Finite Group Databasebeta

← #28323037

Subgroups — #28323037

Order 13568.

882 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811654C211yesmaximal, characteristic, complemented
2C2×#16811647C211yesmaximal, characteristic, complemented
3#20290839C211yesmaximal, characteristic, complemented
4#20290836C211yesmaximal, characteristic, complemented
5#20290836C211yesmaximal, characteristic, complemented
6#20290814C211yesmaximal, characteristic, complemented
7#20290788C211yesmaximal, characteristic, complemented
8#20290785C211yesmaximal, characteristic, complemented
9#20290692C211yesmaximal, characteristic, complemented
10#20290688C211yesmaximal, characteristic, complemented
11#20290662C211yesmaximal, characteristic, complemented
12#20290658C211yesmaximal, characteristic, complemented
13#20290573C211yesmaximal, characteristic, complemented
14#20290514C211yesmaximal, characteristic, complemented
15#20277950C211yesmaximal, characteristic
16C22×#11719940C2211yescharacteristic
17C23×#88324C2211yescharacteristic
18#16811654—24no—
19#16811647—24no—
20C2×#13133284C2211yescharacteristic
21C2×#13133284C2211yescharacteristic
22C2×#13133284C2211yescharacteristic
23C2×C4⋊#88324C2211yescharacteristic
24C2×C4⋊#88324C2211yescharacteristic
25C2×C4⋊#88324C2211yescharacteristic
26C2×C22⋊#88324C2211yescharacteristic
27C2×C22⋊#88324C2211yescharacteristic
28C2×C22⋊#88324C2211yescharacteristic
29C2×C22⋊#88324C2211yescharacteristic
30C2×C22⋊#88324C2211yescharacteristic
31C2×C22⋊#88324C2211yescharacteristic
32C2×C22⋊#88324C2211yescharacteristic
33C2×C22⋊#88324C2211yescharacteristic
34C2×C22⋊#88324C2211yescharacteristic
35C2×C22⋊#88324C2211yescharacteristic
36C2×#13133272C2211yescharacteristic
37C2×#13133272C2211yescharacteristic
38C2×C4×#88324C2211yescharacteristic
39C2×C4×#88324C2211yescharacteristic
40#16811489C2211yescharacteristic
41#16811489C2211yescharacteristic
42#16811489C2211yescharacteristic
43#16811489C2211yescharacteristic
44#16811489C2211yescharacteristic
45#16811489C2211yescharacteristic
46C2×D4×Dic53C2211yescharacteristic
47C2×D4×Dic53C2211yescharacteristic
48C2×D4×Dic53C2211yescharacteristic
49C2×#13133173C2211yescharacteristic
50#16810555C411yescharacteristic
51#16810548C411yescharacteristic
52#16810546C411yescharacteristic
53#16810546C411yescharacteristic
54#16810537C411yescharacteristic
55#16810537C411yescharacteristic
56#16810537C411yescharacteristic
57#16810474C2211yescharacteristic
58C22⋊C4×Dic53C2211yescharacteristic
59C22⋊C4×Dic53C2211yescharacteristic
60C53×#392C411yescharacteristic
61C2×#11719940—22no—
62C2×#11719940—41no—
63C2×#11719940—41no—
64C22×#88324—22no—
65C22×#88324—41no—
66C22×#88324—41no—
67C22×#88324C2311yescharacteristic
68C22×#88324C2311yescharacteristic
69C22×#88324C2311yescharacteristic
70C22×#88324C2311yescharacteristic
71C22×#88324C2311yescharacteristic
72C22×#88324C2311yescharacteristic
73C22×#88324C2311yescharacteristic
74C22×#88324C2311yescharacteristic
75#13133284—22no—
76#13133284—22no—
77#13133284—41no—
78C4⋊#88324—22no—
79C4⋊#88324—22no—
80C4⋊#88324—41no—
81C22⋊#88324—22no—
82C22⋊#88324—22no—
83C22⋊#88324—22no—
84C22⋊#88324—22no—
85C22⋊#88324—41no—
86C22⋊#88324—41no—
87C22⋊#88324—41no—
88C22⋊#88324—41no—
89C22⋊#88324—41no—
90C22⋊#88324—41no—
91#13133272—41no—
92#13133272D414yescomplemented
93C4×#88324—22no—
94C4×#88324—41no—
95C23×Dic53C2311yescharacteristic
96C23×Dic53C2311yescharacteristic
97C23×Dic53C2311yescharacteristic
98D4×Dic53—22no—
99D4×Dic53—22no—
100D4×Dic53—41no—
101D4×Dic53—41no—
102D4×Dic53—41no—
103D4×Dic53—41no—
104#13133173—22no—
