Finite Group Databasebeta

← #27309567

Subgroups — #27309567

Order 13568.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic53C211yesmaximal, characteristic
2C2×#16810522C211yesmaximal, characteristic, complemented
3C2×#16810516C211yesmaximal, characteristic, complemented
4C2×#16810498C211yesmaximal, characteristic, complemented
5C2×#16810498C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
7#20272964C211yesmaximal, characteristic, complemented
8#20272960C211yesmaximal, characteristic, complemented
9#20272956C211yesmaximal, characteristic
10#20272952C211yesmaximal, characteristic, complemented
11#20272949C211yesmaximal, characteristic, complemented
12#20272949C211yesmaximal, characteristic, complemented
13#20272947C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic, complemented
15C2×C53×#394C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C2×D4×Dic53—24no—
19C2×D4×Dic53—24no—
20C2×D4×Dic53—24no—
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C4⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34#16810522—24no—
35#16810516—24no—
36#16810498—24no—
37#16810498—24no—
38C22⋊C4×Dic53—24no—
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C23×D4×C53C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C22⋊C4×C53C2211yescharacteristic
57C22×C22⋊C4×C53C2211yescharacteristic
58C53×#394C418yescomplemented
59C2×#95×C53C2211yescharacteristic
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—22no—
63C23×Dic53—22no—
64C23×Dic53—22no—
65C23×Dic53—22no—
66C23×Dic53—22no—
67C23×Dic53—22no—
68C23×Dic53—22no—
69C23×Dic53—41no—
70C23×Dic53—41no—
71C23×Dic53—41no—
72C23×Dic53—41no—
73C23×Dic53D414yes—
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82D4×Dic53—232no—
83C2×C4⋊Dic53—22no—
84C2×C4⋊Dic53—22no—
85C2×C4⋊Dic53—22no—
86C2×C4⋊Dic53—22no—
87C2×C4⋊Dic53—22no—
88C2×C4⋊Dic53—22no—
89C2×C4⋊Dic53—22no—
90C2×C4⋊Dic53—22no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53—41no—
94C2×C4⋊Dic53D414yes—
95C2×C22⋊Dic53—22no—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—22no—
98C2×C22⋊Dic53—22no—
99C2×C22⋊Dic53—22no—
100C2×C22⋊Dic53—22no—
101C2×C22⋊Dic53—22no—
102C2×C22⋊Dic53—22no—
103C2×C22⋊Dic53—22no—
104C2×C22⋊Dic53—22no—
105C2×C22⋊Dic53—22no—
106C2×C22⋊Dic53—22no—
107C2×C22⋊Dic53—22no—
108C2×C22⋊Dic53—41no—
109C2×C22⋊Dic53—41no—
110C2×C22⋊Dic53—41no—
111C2×C22⋊Dic53—41no—
112C2×C22⋊Dic53D414yes—
113C2×C4×Dic53—22no—
114C2×C4×Dic53—22no—
115C2×C4×Dic53—22no—
116C2×C4×Dic53—22no—
117C2×C4×Dic53—22no—
118C2×C4×Dic53—22no—
119C2×C4×Dic53—22no—
120C2×C4×Dic53—41no—
121C2×C4×Dic53—41no—
122#13133124—22no—
123#13133124—22no—
124#13133124—22no—
125#13133124—22no—
126#13133124—22no—
127#13133124—22no—
128#13133124—22no—
129#13133124—22no—
130#13133124—22no—
131#13133124—22no—
132#13133124—22no—
133#13133124—41no—
134#13133124D414yescomplemented
135C25×C53C2311yescharacteristic
136C25×C53C2311yescharacteristic
137C22×D4×C53—22no—
138C22×D4×C53—22no—
139C22×D4×C53—22no—
140C22×D4×C53—22no—
141C22×D4×C53—22no—
142C22×D4×C53—22no—
143C22×D4×C53C2×C414yes—
