Finite Group Databasebeta

← #27291981

Subgroups — #27291981

Order 13568.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810498C211yesmaximal, characteristic
2C2×#16810481C211yesmaximal, characteristic
3C2×#16810390C211yesmaximal, characteristic
4C2×#16810389C211yesmaximal, characteristic
5C2×#16810389C211yesmaximal, characteristic
6#20272937C211yesmaximal, characteristic
7C2×C53×#342C211yesmaximal, characteristic
8C24×Dic53C2211yescharacteristic
9C22×C4⋊Dic53C412yescomplemented
10C22×#11719919—21no—
11C22×C22⋊Dic53C2211yescharacteristic
12C22×C22⋊Dic53C2211yescharacteristic
13C22×C22⋊Dic53C2211yescharacteristic
14#16810498—21no—
15#16810498—22no—
16#16810498—21no—
17#16810481—22no—
18#16810481—22no—
19C2×#13133124—21no—
20C2×#13133124—22no—
21C2×#13133124C412yescomplemented
22#16810390—22no—
23#16810389—22no—
24#16810389—22no—
25C22×C22⋊C4×C53C2211yescharacteristic
26C22×C22⋊C4×C53C2211yescharacteristic
27C22×C22⋊C4×C53C2211yescharacteristic
28C53×#342—22no—
29C23×Dic53—21no—
30C23×Dic53—21no—
31C23×Dic53—21no—
32C23×Dic53—21no—
33C23×Dic53—21no—
34C23×Dic53—21no—
35C23×Dic53—44no—
36C23×Dic53C2×C412yes—
37C23×Dic53C2×C411yescharacteristic
38C23×Dic53C2×C411yescharacteristic
39C23×Dic53D411yescharacteristic
40C23×Dic53D412yes—
41C23×Dic53D411yescharacteristic
42C2×C4⋊Dic53—22no—
43C2×C4⋊Dic53—22no—
44C2×C4⋊Dic53—44no—
45C2×#11719919—24no—
46C2×#11719919—44no—
47C2×C22⋊Dic53—21no—
48C2×C22⋊Dic53—21no—
49C2×C22⋊Dic53—21no—
50C2×C22⋊Dic53—21no—
51C2×C22⋊Dic53—21no—
52C2×C22⋊Dic53—21no—
53C2×C22⋊Dic53—21no—
54C2×C22⋊Dic53—21no—
55C2×C22⋊Dic53—21no—
56C2×C22⋊Dic53—21no—
57C2×C22⋊Dic53—21no—
58C2×C22⋊Dic53—21no—
59C2×C22⋊Dic53—21no—
60C2×C22⋊Dic53—21no—
61C2×C22⋊Dic53—21no—
62C2×C22⋊Dic53—21no—
63C2×C22⋊Dic53D412yes—
64C2×C22⋊Dic53Q812yes—
65#13133124—24no—
66#13133124—22no—
67#13133124—22no—
68#13133124—44no—
69C25×C53C2311yescharacteristic
70C23×C4×C53—21no—
71C23×C4×C53—21no—
72C23×C4×C53C2×C412yes—
73C2×C22⋊C4×C53—21no—
74C2×C22⋊C4×C53—21no—
75C2×C22⋊C4×C53—21no—
76C2×C22⋊C4×C53—21no—
77C2×C22⋊C4×C53—21no—
78C2×C22⋊C4×C53—21no—
79C2×C22⋊C4×C53—21no—
80C2×C22⋊C4×C53—21no—
81C2×C22⋊C4×C53—21no—
82C2×C22⋊C4×C53—21no—
83C2×C22⋊C4×C53—21no—
84C2×C22⋊C4×C53—21no—
85C2×C22⋊C4×C53—21no—
86C2×C22⋊C4×C53—21no—
87C2×C22⋊C4×C53D412yes—
88C2×C22⋊C4×C53D412yes—
89C2×C22⋊C4×C53Q812yes—
90C2×C22⋊C4×C53Q812yes—
91C24×C53—42no—
92C24×C53—42no—
93C24×C53C22×C411yescharacteristic
94C24×C53C2×D411yescharacteristic
95C24×C53C2×D411yescharacteristic
96C24×C53C2×D411yescharacteristic
97C24×C53C2×D411yescharacteristic
98C24×C53C2×D411yescharacteristic
99C24×C53C2×Q811yescharacteristic
100C24×C53C2×Q811yescharacteristic
101C24×C53C2×Q811yescharacteristic
102C24×C53#4111yescharacteristic
103C24×C53#4111yescharacteristic
104C24×C53#4111yescharacteristic
105C24×C53#4111yescharacteristic
106C24×C53#4111yescharacteristic
107C24×C53#4111yescharacteristic
108C22×C4×C53—22no—
109C22×C4×C53—22no—
110C22×C4×C53—22no—
111C22×C4×C53—22no—
112C22×C4×C53—42no—
113C22×C4×C53—42no—
114C22×C4×C53—42no—
115C22×C4×C53—42no—
116C22×C4×C53—42no—
117C22×C4×C53—42no—
118C22×C4×C53—41no—
