Finite Group Databasebeta

← #28318689

Subgroups — #28318689

Order 13568.

1126 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811597C211yesmaximal, characteristic
2C2×#16811596C211yesmaximal, characteristic
3#20290457C211yesmaximal, characteristic, complemented
4#20290457C211yesmaximal, characteristic, complemented
5#20290456C211yesmaximal, characteristic, complemented
6#20290456C211yesmaximal, characteristic, complemented
7#20290453C211yesmaximal, characteristic, complemented
8#20290452C211yesmaximal, characteristic, complemented
9#20290449C211yesmaximal, characteristic, complemented
10C22⋊C4×#88324C211yesmaximal, characteristic, complemented
11#20290445C211yesmaximal, characteristic, complemented
12#20290445C211yesmaximal, characteristic, complemented
13#20290441C211yesmaximal, characteristic, complemented
14C4×C22⋊#88324C211yesmaximal, characteristic, complemented
15#20277200C211yesmaximal, characteristic
16C22×#11719936C2211yescharacteristic
17C22×#11719940C2211yescharacteristic
18C22×D53⋊C8C2211yescharacteristic
19C23×#88324C2211yescharacteristic
20#16811597C418yescomplemented
21#16811596C418yescomplemented
22C2×#13133274C2211yescharacteristic
23C2×#13133274C2211yescharacteristic
24C2×C22⋊#88324C2211yescharacteristic
25C2×C22⋊#88324C2211yescharacteristic
26C2×C22⋊#88324C2211yescharacteristic
27C2×C22⋊#88324C2211yescharacteristic
28C2×C22⋊#88324C2211yescharacteristic
29C2×C22⋊#88324C2211yescharacteristic
30C2×#13133272C2211yescharacteristic
31C2×#13133272C2211yescharacteristic
32C2×#13133272C2211yescharacteristic
33C2×#13133272C2211yescharacteristic
34C2×C4×#88324C2211yescharacteristic
35C2×C4×#88324C2211yescharacteristic
36C2×C4×#88324C2211yescharacteristic
37C2×C4×#88324C2211yescharacteristic
38#16811489C2211yescharacteristic
39#16811489C2211yescharacteristic
40#16811489C2211yescharacteristic
41#16811489C2211yescharacteristic
42#16811489C2211yescharacteristic
43#16811489C2211yescharacteristic
44#16811489C2211yescharacteristic
45#16811489C2211yescharacteristic
46C22×#11719947C2211yescharacteristic
47C2×#13133173C2211yescharacteristic
48C22×C4×Dic53C2211yescharacteristic
49#16810527C411yescharacteristic
50#16810527C411yescharacteristic
51#16810523C411yescharacteristic
52#16810523C411yescharacteristic
53#16810503C411yescharacteristic
54#16810502C411yescharacteristic
55#16810500C411yescharacteristic
56C22⋊C4×Dic53C2211yescharacteristic
57C22⋊C4×Dic53C2211yescharacteristic
58#16810470C2211yescharacteristic
59#16810470C2211yescharacteristic
60C53×#386C411yescharacteristic
61C2×#11719936—41no—
62C2×#11719936—41no—
63C2×#11719936C2×C414yescomplemented
64C2×#11719940—41no—
65C2×#11719940—41no—
66C2×#11719940C2×C414yescomplemented
67C2×D53⋊C8—41no—
68C2×D53⋊C8—41no—
69C2×D53⋊C8C2×C414yescomplemented
70C22×#88324—41no—
71C22×#88324—41no—
72C22×#88324C2×C414yescomplemented
73C22×#88324C2311yescharacteristic
74C22×#88324C2311yescharacteristic
75C22×#88324C2311yescharacteristic
76C22×#88324C2311yescharacteristic
77C22×#88324C2311yescharacteristic
78C22×#88324C2311yescharacteristic
79C22×#88324C2311yescharacteristic
80C22×#88324C2311yescharacteristic
81#13133274C2×C414yescomplemented
82#13133274C2×C414yescomplemented
83C22⋊#88324C2×C414yes—
84C22⋊#88324C2×C414yes—
85C22⋊#88324C2×C414yes—
86C22⋊#88324C2×C414yes—
87C22⋊#88324C2×C414yescomplemented
88C22⋊#88324C2×C414yescomplemented
