Finite Group Databasebeta

← #27400643

Subgroups — #27400643

Order 13568.

1114 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×#16811328C211yesmaximal, characteristic
2#20277592C211yesmaximal, characteristic, complemented
3#20275700C211yesmaximal, characteristic, complemented
4#20275700C212yesmaximal, complemented
5#20275699C211yesmaximal, characteristic, complemented
6#20275699C212yesmaximal, complemented
7#20274700C211yesmaximal, characteristic
8#20274700C212yesmaximal
9C4×#13133131C211yesmaximal, characteristic
10C4×#13133131C212yesmaximal
11C53×#2345C211yesmaximal, characteristic, complemented
12#16811328—22no—
13#16811328—21no—
14#16811328—21no—
15#16811328—21no—
16#16811328—22no—
17#16811328—21no—
18C2×#13133216C411yescharacteristic, complemented
19C2×#13133207C412yescomplemented
20C2×#13133197C411yescharacteristic, complemented
21C2×#13133196C2211yescharacteristic
22C2×#13133196C2212yes—
23C2×#13133195C412yescomplemented
24C2×#13133182C411yescharacteristic, complemented
25C2×C4×C22⋊D53C2211yescharacteristic
26C2×C4×C22⋊D53C2212yes—
27C2×C4⋊C4×D53C411yescharacteristic, complemented
28C2×#13133131C2211yescharacteristic
29C2×#13133131C2212yes—
30C2×#13133131C2211yescharacteristic
31#16810522—21no—
32#16810509—22no—
33#16810483C2211yescharacteristic
34#16810483C2212yes—
35C4⋊C4×Dic53—21no—
36C4×C22⋊Dic53C2211yescharacteristic
37C4×C22⋊Dic53C2212yes—
38#16810389C2212yes—
39#16810389C2212yes—
40#16810389C2212yes—
41#16810389C2212yes—
42#16810389C2211yescharacteristic
43#16810389C2212yes—
44#16810389C2211yescharacteristic
45C22×C4⋊C4×C53C2211yescharacteristic
46C53×#389—21no—
47C53×#387—22no—
48C53×#380C2212yes—
49C53×#380C2211yescharacteristic
50C4×C4⋊C4×C53—21no—
51C4×C22⋊C4×C53C2211yescharacteristic
52C4×C22⋊C4×C53C2212yes—
53C22×Dic106C2×C411yescharacteristic
54C22×Dic106C2×C412yes—
55C22×C22⋊D53C2311yescharacteristic
56C22×C4×D53C2×C411yescharacteristic
57C22×C4×D53C2×C412yes—
58#13133216—22no—
59#13133216—21no—
60#13133216—21no—
61#13133207—22no—
62#13133207—22no—
63#13133207—22no—
64#13133207—22no—
65#13133197—22no—
66#13133197—21no—
67#13133197—21no—
68#13133196—21no—
69#13133196—21no—
70#13133196—21no—
71#13133196—21no—
72#13133196—22no—
73#13133196—22no—
74#13133196—22no—
75#13133196—22no—
76#13133195—22no—
77#13133195—22no—
78#13133195—22no—
79#13133195—22no—
80#13133182—22no—
81#13133182—21no—
82#13133182—21no—
83C4×C22⋊D53—21no—
84C4×C22⋊D53—21no—
85C4×C22⋊D53—21no—
86C4×C22⋊D53—21no—
87C4×C22⋊D53—22no—
88C4×C22⋊D53—22no—
89C4×C22⋊D53—22no—
90C4×C22⋊D53—22no—
91C2×C4⋊Dic53—21no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53C2×C411yescharacteristic
94C2×C4⋊Dic53C2×C412yes—
95C2×#11719919C2×C412yes—