119C22×C4×C53—41no—
120C22×C4×C53—41no—
121C22×C4×C53—41no—
122C22×C4×C53C4⋊C414yescomplemented
123C22×Dic53—21no—
124C22×Dic53—21no—
125C22×Dic53—24no—
126C22×Dic53—22no—
127C22×Dic53—22no—
128C22×Dic53—21no—
129C22×Dic53—22no—
130C22×Dic53—22no—
131C22×Dic53—21no—
132C22×Dic53—24no—
133C22×Dic53—24no—
134C22×Dic53—21no—
135C22×Dic53—21no—
136C22×Dic53—22no—
137C22×Dic53—22no—
138C22×Dic53—21no—
139C22×Dic53—21no—
140C22×Dic53—21no—
141C22×Dic53—21no—
142C22×Dic53—42no—
143C22×Dic53—42no—
144C22×Dic53—42no—
145C22×Dic53—44no—
146C22×Dic53—44no—
147C22×Dic53—44no—
148C22×Dic53—44no—
149C22×Dic53—42no—
150C22×Dic53—42no—
151C22×Dic53—42no—
152C22×Dic53—42no—
153C22×Dic53—41no—
154C22×Dic53—41no—
155C22×Dic53—41no—
156C22×Dic53—41no—
157C22×Dic53—42no—
158C22×Dic53—42no—
159C22×Dic53C22⋊C412yes—
160C22×Dic53C22⋊C412yes—
161C22⋊C4×C53—22no—
162C22⋊C4×C53—22no—
163C22⋊C4×C53—22no—
164C22⋊C4×C53—22no—
165C22⋊C4×C53—22no—
166C22⋊C4×C53—22no—
167C22⋊C4×C53—22no—
168C22⋊C4×C53—22no—
169C22⋊C4×C53—41no—
170C22⋊C4×C53—41no—
171C22⋊C4×C53—41no—
172C22⋊C4×C53—41no—
173C22⋊Dic53—22no—
174C22⋊Dic53—22no—
175C22⋊Dic53—22no—
176C22⋊Dic53—22no—
177C22⋊Dic53—41no—
178C22⋊Dic53—41no—
179C22⋊Dic53—41no—
180C22⋊Dic53—41no—
181C22⋊Dic53—41no—
182C22⋊Dic53—41no—
183C22⋊Dic53—41no—
184C22⋊Dic53—41no—
185C4⋊Dic53—44no—
186C4⋊Dic53—44no—
187#11719919—48no—
188C23×C53—22no—
189C23×C53—22no—
190C23×C53—22no—
191C23×C53—22no—
192C23×C53—22no—
193C23×C53—22no—
194C23×C53—41no—
195C23×C53—41no—
196C23×C53—41no—
197C23×C53—41no—
198C23×C53—41no—
199C23×C53—41no—
200C23×C53—42no—
201C23×C53—42no—
202C23×C53—42no—
203C23×C53—42no—
204C23×C53—41no—
205C23×C53—42no—
206C23×C53—42no—
207C23×C53—42no—
208C23×C53—42no—
209C23×C53—41no—
210C23×C53C2×C22⋊C411yescharacteristic
211C23×C53C2×C4⋊C411yescharacteristic
212C23×C53#11711yescharacteristic
213C23×C53C4×D411yescharacteristic
214C23×C53C4×D411yescharacteristic
215C23×C53C4×Q811yescharacteristic
216C23×C53C4×Q811yescharacteristic
217C23×C53#12011yescharacteristic
218C23×C53#12111yescharacteristic
219C23×C53#12111yescharacteristic
220C23×C53#12111yescharacteristic
221C23×C53#12111yescharacteristic
222C23×C53#12111yescharacteristic
223C23×C53#12111yescharacteristic
224C23×C53C22⋊Q811yescharacteristic
225C23×C53C22⋊Q811yescharacteristic
226C23×C53C22⋊Q811yescharacteristic
227C23×C53C22⋊Q811yescharacteristic
228C23×C53C22⋊Q811yescharacteristic
229C23×C53C22⋊Q811yescharacteristic
230C23×C53C22⋊Q811yescharacteristic
231C23×C53C22⋊Q811yescharacteristic
232C23×C53#12311yescharacteristic
233C23×C53#12311yescharacteristic
234C23×C53#12311yescharacteristic
235C23×C53#12411yescharacteristic
236C23×C53#12511yescharacteristic
237C23×C53#12511yescharacteristic
238C23×C53#12511yescharacteristic
239C23×C53#12511yescharacteristic
240C23×C53#12611yescharacteristic
241C23×C53#12611yescharacteristic
242C23×C53C4⋊Q811yescharacteristic
243C23×C53C4⋊Q811yescharacteristic
244C23×C53C4⋊Q811yescharacteristic
245C2×C4×C53—24no—
246C2×C4×C53—44no—
247C2×C4×C53—42no—
248C2×C4×C53—42no—
249C2×C4×C53—44no—
250C2×C4×C53—42no—
251C2×C4×C53—44no—
252C2×C4×C53—42no—
253C2×C4×C53—42no—