89#13133272—41no—
90#13133272—41no—
91#13133272—41no—
92#13133272—41no—
93C4×#88324—41no—
94C4×#88324—41no—
95C4×#88324—41no—
96C4×#88324—41no—
97C2×#11719947—41no—
98C2×#11719947—41no—
99C2×#11719947—41no—
100C2×#11719947—41no—
101C2×#11719947C2×C414yes—
102C2×#11719947C2×C414yes—
103C22×Dic106C2×C411yescharacteristic
104C22×C22⋊D53C2×C411yescharacteristic
105C22×C22⋊D53C2×C411yescharacteristic
106C23×Dic53C2×C411yescharacteristic
107C23×Dic53C2311yescharacteristic
108C23×Dic53C2311yescharacteristic
109C22×C4×D53C2311yescharacteristic
110#13133173—41no—
111#13133173—41no—
112C2×#11719919C2×C411yescharacteristic
113C2×#11719919C2×C411yescharacteristic
114C2×C22⋊Dic53C2×C411yescharacteristic
115C2×C22⋊Dic53C2×C411yescharacteristic
116C2×C22⋊Dic53C2×C411yescharacteristic
117C2×#11719921C2×C411yescharacteristic
118C2×#11719921C2×C411yescharacteristic
119C2×#11719921C2×C411yescharacteristic
120C2×#11719921C2×C411yescharacteristic
121C2×C4×Dic53—41no—
122C2×C4×Dic53—41no—
123C2×C4×Dic53C2×C411yescharacteristic
124C2×C4×Dic53C2×C411yescharacteristic
125C2×C4×Dic53C2311yescharacteristic
126C2×C4×Dic53C2311yescharacteristic
127C2×C4×Dic53C2311yescharacteristic
128C2×C4×Dic53C2311yescharacteristic
129#13133124C2×C411yescharacteristic
130#13133124C2×C411yescharacteristic
131#13133124C2×C411yescharacteristic
132#13133124C2×C411yescharacteristic
133#13133124C2×C411yescharacteristic
134#13133124C2×C411yescharacteristic
135C22×D4×C53C2×C411yescharacteristic
136C23×C4×C53C2×C411yescharacteristic
137C2×C22⋊C4×C53C2×C411yescharacteristic
138C2×C22⋊C4×C53C2×C411yescharacteristic
139C2×C22⋊C4×C53C2×C411yescharacteristic
140#95×C53C2×C411yescharacteristic
141#95×C53C2×C411yescharacteristic
142C24×C53C22×C411yescharacteristic
143C24×C53C22×C411yescharacteristic
144C23×D53C22×C411yescharacteristic
145C2×D4×C53—41no—
146C2×D4×C53—41no—
147C2×D4×C53C4214yes—
148C22×C4×C53—22no—
149C22×C4×C53—41no—
150C22×C4×C53—41no—
151C22×C4×C53C22×C411yescharacteristic
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C22×C411yescharacteristic
154C22×C4×C53C22×C411yescharacteristic
155C22×C4×C53C22×C411yescharacteristic
156C2×C22⋊D53—41no—
157C2×C22⋊D53—41no—
158C2×C22⋊D53—41no—
159C2×C22⋊D53—41no—
160C2×C22⋊D53C4214yes—
161C2×C22⋊D53C4214yes—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—22no—
171C22×Dic53—41no—
172C22×Dic53—41no—
173C22×Dic53C22×C411yescharacteristic
174C22×Dic53C22×C411yescharacteristic
175C22×Dic53C22×C411yescharacteristic
176C22×Dic53C22×C411yescharacteristic
177C22×Dic53C22×C411yescharacteristic
178C22×Dic53C22×C412yes—
179C22×Dic53C22×C412yes—
180C22×Dic53C22×C412yes—
181C22×Dic53C22×C412yes—
182C22×Dic53C22×C411yescharacteristic
183C22×Dic53C2411yescharacteristic
184#11719947—44no—
185#11719947—44no—
186#11719947—44no—
187#11719947—44no—
188C2×C4×D53—21no—
189C2×C4×D53—21no—
190C2×C4×D53—21no—
191C2×C4×D53—21no—
192C2×C4×D53C22×C412yes—
193C2×C4×D53C22×C412yes—
194C2×Dic106—41no—
195C2×Dic106—41no—
196C2×Dic106C4214yes—
197#11719940—44no—
198C2×#88324—21no—
199C2×#88324—21no—
200C2×#88324—21no—
201C2×#88324—21no—
202C2×#88324—21no—
203C2×#88324—21no—
204C2×#88324—21no—
205C2×#88324—21no—
206C2×#88324—21no—
207C2×#88324—21no—
208C2×#88324—21no—
209C2×#88324—21no—
210C2×#88324—21no—
211C2×#88324—21no—
212C2×#88324—21no—
213C2×#88324—21no—
214C2×#88324—44no—
