yes—
134C22×C8×C53C2311yescharacteristic
135C22×C8×C53C2311yescharacteristic
136#121×C53—22no—
137#121×C53C2×C414yes—
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53—21no—
140#103×C53C2×C414yescomplemented
141#103×C53C2×C414yescomplemented
142C22⋊C8×C53C2×C414yescomplemented
143C24×C53—21no—
144C24×C53C2×D411yescharacteristic
145C2×Q8×C53—24no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53—28no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53—42no—
156C2×Q8×C53—42no—
157C2×Q8×C53—44no—
158C2×Q8×C53—44no—
159C2×Q8×C53—44no—
160C2×Q8×C53C22×C412yes—
161C2×Q8×C53C22×C412yes—
162C2×Q8×C53C2×D412yes—
163C2×Q8×C53#4112yes—
164C2×D4×C53—24no—
165C2×D4×C53—21no—
166C2×D4×C53—21no—
167C2×D4×C53—21no—
168C2×D4×C53—21no—
169C2×D4×C53—21no—
170C2×D4×C53—81no—
171C2×D4×C53—81no—
172C2×D4×C53C22×C412yes—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—24no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—42no—
182C22×C4×C53—42no—
183C22×C4×C53C22×C412yes—
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53#4112yes—
186C22×C4×C53C2411yescharacteristic
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—42no—
192C22×Dic53—42no—
193C22×Dic53—81no—
194C22×Dic53C2×D411yescharacteristic
195C22×Dic53C2×D411yescharacteristic
196C22×Dic53C2×D411yescharacteristic
197C22×Dic53C2×D411yescharacteristic
198SD16×C53—28no—
199SD16×C53—44no—
200C2×C8×C53—21no—
201C2×C8×C53—21no—
202C2×C8×C53—21no—
203C2×C8×C53—21no—
204C2×C8×C53C22×C412yes—
205C2×C8×C53C22×C412yes—
206C4⋊C4×C53—21no—
207C4⋊C4×C53C22×C412yes—
208C22⋊C4×C53—24no—
209C22⋊Dic53—22no—
210C22⋊Dic53—41no—
211C22⋊Dic53—42no—
212C22⋊Dic53—42no—
213C22⋊Dic53—42no—
214C22⋊Dic53—42no—
215C22⋊Dic53—81no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—42no—
224C4⋊Dic53—42no—
225C4⋊Dic53—81no—
226C4⋊Dic53C2×D412yes—
227C4×Dic53—21no—
228C4×Dic53—21no—
229C4×Dic53—21no—
230C4×Dic53—21no—
231C4×Dic53—42no—
232C4×Dic53—42no—
233C4×Dic53—42no—
234C4×Dic53—81no—
235#11719917—44no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322C2×D412yes—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—22no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53C4×D412yes—
256C23×C53C22×D411yescharacteristic
257Q8×C53—22no—
258Q8×C53—22no—
259Q8×C53—22no—
260Q8×C53—22no—
261Q8×C53—22no—
262Q8×C53—48no—
263Q8×C53—41no—
264Q8×C53—41no—
265Q8×C53C4×D414yes—
266D4×C53—22no—
267D4×C53—22no—
268D4×C53—41no—
269D4×C53—41no—
270D4×C53—84no—
271C2×C4×C53—22no—
272C2×C4×C53—21no—
273C2×C4×C53—22no—
274C2×C4×C53—21no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—48no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53C4×D412yes—
288C2×C4×C53C23×C411yescharacteristic
289C2×C4×C53C22×D411yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53C2×#4111yescharacteristic
292C2×C4×C53H(5,𝔽2)11yescharacteristic
293C2×C4×C53H(5,𝔽2)11yescharacteristic
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—22no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—84no—
318C2×Dic53#13712yes—
319C8×C53—22no—
320C8×C53—22no—
321#88322—22no—
322#88322—41no—
323#22885—531nomaximal, Sylow
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—81no—
335C22×C53—81no—
336C22×C53—81no—
337C22×C53—81no—
338C22×C53C2×C4×D411yescharacteristic
339C22×C53D4211yescharacteristic
340C22×C53#54611yescharacteristic
341C22×C53C2×#13711yescharacteristic
342C22×C53#57511yescharacteristic
343C22×C53#57711yescharacteristic
344C22×C53#57711yescharacteristic
345C4×C53—22no—
346C4×C53—24no—
347C4×C53—42no—
348C4×C53—42no—
349C4×C53C2×C4×D411yescharacteristic
350C4×C53#51811yescharacteristic
