Finite Group Databasebeta

← #27406315

Subgroups — #27406315

Order 13568.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810702C211yesmaximal, characteristic, complemented
2C2×#16810700C211yesmaximal, characteristic, complemented
3C2×#16810693C211yesmaximal, characteristic, complemented
4C2×#16810648C211yesmaximal, characteristic, complemented
5#20277955C211yesmaximal, characteristic
6#20275512C211yesmaximal, characteristic, complemented
7#20275326C211yesmaximal, characteristic, complemented
8#20275319C211yesmaximal, characteristic, complemented
9#20275011C211yesmaximal, characteristic, complemented
10#20275006C211yesmaximal, characteristic, complemented
11#20274896C211yesmaximal, characteristic, complemented
12#20274896C211yesmaximal, characteristic, complemented
13#20274590C211yesmaximal, characteristic, complemented
14#20274482C211yesmaximal, characteristic, complemented
15C53×#1939C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×C4×D212C2211yescharacteristic
22C2×C4×D212C2211yescharacteristic
23C2×#13133174C2211yescharacteristic
24#16810702—24no—
25#16810700—24no—
26#16810693—24no—
27#16810648—24no—
28C2×C4⋊#88322C2211yescharacteristic
29C2×#13133146C2211yescharacteristic
30C2×#13133146C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133129C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×#13133129C2211yescharacteristic
39C2×#13133128C2211yescharacteristic
40C2×#13133128C2211yescharacteristic
41C2×C4×#88322C2211yescharacteristic
42#16810555C411yescharacteristic
43#16810550C411yescharacteristic
44#16810545C411yescharacteristic
45#16810545C411yescharacteristic
46#16810541C411yescharacteristic
47#16810540C411yescharacteristic
48#16810540C411yescharacteristic
49#16810533C411yescharacteristic
50C4×#11719921C2211yescharacteristic
51C4×#11719921C2211yescharacteristic
52#16810378C2211yescharacteristic
53#16810378C2211yescharacteristic
54#16810377C2211yescharacteristic
55#16810377C2211yescharacteristic
56C2×C4⋊C8×C53C2211yescharacteristic
57C2×C4⋊C8×C53C2211yescharacteristic
58C2×C4⋊C8×C53C2211yescharacteristic
59C2×C4×C8×C53C2211yescharacteristic
60C4×C4⋊C4×C53C2211yescharacteristic
61C53×#336C2211yescharacteristic
62C53×#336C2211yescharacteristic
63C22×D212C2×C411yescharacteristic
64C22×D212C2×C411yescharacteristic
65C22×D212C2×C411yescharacteristic
66C22×C4×D53C2311yescharacteristic
67C22×C4×D53C2311yescharacteristic
68C22×C4×D53C2311yescharacteristic
69C2×#11719912—22no—
70C2×#11719912—22no—
71C2×#11719912—22no—
72C2×#11719912—22no—
73C2×#11719912—22no—
74C2×#11719912—22no—
75C2×#11719912—41no—
76C2×#11719912—41no—
77C2×#11719912—41no—
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80C22×#88322C2311yescharacteristic
81C22×#88322C2311yescharacteristic
82C2×C8×D53—22no—
83C2×C8×D53—22no—
84C2×C8×D53—41no—
85C4×D212—22no—
86C4×D212—22no—
87C4×D212—22no—
88C4×D212—22no—
89C4×D212—22no—
90C4×D212—22no—
91#13133174—22no—
92#13133174—22no—
93C2×C4⋊Dic53C2×C411yescharacteristic
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×C4⋊Dic53C2×C411yescharacteristic
96C2×#11719919C2×C411yescharacteristic
97C2×#11719919C2×C411yescharacteristic
98C2×#11719921C2×C411yescharacteristic
99C2×#11719921C2×C411yescharacteristic