254C2×C4×C53—42no—
255C2×C4×C53—82no—
256C2×C4×C53—82no—
257C2×C4×C53—81no—
258C2×C4×C53—81no—
259C2×C4×C53—82no—
260C2×Dic53—24no—
261C2×Dic53—24no—
262C2×Dic53—22no—
263C2×Dic53—22no—
264C2×Dic53—22no—
265C2×Dic53—22no—
266C2×Dic53—22no—
267C2×Dic53—44no—
268C2×Dic53—44no—
269C2×Dic53—44no—
270C2×Dic53—44no—
271C2×Dic53—42no—
272C2×Dic53—42no—
273C2×Dic53—42no—
274C2×Dic53—44no—
275C2×Dic53—42no—
276C2×Dic53—41no—
277C2×Dic53—41no—
278C2×Dic53—42no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—82no—
283C2×Dic53—82no—
284C2×Dic53—81no—
285C2×Dic53—81no—
286C2×Dic53—82no—
287C2×Dic53—81no—
288C2×Dic53—81no—
289C2×Dic53—81no—
290C2×Dic53—81no—
291C2×Dic53#9914yes—
292#11203—531nomaximal, Sylow
293C22×C53—22no—
294C22×C53—22no—
295C22×C53—22no—
296C22×C53—22no—
297C22×C53—22no—
298C22×C53—22no—
299C22×C53—21no—
300C22×C53—21no—
301C22×C53—21no—
302C22×C53—21no—
303C22×C53—21no—
304C22×C53—21no—
305C22×C53—21no—
306C22×C53—21no—
307C22×C53—21no—
308C22×C53—21no—
309C22×C53—21no—
310C22×C53—21no—
311C22×C53—22no—
312C22×C53—22no—
313C22×C53—22no—
314C22×C53—22no—
315C22×C53—22no—
316C22×C53—22no—
317C22×C53—41no—
318C22×C53—41no—
319C22×C53—41no—
320C22×C53—41no—
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#38011yescharacteristic
334C22×C53#38611yescharacteristic
335C22×C53#38711yescharacteristic
336C22×C53#38711yescharacteristic
337C22×C53#38911yescharacteristic
338C22×C53#38911yescharacteristic
339C22×C53#39111yescharacteristic
340C22×C53#39411yescharacteristic
341C22×C53#39511yescharacteristic
342C22×C53#39611yescharacteristic
343C22×C53#39611yescharacteristic
344C22×C53#39811yescharacteristic
345C22×C53#39811yescharacteristic
346C22×C53#39811yescharacteristic
347C22×C53#40011yescharacteristic
348C22×C53C2×#9912yes—
349C22×C53#41012yes—
350C4×C53—44no—
351C4×C53—82no—
352C4×C53—82no—
353Dic53—24no—
354Dic53—42no—
355Dic53—82no—
356Dic53—82no—
357Dic53—81no—
358Dic53—81no—
359C2×#385—531no—
360C2×#380—531no—
361C2×#342—531no—
362C2×#342—531no—
363C2×#342—531no—
364C2×#342D5311yescharacteristic
365C22⋊#95—531no—
366C2×C53—21no—
367C2×C53—21no—
368C2×C53—21no—
369C2×C53—21no—
370C2×C53—21no—
371C2×C53—21no—
372C2×C53—21no—
373C2×C53—21no—
374C2×C53—21no—
375C2×C53—21no—
376C2×C53—21no—
377C2×C53—21no—
378C2×C53#144111yescharacteristic
379C2×C53#179912yes—
380C2×C53#189811yescharacteristic
381C2×C53#189911yescharacteristic
382C2×C53#199612yes—
383C24×C4—531no—
384C22×C4⋊C4—532no—
385C22×C4⋊C4—1061no—
386C22×C22⋊C4—531no—
387C22×C22⋊C4—531no—
388C22×C22⋊C4—531no—
389C22×C22⋊C4C2×D5311yescharacteristic
390C22×C22⋊C4C2×D5311yescharacteristic
391C22×C22⋊C4C2×D5311yescharacteristic
392#385—1061no—
393#385—1062no—
394#385—1061no—
395#380—1062no—
396#380—1062no—
397C2×#95—532no—
398C2×#95—1061no—
399C2×#95—1062no—
400#342—22no—
401#342—1062no—
402#342—1062no—
403#342—1062no—
404C53#1120311yescharacteristic, complemented, Sylow
405C25C22×D5311yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—531no—
409C23×C4—532no—
410C23×C4—532no—
411C23×C4—531no—
412C23×C4—531no—
413C23×C4—531no—
414C23×C4—1061no—
415C23×C4—1061no—
416C23×C4—1061no—