96C2×#11719919C2×C411yescharacteristic
97C2×#11719919C2×C412yes—
98C2×#11719919C2×C412yes—
99C2×#11719919C2×C412yes—
100C4⋊C4×D53—22no—
101C4⋊C4×D53—21no—
102C4⋊C4×D53—21no—
103C2×C22⋊Dic53C2311yescharacteristic
104C2×C22⋊Dic53C2312yes—
105C2×C22⋊Dic53C2311yescharacteristic
106C2×C22⋊Dic53C2312yes—
107C2×C22⋊Dic53C2311yescharacteristic
108C2×#11719921C2×C411yescharacteristic
109C2×#11719921C2×C412yes—
110C2×C4×Dic53—21no—
111C2×C4×Dic53—22no—
112C2×C4×Dic53C2×C412yes—
113C2×C4×Dic53C2×C411yescharacteristic
114#13133131—22no—
115#13133131—24no—
116#13133131Q814yescomplemented
117#13133124—21no—
118#13133124—21no—
119#13133124—22no—
120#13133124—22no—
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2312yes—
123C2×C4⋊C4×C53—21no—
124C2×C4⋊C4×C53—22no—
125C2×C4⋊C4×C53C2×C411yescharacteristic
126C2×C4⋊C4×C53C2×C412yes—
127C2×C4⋊C4×C53C2×C411yescharacteristic
128C2×C4⋊C4×C53D412yes—
129C2×C4⋊C4×C53D411yescharacteristic
130C2×C4⋊C4×C53D411yescharacteristic
131C2×C4⋊C4×C53D411yescharacteristic
132C2×C4⋊C4×C53D412yes—
133C2×C4⋊C4×C53D411yescharacteristic
134C2×C22⋊C4×C53C2311yescharacteristic
135C2×C22⋊C4×C53C2312yes—
136C2×C22⋊C4×C53C2311yescharacteristic
137C2×C42×C53—21no—
138C2×C42×C53—22no—
139#95×C53—21no—
140#95×C53—22no—
141#95×C53—22no—
142#95×C53—21no—
143C24×C53C2411yescharacteristic
144C23×D53C22×C411yescharacteristic
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—22no—
148C22×C4×C53—42no—
149C22×C4×C53—82no—
150C22×C4×C53C22×C411yescharacteristic
151C22×C4×C53C22×C412yes—
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C22×C412yes—
154C22×C4×C53C2×D411yescharacteristic
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2×D412yes—
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×D412yes—
162C2×C22⋊D53—21no—
163C2×C22⋊D53—21no—
164C2×C22⋊D53—21no—
165C2×C22⋊D53—21no—
166C2×C22⋊D53C2×Q812yes—
167C2×C22⋊D53#4112yes—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—22no—
171C22×Dic53C22×C411yescharacteristic
172C22×Dic53C22×C412yes—
173C22×Dic53C22×C411yescharacteristic
174C22×Dic53C22×C411yescharacteristic
175C22×Dic53C22×C412yes—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—22no—
179C2×C4×D53—22no—
180C2×C4×D53—42no—
181C2×C4×D53—82no—
182C2×Dic106—21no—
183C2×Dic106—21no—
184C2×Dic106—22no—
185C2×Dic106—22no—
186C2×Dic106—42no—
187C2×Dic106—82no—
188C4⋊C4×C53—42no—
189C4⋊C4×C53—82no—
190C4⋊C4×C53C22⋊C412yes—
191C4⋊C4×C53C22⋊C411yescharacteristic
192C4⋊C4×C53C22⋊C411yescharacteristic
193C4⋊C4×C53C22⋊C412yes—
194C4⋊C4×C53C22⋊C412yes—
195C4⋊C4×C53C22⋊C412yes—
196C4⋊C4×C53C22⋊C412yes—
197C4⋊C4×C53C22⋊C412yes—
198C4⋊C4×C53C22⋊C411yescharacteristic
199C4⋊C4×C53C22⋊C411yescharacteristic
200C22⋊C4×C53—21no—
201C22⋊C4×C53—21no—