105#13133173—22no—
106C2×C4⋊Dic53C2×C411yescharacteristic
107C2×C4⋊Dic53C2×C411yescharacteristic
108C2×C4⋊Dic53C2×C411yescharacteristic
109C2×#11719919C2×C411yescharacteristic
110C2×#11719919C2×C411yescharacteristic
111C2×#11719919C2×C411yescharacteristic
112C2×#11719919C2×C411yescharacteristic
113C2×C22⋊Dic53C2×C411yescharacteristic
114C2×C22⋊Dic53C2×C411yescharacteristic
115C2×C22⋊Dic53C2×C411yescharacteristic
116C2×C22⋊Dic53C2×C411yescharacteristic
117C2×C22⋊Dic53C2×C411yescharacteristic
118C2×C22⋊Dic53C2×C411yescharacteristic
119C2×C22⋊Dic53C2×C411yescharacteristic
120C2×C22⋊Dic53C2×C411yescharacteristic
121C2×C22⋊Dic53C2×C411yescharacteristic
122C2×C4×Dic53C2311yescharacteristic
123C2×C4×Dic53C2311yescharacteristic
124C2×C4×Dic53C2311yescharacteristic
125C2×C4×Dic53C2311yescharacteristic
126#13133124C2×C411yescharacteristic
127#13133124C2×C411yescharacteristic
128#13133124C2×C411yescharacteristic
129#13133124C2×C411yescharacteristic
130#13133124C2×C411yescharacteristic
131C22×D4×C53C2×C411yescharacteristic
132C22×D4×C53C2×C411yescharacteristic
133C22×D4×C53C2×C411yescharacteristic
134C2×C22⋊C4×C53C2×C411yescharacteristic
135C2×C22⋊C4×C53C2×C411yescharacteristic
136C2×C22⋊C4×C53C2×C411yescharacteristic
137#95×C53C2×C411yescharacteristic
138C24×C53C22×C411yescharacteristic
139C24×C53C22×C411yescharacteristic
140C24×C53C22×C411yescharacteristic
141C2×D4×C53—22no—
142C2×D4×C53—22no—
143C2×D4×C53—22no—
144C2×D4×C53—22no—
145C2×D4×C53—41no—
146C2×D4×C53—41no—
147C2×D4×C53—41no—
148C2×D4×C53—41no—
149C2×D4×C53—41no—
150C22×C4×C53C22×C411yescharacteristic
151C22×C4×C53C22×C411yescharacteristic
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C22×C411yescharacteristic
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×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—21no—
171C22×Dic53—21no—
172C22×Dic53C22×C411yescharacteristic
173C22×Dic53C22×C411yescharacteristic
174C22×Dic53C22×C411yescharacteristic
175C22×Dic53C22×C411yescharacteristic
176C22×Dic53C22×C411yescharacteristic
177C22×Dic53C22×C411yescharacteristic
178C22×Dic53C22×C411yescharacteristic
179C22×Dic53C2411yescharacteristic
180#11719940—44no—
181C2×#88324—21no—
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—44no—
204C2×#88324C2×D412yes—
205C2×#88324C2×D412yes—
206C22⋊C4×C53—22no—
207C22⋊C4×C53—22no—
208C22⋊C4×C53—41no—
209C22⋊Dic53—22no—
210C22⋊Dic53—22no—
211C22⋊Dic53—22no—
212C22⋊Dic53—22no—
213C22⋊Dic53—41no—
214C22⋊Dic53—41no—
215C22⋊Dic53—41no—
216C22⋊Dic53—41no—
217C22⋊Dic53—41no—
218C4⋊Dic53—22no—
219C4⋊Dic53—41no—
220C4⋊Dic53—41no—
221#11719919—22no—
222#11719919—22no—
223#11719919—22no—
224#11719919—41no—
225C4×Dic53—21no—
226C4×Dic53—21no—
227C4×Dic53—21no—
228C4×Dic53—21no—
229C4×Dic53—21no—
230C4×Dic53—21no—
231C4×Dic53C2×D412yes—
232C4×Dic53#4112yes—
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×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53#13112yes—
254C23×C53C23×C411yescharacteristic
255D4×C53—44no—
256D4×C53—44no—
257D4×C53—44no—
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×C53C4×D412yes—
269C2×C4×C53#13112yes—
270C2×Dic53—21no—
271C2×Dic53—21no—
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—21no—
289C2×Dic53—21no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53C4×D412yes—
303C2×Dic53C22×D411yescharacteristic
304C2×Dic53C2×#4111yescharacteristic
305C2×Dic53H(5,𝔽2)11yescharacteristic
306C2×Dic53H(5,𝔽2)11yescharacteristic
307C2×Dic53H(5,𝔽2)11yescharacteristic
308C2×Dic532−1+411yescharacteristic
309#88324—22no—
310#88324—22no—
311#88324—41no—