100C2×#11719921C2×C411yescharacteristic
101C2×#11719921C2×C411yescharacteristic
102C2×#11719921C2×C411yescharacteristic
103C2×#11719921C2×C411yescharacteristic
104C2×#11719921C2×C411yescharacteristic
105C2×#11719921C2×C411yescharacteristic
106C2×#11719921C2×C411yescharacteristic
107C2×#11719921C2×C411yescharacteristic
108C2×#11719921C2×C411yescharacteristic
109C2×#11719921C2×C411yescharacteristic
110C2×C4×Dic53C2311yescharacteristic
111C4⋊#88322D414yescomplemented
112#13133146—22no—
113#13133146—22no—
114#13133129—22no—
115#13133129—22no—
116#13133129—22no—
117#13133129—22no—
118#13133129—22no—
119#13133129—41no—
120#13133129—41no—
121#13133129D414yescomplemented
122#13133128—22no—
123#13133128—22no—
124C4×#88322—22no—
125#13133124C2×C411yescharacteristic
126#13133124C2×C411yescharacteristic
127#13133124C2×C411yescharacteristic
128#13133124C2×C411yescharacteristic
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133C2×C4⋊C4×C53C2×C411yescharacteristic
134C2×C4⋊C4×C53C2×C411yescharacteristic
135C2×C42×C53C2311yescharacteristic
136C2×C42×C53C2311yescharacteristic
137C2×C42×C53C2311yescharacteristic
138C4⋊C8×C53—22no—
139C4⋊C8×C53—22no—
140C4⋊C8×C53—22no—
141C4×C8×C53—22no—
142#95×C53C2×C411yescharacteristic
143#95×C53C2×C411yescharacteristic
144C23×D53C22×C411yescharacteristic
145C23×D53C22×C411yescharacteristic
146C23×D53C22×C411yescharacteristic
147C22×C4×C53C22×C411yescharacteristic
148C22×C4×C53C22×C411yescharacteristic
149C22×C4×C53C22×C411yescharacteristic
150C22×C4×C53C22×C411yescharacteristic
151C22×C4×C53C22×C411yescharacteristic
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C2411yescharacteristic
154C22×Dic53C22×C411yescharacteristic
155C22×Dic53C22×C411yescharacteristic
156C22×Dic53C22×C411yescharacteristic
157C22×Dic53C22×C411yescharacteristic
158C22×Dic53C22×C411yescharacteristic
159C2×D212—22no—
160C2×D212—22no—
161C2×D212—22no—
162C2×D212—22no—
163C2×D212—41no—
164C2×D212—41no—
165C2×D212—41no—
166C2×D212—41no—
167C2×D212—41no—
168C2×C4×D53—21no—
169C2×C4×D53—21no—
170C2×C4×D53—21no—
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53—21no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—21no—
181C2×C4×D53—21no—
182C2×C4×D53—21no—
183C2×C4×D53—21no—
184C2×C4×D53C2×D412yes—
185C2×C4×D53#4112yes—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53C2×D412yes—
198C4⋊C4×C53—22no—
199C4⋊C4×C53—41no—
200C42×C53—21no—
201C42×C53—21no—
202C42×C53—21no—
203C42×C53—21no—
204C42×C53C2×D412yes—
205C42×C53#4112yes—
206#11719921—22no—
207#11719921—22no—
208#11719921—22no—
209#11719921—22no—
210#11719921—22no—
211#11719921—22no—
212#11719921—22no—
213#11719921—22no—
214#11719921—22no—
215#11719921—41no—
216#11719921—41no—
217#11719921—41no—
218C4⋊Dic53—22no—
219C4⋊Dic53—22no—
220C4⋊Dic53—22no—
221#11719919—22no—
222#11719919—22no—
223C4×Dic53—21no—
224C4×Dic53—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322C2×D412yes—
235C2×#88322C2×D412yes—
236C2×#88322C2×D412yes—
237#11719912—44no—
238#11719912—44no—
239#11719912—44no—
240C8×D53—44no—
241C23×C53C23×C411yescharacteristic
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53—21no—
247C22×D53—21no—
248C22×D53—21no—
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53—21no—
