Finite Group Databasebeta

← #28323696

Subgroups — #28323696

Order 13568.

884 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20290840C211yesmaximal, characteristic, complemented
2#20290838C211yesmaximal, characteristic, complemented
3#20290785C211yesmaximal, characteristic, complemented
4#20290784C211yesmaximal, characteristic, complemented
5#20290775C211yesmaximal, characteristic, complemented
6#20290768C211yesmaximal, characteristic, complemented
7#20290694C211yesmaximal, characteristic, complemented
8#20290692C211yesmaximal, characteristic, complemented
9#20290690C211yesmaximal, characteristic, complemented
10#20290688C211yesmaximal, characteristic, complemented
11#20290607C211yesmaximal, characteristic, complemented
12#20290457C211yesmaximal, characteristic, complemented
13C22⋊C4×#88324C211yesmaximal, characteristic, complemented
14C4×#13133274C211yesmaximal, characteristic, complemented
15#20277231C211yesmaximal, characteristic
16C22×#11719940C2211yescharacteristic
17C23×#88324C2211yescharacteristic
18C2×#13133284C2211yescharacteristic
19C2×C4⋊#88324C2211yescharacteristic
20C2×#13133274C2211yescharacteristic
21C2×#13133274C2211yescharacteristic
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×C4×#88324C2211yescharacteristic
32C2×C4×#88324C2211yescharacteristic
33C2×C4×#88324C2211yescharacteristic
34#16811489C2211yescharacteristic
35#16811489C2211yescharacteristic
36#16811489C2211yescharacteristic
37#16811489C2211yescharacteristic
38#16811489C2211yescharacteristic
39#16811489C2211yescharacteristic
40#16811489C2211yescharacteristic
41#16811489C2211yescharacteristic
42#16811489C2211yescharacteristic
43#16811489C2211yescharacteristic
44C2×#13133188C411yescharacteristic
45C2×D4×Dic53C2211yescharacteristic
46C2×#13133177C2211yescharacteristic
47C2×#13133177C2211yescharacteristic
48C2×C42×D53C2211yescharacteristic
49#16810521C411yescharacteristic
50#16810517C411yescharacteristic
51#16810517C411yescharacteristic
52#16810499C411yescharacteristic
53#16810499C411yescharacteristic
54#16810480C411yescharacteristic
55C4⋊C4×Dic53C2211yescharacteristic
56C22⋊C4×Dic53C2211yescharacteristic
57C22⋊C4×Dic53C2211yescharacteristic
58C53×#390C411yescharacteristic
59C2×#11719940—22no—
60C2×#11719940—41no—
61C2×#11719940—41no—
62C22×#88324—22no—
63C22×#88324—41no—
64C22×#88324—41no—
65C22×#88324C2311yescharacteristic
66C22×#88324C2311yescharacteristic
67C22×#88324C2311yescharacteristic
68C22×#88324C2311yescharacteristic
69C22×#88324C2311yescharacteristic
70C22×#88324C2311yescharacteristic
71C22×#88324C2311yescharacteristic
72C22×#88324C2311yescharacteristic
73#13133284—41no—
74C4⋊#88324—41no—
75#13133274—22no—
76#13133274—22no—
77#13133274—41no—
78#13133274—41no—
79C22⋊#88324—22no—
80C22⋊#88324—22no—
81C22⋊#88324—41no—
82C22⋊#88324—41no—
83C22⋊#88324—41no—
84C22⋊#88324—41no—
85#13133272—41no—
86C4×#88324—41no—
87C4×#88324—41no—
88C4×#88324—41no—
89C22×C22⋊D53C2×C411yescharacteristic
90C22×C22⋊D53C2×C411yescharacteristic
91C23×Dic53C2311yescharacteristic
92C23×Dic53C2311yescharacteristic