312#88324—41no—
313#88324—41no—
314#88324—41no—
315#88324—41no—
316#88324—41no—
317#22142—531nomaximal, Sylow
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—41no—
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×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53C2×C4×D411yescharacteristic
340C22×C53#51811yescharacteristic
341C22×C53#52011yescharacteristic
342C22×C53C2×#13111yescharacteristic
343C22×C53C2×#13111yescharacteristic
344C22×C53#56811yescharacteristic
345C22×C53#56811yescharacteristic
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—41no—
349C4×C53—41no—
350Dic53—22no—
351Dic53—41no—
352Dic53—41no—
353Dic53—41no—
354Dic53—41no—
355Dic53—41no—
356Dic53—41no—
357Dic53#53511yescharacteristic
358Dic53#53711yescharacteristic
359Dic53#54011yescharacteristic
360Dic53#54211yescharacteristic
361C2×#435—531no—
362C2×#433—531no—
363#2392—531no—
364#1955—531no—
365#1954—531no—
366#1954—531no—
367#1939—531no—
368#1924—531no—
369#1923—531no—
370#1870—531no—
371#1869—531no—
372#1851—531no—
373#1850—531no—
374#1798—531no—
375#1771—531no—
376C2×C53—42no—
377C2×C53—81no—
378C2×C53—81no—
379C2×C53#232411yescharacteristic
380C2×C53#293311yescharacteristic
381C2×C53#293511yescharacteristic
382C2×C53#297611yescharacteristic
383C2×C53#297611yescharacteristic
384C2×C53#299411yescharacteristic
385C2×C53#299511yescharacteristic
386C22×M16—531no—
387C23×C8—531no—
388C2×C4×D4—531no—
389C2×C4×D4—531no—
390C2×C4×D4—531no—
391C2×#117—531no—
392#435—1064no—
393#433—1064no—
394C2×C4⋊C8—531no—
395C2×C4⋊C8—531no—
396C2×C4⋊C8—531no—
397C2×C4⋊C8—531no—
398C2×C4⋊C8—531no—
399C2×C4⋊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×C22⋊C8—531no—
407C2×C22⋊C8—531no—
408C2×C22⋊C8—531no—
409C2×C22⋊C8—531no—
410C2×#97—531no—
411C2×#97—531no—
412C2×C4×C8—531no—
413C2×C4×C8—531no—
414#398—531no—
415#397—531no—
416#396—531no—
417#396—531no—
418#394—531no—
419#394—531no—
420#394—531no—
421#392#615711yescharacteristic
422C4×C4⋊C4—531no—
423C4×C22⋊C4—531no—
424C4×C22⋊C4—531no—
425#336—531no—
426#336—531no—
427#336—531no—
428#336—531no—
429#336—531no—
430#336—531no—
431C53#2214211yescharacteristic, complemented, Sylow
432C22×D4C2×#615711yescharacteristic
433C22×D4C2×#615711yescharacteristic
434C22×D4C2×#615711yescharacteristic
435C23×C4—531no—
436C23×C4—531no—
437C23×C4—531no—
438C2×M16—1062no—
439C2×M16—2121no—
440C2×M16—2121no—
441C22×C8—531no—
442C22×C8—531no—
443C22×C8—531no—
444C22×C8—531no—
445C22×C8—531no—
446C22×C8—531no—
447C22×C8—531no—
448C22×C8—531no—
449C22×C8—1062no—
450C22×C8—2121no—
451C22×C8—2121no—
452C4×D4—1062no—
453C4×D4—1062no—
454C4×D4—2121no—
455C4×D4—2121no—
456C4×D4—2121no—
457C4×D4—2121no—
458#117—1062no—
459#117—1062no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—531no—
467C2×C22⋊C4—531no—
468C2×C22⋊C4—531no—
469C2×C22⋊C4—531no—
470C2×C22⋊C4—531no—
471C2×C22⋊C4—531no—
472C2×C22⋊C4—531no—
473C2×C22⋊C4—531no—
474C2×C22⋊C4—531no—
475C2×C22⋊C4—531no—
476C2×C22⋊C4C2×#615711yescharacteristic
477C2×C22⋊C4C2×#615711yescharacteristic
478C2×C22⋊C4C2×#615711yescharacteristic
479C2×C42—531no—
480C2×C42—531no—
481C2×C42—531no—
482C2×C42—531no—
483C4⋊C8—1062no—
484C4⋊C8—1062no—
485C4⋊C8—1062no—
486C4⋊C8—1062no—
487C4⋊C8—2121no—
488C4⋊C8—2121no—
489C22⋊C8—1062no—
490C22⋊C8—1062no—
491C22⋊C8—1062no—
492C22⋊C8—1062no—
493C22⋊C8—2121no—
494C22⋊C8—2121no—
495C22⋊C8—2121no—
496C22⋊C8—2121no—
497C22⋊C8—2121no—
498C22⋊C8—2121no—
499#97—534no—
500#97—2121no—
501C4×C8—1062no—
502C4×C8—2121no—
503#95—531no—
504#95—531no—
505#95—531no—
506#95—531no—
507#95—531no—
508#95C2×#615711yescharacteristic