202C22⋊C4×C53—22no—
203C22⋊C4×C53—21no—
204C22⋊C4×C53—22no—
205C22⋊C4×C53C2×Q812yes—
206C42×C53—42no—
207C42×C53—82no—
208C22⋊Dic53—21no—
209C22⋊Dic53—21no—
210C22⋊Dic53—22no—
211C22⋊Dic53—22no—
212C22⋊Dic53—21no—
213C22⋊Dic53—21no—
214C22⋊Dic53—22no—
215C22⋊Dic53—21no—
216C22⋊Dic53—22no—
217C22⋊Dic53C2×Q812yes—
218#11719921—21no—
219#11719921—21no—
220#11719921—22no—
221#11719921—22no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—22no—
225C4⋊Dic53—22no—
226C4⋊Dic53—42no—
227C4⋊Dic53—82no—
228#11719919—22no—
229#11719919—22no—
230#11719919—21no—
231#11719919—21no—
232#11719919—22no—
233#11719919—22no—
234#11719919—22no—
235#11719919—22no—
236#11719919—22no—
237#11719919—22no—
238C4×Dic53—22no—
239C4×Dic53—22no—
240C4×Dic53—21no—
241C4×Dic53—21no—
242C4×Dic53—42no—
243C4×Dic53—82no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53C23×C411yescharacteristic
247C23×C53C22×D411yescharacteristic
248C23×C53C22×D411yescharacteristic
249C23×C53C22×Q811yescharacteristic
250C23×C53C2×#4111yescharacteristic
251C23×C532−1+411yescharacteristic
252C23×C532−1+411yescharacteristic
253C22×D53—21no—
254C22×D53—21no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53C4×Q812yes—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—42no—
263C2×C4×C53—42no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—42no—
268C2×C4×C53—42no—
269C2×C4×C53—42no—
270C2×C4×C53—42no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—42no—
275C2×C4×C53—42no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—42no—
279C2×C4×C53C2×C22⋊C411yescharacteristic
280C2×C4×C53C2×C22⋊C412yes—
281C2×C4×C53C2×C22⋊C412yes—
282C2×C4×C53C2×C22⋊C412yes—
283C2×C4×C53C2×C22⋊C412yes—
284C2×C4×C53C2×C22⋊C411yescharacteristic
285C2×C4×C53C2×C22⋊C411yescharacteristic
286C2×C4×C53C2×C22⋊C411yescharacteristic
287C22⋊D53—22no—
288C22⋊D53—22no—
289C22⋊D53—22no—
290C22⋊D53—22no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—21no—
297C2×Dic53—22no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—42no—
301C2×Dic53—41no—
302C2×Dic53—42no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—42no—
310C2×Dic53C4×Q812yes—
311C4×D53—42no—
312C4×D53—42no—
313C4×D53—82no—
314C4×D53—82no—
315Dic106—42no—
316Dic106—42no—
317Dic106—82no—
318Dic106—82no—
319#22513—531nomaximal, Sylow
320C22×C53—21no—
321C22×C53—21no—
322C22×C53—21no—
323C22×C53—21no—
324C22×C53—21no—
325C22×C53—21no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53C22×C22⋊C411yescharacteristic
331C22×C53C2×C4×Q811yescharacteristic
332C22×C53#51911yescharacteristic
333C22×C53#54811yescharacteristic
334C22×C53#54811yescharacteristic
335C22×C53D4×Q811yescharacteristic
336C22×C53D4×Q811yescharacteristic
337C2×D53—22no—
338C2×D53—42no—