215C2×#88324C22×C412yes—
216C2×#88324C22×C412yes—
217C2×#88324C22×C412yes—
218C2×#88324C22×C412yes—
219C2×#88324C22×C412yes—
220C2×#88324C22×C412yes—
221C2×#88324C22×C412yes—
222C2×#88324C22×C412yes—
223#11719936—44no—
224D53⋊C8—44no—
225C22⋊C4×C53—22no—
226C22⋊C4×C53—41no—
227C22⋊C4×C53—41no—
228C22⋊Dic53—22no—
229C22⋊Dic53—41no—
230C22⋊Dic53—41no—
231#11719921—22no—
232#11719921—22no—
233#11719921—41no—
234#11719921—41no—
235#11719919—41no—
236#11719919—41no—
237C4×Dic53—21no—
238C4×Dic53—21no—
239C4×Dic53—21no—
240C4×Dic53—21no—
241C4×Dic53—21no—
242C4×Dic53—21no—
243C4×Dic53—21no—
244C4×Dic53—21no—
245C4×Dic53—41no—
246C4×Dic53—41no—
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×C53—21no—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53C2×C4212yes—
260C23×C53C2×C4212yes—
261C23×C53C23×C411yescharacteristic
262C22×D53—21no—
263C22×D53—21no—
264C22×D53—21no—
265C22×D53—21no—
266C22×D53—21no—
267C22×D53—21no—
268C22×D53C2×C4212yes—
269D4×C53—44no—
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×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—44no—
284C2×C4×C53C2×C4212yes—
285C2×C4×C53#13112yes—
286C22⋊D53—44no—
287C22⋊D53—44no—
288C2×Dic53—21no—
289C2×Dic53—21no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53—44no—
312C2×Dic53C2×C4212yes—
313C2×Dic53C2×C4212yes—
314C2×Dic53#13112yes—
315C2×Dic53C23×C411yescharacteristic
316C2×Dic53C23×C411yescharacteristic
317C2×Dic53H(5,𝔽2)11yescharacteristic
318C2×Dic53H(5,𝔽2)11yescharacteristic
319C2×Dic53H(5,𝔽2)11yescharacteristic
320C2×Dic53H(5,𝔽2)11yescharacteristic
321C4×D53—22no—
322C4×D53—22no—
323C4×D53—22no—
324C4×D53—22no—
325Dic106—44no—
326#88324—22no—
327#88324—22no—
328#88324—22no—
329#88324—22no—
330#88324—22no—
331#88324—22no—
332#88324—22no—
333#88324—22no—
334#20531—531nomaximal, Sylow
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—41no—
346C22×C53—41no—
347C22×C53—41no—
348C22×C53—41no—
349C22×C53C22×C4211yescharacteristic
350C22×C53#51811yescharacteristic
351C22×C53#51811yescharacteristic
352C22×C53C2×#13111yescharacteristic
353C22×C53C2×#13111yescharacteristic
354C22×C53#56811yescharacteristic
355C22×C53#56811yescharacteristic
356C2×D53—22no—
357C2×D53—22no—
358C2×D53—22no—
359C2×D53—41no—
360C2×D53—41no—
361C2×D53—41no—
362C2×D53—41no—
363C4×C53—22no—
364C4×C53—22no—
365C4×C53—41no—
366C4×C53—41no—
367C4×C53—41no—
368Dic53—22no—
369Dic53—22no—
370Dic53—22no—
371Dic53—41no—
372Dic53—41no—
373Dic53—41no—
374Dic53#51811yescharacteristic
375Dic53#51811yescharacteristic
376Dic53#51811yescharacteristic
377Dic53#51811yescharacteristic
378C2×#408—531no—
379C2×#408—531no—
380#2297—531no—
381#1753—531no—
382#1753—531no—
383#1753—531no—
384#1753—531no—
385#1752—531no—
386#1752—531no—
387C8×C22⋊C4—531no—
388C8×C22⋊C4—531no—
389#1750—531no—
390#1750—531no—
391#1749—531no—
392C4×C22⋊C8—531no—
393C2×C53—42no—
394C2×C53—42no—
395C2×C53#227311yescharacteristic
396C2×C53C4×#13111yescharacteristic
397C2×C53#287511yescharacteristic
398C2×C53#297611yescharacteristic
399C2×C53#297611yescharacteristic
400C2×C53#298111yescharacteristic
401C2×C53#298111yescharacteristic
402D53—42no—
403C22×#41—531no—
404C22×M16—531no—
405C22×M16—531no—
406C23×C8—531no—
407C23×C8—531no—
408C2×#117—531no—
409C22×C42—531no—
410#408—538no—
411#408—538no—
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×#97—531no—