417C23×C4—1061no—
418C23×C4—1061no—
419C23×C4—1061no—
420C23×C4—2124no—
421C23×C4C4×D5312yes—
422C2×C4⋊C4—1062no—
423C2×C4⋊C4—1062no—
424C2×C4⋊C4—1064no—
425C2×C4⋊C4—2124no—
426C2×C4⋊C4—2124no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—532no—
442C2×C22⋊C4—532no—
443C2×C22⋊C4—1061no—
444C2×C22⋊C4—1061no—
445C2×C22⋊C4—1061no—
446C2×C22⋊C4—1061no—
447C2×C22⋊C4—1061no—
448C2×C22⋊C4—1061no—
449C2×C22⋊C4—1061no—
450C2×C22⋊C4—1061no—
451C2×C22⋊C4—1061no—
452C2×C22⋊C4—1061no—
453C2×C22⋊C4—1061no—
454C2×C22⋊C4—1061no—
455C2×C22⋊C4—1061no—
456C2×C22⋊C4—1061no—
457C2×C22⋊C4—1061no—
458C2×C22⋊C4—1061no—
459C2×C22⋊C4Dic10612yes—
460C2×C22⋊C4Dic10612yes—
461C2×C22⋊C4D21212yes—
462C2×C22⋊C4C22⋊D5312yes—
463#95—1062no—
464#95—1062no—
465#95—1064no—
466#95—2124no—
467C24—42no—
468C24—42no—
469C24C2×Dic10611yescharacteristic
470C24C2×Dic10611yescharacteristic
471C24C2×C4×D5311yescharacteristic
472C24C2×D21211yescharacteristic
473C24#1171994511yescharacteristic
474C24#1171994511yescharacteristic
475C24D4×D5311yescharacteristic
476C24D4×D5311yescharacteristic
477C24D4×D5311yescharacteristic
478C24#1171994711yescharacteristic
479C24#1171994711yescharacteristic
480C24#1171994711yescharacteristic
481C24Q8×D5311yescharacteristic
482C24#1171994911yescharacteristic
483C24C2×C22⋊D5311yescharacteristic
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—532no—
499C22×C4—532no—
500C22×C4—1064no—
501C22×C4—1064no—
502C22×C4—1064no—
503C22×C4—1061no—
504C22×C4—1061no—
505C22×C4—1062no—
506C22×C4—1062no—
507C22×C4—1061no—
508C22×C4—1062no—
509C22×C4—1062no—
510C22×C4—1061no—
511C22×C4—1061no—
512C22×C4—1061no—
513C22×C4—1061no—
514C22×C4—1061no—
515C22×C4—1061no—
516C22×C4—1061no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—2122no—
520C22×C4—2122no—
521C22×C4—2122no—
522C22×C4—2124no—
523C22×C4—2124no—
524C22×C4—2124no—
525C22×C4—2124no—
526C22×C4—2122no—
527C22×C4—2122no—
528C22×C4—2122no—
529C22×C4—2122no—
530C22×C4—2121no—
531C22×C4—2121no—
532C22×C4—2121no—
533C22×C4—2121no—
534C22×C4—2122no—
535C22×C4—2122no—
536C22×C4#1171991914yescomplemented
537C4⋊C4—2124no—
538C4⋊C4—2128no—
539C4⋊C4—2124no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—1062no—
553C22⋊C4—1062no—
554C22⋊C4—1062no—
555C22⋊C4—1062no—
556C22⋊C4—2121no—
557C22⋊C4—2121no—
558C22⋊C4—2121no—
559C22⋊C4—2121no—
560C22⋊C4—2121no—
561C22⋊C4—2121no—
562C22⋊C4—2121no—
563C22⋊C4—2121no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—42no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—41no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—41no—
585C23—42no—
586C23C22⋊C4×D5311yescharacteristic
587C23C2×#1171991911yescharacteristic
588C23#1313317311yescharacteristic
589C23#1313317911yescharacteristic
590C23C4×D21211yescharacteristic
591C23#1313318211yescharacteristic
592C23C4×Dic10611yescharacteristic
593C23#1313318711yescharacteristic
594C23#1313318811yescharacteristic
595C23#1313318911yescharacteristic
596C23#1313318911yescharacteristic
597C23#1313319011yescharacteristic
598C23#1313319111yescharacteristic
599C23#1313319211yescharacteristic
600C23#1313319311yescharacteristic