339C2×D53—41no—
340C2×D53—41no—
341C2×D53—42no—
342C4×C53—21no—
343C4×C53—21no—
344C4×C53—21no—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—42no—
350C4×C53—81no—
351C4×C53—82no—
352C4×C53#41012yes—
353Dic53—22no—
354Dic53—42no—
355Dic53—42no—
356Dic53—41no—
357Dic53—41no—
358Dic53—42no—
359Dic53—81no—
360Dic53—82no—
361C2×#554—531no—
362#2345—531no—
363#2345D5311yescharacteristic, complemented
364#1996—532no—
365#1996—531no—
366#1996—532no—
367#1996—531no—
368#1799—532no—
369#1799—531no—
370C4×#99—532no—
371C4×#99—531no—
372C2×C53—21no—
373C2×C53—21no—
374C2×C53—21no—
375C2×C53—21no—
376C2×C53—21no—
377C2×C53—21no—
378C2×C53Q8×C22⋊C411yescharacteristic
379C2×C53C2×#41011yescharacteristic
380C2×C53#288311yescharacteristic
381D53—42no—
382#554—1061no—
383#554—1062no—
384#554—1061no—
385#554—1061no—
386#554—1062no—
387#554—1061no—
388C2×C4⋊Q8—531no—
389C2×#125—532no—
390C2×C22⋊Q8—532no—
391C2×C22⋊Q8—531no—
392C2×C22⋊Q8—532no—
393C2×C22⋊Q8—531no—
394C2×C4×Q8—531no—
395C2×C4×D4—532no—
396C2×C4×D4—531no—
397C22×C4⋊C4—531no—
398C22×C4⋊C4C2×D5311yescharacteristic
399C2×#99—531no—
400C2×#99—532no—
401C2×#99—531no—
402#389—21no—
403#389—1061no—
404#387—22no—
405#387—1062no—
406#380—532no—
407#380—531no—
408#380C2×D5312yes—
409#380C2×D5311yescharacteristic
410C4×C4⋊C4—21no—
411C4×C4⋊C4—1061no—
412C4×C22⋊C4—531no—
413C4×C22⋊C4—532no—
414C4×C22⋊C4C2×D5311yescharacteristic
415C4×C22⋊C4C2×D5312yes—
416#342—532no—
417#342—532no—
418#342—532no—
419#342—532no—
420#342—531no—
421#342—532no—
422#342—531no—
423C53#2251311yescharacteristic, complemented, Sylow
424C22×Q8—532no—
425C22×Q8—531no—
426C22×D4—531no—
427C23×C4—532no—
428C23×C4—531no—
429C23×C4C22×D5311yescharacteristic
430C23×C4C22×D5312yes—
431C4⋊Q8—1062no—
432C4⋊Q8—1061no—
433C4⋊Q8—1061no—
434#125—1062no—
435#125—1062no—
436#125—1062no—
437#125—1062no—
438C22⋊Q8—1062no—
439C22⋊Q8—1062no—
440C22⋊Q8—1061no—
441C22⋊Q8—1061no—
442C22⋊Q8—1062no—
443C22⋊Q8—1062no—
444C22⋊Q8—1061no—
445C22⋊Q8—1061no—
446C22⋊Q8—1062no—
447C22⋊Q8—1062no—
448C22⋊Q8—1062no—
449C22⋊Q8—1062no—
450C22⋊Q8—1062no—
451C22⋊Q8—1061no—
452C22⋊Q8—1061no—
453C4×Q8—1062no—
454C4×Q8—1061no—
455C4×Q8—1061no—
456C4×D4—1062no—
457C4×D4—1062no—
458C4×D4—1061no—
459C4×D4—1061no—
460C4×D4—1062no—
461C4×D4—1062no—
462C4×D4—1061no—
463C4×D4—1061no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—532no—
467C2×C4⋊C4—531no—
468C2×C4⋊C4—531no—
469C2×C4⋊C4—532no—
470C2×C4⋊C4—532no—
471C2×C4⋊C4—532no—
472C2×C4⋊C4—532no—
473C2×C4⋊C4—1062no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1062no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4C4×D5311yescharacteristic
479C2×C4⋊C4C4×D5312yes—
480C2×C4⋊C4C4×D5311yescharacteristic
