Finite Group Databasebeta

← #27394388

Subgroups — #27394388

Order 13568.

1010 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×#16810590C211yesmaximal, characteristic
2#20277307C211yesmaximal, characteristic
3#20274914C211yesmaximal, characteristic, complemented
4#20274914C211yesmaximal, characteristic, complemented
5#20274912C211yesmaximal, characteristic, complemented
6#20274912C211yesmaximal, characteristic, complemented
7#20274908C211yesmaximal, characteristic, complemented
8#20274907C211yesmaximal, characteristic, complemented
9#20274903C211yesmaximal, characteristic, complemented
10#20274902C211yesmaximal, characteristic, complemented
11#20274746C211yesmaximal, characteristic, complemented
12#20274746C211yesmaximal, characteristic, complemented
13#20274742C211yesmaximal, characteristic, complemented
14#20274738C211yesmaximal, characteristic, complemented
15C53×#2311C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133176C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C2×#13133150C2211yescharacteristic
21C2×#13133150C2211yescharacteristic
22C2×#13133150C2211yescharacteristic
23C2×#13133150C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×#13133148C2211yescharacteristic
27C2×#13133148C2211yescharacteristic
28#16810590C418yescomplemented
29C2×C22⋊#88322C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33#16810530—21no—
34#16810526—21no—
35#16810503—21no—
36#16810503—21no—
37#16810483C2211yescharacteristic
38#16810483C2211yescharacteristic
39#16810483C2211yescharacteristic
40#16810483C2211yescharacteristic
41#16810385C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49C22×#41×C53C2211yescharacteristic
50C2×#117×C53C2211yescharacteristic
51C22×C4⋊C4×C53C2211yescharacteristic
52C53×#391—21no—
53C53×#390—21no—
54C53×#386—21no—
55C53×#386—21no—
56C53×#380C2211yescharacteristic
57C53×#380C2211yescharacteristic
58C53×#380C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C23×Dic53—21no—
61C2×#11719917—41no—
62C2×#11719917—41no—
63C2×#11719917C2×C414yescomplemented
64C22×#88322—41no—
65C22×#88322—41no—
66C22×#88322C2×C414yescomplemented
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71#13133176—41no—
72#13133176—41no—
73C2×C4⋊Dic53—21no—
74C2×C4⋊Dic53—41no—
75C2×C4⋊Dic53—41no—
76C2×C4⋊Dic53C2311yescharacteristic
77C2×C4⋊Dic53C2311yescharacteristic
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C4×Dic53—21no—
86#13133150—41no—
87#13133150—41no—
88#13133150—41no—
89#13133150—41no—
90#13133148—41no—
91#13133148—41no—
92#13133148—41no—
93#13133148—41no—
94C22⋊#88322C2×C414yescomplemented
95C22⋊#88322C2×C414yescomplemented
96C22⋊#88322C2×C414yescomplemented
97C22⋊#88322C2×C414yescomplemented
98#13133124—21no—
99#13133124—21no—
100#13133124—21no—
101#13133124—21no—
102C2×#41×C53—41no—
103C2×#41×C53—41no—
104C2×#41×C53—41no—
105C2×#41×C53—41no—
106C2×#41×C53C2×C414yes—
107C2×#41×C53Q814yes—
108C22×Q8×C53D411yescharacteristic
109C22×D4×C53D411yescharacteristic
110C22×D4×C53D411yescharacteristic
111C22×D4×C53D411yescharacteristic
112C23×C4×C53—21no—
113C23×C4×C53C2311yescharacteristic
114C23×C4×C53C2311yescharacteristic
115C23×C4×C53C2311yescharacteristic
116#117×C53—41no—
117#117×C53—41no—
118C2×C4⋊C4×C53—21no—