601C23#1313319411yescharacteristic
602C23#1313319411yescharacteristic
603C23#1313319411yescharacteristic
604C23#1313319411yescharacteristic
605C23#1313319511yescharacteristic
606C23#1313319611yescharacteristic
607C23#1313319711yescharacteristic
608C23#1313319911yescharacteristic
609C23#1313320111yescharacteristic
610C23#1313320211yescharacteristic
611C23#1313320311yescharacteristic
612C23#1313320711yescharacteristic
613C23#1313320811yescharacteristic
614C23#1313320811yescharacteristic
615C23#1313320911yescharacteristic
616C23#1313321011yescharacteristic
617C23#1313321211yescharacteristic
618C23#1313321611yescharacteristic
619C23#1313321611yescharacteristic
620C23#1313321711yescharacteristic
621C2×C4—24no—
622C2×C4—44no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—44no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—44no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—82no—
632C2×C4—82no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—82no—
636C2×C4—534no—
637C2×C4—1064no—
638C2×C4—1064no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—4242no—
645C2×C4—4242no—
646C2×C4—4241no—
647C2×C4—4241no—
648C2×C4—4242no—
649C2×C4—4241no—
650C2×C4—4241no—
651C2×C4—4241no—
652C2×C4—4241no—
653C2×C4—2124no—
654C2×C4—2124no—
655C2×C4—2124no—
656C2×C4—2124no—
657C2×C4—2122no—
658C2×C4—2122no—
659C2×C4—2124no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4—2122no—
663C2×C4—2122no—
664C2×C4—2122no—
665C2×C4—2122no—
666C2×C4—2122no—
667C2×C4—2122no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
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#1681048111yescharacteristic
709C22#1681050111yescharacteristic
710C22#1681050611yescharacteristic
711C22#1681050811yescharacteristic
712C22#1681051911yescharacteristic
713C22#1681052111yescharacteristic
714C22#1681052711yescharacteristic
715C22#1681053911yescharacteristic
716C22#1681054411yescharacteristic
717C22#1681054511yescharacteristic
718C22#1681054611yescharacteristic
719C22#1681055511yescharacteristic
720C22#1681055611yescharacteristic
721C22#1681055711yescharacteristic
722C22#1681056511yescharacteristic
723C22#99×D5312yes—
724C22#1681059512yes—
725C4—44no—
726C4—82no—
727C4—82no—
728C4—1064no—
729C4—4242no—
730C4—4242no—
731C4—4241no—
732C4—4241no—
733C4—2122no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—21no—
741C2—21no—
742C2—21no—
743C2—21no—
744C2—21no—
745C2—21no—
746C2#2027296711yescharacteristic
747C2#2027470112yes—
748C2#2027516711yescharacteristic
749C2#2027517211yescharacteristic
750C2#2027569812yes—
subgroupG/H
centerC23C22⋊C4×D53
commutatorC24×C53C22×C4
FrattiniC25C22×D53
FittingC2×C53×#342C2
socleC23×C53C2×C22⋊C4
prime radical, cosocleC25×C53C23
hypercenterC2×#342D53
hypocenterC53#11203
LCSG ▷ C24×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
9. C22×C4⋊Dic53C4semidirect
21. C2×#13133124C4semidirect
122. C22×C4×C53C4⋊C4semidirect
404. C53#11203semidirect
536. C22×C4#11719919semidirect

Maximal subgroups

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

subgroupindex
C2×#168104982
C2×#168104812
C2×#168103902
C2×#168103892
#202729372
C2×C53×#3422
#1120353