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C23×C4×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149C2×C4⋊C4×C53—22no—
150C2×C4⋊C4×C53—22no—
151C2×C4⋊C4×C53C2×C414yescomplemented
152C2×C22⋊C4×C53—22no—
153C2×C22⋊C4×C53—22no—
154C2×C22⋊C4×C53—22no—
155C2×C22⋊C4×C53—22no—
156C2×C22⋊C4×C53—22no—
157C2×C22⋊C4×C53—22no—
158C2×C22⋊C4×C53—22no—
159C2×C22⋊C4×C53—22no—
160C2×C22⋊C4×C53C2×C414yescomplemented
161C2×C22⋊C4×C53C2×C414yescomplemented
162C2×C22⋊C4×C53C2×C414yescomplemented
163C2×C22⋊C4×C53C2×C414yescomplemented
164#95×C53C2×C414yescomplemented
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53—21no—
189C24×C53C22×C412yes—
190C24×C53C22×C412yes—
191C24×C53C2×D412yes—
192C24×C53C2×D412yes—
193C24×C53#4112yes—
194C24×C53#4112yes—
195C24×C53C2411yescharacteristic
196C2×D4×C53—28no—
197C2×D4×C53—28no—
198C2×D4×C53—28no—
199C2×D4×C53—28no—
200C2×D4×C53—28no—
201C2×D4×C53—28no—
202C2×D4×C53—28no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53C22×C412yes—
230C22×C4×C53C22×C412yes—
231C22×C4×C53C22×C412yes—
232C22×C4×C53C22×C412yes—
233C22×C4×C53C22×C412yes—
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2×D412yes—
236C22×C4×C53#4112yes—
237C22×C4×C53#4112yes—
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—28no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—21no—
261C22×Dic53—21no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264C22×Dic53—21no—
265C22×Dic53—21no—
266C22×Dic53—21no—
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—28no—
272C22×Dic53—28no—
273C22×Dic53—21no—
274C22×Dic53—21no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278C22×Dic53—21no—
279C22×Dic53—21no—
280C22×Dic53—21no—
281C22×Dic53—21no—
282C22×Dic53—21no—
283C22×Dic53—21no—
284C22×Dic53—21no—
285C22×Dic53—21no—
286C22×Dic53—21no—
287C22×Dic53—44no—
288C22×Dic53—44no—
289C22×Dic53—44no—
290C22×Dic53—44no—
291C22×Dic53—44no—
292C22×Dic53—44no—
293C22×Dic53—44no—
294C22×Dic53—44no—
295C22×Dic53—44no—
296C22×Dic53—44no—
297C22×Dic53—44no—
298C22×Dic53C2×D412yes—
299C22×Dic53C2×D412yes—
300C22×Dic53C2×D412yes—
301C22×Dic53C2×D412yes—
302C22×Dic53C2×D412yes—
303C22×Dic53C2×D412yes—
304C22×Dic53C2×D412yes—
305C22×Dic53C2×D412yes—
306C22×Dic53#4112yes—
307C22×Dic53#4112yes—
308C4⋊C4×C53—28no—
309C22⋊C4×C53—28no—
310C22⋊C4×C53—28no—
311C22⋊C4×C53—28no—
312C22⋊C4×C53—28no—
313C22⋊Dic53—28no—
314C22⋊Dic53—28no—
315C22⋊Dic53—28no—
316C22⋊Dic53—44no—
317C22⋊Dic53—44no—
318C22⋊Dic53—44no—
319C4⋊Dic53—28no—
320C4⋊Dic53—44no—
321C4⋊Dic53—44no—
322C4⋊Dic53—44no—
323C4×Dic53—28no—
324C4×Dic53—44no—
325C4×Dic53—44no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—22no—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—22no—
339C23×C53—22no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—22no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53—41no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—41no—
379C23×C53—41no—
380C23×C53—41no—
381C23×C53—41no—
382C23×C53—41no—
383C23×C53—41no—
384C23×C53—41no—
385C23×C53—41no—
386C23×C53—41no—
387C23×C53—41no—
388C23×C53—41no—