119C2×C4⋊C4×C53—41no—
120C2×C4⋊C4×C53—41no—
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C42×C53—21no—
131#95×C53—21no—
132#95×C53—21no—
133#95×C53—21no—
134#95×C53—21no—
135C24×C53C2×D411yescharacteristic
136C24×C53C2×D411yescharacteristic
137C24×C53C2×D411yescharacteristic
138#41×C53—44no—
139#41×C53—44no—
140#41×C53—44no—
141#41×C53—44no—
142C2×Q8×C53—41no—
143C2×Q8×C53—41no—
144C2×Q8×C53C4⋊C414yes—
145C2×D4×C53—41no—
146C2×D4×C53—41no—
147C2×D4×C53—41no—
148C2×D4×C53—41no—
149C2×D4×C53—41no—
150C2×D4×C53—41no—
151C2×D4×C53C4⋊C414yes—
152C2×D4×C53C4⋊C414yes—
153C2×D4×C53C4⋊C414yes—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—42no—
171C22×C4×C53—81no—
172C22×C4×C53—81no—
173C22×C4×C53C22×C412yes—
174C22×C4×C53C22×C412yes—
175C22×C4×C53C22×C412yes—
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×Q812yes—
180C22×C4×C53C2×Q812yes—
181C22×C4×C53C2×Q812yes—
182C22×C4×C53C2411yescharacteristic
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—42no—
188C22×Dic53—81no—
189C22×Dic53—81no—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—42no—
199C22⋊C4×C53—42no—
200C22⋊C4×C53—81no—
201C22⋊C4×C53—81no—
202C22⋊C4×C53—81no—
203C22⋊C4×C53—81no—
204C42×C53—42no—
205C22⋊Dic53—42no—
206C22⋊Dic53—81no—
207C22⋊Dic53—81no—
208C22⋊Dic53—81no—
209C22⋊Dic53—81no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—42no—
219C4×Dic53—42no—
220#11719917—44no—
221C2×#88322—21no—
222C2×#88322—21no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—44no—
230C2×#88322C22×C412yes—
231C2×#88322C22×C412yes—
232C2×#88322C22×C412yes—
233C2×#88322C22×C412yes—
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×C53C2×C4⋊C412yes—
253C23×C53C2×C4⋊C412yes—
254C23×C53C2×C4⋊C412yes—
255C23×C53C22×D411yescharacteristic
256Q8×C53—44no—
257D4×C53—44no—
258D4×C53—44no—
259D4×C53—44no—
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—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—84no—
291C2×C4×C53C2×C4⋊C412yes—
292C2×C4×C53C2×C4⋊C412yes—
293C2×C4×C53C2×C4⋊C412yes—
294C2×C4×C53C23×C411yescharacteristic
295C2×C4×C53C22×Q811yescharacteristic
296C2×C4×C53H(5,𝔽2)11yescharacteristic
297C2×C4×C53H(5,𝔽2)11yescharacteristic
298C2×C4×C53H(5,𝔽2)11yescharacteristic
299C2×C4×C53H(5,𝔽2)11yescharacteristic
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—84no—
313#88322—22no—
314#88322—22no—
315#88322—22no—
316#88322—22no—
317#21945—531nomaximal, Sylow
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—22no—
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—22no—
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×C53C22×C4⋊C411yescharacteristic
340C22×C53#53411yescharacteristic
341C22×C53#53411yescharacteristic
342C22×C53#57611yescharacteristic
343C22×C53#57711yescharacteristic
344C22×C53#57711yescharacteristic
345C22×C53#57811yescharacteristic
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—81no—
350C4×C53—81no—
351C4×C53—81no—
352C4×C53—81no—
353C4×C53#51811yescharacteristic
354C4×C53#51811yescharacteristic
355C4×C53#54311yescharacteristic
356C4×C53#54311yescharacteristic
357Dic53—81no—
358Dic53—81no—
359Dic53—81no—
360Dic53—81no—
361C2×#408—531no—
362#2311—531no—
363#2311D5311yescharacteristic
364#1854—531no—
365#1854—531no—
366#1854—531no—
367#1854—531no—
