Finite Group Databasebeta

← #27308567

Subgroups — #27308567

Order 13568.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133203C211yesmaximal, characteristic
2C2×#16810529C211yesmaximal, characteristic, complemented
3C2×#16810516C211yesmaximal, characteristic, complemented
4C2×#16810502C211yesmaximal, characteristic
5#20272985C211yesmaximal, characteristic, complemented
6#20272962C211yesmaximal, characteristic, complemented
7#20272961C211yesmaximal, characteristic, complemented
8#20272954C211yesmaximal, characteristic
9#20272953C211yesmaximal, characteristic, complemented
10#20272953C211yesmaximal, characteristic, complemented
11#20272951C211yesmaximal, characteristic, complemented
12#20272939C211yesmaximal, characteristic, complemented
13#20272938C211yesmaximal, characteristic, complemented
14C4×#13133124C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
16C23×Dic106C2211yescharacteristic
17C23×C22⋊D53C2211yescharacteristic
18C2×#13133203—24no—
19C2×#13133203—24no—
20C2×#13133203C418yescomplemented
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810529—24no—
34#16810516—24no—
35#16810502—24no—
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C24×C4×C53C2211yescharacteristic
51C22×C22⋊C4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2211yescharacteristic
53C22×C42×C53C2211yescharacteristic
54C22×C42×C53C2211yescharacteristic
55C4×C22⋊C4×C53—24no—
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C24×D53C2311yescharacteristic
59C22×Dic106—22no—
60C22×Dic106—22no—
61C22×Dic106—22no—
62C22×Dic106—22no—
63C22×Dic106—41no—
64C22×Dic106—41no—
65C22×Dic106C2×C414yescomplemented
66C22×C22⋊D53—22no—
67C22×C22⋊D53—22no—
68C22×C22⋊D53—22no—
69C22×C22⋊D53—22no—
70C22×C22⋊D53—41no—
71C22×C22⋊D53—41no—
72C22×C22⋊D53C2×C414yes—
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80#13133203—232no—
81C2×C4⋊Dic53—22no—
82C2×C4⋊Dic53—22no—
83C2×C4⋊Dic53—41no—
84C2×C22⋊Dic53—22no—
85C2×C22⋊Dic53—22no—
86C2×C22⋊Dic53—22no—
87C2×C22⋊Dic53—22no—
88C2×C22⋊Dic53—22no—
89C2×C22⋊Dic53—22no—
90C2×C22⋊Dic53—41no—
91C2×C22⋊Dic53—41no—
92C2×C22⋊Dic53C2×C414yes—
93C2×#11719921—22no—
94C2×#11719921—22no—
95C2×#11719921—22no—
96C2×#11719921—22no—
97C2×#11719921—22no—
98C2×#11719921—22no—
99C2×#11719921—22no—
100C2×#11719921—22no—
101C2×#11719921—22no—
102C2×#11719921—22no—
103C2×#11719921—22no—
104C2×#11719921—22no—
105C2×#11719921—41no—
106C2×#11719921—41no—
107C2×#11719921—41no—
108C2×#11719921—41no—
109C2×#11719921C2×C414yescomplemented
110C2×#11719921C2×C414yescomplemented
111C2×C4×Dic53—22no—
112C2×C4×Dic53—22no—
113C2×C4×Dic53—22no—
114C2×C4×Dic53—22no—
115C2×C4×Dic53—41no—
116C2×C4×Dic53C2×C414yescomplemented
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—22no—
126#13133124—22no—
127#13133124—22no—
128#13133124—41no—
129#13133124—41no—
130#13133124D414yes—
131C25×C53C2311yescharacteristic
132C23×C4×C53—22no—
133C23×C4×C53—22no—
134C23×C4×C53—22no—
135C23×C4×C53—22no—
136C23×C4×C53—22no—
137C23×C4×C53—41no—
138C23×C4×C53—41no—
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C2×C22⋊C4×C53—22no—
146C2×C22⋊C4×C53—22no—