389C23×C53—41no—
390C23×C53—41no—
391C23×C53—41no—
392C23×C53—41no—
393C23×C53—41no—
394C23×C53C4×D414yes—
395C23×C53C4×D414yes—
396C23×C53C23×C411yescharacteristic
397C23×C53C22×D411yescharacteristic
398C23×C53C22×D411yescharacteristic
399C23×C53C22×D411yescharacteristic
400C23×C53C22×D411yescharacteristic
401C23×C53C2×#4111yescharacteristic
402C23×C53C2×#4111yescharacteristic
403C23×C53C2×#4111yescharacteristic
404C23×C53C2×#4111yescharacteristic
405C23×C53C2×#4111yescharacteristic
406C23×C53C2×#4111yescharacteristic
407C23×C53H(5,𝔽2)11yescharacteristic
408C23×C53H(5,𝔽2)11yescharacteristic
409C23×C532−1+411yescharacteristic
410C23×C532−1+411yescharacteristic
411D4×C53—232no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—22no—
416C2×C4×C53—22no—
417C2×C4×C53—22no—
418C2×C4×C53—22no—
419C2×C4×C53—22no—
420C2×C4×C53—22no—
421C2×C4×C53—22no—
422C2×C4×C53—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—22no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—22no—
433C2×C4×C53—41no—
434C2×C4×C53—41no—
435C2×C4×C53—41no—
436C2×C4×C53—41no—
437C2×C4×C53—41no—
438C2×C4×C53—41no—
439C2×C4×C53—41no—
440C2×C4×C53—41no—
441C2×C4×C53—41no—
442C2×C4×C53—41no—
443C2×C4×C53—41no—
444C2×C4×C53—41no—
445C2×C4×C53C4×D414yes—
446C2×C4×C53C4×D414yescomplemented
447C2×Dic53—22no—
448C2×Dic53—22no—
449C2×Dic53—22no—
450C2×Dic53—22no—
451C2×Dic53—22no—
452C2×Dic53—22no—
453C2×Dic53—22no—
454C2×Dic53—22no—
455C2×Dic53—22no—
456C2×Dic53—22no—
457C2×Dic53—22no—
458C2×Dic53—22no—
459C2×Dic53—22no—
460C2×Dic53—22no—
461C2×Dic53—22no—
462C2×Dic53—22no—
463C2×Dic53—22no—
464C2×Dic53—22no—
465C2×Dic53—22no—
466C2×Dic53—22no—
467C2×Dic53—22no—
468C2×Dic53—22no—
469C2×Dic53—22no—
470C2×Dic53—22no—
471C2×Dic53—416no—
472C2×Dic53—416no—
473C2×Dic53—41no—
474C2×Dic53—41no—
475C2×Dic53—41no—
476C2×Dic53—41no—
477C2×Dic53—41no—
478C2×Dic53—41no—
479C2×Dic53—41no—
480C2×Dic53—41no—
481C2×Dic53—41no—
482C2×Dic53—41no—
483C2×Dic53—41no—
484C2×Dic53—41no—
485C2×Dic53—41no—
486C2×Dic53—41no—
487C2×Dic53—41no—
488C2×Dic53—41no—
489C2×Dic53—41no—
490C2×Dic53—41no—
491C2×Dic53—41no—
492C2×Dic53—41no—
493C2×Dic53—41no—
494C2×Dic53—41no—
495C2×Dic53—41no—
496C2×Dic53—41no—
497C2×Dic53—41no—
498C2×Dic53—41no—
499C2×Dic53—41no—
500C2×Dic53—41no—
501C2×Dic53—41no—
502C2×Dic53—41no—
503C2×Dic53#12014yes—
504C2×Dic53#12114yes—
505#14185—531nomaximal, Sylow
506C22×C53—24no—
507C22×C53—24no—
508C22×C53—24no—
509C22×C53—24no—
510C22×C53—24no—
511C22×C53—24no—
512C22×C53—42no—
513C22×C53—42no—
514C22×C53—42no—
515C22×C53—42no—
516C22×C53—42no—
517C22×C53—42no—
518C22×C53—42no—
519C22×C53—42no—
520C22×C53—42no—
521C22×C53—42no—
522C22×C53—42no—
523C22×C53—42no—
524C22×C53—42no—
525C22×C53—42no—
526C22×C53—42no—
527C22×C53—42no—
528C22×C53—42no—
529C22×C53—42no—
530C22×C53—42no—
531C22×C53—42no—
532C22×C53—42no—
533C22×C53—42no—
534C22×C53—42no—
535C22×C53—42no—
536C22×C53C2×C4×D411yescharacteristic
537C22×C53C2×C4×D411yescharacteristic
538C22×C53C2×C4×D411yescharacteristic
539C22×C53C2×C4×D411yescharacteristic
540C22×C53C4×#4111yescharacteristic