368#1853—531no—
369#1853—531no—
370#1852—531no—
371#1852—531no—
372#1809—531no—
373#1809—531no—
374#1808—531no—
375#1807—531no—
376C2×C53—42no—
377C2×C53—42no—
378C2×C53—42no—
379C2×C53#231511yescharacteristic
380C2×C53#291211yescharacteristic
381C2×C53#291311yescharacteristic
382C2×C53#319811yescharacteristic
383C2×C53#319811yescharacteristic
384C2×C53#320111yescharacteristic
385C2×C53#320111yescharacteristic
386C22×#41C2×D5311yescharacteristic
387C22×M16—531no—
388C23×C8—531no—
389C2×#117—531no—
390C2×#117C2×D5311yescharacteristic
391C22×C4⋊C4—531no—
392C22×C4⋊C4C2×D5311yescharacteristic
393C2×#107—531no—
394C2×#107—531no—
395C2×#107—531no—
396C2×#107—531no—
397C2×#106—531no—
398C2×#106—531no—
399C2×#106—531no—
400C2×#106—531no—
401#408—538no—
402C2×C22⋊C8—531no—
403C2×C22⋊C8—531no—
404C2×C22⋊C8—531no—
405C2×C22⋊C8—531no—
406#391—21no—
407#391—1061no—
408#390—21no—
409#390—1061no—
410#386—21no—
411#386—21no—
412#386—1061no—
413#386—1061no—
414#380—531no—
415#380—531no—
416#380—531no—
417#380—531no—
418#380C2×D5311yescharacteristic
419#380C2×D5311yescharacteristic
420#380C2×D5311yescharacteristic
421#380C2×D5311yescharacteristic
422#340—531no—
423#340—531no—
424#340—531no—
425#340—531no—
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430C53#2194511yescharacteristic, complemented, Sylow
431C2×#41—41no—
432C2×#41—41no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41Dic10614yes—
436C2×#41C4×D5314yes—
437C22×Q8C22⋊D5311yescharacteristic
438C22×D4C22⋊D5311yescharacteristic
439C22×D4C22⋊D5311yescharacteristic
440C22×D4C22⋊D5311yescharacteristic
441C23×C4—21no—
442C23×C4—1061no—
443C23×C4C22×D5311yescharacteristic
444C23×C4C22×D5311yescharacteristic
445C23×C4C22×D5311yescharacteristic
446C2×M16—534no—
447C2×M16—2121no—
448C2×M16—2121no—
449C22×C8—531no—
450C22×C8—531no—
451C22×C8—531no—
452C22×C8—531no—
453C22×C8—534no—
454C22×C8—2121no—
455C22×C8—2121no—
456#117—41no—
457#117—41no—
458#117—2121no—
459#117—2121no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—531no—
467C2×C4⋊C4—1061no—
468C2×C4⋊C4—2121no—
469C2×C4⋊C4—2121no—
470C2×C4⋊C4C22×D5311yescharacteristic
471C2×C4⋊C4C22×D5311yescharacteristic
472C2×C4⋊C4C22×D5311yescharacteristic
473C2×C4⋊C4C22×D5311yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1061no—
480C2×C22⋊C4—1061no—
481C2×C22⋊C4—1061no—
482C2×C22⋊C4—1061no—
483C2×C22⋊C4—1061no—
484C2×C42—21no—
485C2×C42—1061no—
486#107—2121no—
487#107—2121no—
488#107—2121no—
489#107—2121no—
490#106—2121no—
491#106—2121no—
492#106—2121no—
493#106—2121no—
494C22⋊C8—534no—
495C22⋊C8—534no—
496C22⋊C8—534no—
497C22⋊C8—534no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—1061no—
503#95—1061no—
504#95—1061no—
505#95—1061no—
506C24C2×C22⋊D5311yescharacteristic
507C24C2×C22⋊D5311yescharacteristic
508C24C2×C22⋊D5311yescharacteristic
509#41—44no—
510#41—44no—
511#41—44no—
512#41—44no—
513C2×Q8—41no—
514C2×Q8—41no—
515C2×Q8#1171991914yes—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4#1171991914yes—
523C2×D4#1171991914yes—
524C2×D4#1171991914yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4—1061no—
548C22×C4—4241no—
549C22×C4—4241no—
550C22×C4—2122no—
551C22×C4C2×Dic10612yes—
552C22×C4C2×Dic10612yes—
553C22×C4C2×Dic10612yes—