255C22×D53—21no—
256C22×D53—21no—
257C22×D53—21no—
258C22×D53—21no—
259C22×D53—21no—
260C22×D53—21no—
261C22×D53—21no—
262C22×D53C4×D412yes—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
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—21no—
278C2×C4×C53C4×D412yes—
279C2×C4×C53C4×D412yes—
280C2×C4×C53#13112yes—
281C2×C4×C53C22×D411yescharacteristic
282C2×C4×C53C22×D411yescharacteristic
283C2×C4×C53C2×#4111yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53H(5,𝔽2)11yescharacteristic
286C2×C4×C532−1+411yescharacteristic
287C2×Dic53—21no—
288C2×Dic53—21no—
289C2×Dic53—21no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53C4×D412yes—
302D212—44no—
303D212—44no—
304D212—44no—
305C4×D53—22no—
306C4×D53—22no—
307C4×D53—22no—
308C4×D53—22no—
309C4×D53—41no—
310C4×D53—41no—
311C4×D53—41no—
312C4×D53—41no—
313C4×D53—41no—
314C4×D53—41no—
315C4×D53—41no—
316C4×D53—41no—
317C8×C53—22no—
318C8×C53—41no—
319C8×C53—41no—
320C8×C53—41no—
321#88322—22no—
322#88322—22no—
323#88322—22no—
324#88322—41no—
325#22994—531nomaximal, Sylow
326C22×C53C2×C4×D411yescharacteristic
327C22×C53C2×C4×D411yescharacteristic
328C22×C53#52011yescharacteristic
329C22×C53C2×#13111yescharacteristic
330C22×C53#56811yescharacteristic
331C22×C53#56811yescharacteristic
332C22×C53#56811yescharacteristic
333C2×D53—22no—
334C2×D53—22no—
335C2×D53—22no—
336C2×D53—41no—
337C2×D53—41no—
338C2×D53—41no—
339C2×D53—41no—
340C2×D53—41no—
341C2×D53—41no—
342C2×D53—41no—
343C2×D53—41no—
344C2×D53—41no—
345C2×D53—41no—
346C2×D53—41no—
347C2×D53—41no—
348C2×D53—41no—
349C2×D53—41no—
350C2×D53—41no—
351C2×D53—41no—
352C2×D53—41no—
353C2×D53—41no—
354C4×C53—22no—
355C4×C53—22no—
356C4×C53—22no—
357C4×C53—41no—
358C4×C53—41no—
359C4×C53—41no—
360C4×C53D4211yescharacteristic
361C4×C53#54711yescharacteristic
362C4×C53#54811yescharacteristic
363C4×C53#55311yescharacteristic
364Dic53—22no—
365Dic53—41no—
366Dic53—41no—
367Dic53—41no—
368Dic53—41no—
369C2×#436—531no—
370C2×#436—531no—
371C2×#435—531no—
372C2×#424—531no—
373#2392—531no—
374#1955—531no—
375#1939D5311yescharacteristic, complemented
376#1924—531no—
377#1923—531no—
378#1870—531no—
379#1869—531no—
380#1851—531no—
381#1851—531no—
382#1771—531no—
383#1750—531no—
384C2×C53#236111yescharacteristic
385C2×C53#293011yescharacteristic
386C2×C53#293011yescharacteristic
387C2×C53#293311yescharacteristic
388C2×C53#293511yescharacteristic
389C2×C53#299311yescharacteristic
390C2×C53#299511yescharacteristic
391D53—42no—
392D53—81no—
393D53—81no—
394C22×M16—531no—
395C22×M16—531no—
396C22×M16—531no—
397C23×C8—531no—
398C2×C4×D4—531no—
399C2×C4×D4—531no—
400C2×C4×D4—531no—
401C2×#117—531no—
402#436—1064no—
403#436—1064no—
404#435—1064no—
405#424—1064no—
406C2×C4⋊C8—531no—
407C2×C4⋊C8—531no—
408C2×C4⋊C8—531no—
409C2×C4⋊C8C2×D5311yescharacteristic
410C2×C4⋊C8C2×D5311yescharacteristic
411C2×C4⋊C8C2×D5311yescharacteristic
412C2×C22⋊C8—531no—
413C2×C22⋊C8—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8—531no—
416C2×C22⋊C8—531no—
417C2×C22⋊C8—531no—
418C2×C22⋊C8—531no—
419C2×C22⋊C8—531no—
420C2×#97—531no—
421C2×#97—531no—
422C2×C4×C8—531no—
423C2×C4×C8C2×D5311yescharacteristic
424#398—531no—
425#397—531no—
426#396—531no—
427#396—531no—