423C2×#97—531no—
424C2×C4×C8—531no—
425C2×C4×C8—531no—
426C2×C4×C8—531no—
427C2×C4×C8—531no—
428#391—531no—
429#391—531no—
430#390—531no—
431#390—531no—
432#386—531no—
433#386—531no—
434#386—531no—
435#386#615711yescharacteristic
436C4×C22⋊C4—531no—
437C4×C22⋊C4—531no—
438C4×C22⋊C4—531no—
439C4×C22⋊C4—531no—
440#336—531no—
441#336—531no—
442#336—531no—
443#336—531no—
444#336—531no—
445#336—531no—
446#336—531no—
447#336—531no—
448C53#2053111yescharacteristic, complemented, Sylow
449C2×#41—534no—
450C2×#41—534no—
451C2×#41—2121no—
452C2×#41—2121no—
453C2×#41—2121no—
454C2×#41—2121no—
455C22×Q8—531no—
456C22×D4—531no—
457C22×D4—531no—
458C22×D4C2×#615711yescharacteristic
459C23×C4—531no—
460C23×C4—531no—
461C23×C4—531no—
462C23×C4—531no—
463C23×C4C2×#615711yescharacteristic
464C2×M16—534no—
465C2×M16—534no—
466C2×M16—2121no—
467C2×M16—2121no—
468C2×M16—2121no—
469C2×M16—2121no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—531no—
474C22×C8—531no—
475C22×C8—531no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8—534no—
479C22×C8—534no—
480C22×C8—2121no—
481C22×C8—2121no—
482C22×C8—2121no—
483C22×C8—2121no—
484#117—2121no—
485#117—2121no—
486C2×C4⋊C4—531no—
487C2×C4⋊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×C22⋊C4C2×#615711yescharacteristic
496C2×C22⋊C4C2×#615711yescharacteristic
497C2×C22⋊C4C2×#615711yescharacteristic
498C2×C42—531no—
499C2×C42—531no—
500C2×C42—531no—
501C2×C42—531no—
502C2×C42—531no—
503C2×C42—531no—
504C2×C42—2121no—
505C2×C42—2121no—
506C22⋊C8—534no—
507C22⋊C8—534no—
508C22⋊C8—534no—
509C22⋊C8—534no—
510C22⋊C8—534no—
511C22⋊C8—534no—
512C22⋊C8—534no—
513C22⋊C8—534no—
514#97—2121no—
515#97—2121no—
516#97—2121no—
517#97—2121no—
518C4×C8—2121no—
519C4×C8—2121no—
520C4×C8—2121no—
521C4×C8—2121no—
522#95—531no—
523#95—531no—
524#95—531no—
525#95—531no—
526#95—531no—
527#95—531no—
528#95C2×#615711yescharacteristic
529#95C2×#615711yescharacteristic
530C24—531no—
531C24C22×#615711yescharacteristic
532C24C22×#615711yescharacteristic
533#41—2124no—
534#41—2124no—
535#41—2124no—
536#41—2124no—
537C2×Q8—534no—
538C2×Q8—2121no—
539C2×Q8—2121no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—534no—
543C2×D4—534no—
544C2×D4—2121no—
545C2×D4—2121no—
546C2×D4—2121no—
547C2×D4—2121no—
548C2×D4C4×#615714yes—
549C22×C4—22no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—531no—
553C22×C4—532no—
554C22×C4—532no—
555C22×C4—532no—
556C22×C4—532no—
557C22×C4—531no—
558C22×C4—531no—
559C22×C4—531no—
560C22×C4—532no—
561C22×C4—532no—
562C22×C4—531no—
563C22×C4—531no—
564C22×C4—531no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1062no—
578C22×C4—2121no—
579C22×C4—2121no—
580C22×C4C22×#615711yescharacteristic
581C22×C4C22×#615711yescharacteristic
582C22×C4C22×#615711yescharacteristic
583C22×C4C22×#615711yescharacteristic
584C22×C4C22×#615711yescharacteristic
585M16—2124no—
586M16—2124no—
587C2×C8—532no—
588C2×C8—532no—
589C2×C8—532no—
590C2×C8—532no—
591C2×C8—532no—
592C2×C8—532no—
593C2×C8—532no—
594C2×C8—532no—
595C2×C8—1061no—
596C2×C8—1061no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—1061no—
600C2×C8—1061no—
601C2×C8—1061no—
602C2×C8—1061no—
603C2×C8—1061no—
604C2×C8—1061no—
605C2×C8—1061no—
606C2×C8—1061no—
607C2×C8—1061no—
608C2×C8—1061no—
609C2×C8—1061no—
610C2×C8—1061no—
611C2×C8—2124no—
612C2×C8—2124no—
613C4⋊C4—2121no—