554C22×C4C2×C4×D5312yes—
555C22×C4C2×C4×D5312yes—
556C22×C4C2×C4×D5312yes—
557C22×C4C2×C22⋊D5311yescharacteristic
558C22×C4C2×C22⋊D5311yescharacteristic
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C23×D5311yescharacteristic
561M16—2124no—
562C2×C8—532no—
563C2×C8—532no—
564C2×C8—532no—
565C2×C8—532no—
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—2124no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—1061no—
585C4⋊C4—1061no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—2122no—
593C22⋊C4—42no—
594C22⋊C4—81no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—4241no—
599C22⋊C4—4241no—
600C22⋊C4—4241no—
601C22⋊C4—4241no—
602C22⋊C4—2122no—
603C42—42no—
604C42—2122no—
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—
623C23C2×#1171991912yes—
624C23C2×#1171991912yes—
625C23C2×#1171991912yes—
626C23C22×C22⋊D5311yescharacteristic
627Q8—44no—
628D4—44no—
629D4—44no—
630D4—44no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—4244no—
663C2×C4—2121no—
664C2×C4—2121no—
665C2×C4—2121no—
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×C4C2×#1171991912yes—
676C2×C4C2×#1171991912yes—
677C2×C4C2×#1171991912yes—
678C2×C4C22×C4×D5311yescharacteristic
679C2×C4C22×Dic10611yescharacteristic
680C2×C4#1313326211yescharacteristic
681C2×C4#1313326211yescharacteristic
682C2×C4#1313326211yescharacteristic
683C2×C4#1313326211yescharacteristic
684C8—1062no—
685C8—1062no—
686C8—1062no—
687C8—1062no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22C22×#1171991911yescharacteristic
710C22#1681118211yescharacteristic
711C22#1681118211yescharacteristic
712C22#1681142611yescharacteristic
713C22#1681143111yescharacteristic
714C22#1681143411yescharacteristic
715C22#1681143811yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4—81no—
723C4—4241no—
724C4—4241no—
725C4—4241no—
726C4—4241no—
727C4#1681109611yescharacteristic
728C4#1681109611yescharacteristic
729C4#1681124911yescharacteristic
730C4#1681124911yescharacteristic
731C2—42no—
732C2—42no—
733C2—42no—
734C2#2027732711yescharacteristic
735C2#2028330811yescharacteristic
736C2#2028331311yescharacteristic
737C2#2028556111yescharacteristic
738C2#2028556711yescharacteristic
739C2#2028559111yescharacteristic
740C2#2028559711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2311C2
socleC23×C53C22×D4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenter#2311D53
hypocenterC53#21945
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
3. #20274914C2semidirect
4. #20274914C2semidirect
5. #20274912C2semidirect
6. #20274912C2semidirect
7. #20274908C2semidirect
8. #20274907C2semidirect
9. #20274903C2semidirect
10. #20274902C2semidirect
11. #20274746C2semidirect
12. #20274746C2semidirect
13. #20274742C2semidirect
14. #20274738C2semidirect
28. #16810590C4semidirect
63. C2×#11719917C2×C4semidirect
66. C22×#88322C2×C4semidirect
94. C22⋊#88322C2×C4semidirect
95. C22⋊#88322C2×C4semidirect
96. C22⋊#88322C2×C4semidirect
97. C22⋊#88322C2×C4semidirect
430. C53#21945semidirect

Maximal subgroups

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

subgroupindex
C2×#168105902
#202773072
#202749142
#202749122
#202749082
#202749072
#202749032
#202749022
#202747462
#202747422
#202747382
C53×#23112
#2194553