428#394—531no—
429#394—531no—
430#394—531no—
431#392—531no—
432C4×C4⋊C4C2×D5311yescharacteristic
433C4×C22⋊C4—531no—
434C4×C22⋊C4—531no—
435#336—531no—
436#336—531no—
437#336—531no—
438#336—531no—
439#336C2×D5311yescharacteristic
440#336C2×D5311yescharacteristic
441C53#2299411yescharacteristic, complemented, Sylow
442C22×D4—531no—
443C22×D4—531no—
444C22×D4—531no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4—531no—
448C2×M16—1062no—
449C2×M16—1062no—
450C2×M16—1062no—
451C2×M16—1062no—
452C2×M16—1062no—
453C2×M16—1062no—
454C2×M16—2121no—
455C2×M16—2121no—
456C2×M16—2121no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—531no—
461C22×C8—1062no—
462C22×C8—1062no—
463C22×C8—2121no—
464C22×C8C22×D5311yescharacteristic
465C22×C8C22×D5311yescharacteristic
466C22×C8C22×D5311yescharacteristic
467C22×C8C22×D5311yescharacteristic
468C4×D4—1062no—
469C4×D4—1062no—
470C4×D4—1062no—
471C4×D4—1062no—
472C4×D4—1062no—
473C4×D4—1062no—
474#117—1062no—
475#117—1062no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4C4×D5311yescharacteristic
482C2×C4⋊C4C4×D5311yescharacteristic
483C2×C22⋊C4—531no—
484C2×C22⋊C4—531no—
485C2×C22⋊C4—531no—
486C2×C22⋊C4—531no—
487C2×C22⋊C4—531no—
488C2×C22⋊C4—531no—
489C2×C22⋊C4—531no—
490C2×C22⋊C4—531no—
491C2×C22⋊C4—531no—
492C2×C22⋊C4—531no—
493C2×C22⋊C4—531no—
494C2×C22⋊C4—531no—
495C2×C42—531no—
496C2×C42C22×D5311yescharacteristic
497C2×C42C22×D5311yescharacteristic
498C2×C42C22×D5311yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—534no—
503C4⋊C8—1062no—
504C4⋊C8—1062no—
505C22⋊C8—534no—
506C22⋊C8—1062no—
507C22⋊C8—1062no—
508C22⋊C8—1062no—
509C22⋊C8—1062no—
510C22⋊C8—1062no—
511C22⋊C8—2121no—
512C22⋊C8—2121no—
513#97—1062no—
514#97—1062no—
515C4×C8—22no—
516C4×C8—1062no—
517#95—531no—
518#95—531no—
519#95—531no—
520#95—531no—
521#95C4×D5311yescharacteristic
522#95C4×D5311yescharacteristic
523C24—531no—
524C24—531no—
525C24—531no—
526C2×D4—1062no—
527C2×D4—1062no—
528C2×D4—1062no—
529C2×D4—1062no—
530C2×D4—2121no—
531C2×D4—2121no—
532C2×D4—2121no—
533C2×D4—2121no—
534C2×D4—2121no—
535C22×C4—531no—
536C22×C4—532no—
537C22×C4—532no—
538C22×C4—531no—
539C22×C4—531no—
540C22×C4—531no—
541C22×C4—531no—
542C22×C4—1061no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4C2×C4×D5311yescharacteristic
559C22×C4C2×C4×D5311yescharacteristic
560C22×C4C2×C4×D5311yescharacteristic
561C22×C4C2×C4×D5311yescharacteristic
562C22×C4C2×C4×D5311yescharacteristic
563C22×C4C2×C4×D5311yescharacteristic
564C22×C4C23×D5311yescharacteristic
565M16—2124no—
566M16—2124no—
567M16—2124no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—532no—
580C2×C8—532no—
581C2×C8—532no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C2×C8—1061no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—1061no—
591C2×C8—2124no—
592C2×C8D4×D5312yes—
593C4⋊C4—22no—
594C4⋊C4—41no—
595C4⋊C4—1062no—
596C4⋊C4—1062no—
597C4⋊C4—1062no—
598C4⋊C4—1062no—
599C4⋊C4—1062no—
600C22⋊C4—1062no—
601C22⋊C4—1062no—
602C22⋊C4—1062no—
603C22⋊C4—1062no—
604C22⋊C4—1062no—
605C22⋊C4—1062no—
606C22⋊C4—1062no—
607C22⋊C4—1062no—
608C22⋊C4—1062no—
609C22⋊C4—2121no—
610C22⋊C4—2121no—
611C22⋊C4—2121no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—1061no—