147C2×C22⋊C4×C53—22no—
148C2×C22⋊C4×C53C2×C414yes—
149C2×C22⋊C4×C53D414yes—
150C2×C22⋊C4×C53D414yes—
151C2×C42×C53—22no—
152C2×C42×C53—22no—
153C2×C42×C53—22no—
154C2×C42×C53—22no—
155C2×C42×C53—41no—
156C2×C42×C53—41no—
157#95×C53—22no—
158#95×C53—22no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53C22×C412yes—
172C24×C53C2×D412yes—
173C24×C53C2×D412yes—
174C24×C53C2411yescharacteristic
175C23×D53—21no—
176C23×D53—21no—
177C23×D53—21no—
178C23×D53—21no—
179C23×D53—21no—
180C23×D53—21no—
181C23×D53—21no—
182C23×D53—21no—
183C23×D53—21no—
184C23×D53—21no—
185C23×D53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—21no—
189C23×D53C22×C412yes—
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×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—44no—
222C22×C4×C53—44no—
223C22×C4×C53—44no—
224C22×C4×C53—44no—
225C22×C4×C53—44no—
226C22×C4×C53—44no—
227C22×C4×C53C22×C412yes—
228C22×C4×C53C22×C412yes—
229C22×C4×C53C2×D412yes—
230C22×C4×C53C2×D412yes—
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53#4112yes—
235C22×C4×C53#4112yes—
236C22×C4×C53#4112yes—
237C22×C4×C53#4112yes—
238C22×C4×C53#4112yes—
239C2×C22⋊D53—28no—
240C2×C22⋊D53—28no—
241C2×C22⋊D53—44no—
242C2×C22⋊D53—44no—
243C2×C22⋊D53—44no—
244C2×C22⋊D53—44no—
245C2×C22⋊D53—44no—
246C22×Dic53—21no—
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—21no—
272C22×Dic53—21no—
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—21no—
288C22×Dic53C22×C412yes—
289C22×Dic53C22×C412yes—
290C22×Dic53C22×C412yes—
291C22×Dic53C2×D412yes—
292C22×Dic53C2×D412yes—
293C22×Dic53#4112yes—
294C22×Dic53#4112yes—
295C2×Dic106—28no—
296C2×Dic106—28no—
297C2×Dic106—44no—
298C2×Dic106—44no—
299C2×Dic106—44no—
300C2×Dic106—44no—
301C2×Dic106—44no—
302C22⋊C4×C53—28no—
303C22⋊C4×C53C22⋊C4116yescomplemented
304C42×C53—44no—
305C42×C53—44no—
306C22⋊Dic53—28no—
307C22⋊Dic53—44no—
308C22⋊Dic53—44no—
309#11719921—28no—
310#11719921—28no—
311#11719921—44no—
312#11719921—44no—
313#11719921—44no—
314#11719921—44no—
315C4⋊Dic53—44no—
316C4×Dic53—28no—
317C4×Dic53—44no—
318C23×C53—22no—
319C23×C53—22no—
320C23×C53—22no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
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—41no—
337C23×C53—41no—
338C23×C53—41no—
339C23×C53—41no—
340C23×C53—41no—
341C23×C53—41no—
342C23×C53—41no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53C2×C22⋊C414yes—
353C23×C53C23×C411yescharacteristic
354C23×C53C22×D411yescharacteristic
355C23×C53C22×D411yescharacteristic
356C23×C53C22×D411yescharacteristic
357C23×C53C2×#4111yescharacteristic
358C23×C53C2×#4111yescharacteristic
359C23×C53C2×#4111yescharacteristic
360C23×C53C2×#4111yescharacteristic
361C23×C53C2×#4111yescharacteristic
362C23×C53C2×#4111yescharacteristic
363C23×C53C2×#4111yescharacteristic
364C23×C53H(5,𝔽2)11yescharacteristic
365C23×C53H(5,𝔽2)11yescharacteristic
366C23×C53H(5,𝔽2)11yescharacteristic
367C23×C532−1+411yescharacteristic
368C22×D53—22no—
369C22×D53—22no—
370C22×D53—22no—
371C22×D53—22no—
372C22×D53—22no—
373C22×D53—22no—
374C22×D53—22no—
375C22×D53—41no—
376C22×D53—41no—
377C22×D53—41no—
378C22×D53—41no—
