Finite Group Databasebeta

← #27309762

Subgroups — #27309762

Order 13568.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810545C211yesmaximal, characteristic
2C2×#16810520C211yesmaximal, characteristic, complemented
3C2×#16810515C211yesmaximal, characteristic
4C2×#16810512C211yesmaximal, characteristic
5C2×#16810512C211yesmaximal, characteristic
6C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
8#20272967C211yesmaximal, characteristic, complemented
9#20272957C211yesmaximal, characteristic
10#20272951C211yesmaximal, characteristic
11#20272951C211yesmaximal, characteristic
12#20272950C211yesmaximal, characteristic, complemented
13#20272946C211yesmaximal, characteristic, complemented
14#20272940C211yesmaximal, characteristic, complemented
15C53×#1441C211yesmaximal, characteristic, complemented
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×#11719921C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30C22×C4×Dic53C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810545C418yescomplemented
34#16810520—24no—
35#16810515—24no—
36#16810512—24no—
37#16810512—24no—
38C4⋊C4×Dic53—24no—
39C4⋊C4×Dic53—24no—
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C22×C4⋊C4×C53C2211yescharacteristic
52C22×C4⋊C4×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C24×D53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C23×Dic53C2311yescharacteristic
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2311yescharacteristic
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53—22no—
69C2×C4⋊Dic53—22no—
70C2×C4⋊Dic53C2×C414yes—
71C2×C4⋊Dic53D414yes—
72C2×#11719919—22no—
73C2×#11719919—22no—
74C2×#11719919—22no—
75C2×#11719919—22no—
76C2×#11719919—22no—
77C2×#11719919—22no—
78C2×#11719919—22no—
79C2×#11719919—41no—
80C2×#11719919C2×C414yes—
81C2×#11719921—22no—
82C2×#11719921—22no—
83C2×#11719921—22no—
84C2×#11719921—22no—
85C2×#11719921—22no—
86C2×#11719921—22no—
87C2×#11719921—22no—
88C2×#11719921—22no—
89C2×#11719921—22no—
90C2×#11719921—22no—
91C2×#11719921—22no—
92C2×#11719921—22no—
93C2×#11719921—22no—
94C2×#11719921—22no—
95C2×#11719921—22no—
96C2×#11719921—22no—
97C2×#11719921—41no—
98C2×#11719921—41no—
99C2×#11719921C2×C414yes—
100C2×#11719921C2×C414yes—
101C2×#11719921C2×C414yes—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—22no—
106C2×C4×Dic53—22no—
107C2×C4×Dic53—22no—
108C2×C4×Dic53—22no—
109C2×C4×Dic53—22no—
110C2×C4×Dic53—22no—
111C2×C4×Dic53—22no—
112C2×C4×Dic53—22no—
113C2×C4×Dic53—22no—
114C2×C4×Dic53—41no—
115C2×C4×Dic53—41no—
116C2×C4×Dic53D414yes—
117#13133124—22no—
118#13133124—22no—
119#13133124—22no—
120#13133124—22no—
121#13133124—22no—
122#13133124—22no—
123#13133124—22no—
124#13133124—22no—
125#13133124—41no—
126#13133124C2×C414yes—
127#13133124D414yes—
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53—22no—