614C4⋊C4—2121no—
615C22⋊C4—22no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—1062no—
619C22⋊C4—1062no—
620C22⋊C4—1062no—
621C22⋊C4—2121no—
622C22⋊C4—2121no—
623C22⋊C4—2121no—
624C22⋊C4—2121no—
625C42—1061no—
626C42—1061no—
627C42—1061no—
628C42—1061no—
629C42—1061no—
630C42—1061no—
631C42—1061no—
632C42—1061no—
633C42—2121no—
634C42—2121no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—532no—
648C23—1061no—
649C23—1061no—
650C23—1061no—
651C23—1061no—
652C23—1061no—
653C23—1061no—
654C23C2×C4×#615712yes—
655C23C2×C4×#615712yes—
656C23C23×#615711yescharacteristic
657Q8—2124no—
658D4—44no—
659D4—2124no—
660D4—2124no—
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—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—44no—
675C2×C4—531no—
676C2×C4—531no—
677C2×C4—531no—
678C2×C4—531no—
679C2×C4—531no—
680C2×C4—531no—
681C2×C4—532no—
682C2×C4—532no—
683C2×C4—532no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1061no—
697C2×C4—1061no—
698C2×C4—1061no—
699C2×C4—1061no—
700C2×C4—1061no—
701C2×C4—1061no—
702C2×C4—1061no—
703C2×C4—1061no—
704C2×C4—1061no—
705C2×C4—1061no—
706C2×C4—1061no—
707C2×C4—1061no—
708C2×C4—1061no—
709C2×C4—1061no—
710C2×C4—1061no—
711C2×C4—2124no—
712C2×C4C2×C4×#615712yes—
713C2×C4#1313330412yes—
714C8—1062no—
715C8—1062no—
716C8—1062no—
717C8—1062no—
718C8—1062no—
719C8—1062no—
720C8—1062no—
721C8—1062no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—1062no—
737C22—1062no—
738C22—1062no—
739C22—2121no—
740C22—2121no—
741C22—2121no—
742C22—2121no—
743C22C22×C4×#615711yescharacteristic
744C22#1681169011yescharacteristic
745C22#1681169011yescharacteristic
746C22C2×#1313330411yescharacteristic
747C22D53⋊#13111yescharacteristic
748C22#1681170111yescharacteristic
749C22#1681170211yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—531no—
756C4—531no—
757C4—531no—
758C4—531no—
759C4—1062no—
760C4—1062no—
761C4—1062no—
762C4—2121no—
763C4—2121no—
764C4—2121no—
765C2—42no—
766C2—42no—
767C2—2122no—
768C2#2029115111yescharacteristic
769C2C4×#1313330411yescharacteristic
770C2#2029128611yescharacteristic
771C2#2029158111yescharacteristic
772C2#2029158311yescharacteristic
773C2#2029160311yescharacteristic
774C2#2029160511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutatorC22×C53C22×C42
FittingC53×#386C4
socleC23×C53C23×C4
prime radicalC22×#11719947C22
cosocleC22×Dic53C24
hypercenter#386#6157
hypocenterC53#20531
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #20290457C2semidirect
4. #20290457C2semidirect
5. #20290456C2semidirect
6. #20290456C2semidirect
7. #20290453C2semidirect
8. #20290452C2semidirect
9. #20290449C2semidirect
10. C22⋊C4×#88324C2semidirect
11. #20290445C2semidirect
12. #20290445C2semidirect
13. #20290441C2semidirect
14. C4×C22⋊#88324C2semidirect
20. #16811597C4semidirect
21. #16811596C4semidirect
63. C2×#11719936C2×C4semidirect
66. C2×#11719940C2×C4semidirect
69. C2×D53⋊C8C2×C4semidirect
72. C22×#88324C2×C4semidirect
81. #13133274C2×C4semidirect
82. #13133274C2×C4semidirect
87. C22⋊#88324C2×C4semidirect
88. C22⋊#88324C2×C4semidirect
448. C53#20531semidirect

Maximal subgroups

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

subgroupindex
C2×#168115972
C2×#168115962
#202904572
#202904562
#202904532
#202904522
#202904492
C22⋊C4×#883242
#202904452
#202904412
C4×C22⋊#883242
#202772002
#2053153