379C22×D53—41no—
380C22×D53—41no—
381C22×D53—41no—
382C22×D53—41no—
383C22×D53—41no—
384C22×D53—41no—
385C22×D53—41no—
386C22×D53—41no—
387C22×D53—41no—
388C22×D53—41no—
389C22×D53—41no—
390C22×D53—41no—
391C22×D53—41no—
392C22×D53—41no—
393C22×D53—41no—
394C22×D53—41no—
395C22×D53—41no—
396C22×D53—41no—
397C22×D53—41no—
398C22×D53—41no—
399C22×D53—41no—
400C22×D53—41no—
401C22×D53—41no—
402C22×D53—41no—
403C2×C4×C53—22no—
404C2×C4×C53—22no—
405C2×C4×C53—22no—
406C2×C4×C53—22no—
407C2×C4×C53—22no—
408C2×C4×C53—22no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—22no—
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—416no—
431C2×C4×C53—41no—
432C2×C4×C53—41no—
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×C53C2×C22⋊C414yes—
444C2×C4×C53C2×C22⋊C414yes—
445C2×C4×C53#12414yescomplemented
446C22⋊D53—416no—
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—41no—
466C2×Dic53—41no—
467C2×Dic53—41no—
468C2×Dic53—41no—
469C2×Dic53—41no—
470C2×Dic53—41no—
471C2×Dic53—41no—
472C2×Dic53—41no—
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×Dic53C4×D414yes—
496Dic106—416no—
497#14098—531nomaximal, Sylow
498C22×C53—24no—
499C22×C53—24no—
500C22×C53—24no—
501C22×C53—42no—
502C22×C53—42no—
503C22×C53—42no—
504C22×C53—42no—
505C22×C53—42no—
506C22×C53—42no—
507C22×C53—42no—
508C22×C53—42no—
509C22×C53—42no—
510C22×C53—42no—
511C22×C53—42no—
512C22×C53—42no—
513C22×C53C22×C22⋊C411yescharacteristic
514C22×C53C2×C4×D411yescharacteristic
515C22×C53C4×#4111yescharacteristic
516C22×C53C4×#4111yescharacteristic
517C22×C53C4×#4111yescharacteristic
518C22×C53#51811yescharacteristic
519C22×C53#52011yescharacteristic
520C22×C53#52511yescharacteristic
521C22×C53#52511yescharacteristic
522C22×C53C2×#12411yescharacteristic
523C22×C53#52911yescharacteristic
524C22×C53#52911yescharacteristic
525C22×C53#53211yescharacteristic
526C22×C53#53211yescharacteristic
527C22×C53#53211yescharacteristic
528C22×C53#53811yescharacteristic
529C22×C53#53811yescharacteristic
530C22×C53#54211yescharacteristic
531C22×C53#54211yescharacteristic
532C22×C53D4211yescharacteristic
533C22×C53D4211yescharacteristic
534C22×C53#54611yescharacteristic
535C22×C53#54611yescharacteristic
536C22×C53#54611yescharacteristic
537C22×C53#54611yescharacteristic
538C22×C53#54611yescharacteristic
539C22×C53#54711yescharacteristic
540C22×C53#54711yescharacteristic
541C22×C53#54811yescharacteristic
542C22×C53#55111yescharacteristic
543C22×C53#55111yescharacteristic
544C22×C53#55511yescharacteristic
545C22×C53#55511yescharacteristic
546C22×C53#55611yescharacteristic
547C22×C53#55911yescharacteristic
548C2×D53—42no—
549C2×D53—42no—
550C2×D53—42no—
551C2×D53—42no—
552C2×D53—42no—
553C2×D53—42no—
554C2×D53—42no—
555C2×D53—81no—
556C2×D53—81no—
557C2×D53—81no—
558C2×D53—81no—
559C2×D53—81no—
560C2×D53—81no—
561C2×D53—81no—
562C2×D53—81no—
563C4×C53—24no—
564C4×C53—24no—
565C4×C53—24no—
566C4×C53—42no—
567C4×C53—42no—
568C4×C53—42no—
569Dic53—24no—
570Dic53—42no—
571Dic53—42no—
572Dic53—42no—
573Dic53—42no—
574Dic53—81no—
575Dic53—81no—
576C22×#124—531no—
577C2×#391—531no—
578C2×#388—531no—