136C2×C4⋊C4×C53—22no—
137C2×C4⋊C4×C53—22no—
138C2×C4⋊C4×C53—22no—
139C2×C4⋊C4×C53—22no—
140C2×C4⋊C4×C53C2×C414yes—
141#95×C53—22no—
142#95×C53—22no—
143#95×C53—22no—
144#95×C53—22no—
145#95×C53—22no—
146C24×C53C2411yescharacteristic
147C23×D53—21no—
148C23×D53—21no—
149C23×D53—21no—
150C23×D53—21no—
151C23×D53—21no—
152C23×D53—21no—
153C23×D53—21no—
154C23×D53—21no—
155C23×D53—21no—
156C23×D53—21no—
157C23×D53—21no—
158C23×D53—21no—
159C23×D53—21no—
160C23×D53—21no—
161C23×D53C22×C412yes—
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—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53C22×C412yes—
203C22×C4×C53C22×C412yes—
204C22×C4×C53C22×C412yes—
205C22×C4×C53C2×D412yes—
206C22×C4×C53C2×D412yes—
207C22×C4×C53C2×D412yes—
208C22×C4×C53#4112yes—
209C22×C4×C53#4112yes—
210C22×C4×C53#4112yes—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53C22×C412yes—
248C22×Dic53C22×C412yes—
249C22×Dic53C22×C412yes—
250C22×Dic53C2×D412yes—
251C22×Dic53C2×D412yes—
252C22×Dic53C2×D412yes—
253C22×Dic53C2×D412yes—
254C22×Dic53C2×D412yes—
255C22×Dic53C2×D412yes—
256C22×Dic53#4112yes—
257C22×Dic53#4112yes—
258C22×Dic53#4112yes—
259C22×Dic53#4112yes—
260C4⋊C4×C53—28no—
261C4⋊C4×C53—28no—
262#11719921—28no—
263#11719921—28no—
264#11719921—28no—
265#11719921—44no—
266#11719921—44no—
267#11719921—44no—
268#11719921—44no—
269C4⋊Dic53—28no—
270C4⋊Dic53—28no—
271#11719919—28no—
272#11719919—44no—
273#11719919—44no—
274C4×Dic53—28no—
275C4×Dic53—28no—
276C4×Dic53—44no—
277C4×Dic53—44no—
278C4×Dic53—44no—
279C23×C53C23×C411yescharacteristic
280C23×C53C22×D411yescharacteristic
281C23×C53C22×D411yescharacteristic
282C23×C53C22×D411yescharacteristic
283C23×C53C2×#4111yescharacteristic
284C23×C53C2×#4111yescharacteristic
285C23×C53C2×#4111yescharacteristic
286C23×C53C2×#4111yescharacteristic
287C23×C53C2×#4111yescharacteristic
288C23×C53C2×#4111yescharacteristic
289C23×C53C2×#4111yescharacteristic
290C23×C53H(5,𝔽2)11yescharacteristic
291C23×C532−1+411yescharacteristic
292C23×C532−1+411yescharacteristic
293C23×C532−1+411yescharacteristic
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—41no—
302C22×D53—41no—
303C22×D53—41no—
304C22×D53—41no—
305C22×D53—41no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—41no—
312C22×D53—41no—
313C22×D53—41no—
314C22×D53—41no—
315C22×D53—41no—
316C22×D53—41no—
317C22×D53—41no—
318C22×D53—41no—
319C22×D53—41no—
320C22×D53—41no—
321C22×D53—41no—
322C22×D53—41no—
323C22×D53—41no—
324C22×D53—41no—
325C22×D53—41no—
326C22×D53—41no—
327C22×D53—41no—
328C22×D53—41no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53C4×D414yes—
377C2×C4×C53C4×D414yes—
378C2×Dic53—22no—
379C2×Dic53—22no—
380C2×Dic53—22no—
381C2×Dic53—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—22no—
393C2×Dic53—22no—
394C2×Dic53—22no—
395C2×Dic53—22no—
396C2×Dic53—22no—