541C22×C53#52011yescharacteristic
542C22×C53#52011yescharacteristic
543C22×C53C2×#12011yescharacteristic
544C22×C53C2×#12111yescharacteristic
545C22×C53#52511yescharacteristic
546C22×C53#52511yescharacteristic
547C22×C53#52511yescharacteristic
548C22×C53#52511yescharacteristic
549C22×C53#52911yescharacteristic
550C22×C53#53211yescharacteristic
551C22×C53#53411yescharacteristic
552C22×C53#53611yescharacteristic
553C22×C53#53911yescharacteristic
554C22×C53#53911yescharacteristic
555C22×C53D4211yescharacteristic
556C22×C53D4211yescharacteristic
557C22×C53#54611yescharacteristic
558C22×C53#54611yescharacteristic
559C22×C53#54711yescharacteristic
560C22×C53#54711yescharacteristic
561C22×C53#54711yescharacteristic
562C22×C53#54811yescharacteristic
563C22×C53#54811yescharacteristic
564C22×C53#54811yescharacteristic
565C22×C53#55111yescharacteristic
566C22×C53#55211yescharacteristic
567C22×C53#55311yescharacteristic
568C22×C53#55311yescharacteristic
569C22×C53#55611yescharacteristic
570C22×C53#55911yescharacteristic
571C4×C53—24no—
572C4×C53—24no—
573C4×C53—42no—
574C4×C53—42no—
575C4×C53—42no—
576Dic53—24no—
577Dic53—24no—
578Dic53—42no—
579Dic53—42no—
580Dic53—42no—
581Dic53—42no—
582Dic53—81no—
583Dic53—81no—
584C22×C4×D4—531no—
585C2×#394D5311yescharacteristic
586C2×#389—531no—
587C2×#388—531no—
588C2×#385—531no—
589C2×#385—531no—
590C2×C4×C22⋊C4—531no—
591#1440—531no—
592#1439—531no—
593#1438—531no—
594#1437—531no—
595#1436—531no—
596#1436—531no—
597#1436—531no—
598C22⋊#95—531no—
599C2×C53—44no—
600C2×C53—44no—
601C2×C53C4×#12011yescharacteristic
602C2×C53C4×#12111yescharacteristic
603C2×C53#232211yescharacteristic
604C2×C53#235911yescharacteristic
605C2×C53#236111yescharacteristic
606C2×C53#236111yescharacteristic
607C2×C53#236711yescharacteristic
608C2×C53#241011yescharacteristic
609C2×C53#241511yescharacteristic
610C2×C53#243211yescharacteristic
611C2×C53#245511yescharacteristic
612C2×C53#246011yescharacteristic
613C2×C53#246311yescharacteristic
614C2×C53#246611yescharacteristic
615C2×C53#260211yescharacteristic
616C23×D4C2×D5311yescharacteristic
617C24×C4—531no—
618C24×C4—531no—
619C2×C4×D4—1064no—
620C2×C4×D4—1064no—
621C2×C4×D4—1064no—
622C22×C4⋊C4—531no—
623C22×C4⋊C4—531no—
624C22×C4⋊C4—531no—
625C22×C4⋊C4—531no—
626C22×C4⋊C4C2×D5311yescharacteristic
627C22×C22⋊C4—531no—
628C22×C22⋊C4—531no—
629C22×C22⋊C4—531no—
630C22×C22⋊C4—531no—
631C22×C22⋊C4—531no—
632C22×C22⋊C4—531no—
633C22×C22⋊C4C2×D5311yescharacteristic
634C22×C22⋊C4C2×D5311yescharacteristic
635C22×C22⋊C4C2×D5311yescharacteristic
636C22×C22⋊C4C2×D5311yescharacteristic
637C22×C42—531no—
638C22×C42—531no—
639C22×C42—531no—
640#394Dic5318yescomplemented
641#389—1064no—
642#388—1064no—
643#385—1064no—
644#385—1064no—
645C4×C22⋊C4—1064no—
646C2×#95—531no—
647C2×#95—531no—
648C2×#95—531no—
649C2×#95—531no—
650C2×#95—531no—
651C2×#95—531no—
652C2×#95—531no—
653C2×#95—531no—
654C2×#95—531no—
655C2×#95—531no—
656C2×#95—531no—
657C2×#95—531no—
658C2×#95—531no—
659C2×#95C2×D5311yescharacteristic