93C22×C4×D53C2×C411yescharacteristic
94C22×C4×D53C2×C411yescharacteristic
95C22×C4×D53C2311yescharacteristic
96#13133188—24no—
97D4×Dic53—41no—
98D4×Dic53—41no—
99#13133177—41no—
100#13133177—41no—
101#13133177—41no—
102#13133177—41no—
103C2×C4⋊Dic53C2×C411yescharacteristic
104C2×C4⋊Dic53C2×C411yescharacteristic
105C2×#11719919C2×C411yescharacteristic
106C2×#11719919C2×C411yescharacteristic
107C2×C22⋊Dic53C2×C411yescharacteristic
108C2×C22⋊Dic53C2×C411yescharacteristic
109C2×C22⋊Dic53C2×C411yescharacteristic
110C2×C22⋊Dic53C2×C411yescharacteristic
111C2×#11719921C2×C411yescharacteristic
112C2×#11719921C2×C411yescharacteristic
113C2×C4×Dic53C2×C411yescharacteristic
114C2×C4×Dic53C2311yescharacteristic
115C2×C4×Dic53C2311yescharacteristic
116C2×C4×Dic53C2311yescharacteristic
117C2×C4×Dic53C2311yescharacteristic
118C42×D53—41no—
119C42×D53—41no—
120#13133124C2×C411yescharacteristic
121#13133124C2×C411yescharacteristic
122#13133124C2×C411yescharacteristic
123#13133124C2×C411yescharacteristic
124#13133124C2×C411yescharacteristic
125#13133124C2×C411yescharacteristic
126C22×D4×C53C2×C411yescharacteristic
127C2×C4⋊C4×C53C2×C411yescharacteristic
128C2×C22⋊C4×C53C2×C411yescharacteristic
129C2×C22⋊C4×C53C2×C411yescharacteristic
130C2×C22⋊C4×C53C2×C411yescharacteristic
131C2×C22⋊C4×C53C2×C411yescharacteristic
132C2×C42×C53C2×C411yescharacteristic
133C24×C53C22×C411yescharacteristic
134C24×C53C22×C411yescharacteristic
135C23×D53C22×C411yescharacteristic
136C2×D4×C53—22no—
137C2×D4×C53—22no—
138C2×D4×C53—41no—
139C22×C4×C53C22×C411yescharacteristic
140C22×C4×C53C22×C411yescharacteristic
141C22×C4×C53C22×C411yescharacteristic
142C22×C4×C53C22×C411yescharacteristic
143C22×C4×C53C22×C411yescharacteristic
144C2×C22⋊D53—22no—
145C2×C22⋊D53—22no—
146C2×C22⋊D53—22no—
147C2×C22⋊D53—22no—
148C2×C22⋊D53—41no—
149C2×C22⋊D53—41no—
150C22×Dic53—21no—
151C22×Dic53—21no—
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53C22×C411yescharacteristic
163C22×Dic53C22×C411yescharacteristic
164C22×Dic53C22×C411yescharacteristic
165C22×Dic53C22×C411yescharacteristic
166C22×Dic53C22×C411yescharacteristic
167C22×Dic53C22×C411yescharacteristic
168C22×Dic53C2411yescharacteristic
169C2×C4×D53—22no—
170C2×C4×D53—22no—
171C2×C4×D53—22no—
172C2×C4×D53—22no—
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—41no—
180C2×C4×D53—41no—
181#11719940—44no—
182C2×#88324—21no—
183C2×#88324—21no—
184C2×#88324—21no—
185C2×#88324—21no—
186C2×#88324—21no—
187C2×#88324—21no—
188C2×#88324—21no—
189C2×#88324—21no—
190C2×#88324—21no—
191C2×#88324—21no—
192C2×#88324—21no—
193C2×#88324—21no—
194C2×#88324—21no—
195C2×#88324—21no—
196C2×#88324—21no—
197C2×#88324—21no—
198C2×#88324—21no—
199C2×#88324—21no—
200C2×#88324—21no—
201C2×#88324—21no—
202C2×#88324—21no—
203C2×#88324—21no—
204C2×#88324—44no—
205C2×#88324#4112yes—
206C2×#88324#4112yes—
207C4⋊C4×C53—22no—
208C22⋊C4×C53—22no—
209C22⋊C4×C53—22no—
210C22⋊C4×C53—41no—
211C22⋊C4×C53—41no—
212C42×C53—41no—
213C22⋊Dic53—22no—
214C22⋊Dic53—41no—
215C22⋊Dic53—41no—