351C4×C53#54611yescharacteristic
352C4×C53#55111yescharacteristic
353Dic53—22no—
354Dic53—41no—
355Dic53—42no—
356Dic53—41no—
357Dic53—41no—
358Dic53—81no—
359Dic53—81no—
360Dic53—81no—
361C2×#448D5311yescharacteristic
362C2×C4×SD16—531no—
363C2×#419—531no—
364#2363—531no—
365Q8×C22⋊C4—531no—
366#1973—531no—
367#1933—531no—
368#1927—531no—
369#1895—531no—
370#1880—531no—
371#1877—531no—
372#1863—531no—
373#1854—531no—
374#1763—531no—
375#1753—531no—
376C2×C53—42no—
377C2×C53—82no—
378C2×C53#235811yescharacteristic
379C2×C53C4×#13711yescharacteristic
380C2×C53#294911yescharacteristic
381C2×C53#326611yescharacteristic
382C2×C53#327111yescharacteristic
383C2×C53#332611yescharacteristic
384C2×C53#332911yescharacteristic
385C23×Q8C2×D5311yescharacteristic
386C22×SD16C2×D5311yescharacteristic
387C22×SD16C2×D5311yescharacteristic
388C22×M16—531no—
389C2×#121C2×D5311yescharacteristic
390C2×C4×Q8—531no—
391C2×C4×Q8—531no—
392C2×C4×D4—531no—
393C2×#117—531no—
394#448Dic5318yescomplemented
395C4×SD16—1064no—
396C2×#107—531no—
397C2×#106—531no—
398#419—1064no—
399C2×#103—531no—
400C2×#103—531no—
401C2×#103—531no—
402C2×#103—531no—
403C2×#103C2×D5311yescharacteristic
404C2×#103C2×D5311yescharacteristic
405C2×#102—531no—
406C2×#102—531no—
407C2×C22⋊C8C2×D5311yescharacteristic
408C2×#97—531no—
409C2×C4×C8—531no—
410#391—531no—
411#391—531no—
412#391—1061no—
413#391—1061no—
414#390—531no—
415#390—1061no—
416#389—531no—
417#388—1061no—
418#386—1061no—
419#380—531no—
420#380—1061no—
421C4×C4⋊C4—531no—
422C4×C22⋊C4—531no—
423C4×C22⋊C4—1061no—
424C4×C22⋊C4—1061no—
425#340—531no—
426#340—531no—
427#340—531no—
428#340—531no—
429#336—531no—
430#336—531no—
431C53#2288511yescharacteristic, complemented, Sylow
432C22×Q8—21no—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C2×Dic5314yescomplemented
439C22×Q8C22×D5311yescharacteristic
440C22×Q8C22×D5311yescharacteristic
441C22×D4—21no—
442C22×D4C22×D5311yescharacteristic
443C23×C4—21no—
444C23×C4—1061no—
445C23×C4C22×D5311yescharacteristic
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16C2×Dic5314yes—
451C2×SD16C2×Dic5314yes—
452C2×M16—1062no—
453C2×M16—1062no—
454C2×M16—2121no—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8C22×D5311yescharacteristic
458C22×C8C22×D5311yescharacteristic
459#121—22no—
460#121C2×Dic5314yes—
461C4×Q8—1062no—
462C4×Q8—1062no—
463C4×Q8—2121no—
464C4×Q8—2121no—
465C4×D4—1062no—
466C4×D4—2121no—
467#117—1062no—
468#117—2121no—
469C2×C4⋊C4—531no—
470C2×C4⋊C4—531no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4C22×D5311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—531no—
479C2×C22⋊C4—531no—
480C2×C22⋊C4—1061no—
481C2×C22⋊C4—1061no—
482C2×C22⋊C4—1061no—
483C2×C22⋊C4—1061no—
484C2×C22⋊C4—1061no—
485C2×C42—531no—
486C2×C42—531no—
487C2×C42—1061no—
488C2×C42—1061no—
489C2×C42—1061no—
490C2×C42—1061no—
491#107—2121no—
492#106—1062no—
493#103—534no—
494#103—1062no—
495#103—1062no—
496#103—1062no—
497#103C2×Dic5314yescomplemented
498#103C2×Dic5314yescomplemented
499#102—1062no—
500#102—2121no—
501C22⋊C8C2×Dic5314yescomplemented
502#97—2121no—
503C4×C8—1062no—
504#95—531no—
505#95—531no—
506#95—1061no—
507#95—1061no—
508#95—1061no—
509#95—1061no—
510#95—1061no—
511#95—1061no—
512#95—1061no—
513C24—21no—
514C24D4×D5311yescharacteristic
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8D4×D5312yes—
531C2×Q8#1171994712yes—
532C2×Q8C22×Dic5312yes—
533C2×Q8C22×Dic5312yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4C22×Dic5312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—531no—
554C22×C4—531no—
555C22×C4—531no—