660C53#1418511yescharacteristic, complemented, Sylow
661C25C22×D5311yescharacteristic
662C25C22×D5311yescharacteristic
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4—22no—
667C22×D4—22no—
668C22×D4—22no—
669C22×D4C2×Dic5314yes—
670C23×C4—531no—
671C23×C4—531no—
672C23×C4—531no—
673C23×C4—531no—
674C23×C4—531no—
675C23×C4—531no—
676C23×C4—534no—
677C23×C4—531no—
678C23×C4—531no—
679C23×C4—1062no—
680C23×C4—1062no—
681C23×C4—1062no—
682C23×C4—1062no—
683C23×C4—1062no—
684C23×C4—1062no—
685C23×C4—1062no—
686C23×C4—1062no—
687C23×C4—1062no—
688C23×C4—2121no—
689C23×C4—2121no—
690C23×C4—2121no—
691C23×C4—2121no—
692C23×C4C22×D5311yescharacteristic
693C23×C4C22×D5311yescharacteristic
694C23×C4C22×D5311yescharacteristic
695C23×C4C22×D5311yescharacteristic
696C23×C4C22×D5311yescharacteristic
697C4×D4—10632no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—534no—
701C2×C4⋊C4—1062no—
702C2×C4⋊C4—1062no—
703C2×C4⋊C4—1062no—
704C2×C4⋊C4—1062no—
705C2×C4⋊C4—1062no—
706C2×C4⋊C4—1062no—
707C2×C4⋊C4—1062no—
708C2×C4⋊C4—1062no—
709C2×C4⋊C4—1062no—
710C2×C4⋊C4—1062no—
711C2×C4⋊C4—2121no—
712C2×C4⋊C4C2×Dic5314yescomplemented
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—534no—
722C2×C22⋊C4—1062no—
723C2×C22⋊C4—1062no—
724C2×C22⋊C4—1062no—
725C2×C22⋊C4—1062no—
726C2×C22⋊C4—1062no—
727C2×C22⋊C4—1062no—
728C2×C22⋊C4—1062no—
729C2×C22⋊C4—1062no—
730C2×C22⋊C4—1062no—
731C2×C22⋊C4—1062no—
732C2×C22⋊C4—1062no—
733C2×C22⋊C4—1062no—
734C2×C22⋊C4—1062no—
735C2×C22⋊C4—2121no—
736C2×C22⋊C4—2121no—
737C2×C22⋊C4—2121no—
738C2×C22⋊C4—2121no—
739C2×C22⋊C4C2×Dic5314yescomplemented
740C2×C22⋊C4C2×Dic5314yescomplemented
741C2×C22⋊C4C2×Dic5314yescomplemented
742C2×C22⋊C4C2×Dic5314yescomplemented
743C2×C42—1062no—
744C2×C42—1062no—
745C2×C42—1062no—
746C2×C42—1062no—
747C2×C42—1062no—
748C2×C42—1062no—
749C2×C42—1062no—
750C2×C42—2121no—
751C2×C42—2121no—
752#95—534no—
753#95—1062no—
754#95—1062no—
755#95—1062no—
756#95—1062no—
757#95—1062no—
758#95—1062no—
759#95—1062no—
760#95—1062no—
761#95—1062no—
762#95—1062no—
763#95—1062no—
764#95—2121no—
765#95C2×Dic5314yescomplemented
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24D4×D5312yes—
791C24D4×D5312yes—
792C24#1171994712yes—
793C24#1171994712yes—
794C24C22×Dic5312yes—
795C24C22×Dic5312yes—
796C24C23×D5311yescharacteristic
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—532no—
831C22×C4—532no—
832C22×C4—532no—
833C22×C4—532no—
834C22×C4—532no—
835C22×C4—532no—
836C22×C4—532no—
837C22×C4—532no—
838C22×C4—532no—
839C22×C4—532no—
840C22×C4—1068no—
841C22×C4—1068no—
842C22×C4—1061no—
843C22×C4—1061no—
844C22×C4—1061no—
845C22×C4—1061no—
846C22×C4—1061no—
847C22×C4—1061no—
848C22×C4—1061no—
849C22×C4—1061no—
850C22×C4—1068no—
851C22×C4—1061no—
852C22×C4—1061no—
853C22×C4—1061no—
854C22×C4—1061no—
855C22×C4—1061no—
856C22×C4—1061no—
857C22×C4—1061no—
858C22×C4—1061no—
859C22×C4—1061no—
860C22×C4—1061no—
861C22×C4—1061no—
862C22×C4—1061no—
863C22×C4—1061no—
864C22×C4—1061no—
865C22×C4—1061no—
866C22×C4—1061no—
867C22×C4—1061no—
868C22×C4—1061no—
869C22×C4—1061no—
870C22×C4—1061no—