481C2×C4⋊C4D21211yescharacteristic
482C2×C4⋊C4D21212yes—
483C2×C4⋊C4D21211yescharacteristic
484C2×C4⋊C4C22⋊D5311yescharacteristic
485C2×C4⋊C4C22⋊D5312yes—
486C2×C4⋊C4C22⋊D5311yescharacteristic
487C2×C22⋊C4—531no—
488C2×C22⋊C4—532no—
489C2×C22⋊C4—531no—
490C2×C22⋊C4—532no—
491C2×C22⋊C4—531no—
492C2×C22⋊C4—532no—
493C2×C22⋊C4—531no—
494C2×C22⋊C4C22×D5311yescharacteristic
495C2×C22⋊C4C22×D5312yes—
496C2×C22⋊C4C22×D5311yescharacteristic
497C2×C42—21no—
498C2×C42—22no—
499C2×C42—532no—
500C2×C42—531no—
501C2×C42—1062no—
502C2×C42—1061no—
503#99—534no—
504#99—1062no—
505#99—1064no—
506#95—21no—
507#95—22no—
508#95—22no—
509#95—21no—
510#95—1061no—
511#95—1062no—
512#95—1062no—
513#95—1061no—
514C24—531no—
515C24C23×D5311yescharacteristic
516C2×Q8—1062no—
517C2×Q8—1062no—
518C2×Q8—1061no—
519C2×Q8—1061no—
520C2×Q8—4242no—
521C2×Q8—2122no—
522C2×D4—532no—
523C2×D4—532no—
524C2×D4—1061no—
525C2×D4—1061no—
526C2×D4—1061no—
527C2×D4—1061no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—82no—
533C22×C4—531no—
534C22×C4—532no—
535C22×C4—531no—
536C22×C4—531no—
537C22×C4—532no—
538C22×C4—1061no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1061no—
542C22×C4—1061no—
543C22×C4—1062no—
544C22×C4—1061no—
545C22×C4—4242no—
546C22×C4—2122no—
547C22×C4C2×C4×D5311yescharacteristic
548C22×C4C2×C4×D5312yes—
549C22×C4C2×C4×D5311yescharacteristic
550C22×C4C2×C4×D5312yes—
551C22×C4C2×D21211yescharacteristic
552C22×C4C2×D21211yescharacteristic
553C22×C4C2×D21212yes—
554C22×C4C2×D21212yes—
555C22×C4C2×C22⋊D5311yescharacteristic
556C22×C4C2×C22⋊D5311yescharacteristic
557C22×C4C2×C22⋊D5312yes—
558C22×C4C2×C22⋊D5312yes—
559C4⋊C4—42no—
560C4⋊C4—82no—
561C4⋊C4—1062no—
562C4⋊C4—1062no—
563C4⋊C4—1061no—
564C4⋊C4—1061no—
565C4⋊C4—1061no—
566C4⋊C4—1061no—
567C4⋊C4—1062no—
568C4⋊C4—1062no—
569C4⋊C4—1062no—
570C4⋊C4—1062no—
571C4⋊C4—1062no—
572C4⋊C4—1062no—
573C4⋊C4—1062no—
574C4⋊C4—1062no—
575C4⋊C4—4242no—
576C4⋊C4—2122no—
577C4⋊C4#1171992112yes—
578C4⋊C4#1171992111yescharacteristic
579C4⋊C4#1171992111yescharacteristic
580C4⋊C4#1171992112yes—
581C4⋊C4#1171992112yes—
582C4⋊C4#1171992112yes—
583C4⋊C4#1171992112yes—
584C4⋊C4#1171992112yes—
585C4⋊C4#1171992111yescharacteristic
586C4⋊C4#1171992111yescharacteristic
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—22no—
590C22⋊C4—21no—
591C22⋊C4—22no—
592C22⋊C4—532no—
593C22⋊C4—1062no—
594C22⋊C4—1061no—
595C22⋊C4—1062no—
596C22⋊C4—1061no—
597C22⋊C4—1061no—
598C22⋊C4—1062no—
599C22⋊C4—1062no—
600C22⋊C4—1061no—
601C22⋊C4—1061no—
602C22⋊C4—1062no—
603C22⋊C4—1061no—
604C22⋊C4—1062no—
605C22⋊C4—1061no—
606C22⋊C4Q8×D5312yes—
607C42—42no—
608C42—82no—
609C42—1062no—
610C42—1062no—
611C42—1061no—
612C42—1061no—
613C42—4242no—
614C42—2122no—