617C42—1061no—
618C42D4×D5312yes—
619C42#1171994912yes—
620C23—532no—
621C23—1061no—
622C23—1061no—
623C23—1061no—
624C23—1061no—
625C23—1061no—
626C23—1061no—
627C23—1061no—
628C23—1061no—
629C23—1061no—
630C23—1061no—
631C23—1061no—
632C23—1061no—
633C23—1061no—
634C23—1061no—
635C23—1061no—
636C23—1061no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23—1061no—
641C23C22×C4×D5311yescharacteristic
642D4—2124no—
643D4—2124no—
644D4—2124no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—532no—
661C2×C4—1061no—
662C2×C4—1061no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1061no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—1061no—
672C2×C4—1061no—
673C2×C4—1061no—
674C2×C4—1061no—
675C2×C4—1061no—
676C2×C4—1061no—
677C2×C4—1061no—
678C2×C4—1061no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4#1313317912yes—
688C2×C4#1313317912yes—
689C2×C4#1313322312yes—
690C2×C4C2×D4×D5311yescharacteristic
691C2×C4C2×D4×D5311yescharacteristic
692C2×C4#41×D5311yescharacteristic
693C2×C4C2×#1171994911yescharacteristic
694C2×C4#1313326311yescharacteristic
695C2×C4#1313326511yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—1062no—
701C8—1062no—
702C8—1062no—
703C8—2121no—
704C22—1062no—
705C22—1062no—
706C22—1062no—
707C22—2121no—
708C22—2121no—
709C22—2121no—
710C22—2121no—
711C22—2121no—
712C22—2121no—
713C22—2121no—
714C22—2121no—
715C22—2121no—
716C22—2121no—
717C22—2121no—
718C22—2121no—
719C22—2121no—
720C22—2121no—
721C22—2121no—
722C22—2121no—
723C22—2121no—
724C22—2121no—
725C22C4×D4×D5311yescharacteristic
726C22C2×#1313317911yescharacteristic
727C22#1681110511yescharacteristic
728C22C2×#1313322311yescharacteristic
729C22#1681138811yescharacteristic
730C22#1681138811yescharacteristic
731C22#1681138911yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—1062no—
739C4—2121no—
740C4—2121no—
741C4—2121no—
742C4—2121no—
743C4#1681125711yescharacteristic
744C4#1681127611yescharacteristic
745C4#1681128311yescharacteristic
746C4#1681132611yescharacteristic
747C2—4241no—
748C2—4241no—
749C2—2122no—
750C2#2027773011yescharacteristic
751C2#2028341511yescharacteristic
752C2#2028341711yescharacteristic
753C2#2028343511yescharacteristic
754C2#2028345811yescharacteristic
755C2#2028386311yescharacteristic
756C2#2028388411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1939C2
prime radical#16810533C4
cosocleC22×C4×C53C24
hypercenter#1939D53
hypocenterC53#22994
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#16810702C2semidirect
2. C2×#16810700C2semidirect
3. C2×#16810693C2semidirect
4. C2×#16810648C2semidirect
6. #20275512C2semidirect
7. #20275326C2semidirect
8. #20275319C2semidirect
9. #20275011C2semidirect
10. #20275006C2semidirect
11. #20274896C2semidirect
12. #20274896C2semidirect
13. #20274590C2semidirect
14. #20274482C2semidirect
15. C53×#1939C2semidirect
111. C4⋊#88322D4semidirect
121. #13133129D4semidirect
375. #1939D53semidirect
441. C53#22994semidirect

Maximal subgroups

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

subgroupindex
C2×#168107022
C2×#168107002
C2×#168106932
C2×#168106482
#202779552
#202755122
#202753262
#202753192
#202750112
#202750062
#202748962
#202745902
#202744822
C53×#19392
#2299453