871C22×C4—1061no—
872C22×C4—1061no—
873C22×C4—1061no—
874C22×C4—1061no—
875C22×C4—1061no—
876C22×C4—1061no—
877C22×C4—1061no—
878C22×C4—1061no—
879C22×C4—1061no—
880C22×C4—1061no—
881C22×C4—1061no—
882C22×C4—1061no—
883C22×C4—1061no—
884C22×C4—1061no—
885C22×C4—1061no—
886C22×C4—1061no—
887C22×C4—1061no—
888C22×C4—1061no—
889C22×C4—2124no—
890C22×C4—2124no—
891C22×C4—2124no—
892C22×C4—2124no—
893C22×C4—2124no—
894C22×C4—2124no—
895C22×C4—2124no—
896C22×C4—2124no—
897C22×C4—2124no—
898C22×C4—2124no—
899C22×C4—2124no—
900C22×C4D4×D5312yes—
901C22×C4D4×D5312yes—
902C22×C4#1171994712yes—
903C22×C4#1171994712yes—
904C22×C4C22×Dic5312yes—
905C22×C4C22×Dic5312yes—
906C22×C4C22×Dic5312yes—
907C22×C4C22×Dic5312yes—
908C22×C4C22×Dic5312yes—
909C4⋊C4—28no—
910C4⋊C4—1068no—
911C4⋊C4—2124no—
912C4⋊C4—2124no—
913C4⋊C4—2124no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—1068no—
919C22⋊C4—1068no—
920C22⋊C4—1068no—
921C22⋊C4—2124no—
922C22⋊C4—2124no—
923C22⋊C4—2124no—
924C42—1068no—
925C42—2124no—
926C42—2124no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23D4×Dic5314yes—
996C23D4×Dic5314yes—
997C23C23×Dic5311yescharacteristic
998C23C2×D4×D5311yescharacteristic
999C23C2×D4×D5311yescharacteristic
1000C23C2×D4×D5311yescharacteristic
1001C23C2×D4×D5311yescharacteristic
1002C23#41×D5311yescharacteristic
1003C23#41×D5311yescharacteristic
1004C23C2×#1171994711yescharacteristic
1005C23C2×#1171994711yescharacteristic
1006C23C2×#1171994711yescharacteristic
1007C23C2×#1171994711yescharacteristic
1008C23#1313326311yescharacteristic
1009C23#1313326311yescharacteristic
1010C23#1313326411yescharacteristic
1011C23#1313326411yescharacteristic
1012D4—232no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—534no—
1047C2×C4—534no—
1048C2×C4—1062no—
1049C2×C4—1062no—
1050C2×C4—1062no—
1051C2×C4—1062no—
1052C2×C4—1062no—
1053C2×C4—1062no—
1054C2×C4—1062no—
1055C2×C4—1062no—
1056C2×C4—1062no—
1057C2×C4—1062no—
1058C2×C4—1062no—
1059C2×C4—1062no—
1060C2×C4—1062no—
1061C2×C4—1062no—
1062C2×C4—1062no—
1063C2×C4—1062no—
1064C2×C4—1062no—
1065C2×C4—1062no—
1066C2×C4—1062no—
1067C2×C4—1062no—
1068C2×C4—1062no—
1069C2×C4—1062no—
1070C2×C4—1062no—
1071C2×C4—1062no—
1072C2×C4—21216no—
1073C2×C4—21216no—
1074C2×C4—2121no—
1075C2×C4—2121no—
1076C2×C4—2121no—
1077C2×C4—2121no—
1078C2×C4—2121no—
1079C2×C4—2121no—
1080C2×C4—2121no—
1081C2×C4—2121no—
1082C2×C4—2121no—
1083C2×C4—2121no—
1084C2×C4—2121no—
1085C2×C4—2121no—
1086C2×C4—2121no—
1087C2×C4—2121no—
1088C2×C4—2121no—
1089C2×C4—2121no—
1090C2×C4—2121no—
1091C2×C4—2121no—
1092C2×C4—2121no—
1093C2×C4—2121no—
1094C2×C4—2121no—
1095C2×C4—2121no—
1096C2×C4—2121no—
1097C2×C4—2121no—
1098C2×C4—2121no—
1099C2×C4—2121no—
1100C2×C4—2121no—
1101C2×C4—2121no—
1102C2×C4—2121no—
1103C2×C4—2121no—
1104C2×C4D4×Dic5314yes—
1105C2×C4D4×Dic5314yescomplemented
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22C2×D4×Dic5311yescharacteristic
1137C22C2×D4×Dic5311yescharacteristic
1138C22C2×D4×Dic5311yescharacteristic
1139C22C2×D4×Dic5311yescharacteristic
1140C22#41×Dic5311yescharacteristic