509C24C22×#615711yescharacteristic
510C24C22×#615711yescharacteristic
511C24C22×#615711yescharacteristic
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C22×C4—531no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—531no—
525C22×C4—531no—
526C22×C4—531no—
527C22×C4—531no—
528C22×C4—531no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
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—1061no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4C22×#615711yescharacteristic
548C22×C4C22×#615711yescharacteristic
549C22×C4C22×#615711yescharacteristic
550C22×C4C22×#615711yescharacteristic
551M16—2124no—
552C2×C8—532no—
553C2×C8—532no—
554C2×C8—1061no—
555C2×C8—1061no—
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—2124no—
577C4⋊C4—1062no—
578C4⋊C4—1062no—
579C4⋊C4—1062no—
580C4⋊C4—1062no—
581C4⋊C4—2121no—
582C4⋊C4—2121no—
583C4⋊C4—2121no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—1062no—
588C22⋊C4—1062no—
589C22⋊C4—1062no—
590C22⋊C4—1062no—
591C22⋊C4—2121no—
592C22⋊C4—2121no—
593C22⋊C4—2121no—
594C22⋊C4—2121no—
595C22⋊C4—2121no—
596C42—532no—
597C42—532no—
598C42—1061no—
599C42—1061no—
600C42—1061no—
601C42—1061no—
602C42—1061no—
603C42—1061no—
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—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23#1313330412yes—
625C23C23×#615711yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
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—531no—
640C2×C4—531no—
641C2×C4—531no—
642C2×C4—531no—
643C2×C4—531no—
644C2×C4—531no—
645C2×C4—532no—
646C2×C4—1061no—
647C2×C4—1061no—
648C2×C4—1061no—
649C2×C4—1061no—
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—2121no—
667C2×C4—2121no—
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×C4D4×#615712yes—
679C2×C4#1313330412yes—
680C8—1062no—
681C8—1062no—
682C8—2121no—
683C8—2121no—
684C8—2121no—
685C8—2121no—
686C8—2121no—
687C8—2121no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22C2×D4×#615711yescharacteristic
710C22#1681169011yescharacteristic
711C22#1681169211yescharacteristic
712C22C2×#1313330411yescharacteristic
713C22C2×#1313330411yescharacteristic
714C22#1681170111yescharacteristic
715C22#1681170111yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—531no—
721C4—531no—
722C4—531no—
723C4—531no—
724C4—1062no—
725C4—2121no—
726C4—2121no—
727C4—2121no—
728C4—2121no—
729C4—2121no—
730C4—2121no—
731C2—42no—
732C2—81no—
733C2—81no—
734C2#2029120311yescharacteristic
735C2#2029144711yescharacteristic
736C2#2029145811yescharacteristic
737C2#2029158111yescharacteristic
738C2#2029158111yescharacteristic
739C2#2029166211yescharacteristic
740C2#2029166811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutator, socleC23×C53C23×C4
Fitting, prime radicalC53×#392C4
cosocleC22×Dic53C24
hypercenter#392#6157
hypocenterC53#22142
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#16811654C2semidirect
2. C2×#16811647C2semidirect
3. #20290839C2semidirect
4. #20290836C2semidirect
5. #20290836C2semidirect
6. #20290814C2semidirect
7. #20290788C2semidirect
8. #20290785C2semidirect
9. #20290692C2semidirect
10. #20290688C2semidirect
11. #20290662C2semidirect
12. #20290658C2semidirect
13. #20290573C2semidirect
14. #20290514C2semidirect
92. #13133272D4semidirect
431. C53#22142semidirect

Maximal subgroups

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

subgroupindex
C2×#168116542
C2×#168116472
#202908392
#202908362
#202908142
#202907882
#202907852
#202906922
#202906882
#202906622
#202906582
#202905732
#202905142
#202779502
#2214253