397C2×Dic53—22no—
398C2×Dic53—22no—
399C2×Dic53—22no—
400C2×Dic53—22no—
401C2×Dic53—22no—
402C2×Dic53—22no—
403C2×Dic53—22no—
404C2×Dic53—22no—
405C2×Dic53—22no—
406C2×Dic53—22no—
407C2×Dic53—22no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53C4×D414yes—
425C2×Dic53#12114yes—
426C2×Dic53#12114yes—
427#14200—531nomaximal, Sylow
428C22×C53C2×C4×D411yescharacteristic
429C22×C53C2×C4×D411yescharacteristic
430C22×C53C2×C4×D411yescharacteristic
431C22×C53C4×#4111yescharacteristic
432C22×C53C4×#4111yescharacteristic
433C22×C53#51911yescharacteristic
434C22×C53#52011yescharacteristic
435C22×C53C2×#12111yescharacteristic
436C22×C53C2×#12111yescharacteristic
437C22×C53#52511yescharacteristic
438C22×C53#52511yescharacteristic
439C22×C53#52911yescharacteristic
440C22×C53#52911yescharacteristic
441C22×C53#53211yescharacteristic
442C22×C53#53211yescharacteristic
443C22×C53#53611yescharacteristic
444C22×C53#53711yescharacteristic
445C22×C53#54111yescharacteristic
446C22×C53#54211yescharacteristic
447C22×C53D4211yescharacteristic
448C22×C53#54711yescharacteristic
449C22×C53#54711yescharacteristic
450C22×C53#54711yescharacteristic
451C22×C53#54811yescharacteristic
452C22×C53#54811yescharacteristic
453C22×C53#54811yescharacteristic
454C22×C53#55111yescharacteristic
455C22×C53#55211yescharacteristic
456C22×C53#55211yescharacteristic
457C22×C53#55211yescharacteristic
458C22×C53#55311yescharacteristic
459C22×C53#55311yescharacteristic
460C22×C53#55611yescharacteristic
461C22×C53#55611yescharacteristic
462C22×C53#55611yescharacteristic
463C2×D53—42no—
464C2×D53—42no—
465C2×D53—42no—
466C2×D53—42no—
467C2×D53—42no—
468C2×D53—42no—
469C2×D53—42no—
470C2×D53—81no—
471C2×D53—81no—
472C2×D53—81no—
473C2×D53—81no—
474C2×D53—81no—
475C2×D53—81no—
476C2×D53—81no—
477C2×D53—81no—
478C4×C53—24no—
479C4×C53—24no—
480C4×C53—42no—
481C4×C53—42no—
482C4×C53—42no—
483C4×C53—81no—
484C4×C53—81no—
485Dic53—24no—
486Dic53—24no—
487Dic53—24no—
488Dic53—42no—
489Dic53—42no—
490Dic53—42no—
491Dic53—42no—
492C2×#396—531no—
493C2×#389—531no—
494C2×#388—531no—
495C2×#388—531no—
496C2×#388—531no—
497C2×C4×C4⋊C4—531no—
498C2×C4×C4⋊C4—531no—
499#1441—531no—
500#1441D5311yescharacteristic, complemented
501#1439—531no—
502#1437—531no—
503#1437—531no—
504#1436—531no—
505#1436—531no—
506#1434—531no—
507C2×C53C4×#12111yescharacteristic
508C2×C53C4×#12111yescharacteristic
509C2×C53#232311yescharacteristic
510C2×C53#236111yescharacteristic
511C2×C53#236211yescharacteristic
512C2×C53#236211yescharacteristic
513C2×C53#237311yescharacteristic
514C2×C53#241311yescharacteristic
515C2×C53#241611yescharacteristic
516C2×C53#246111yescharacteristic
517C2×C53#246911yescharacteristic
518C2×C53#251911yescharacteristic
519C2×C53#252511yescharacteristic
520C2×C53#254511yescharacteristic
521C2×C53#260111yescharacteristic