1141C22#1681110611yescharacteristic
1142C22#1681110611yescharacteristic
1143C22#120×D5311yescharacteristic
1144C22#121×D5311yescharacteristic
1145C22#1681112911yescharacteristic
1146C22#1681112911yescharacteristic
1147C22#1681112911yescharacteristic
1148C22#1681113311yescharacteristic
1149C22#1681115411yescharacteristic
1150C22#1681116811yescharacteristic
1151C22#1681118411yescharacteristic
1152C22#1681119511yescharacteristic
1153C22#1681121711yescharacteristic
1154C22#1681121711yescharacteristic
1155C22#1681125711yescharacteristic
1156C22#1681125711yescharacteristic
1157C22#1681126511yescharacteristic
1158C22#1681126611yescharacteristic
1159C22#1681127111yescharacteristic
1160C22#1681127311yescharacteristic
1161C22#1681127311yescharacteristic
1162C22#1681127911yescharacteristic
1163C22#1681127911yescharacteristic
1164C22#1681128111yescharacteristic
1165C22#1681129611yescharacteristic
1166C22#1681131011yescharacteristic
1167C22#1681132511yescharacteristic
1168C22#1681132511yescharacteristic
1169C22#1681134211yescharacteristic
1170C22#1681135511yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—1064no—
1177C4—1064no—
1178C4—4241no—
1179C4—4241no—
1180C4—2122no—
1181C4—2122no—
1182C4—2122no—
1183C4—2122no—
1184C2—44no—
1185C2—44no—
1186C2#120×Dic5311yescharacteristic
1187C2#121×Dic5311yescharacteristic
1188C2#2027738711yescharacteristic
1189C2#2027771111yescharacteristic
1190C2#2027773511yescharacteristic
1191C2#2027773511yescharacteristic
1192C2#2027779011yescharacteristic
1193C2#2027808411yescharacteristic
1194C2#2027813711yescharacteristic
1195C2#2027833811yescharacteristic
1196C2#2027859311yescharacteristic
1197C2#2027866211yescharacteristic
1198C2#2027870711yescharacteristic
1199C2#2027874611yescharacteristic
1200C2#2028032811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#394C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#394D53
hypocenterC53#14185
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×#16810522C2semidirect
3. C2×#16810516C2semidirect
4. C2×#16810498C2semidirect
5. C2×#16810498C2semidirect
6. C2×C22⋊C4×Dic53C2semidirect
7. #20272964C2semidirect
8. #20272960C2semidirect
10. #20272952C2semidirect
11. #20272949C2semidirect
12. #20272949C2semidirect
13. #20272947C2semidirect
14. #20272937C2semidirect
58. C53×#394C4semidirect
134. #13133124D4semidirect
151. C2×C4⋊C4×C53C2×C4semidirect
160. C2×C22⋊C4×C53C2×C4semidirect
161. C2×C22⋊C4×C53C2×C4semidirect
162. C2×C22⋊C4×C53C2×C4semidirect
163. C2×C22⋊C4×C53C2×C4semidirect
164. #95×C53C2×C4semidirect
446. C2×C4×C53C4×D4semidirect
640. #394Dic53semidirect
660. C53#14185semidirect
712. C2×C4⋊C4C2×Dic53semidirect
739. C2×C22⋊C4C2×Dic53semidirect
740. C2×C22⋊C4C2×Dic53semidirect
741. C2×C22⋊C4C2×Dic53semidirect
742. C2×C22⋊C4C2×Dic53semidirect
765. #95C2×Dic53semidirect
1105. C2×C4D4×Dic53semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic532
C2×#168105222
C2×#168105162
C2×#168104982
C2×C22⋊C4×Dic532
#202729642
#202729602
#202729562
#202729522
#202729492
#202729472
#202729372
C2×C53×#3942
#1418553