216C22⋊Dic53M1614yescomplemented
217#11719921—41no—
218#11719921—41no—
219C4⋊Dic53—22no—
220C4⋊Dic53—41no—
221#11719919—41no—
222#11719919—41no—
223C4×Dic53—21no—
224C4×Dic53—21no—
225C4×Dic53—21no—
226C4×Dic53—21no—
227C4×Dic53—21no—
228C4×Dic53—21no—
229C4×Dic53—21no—
230C4×Dic53—21no—
231C4×Dic53—41no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53C2×M1612yes—
246C23×C53C23×C411yescharacteristic
247C22×D53—21no—
248C22×D53—21no—
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53#13112yes—
254D4×C53—44no—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53#13112yes—
269C2×C4×C53#13112yes—
270C22⋊D53—44no—
271C22⋊D53—44no—
272C2×Dic53—21no—
273C2×Dic53—21no—
274C2×Dic53—21no—
275C2×Dic53—21no—
276C2×Dic53—21no—
277C2×Dic53—21no—
278C2×Dic53—21no—
279C2×Dic53—21no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—21no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53C2×M1612yes—
297C2×Dic53C2×M1612yes—
298C2×Dic53C2×#4111yescharacteristic
299C2×Dic53C2×#4111yescharacteristic
300C2×Dic53H(5,𝔽2)11yescharacteristic
301C2×Dic53H(5,𝔽2)11yescharacteristic
302C2×Dic53H(5,𝔽2)11yescharacteristic
303C2×Dic53H(5,𝔽2)11yescharacteristic
304C4×D53—44no—
305C4×D53—44no—
306C4×D53—41no—
307C4×D53—41no—
308C4×D53—41no—
309C4×D53—41no—
310#88324—22no—
311#88324—22no—
312#88324—41no—
313#88324—41no—
314#88324—41no—
315#88324—41no—
316#88324—41no—
317#88324—41no—
318#22333—531nomaximal, Sylow
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53C4×#4111yescharacteristic
334C22×C53#51811yescharacteristic
335C22×C53#51811yescharacteristic
336C22×C53C22×M1611yescharacteristic
337C22×C53C2×#13111yescharacteristic
338C22×C53C2×#13111yescharacteristic
339C22×C53C2×#13111yescharacteristic
340C2×D53—22no—
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—41no—
344C2×D53—41no—
345C2×D53—41no—
346C2×D53—41no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—41no—
350C4×C53—41no—
351C4×C53—41no—
352Dic53—22no—
353Dic53—22no—
354Dic53—41no—
355Dic53—41no—
356Dic53—41no—
357Dic53—41no—
358Dic53#53811yescharacteristic
359Dic53#53811yescharacteristic
360Dic53#54011yescharacteristic
361Dic53#54011yescharacteristic
362C4×#121—531no—
363#1955—531no—
364#1954—531no—
365#1923—531no—
366#1923—531no—
367#1917—531no—
368#1916—531no—
369#1870—531no—
370#1870—531no—
371#1869—531no—
372#1869—531no—
373#1817—531no—
374#1753—531no—
375C8×C22⋊C4—531no—
376C4×C22⋊C8—531no—
377C2×C53—42no—
378C2×C53—81no—
379C2×C53#233311yescharacteristic
380C2×C53#296511yescharacteristic
381C2×C53#296611yescharacteristic
382C2×C53#297411yescharacteristic
383C2×C53#297411yescharacteristic
384C2×C53#297711yescharacteristic
385C2×C53#297911yescharacteristic
386D53—42no—
387C22×M16—531no—
388C23×C8—531no—
389C2×#121—531no—
390C2×C4×D4—531no—
391C2×C4×D4—531no—
392C2×C4×D4—531no—
393C22×C42—531no—
394C2×C4⋊C8—531no—
395C2×C4⋊C8—531no—
396C2×C22⋊C8—531no—
397C2×C22⋊C8—531no—
398C2×C22⋊C8—531no—
399C2×C22⋊C8—531no—
400C2×C22⋊C8—531no—
401C2×C22⋊C8—531no—
402C2×C22⋊C8—531no—
403C2×C22⋊C8—531no—
404C2×C22⋊C8—531no—