522D53—82no—
523C22×C4⋊C4—531no—
524C22×C4⋊C4—531no—
525C22×C4⋊C4—531no—
526C22×C4⋊C4—531no—
527C22×C4⋊C4—531no—
528C22×C4⋊C4C2×D5311yescharacteristic
529C22×C4⋊C4C2×D5311yescharacteristic
530C22×C22⋊C4—531no—
531C22×C22⋊C4—531no—
532C22×C22⋊C4—531no—
533C22×C22⋊C4—531no—
534C22×C22⋊C4—531no—
535C22×C22⋊C4—531no—
536C22×C22⋊C4—531no—
537C22×C42—531no—
538C22×C42—531no—
539C22×C42—531no—
540C22×C42—531no—
541C22×C42—531no—
542#396—538no—
543#389—1064no—
544#388—1064no—
545#388—1064no—
546#388—1064no—
547C4×C4⋊C4—1064no—
548C4×C4⋊C4—1064no—
549C2×#95—531no—
550C2×#95—531no—
551C2×#95—531no—
552C2×#95—531no—
553C2×#95—531no—
554C2×#95—531no—
555C2×#95—531no—
556C2×#95—531no—
557C2×#95—531no—
558C2×#95—531no—
559C2×#95—531no—
560C2×#95C2×D5311yescharacteristic
561C2×#95C2×D5311yescharacteristic
562C2×#95C2×D5311yescharacteristic
563C2×#95C2×D5311yescharacteristic
564C2×#95C2×D5311yescharacteristic
565C53#1420011yescharacteristic, complemented, Sylow
566C25—531no—
567C23×C4—531no—
568C23×C4—531no—
569C23×C4—531no—
570C23×C4—531no—
571C23×C4—531no—
572C23×C4—531no—
573C23×C4—531no—
574C23×C4C22×D5311yescharacteristic
575C23×C4C22×D5311yescharacteristic
576C23×C4C22×D5311yescharacteristic
577C23×C4C22×D5311yescharacteristic
578C23×C4C22×D5311yescharacteristic
579C23×C4C22×D5311yescharacteristic
580C23×C4C22×D5311yescharacteristic
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—534no—
587C2×C4⋊C4—534no—
588C2×C4⋊C4—534no—
589C2×C4⋊C4—1062no—
590C2×C4⋊C4—1062no—
591C2×C4⋊C4—1062no—
592C2×C4⋊C4—1062no—
593C2×C4⋊C4—1062no—
594C2×C4⋊C4—1062no—
595C2×C4⋊C4—1062no—
596C2×C4⋊C4—1062no—
597C2×C4⋊C4—1062no—
598C2×C4⋊C4—1062no—
599C2×C4⋊C4—1062no—
600C2×C4⋊C4—2121no—
601C2×C4⋊C4C4×D5314yes—
602C2×C22⋊C4—534no—
603C2×C22⋊C4—534no—
604C2×C22⋊C4—534no—
605C2×C22⋊C4—1062no—
606C2×C22⋊C4—1062no—
607C2×C22⋊C4—1062no—
608C2×C22⋊C4—1062no—
609C2×C22⋊C4—1062no—
610C2×C22⋊C4—1062no—
611C2×C22⋊C4—1062no—
612C2×C22⋊C4—1062no—
613C2×C22⋊C4—1062no—
614C2×C22⋊C4—1062no—
615C2×C22⋊C4—1062no—
616C2×C22⋊C4—1062no—
617C2×C22⋊C4—1062no—
618C2×C22⋊C4—1062no—
619C2×C22⋊C4—1062no—
620C2×C22⋊C4—1062no—
621C2×C22⋊C4—2121no—
622C2×C22⋊C4—2121no—
623C2×C42—534no—
624C2×C42—1062no—
625C2×C42—1062no—
626C2×C42—1062no—
627C2×C42—1062no—
628C2×C42—1062no—
629C2×C42—1062no—
630C2×C42—1062no—
631C2×C42—1062no—
632C2×C42—1062no—
633C2×C42—1062no—
634C2×C42—1062no—
635C2×C42—1062no—
636C2×C42—2121no—
637C2×C42—2121no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—534no—
644#95—534no—
645#95—1062no—
646#95—1062no—
647#95—1062no—
648#95—1062no—
649#95—1062no—
650#95—1062no—
651#95—1062no—
652#95—1062no—
653#95—2121no—
654C24—532no—
655C24—1061no—
656C24—1061no—
657C24—1061no—
658C24—1061no—
659C24—1061no—
660C24—1061no—
661C24—1061no—
662C24—1061no—
663C24—1061no—
664C24—1061no—
665C24—1061no—
666C24—1061no—