615C23—41no—
616C23—41no—
617C23—532no—
618C23—1061no—
619C23—1061no—
620C23—2121no—
621C23—2121no—
622C23C22×C4×D5311yescharacteristic
623C23C22×C22⋊D5311yescharacteristic
624C23C22×D21211yescharacteristic
625C23C2×Q8×D5311yescharacteristic
626C23#41×D5311yescharacteristic
627C23#1313326411yescharacteristic
628C23#1313326511yescharacteristic
629Q8—4242no—
630Q8—4242no—
631Q8—2122no—
632Q8—2122no—
633D4—1062no—
634D4—1062no—
635D4—1062no—
636D4—1062no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—532no—
659C2×C4—1061no—
660C2×C4—1061no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1061no—
664C2×C4—1061no—
665C2×C4—1062no—
666C2×C4—4242no—
667C2×C4—4242no—
668C2×C4—2122no—
669C2×C4—2122no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2122no—
678C2×C4—2122no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2122no—
682C2×C4C2×#1171992112yes—
683C2×C4C2×#1171992112yes—
684C2×C4C2×#1171992111yescharacteristic
685C2×C4C2×#1171992111yescharacteristic
686C2×C4C2×#1171992111yescharacteristic
687C2×C4C2×#1171992112yes—
688C2×C4C2×#1171992112yes—
689C2×C4C2×#1171992111yescharacteristic
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—1062no—
701C22—2122no—
702C22—2122no—
703C22—2121no—
704C22—2121no—
705C22C22×#1171992111yescharacteristic
706C22C4×Q8×D5311yescharacteristic
707C22#1681109911yescharacteristic
708C22#1681128011yescharacteristic
709C22#1681128511yescharacteristic
710C22Q8×C22⋊D5311yescharacteristic
711C22Q8×D21211yescharacteristic
712C4—21no—
713C4—21no—
714C4—21no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—22no—
719C4—42no—
720C4—81no—
721C4—82no—
722C4—1062no—
723C4—4242no—
724C4—4241no—
725C4—2122no—
726C4—2121no—
727C4—2122no—
728C4—2122no—
729C4—2121no—
730C4#1681059612yes—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—2122no—
738C2Q8×#1171992111yescharacteristic
739C2C2×#1681059611yescharacteristic
740C2#2028317511yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC23×C53C23×C4
FrattiniC24C23×D53
FittingC53×#2345C2
socleC22×C53C22×C22⋊C4
prime radicalC22×C22⋊D53C23
cosocleC24×C53C24
hypercenter#2345D53
hypocenterC53#22513
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #20277592C2semidirect
3. #20275700C2semidirect
4. #20275700C2semidirect
5. #20275699C2semidirect
6. #20275699C2semidirect
11. C53×#2345C2semidirect
18. C2×#13133216C4semidirect
19. C2×#13133207C4semidirect
20. C2×#13133197C4semidirect
23. C2×#13133195C4semidirect
24. C2×#13133182C4semidirect
27. C2×C4⋊C4×D53C4semidirect
116. #13133131Q8semidirect
363. #2345D53semidirect
423. C53#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#168113282
#202775922
#202757002
#202756992
#202747002
C4×#131331312
C53×#23452
#2251353