405C2×C22⋊C8—531no—
406C2×#97—531no—
407C2×C4×C8—531no—
408C2×C4×C8—531no—
409C2×C4×C8—531no—
410#390#615711yescharacteristic
411#389—531no—
412#388—531no—
413#388—531no—
414#386—531no—
415#386—531no—
416#380—531no—
417C4×C4⋊C4—531no—
418C4×C22⋊C4—531no—
419C4×C22⋊C4—531no—
420#336—531no—
421#336—531no—
422#336—531no—
423#336—531no—
424#336—531no—
425#336—531no—
426#336—531no—
427#336—531no—
428#336—531no—
429#336—531no—
430C53#2233311yescharacteristic, complemented, Sylow
431C22×D4—531no—
432C22×D4—531no—
433C22×D4C2×#615711yescharacteristic
434C23×C4—531no—
435C23×C4—531no—
436C23×C4—531no—
437C23×C4—531no—
438C23×C4—531no—
439C2×M16—1062no—
440C2×M16—2121no—
441C2×M16—2121no—
442C22×C8—531no—
443C22×C8—531no—
444C22×C8—531no—
445C22×C8—531no—
446C22×C8—531no—
447C22×C8—531no—
448C22×C8—531no—
449C22×C8—531no—
450C22×C8—1062no—
451C22×C8—2121no—
452C22×C8—2121no—
453#121—1064no—
454C4×D4—2121no—
455C4×D4—2121no—
456C4×D4—2121no—
457C4×D4—2121no—
458C4×D4—2121no—
459C4×D4—2121no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4C2×#615711yescharacteristic
465C2×C22⋊C4—531no—
466C2×C22⋊C4—531no—
467C2×C22⋊C4—531no—
468C2×C22⋊C4—531no—
469C2×C22⋊C4—531no—
470C2×C22⋊C4—531no—
471C2×C22⋊C4C2×#615711yescharacteristic
472C2×C22⋊C4C2×#615711yescharacteristic
473C2×C22⋊C4C2×#615711yescharacteristic
474C2×C22⋊C4C2×#615711yescharacteristic
475C2×C42—531no—
476C2×C42—531no—
477C2×C42—531no—
478C2×C42—531no—
479C2×C42—531no—
480C2×C42—2121no—
481C2×C42—2121no—
482C2×C42C2×#615711yescharacteristic
483C4⋊C8—2121no—
484C4⋊C8—2121no—
485C22⋊C8—1062no—
486C22⋊C8—1062no—
487C22⋊C8—1062no—
488C22⋊C8—1062no—
489C22⋊C8—2121no—
490C22⋊C8—2121no—
491C22⋊C8—2121no—
492C22⋊C8—2121no—
493C22⋊C8—2121no—
494C22⋊C8—2121no—
495#97—2121no—
496C4×C8—2121no—
497C4×C8—2121no—
498C4×C8—2121no—
499#95—531no—
500#95—531no—
501#95—531no—
502#95—531no—
503#95—531no—
504#95—531no—
505C24—531no—
506C24C22×#615711yescharacteristic
507C24C22×#615711yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—41no—
511C2×D4—1062no—
512C2×D4—1062no—
513C2×D4—1062no—
514C2×D4—1062no—
515C2×D4—2121no—
516C2×D4—2121no—
517C22×C4—531no—
518C22×C4—531no—
519C22×C4—531no—
520C22×C4—531no—
521C22×C4—531no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—1061no—
525C22×C4—1061no—
526C22×C4—1061no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—1061no—
538C22×C4—1061no—
539C22×C4—1061no—
540C22×C4—1061no—
541C22×C4—1061no—
542C22×C4—1061no—
543C22×C4—1061no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—2121no—
547C22×C4—2121no—
548C22×C4C22×#615711yescharacteristic
549C22×C4C22×#615711yescharacteristic
550C22×C4C22×#615711yescharacteristic
551C22×C4C22×#615711yescharacteristic
552C22×C4C22×#615711yescharacteristic
553M16—2124no—
554C2×C8—532no—
555C2×C8—532no—
556C2×C8—1061no—
557C2×C8—1061no—
558C2×C8—1061no—
559C2×C8—1061no—
560C2×C8—1061no—
561C2×C8—1061no—
562C2×C8—1061no—
563C2×C8—1061no—
564C2×C8—1061no—
565C2×C8—1061no—
566C2×C8—1061no—
567C2×C8—1061no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—2124no—