667C24—1061no—
668C24—1061no—
669C24C23×D5311yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—532no—
711C22×C4—532no—
712C22×C4—532no—
713C22×C4—532no—
714C22×C4—532no—
715C22×C4—532no—
716C22×C4—532no—
717C22×C4—532no—
718C22×C4—532no—
719C22×C4—532no—
720C22×C4—532no—
721C22×C4—532no—
722C22×C4—532no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4C2×C4×D5312yes—
760C22×C4C2×C4×D5312yes—
761C22×C4C2×C4×D5312yes—
762C22×C4D4×D5312yes—
763C22×C4D4×D5312yes—
764C22×C4D4×D5312yes—
765C22×C4#1171994712yes—
766C22×C4#1171994712yes—
767C22×C4#1171994912yes—
768C4⋊C4—28no—
769C4⋊C4—28no—
770C4⋊C4—1068no—
771C4⋊C4—1068no—
772C4⋊C4—1068no—
773C4⋊C4—2124no—
774C4⋊C4—2124no—
775C22⋊C4—1068no—
776C22⋊C4—1068no—
777C22⋊C4—1068no—
778C22⋊C4—2124no—
779C22⋊C4—2124no—
780C22⋊C4—2124no—
781C22⋊C4—2124no—
782C42—1068no—
783C42—1068no—
784C42—2124no—
785C42—2124no—
786C42—2124no—
787C23—1062no—
788C23—1062no—
789C23—1062no—
790C23—1062no—
791C23—1062no—
792C23—1062no—
793C23—1062no—
794C23—2121no—
795C23—2121no—
796C23—2121no—
797C23—2121no—
798C23—2121no—
799C23—2121no—
800C23—2121no—
801C23—2121no—
802C23—2121no—
803C23—2121no—
804C23—2121no—
805C23—2121no—
806C23—2121no—
807C23—2121no—
808C23—2121no—
809C23—2121no—
810C23—2121no—
811C23—2121no—
812C23—2121no—
813C23—2121no—
814C23—2121no—
815C23—2121no—
816C23—2121no—
817C23—2121no—
818C23—2121no—
819C23—2121no—
820C23—2121no—
821C23—2121no—
822C23C22×C4×D5311yescharacteristic
823C23C2×D4×D5311yescharacteristic
824C23C2×D4×D5311yescharacteristic
825C23C2×D4×D5311yescharacteristic
826C23#41×D5311yescharacteristic
827C23#41×D5311yescharacteristic
828C23#41×D5311yescharacteristic
829C23#41×D5311yescharacteristic
830C23C2×#1171994711yescharacteristic
831C23C2×#1171994711yescharacteristic
832C23C2×#1171994911yescharacteristic
833C23#1313326311yescharacteristic
834C23#1313326411yescharacteristic
835C23#1313326511yescharacteristic
836C23#1313326511yescharacteristic
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—534no—
885C2×C4—534no—
886C2×C4—534no—
887C2×C4—1062no—
888C2×C4—1062no—
889C2×C4—1062no—
890C2×C4—1062no—
891C2×C4—1062no—
892C2×C4—1062no—
893C2×C4—1062no—
894C2×C4—1062no—
895C2×C4—1062no—
896C2×C4—1062no—
897C2×C4—1062no—
898C2×C4—1062no—
899C2×C4—1062no—
900C2×C4—1062no—
901C2×C4—1062no—
902C2×C4—1062no—
903C2×C4—1062no—
904C2×C4—1062no—
905C2×C4—1062no—
906C2×C4—1062no—
907C2×C4—1062no—
908C2×C4—1062no—
909C2×C4—1062no—
910C2×C4—1062no—
911C2×C4—1062no—
912C2×C4—1062no—
913C2×C4—1062no—
914C2×C4—1062no—
915C2×C4—1062no—
916C2×C4—1062no—
917C2×C4—2121no—
918C2×C4—2121no—
919C2×C4—2121no—
920C2×C4—2121no—
921C2×C4—2121no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4#1313317714yes—
934C2×C4#1313317914yes—
935C22—4241no—
936C22—4241no—
937C22—4241no—
938C22—4241no—
939C22—4241no—
940C22—4241no—