556C22×C4—531no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—4241no—
562C22×C4—2122no—
563C22×C4—2122no—
564C22×C4D4×D5311yescharacteristic
565C22×C4#1171994712yes—
566C22×C4C22×Dic5312yes—
567C22×C4C23×D5311yescharacteristic
568SD16—28no—
569SD16—44no—
570M16—2124no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—532no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8C22×Dic5312yes—
582C2×C8C22×Dic5312yes—
583C4⋊C4—21no—
584C4⋊C4—532no—
585C4⋊C4—1061no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—4241no—
593C4⋊C4—2122no—
594C4⋊C4—2122no—
595C4⋊C4C22×Dic5312yes—
596C22⋊C4—24no—
597C22⋊C4—1062no—
598C22⋊C4—4241no—
599C22⋊C4—2121no—
600C22⋊C4—2122no—
601C22⋊C4—2122no—
602C22⋊C4—2122no—
603C22⋊C4—2122no—
604C42—1061no—
605C42—1061no—
606C42—1061no—
607C42—1061no—
608C42—4241no—
609C42—2122no—
610C42—2122no—
611C42—2122no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23D4×Dic5312yes—
626C23C2×D4×D5311yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8D4×Dic5314yes—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—84no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—532no—
658C2×C4—1061no—
659C2×C4—1061no—
660C2×C4—1061no—
661C2×C4—1061no—
662C2×C4—1061no—
663C2×C4—1061no—
664C2×C4—1061no—
665C2×C4—1061no—
666C2×C4—1061no—
667C2×C4—1062no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—4244no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4D4×Dic5312yes—
683C2×C4C23×Dic5311yescharacteristic
684C2×C4C2×D4×D5311yescharacteristic
685C2×C4C2×#1171994711yescharacteristic
686C2×C4C2×#1171994711yescharacteristic
687C2×C4#1313326211yescharacteristic
688C2×C4#1313326211yescharacteristic
689C8—22no—
690C8—22no—
691C8—1062no—
692C8—2121no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22C2×D4×Dic5311yescharacteristic
708C22#1681125511yescharacteristic
709C22#1681126011yescharacteristic
710C22#137×D5311yescharacteristic
711C22#1681142211yescharacteristic
712C22#1681142911yescharacteristic
713C22#1681142911yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—1062no—
719C4—4241no—
720C4—4241no—
721C4—4241no—
722C4—2122no—
723C4—2121no—
724C4—2121no—
725C4—2121no—
726C4C2×D4×Dic5311yescharacteristic
727C4#1681109811yescharacteristic
728C4#1681126011yescharacteristic
729C4#1681130411yescharacteristic
730C2—42no—
731C2—82no—
732C2#2027769911yescharacteristic
733C2#137×Dic5311yescharacteristic
734C2#2028357511yescharacteristic
735C2#2028622811yescharacteristic
736C2#2028630311yescharacteristic
737C2#2028697211yescharacteristic
738C2#2028700211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#448C2
socleC23×C53C22×D4
prime radicalC2×#121×C53C22
cosocleC22×C4×C53C24
hypercenterC2×#448D53
hypocenterC53#22885
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic53C2semidirect
2. C2×#16810632C2semidirect
4. Q8×C22⋊Dic53C2semidirect
5. #20275598C2semidirect
6. #20275393C2semidirect
7. #20275351C2semidirect
9. #20275072C2semidirect
10. #20275051C2semidirect
11. #20274971C2semidirect
12. #20274916C2semidirect
13. #20274547C2semidirect
14. #20274501C2semidirect
58. C53×#448C4semidirect
101. #13133141D4semidirect
121. C22×Q8×C53C2×C4semidirect
140. #103×C53C2×C4semidirect
141. #103×C53C2×C4semidirect
142. C22⋊C8×C53C2×C4semidirect
394. #448Dic53semidirect
431. C53#22885semidirect
438. C22×Q8C2×Dic53semidirect
497. #103C2×Dic53semidirect
498. #103C2×Dic53semidirect
501. C22⋊C8C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic532
C2×#168106322
#202777572
Q8×C22⋊Dic532
#202755982
#202753932
#202753512
#202751542
#202750722
#202750512
#202749712
#202749162
#202745472
#202745012
C2×C53×#4482
#2288553