579C4⋊C4—22no—
580C4⋊C4—1062no—
581C4⋊C4—2121no—
582C4⋊C4—2121no—
583C4⋊C4—2121no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—534no—
589C22⋊C4—1062no—
590C22⋊C4—2121no—
591C22⋊C4—2121no—
592C22⋊C4—2121no—
593C22⋊C4—2121no—
594C42—41no—
595C42—1061no—
596C42—1061no—
597C42—1061no—
598C42—1061no—
599C42—1061no—
600C42—1061no—
601C42—1061no—
602C42—1061no—
603C42—2121no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—532no—
618C23—1061no—
619C23—1061no—
620C23—1061no—
621C23—1061no—
622C23—1061no—
623C23—1061no—
624C23D53⋊M1612yes—
625C23C23×#615711yescharacteristic
626D4—44no—
627D4—2124no—
628D4—2124no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—531no—
643C2×C4—531no—
644C2×C4—531no—
645C2×C4—531no—
646C2×C4—531no—
647C2×C4—531no—
648C2×C4—532no—
649C2×C4—532no—
650C2×C4—1061no—
651C2×C4—1061no—
652C2×C4—1061no—
653C2×C4—1061no—
654C2×C4—1061no—
655C2×C4—1061no—
656C2×C4—1061no—
657C2×C4—1061no—
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—2124no—
667C2×C4—2124no—
668C2×C4—2121no—
669C2×C4—2121no—
670C2×C4—2121no—
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#1313330412yes—
681C2×C4#1313330412yes—
682C8—1062no—
683C8—1062no—
684C8—2121no—
685C8—2121no—
686C8—2121no—
687C8—2121no—
688C8—2121no—
689C8—2121no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—1062no—
705C22—1062no—
706C22—1062no—
707C22—2121no—
708C22—2121no—
709C22—2121no—
710C22—2121no—
711C22#41×#615711yescharacteristic
712C22#1681169011yescharacteristic
713C22#1681169011yescharacteristic
714C22C2×D53⋊M1611yescharacteristic
715C22C2×#1313330411yescharacteristic
716C22C2×#1313330411yescharacteristic
717C22D53⋊#13111yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—531no—
724C4—531no—
725C4—531no—
726C4—531no—
727C4—1062no—
728C4—1062no—
729C4—2121no—
730C4—2121no—
731C4—2121no—
732C4—2121no—
733C2—42no—
734C2—81no—
735C2—2122no—
736C2#2029121211yescharacteristic
737C2#2029152511yescharacteristic
738C2#2029152911yescharacteristic
739C2#2029157211yescharacteristic
740C2#2029157411yescharacteristic
741C2#2029158811yescharacteristic
742C2#2029159611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutator, socleC23×C53C23×C4
FittingC53×#390C4
prime radicalC2×#13133188C4
cosocleC22×Dic53C24
hypercenter#390#6157
hypocenterC53#22333
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #20290840C2semidirect
2. #20290838C2semidirect
3. #20290785C2semidirect
4. #20290784C2semidirect
5. #20290775C2semidirect
6. #20290768C2semidirect
7. #20290694C2semidirect
8. #20290692C2semidirect
9. #20290690C2semidirect
10. #20290688C2semidirect
11. #20290607C2semidirect
12. #20290457C2semidirect
13. C22⋊C4×#88324C2semidirect
14. C4×#13133274C2semidirect
216. C22⋊Dic53M16semidirect
430. C53#22333semidirect

Maximal subgroups

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

subgroupindex
#202908402
#202908382
#202907852
#202907842
#202907752
#202907682
#202906942
#202906922
#202906902
#202906882
#202906072
#202904572
C22⋊C4×#883242
C4×#131332742
#202772312
#2233353