941C22—4241no—
942C22—4241no—
943C22—2122no—
944C22—2122no—
945C22—2122no—
946C22—2122no—
947C22—2122no—
948C22—2122no—
949C22—2122no—
950C22C4×D4×D5311yescharacteristic
951C22C2×#1313317711yescharacteristic
952C22C2×#1313317911yescharacteristic
953C22C4×#1171994711yescharacteristic
954C22#1681109111yescharacteristic
955C22#1681109911yescharacteristic
956C22#1681110511yescharacteristic
957C22#121×D5311yescharacteristic
958C22#121×D5311yescharacteristic
959C22#1681112911yescharacteristic
960C22#1681113611yescharacteristic
961C22#1681115011yescharacteristic
962C22#1681115911yescharacteristic
963C22#1681116811yescharacteristic
964C22#1681116811yescharacteristic
965C22#1681119611yescharacteristic
966C22#1681120311yescharacteristic
967C22#1681123411yescharacteristic
968C22#1681124211yescharacteristic
969C22#1681125711yescharacteristic
970C22#1681127111yescharacteristic
971C22#1681127511yescharacteristic
972C22#1681127611yescharacteristic
973C22#1681127911yescharacteristic
974C22#1681128311yescharacteristic
975C22#1681128311yescharacteristic
976C22#1681129611yescharacteristic
977C22#1681130511yescharacteristic
978C22#1681130511yescharacteristic
979C22#1681131111yescharacteristic
980C22#1681132411yescharacteristic
981C22#1681132611yescharacteristic
982C22#1681134011yescharacteristic
983C22#1681134411yescharacteristic
984C22#1681134711yescharacteristic
985C4—24no—
986C4—24no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—81no—
991C4—81no—
992C4—1064no—
993C4—1064no—
994C4—1064no—
995C4—2122no—
996C4—2122no—
997C4—2122no—
998C4—2122no—
999C2—4242no—
1000C2#2027722111yescharacteristic
1001C2#2027722511yescharacteristic
1002C2#2027740011yescharacteristic
1003C2#2027773011yescharacteristic
1004C2#2027773711yescharacteristic
1005C2#2027774111yescharacteristic
1006C2#2027782811yescharacteristic
1007C2#2027811511yescharacteristic
1008C2#2027815011yescharacteristic
1009C2#2027867511yescharacteristic
1010C2#2027878911yescharacteristic
1011C2#2027938111yescharacteristic
1012C2#2027946511yescharacteristic
1013C2#2027969011yescharacteristic
1014C2#2028030711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1441C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenter#1441D53
hypocenterC53#14200
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#16810520C2semidirect
6. C2×C4⋊C4×Dic53C2semidirect
7. C2×C4⋊C4×Dic53C2semidirect
8. #20272967C2semidirect
12. #20272950C2semidirect
13. #20272946C2semidirect
14. #20272940C2semidirect
15. C53×#1441C2semidirect
33. #16810545C4semidirect
500. #1441D53semidirect
565. C53#14200semidirect

Maximal subgroups

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

subgroupindex
C2×#168105452
C2×#168105202
C2×#168105152
C2×#168105122
C2×C4⋊C4×Dic532
#202729672
#202729572
#202729512
#202729502
#202729462
#202729402
C53×#14412
#1420053