579C2×#386—531no—
580C2×C4×C22⋊C4D5311yescharacteristic, complemented
581#1446—531no—
582#1440—531no—
583#1439—531no—
584#1438—531no—
585#1437—531no—
586#1437—531no—
587#1437—531no—
588#1434—531no—
589C22⋊#95—531no—
590C4×#95—531no—
591C2×C53—44no—
592C2×C53#229711yescharacteristic
593C2×C53C4×#12411yescharacteristic
594C2×C53#233711yescharacteristic
595C2×C53D4×C22⋊C411yescharacteristic
596C2×C53#233911yescharacteristic
597C2×C53#236711yescharacteristic
598C2×C53#237211yescharacteristic
599C2×C53#245911yescharacteristic
600C2×C53#246111yescharacteristic
601C2×C53#247211yescharacteristic
602C2×C53#247411yescharacteristic
603C2×C53#249111yescharacteristic
604C2×C53#252111yescharacteristic
605C2×C53#255511yescharacteristic
606C2×C53#255711yescharacteristic
607D53—82no—
608C23×Q8—531no—
609C23×D4—531no—
610C24×C4C2×D5311yescharacteristic
611C2×#124—538no—
612C2×#124—1064no—
613C2×#124—1064no—
614C22×C4⋊C4—531no—
615C22×C22⋊C4—531no—
616C22×C22⋊C4—531no—
617C22×C22⋊C4—531no—
618C22×C22⋊C4—531no—
619C22×C22⋊C4—531no—
620C22×C22⋊C4—531no—
621C22×C22⋊C4—531no—
622C22×C22⋊C4—531no—
623C22×C22⋊C4—531no—
624C22×C22⋊C4C2×D5311yescharacteristic
625C22×C22⋊C4C2×D5311yescharacteristic
626C22×C42—531no—
627C22×C42—531no—
628C22×C42C2×D5311yescharacteristic
629C22×C42C2×D5311yescharacteristic
630#391—1064no—
631#388—1064no—
632#386—1064no—
633C4×C22⋊C4—24no—
634C2×#95—531no—
635C2×#95—531no—
636C2×#95—531no—
637C2×#95—531no—
638C2×#95—531no—
639C2×#95—531no—
640C2×#95—531no—
641C2×#95—531no—
642C2×#95—531no—
643C2×#95—531no—
644C2×#95—531no—
645C2×#95—531no—
646C2×#95—531no—
647C2×#95—531no—
648C2×#95C2×D5311yescharacteristic
649C2×#95C2×D5311yescharacteristic
650C53#1409811yescharacteristic, complemented, Sylow
651C25—531no—
652C25C22×D5311yescharacteristic
653C22×Q8—534no—
654C22×Q8—1062no—
655C22×Q8—1062no—
656C22×Q8—1062no—
657C22×Q8—1062no—
658C22×Q8—2121no—
659C22×Q8—2121no—
660C22×D4—534no—
661C22×D4—1062no—
662C22×D4—1062no—
663C22×D4—1062no—
664C22×D4—1062no—
665C22×D4—2121no—
666C22×D4—2121no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4—531no—
675C23×C4—531no—
676C23×C4—531no—
677C23×C4—531no—
678C23×C4—531no—
679C23×C4—531no—
680C23×C4—531no—
681C23×C4C22×D5311yescharacteristic
682C23×C4C22×D5311yescharacteristic
683C23×C4C22×D5311yescharacteristic
684C23×C4C22×D5311yescharacteristic
685C23×C4C22×D5311yescharacteristic
686C23×C4C22×D5311yescharacteristic
687#124—10632no—
688C2×C4⋊C4—1062no—
689C2×C4⋊C4—1062no—
690C2×C4⋊C4—2121no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—534no—
695C2×C22⋊C4—534no—
696C2×C22⋊C4—534no—
697C2×C22⋊C4—1062no—
698C2×C22⋊C4—1062no—
699C2×C22⋊C4—1062no—
700C2×C22⋊C4—1062no—
701C2×C22⋊C4—1062no—
702C2×C22⋊C4—1062no—
703C2×C22⋊C4—1062no—
704C2×C22⋊C4—1062no—
705C2×C22⋊C4—1062no—
706C2×C22⋊C4—1062no—
707C2×C22⋊C4—1062no—
708C2×C22⋊C4—1062no—
709C2×C22⋊C4—1062no—
710C2×C22⋊C4—1062no—
711C2×C22⋊C4—1062no—
712C2×C22⋊C4—1062no—
713C2×C22⋊C4—1062no—
714C2×C22⋊C4—1062no—
715C2×C22⋊C4—2121no—
716C2×C22⋊C4—2121no—
717C2×C22⋊C4—2121no—
718C2×C22⋊C4—2121no—
719C2×C22⋊C4—2121no—
720C2×C22⋊C4—2121no—
721C2×C22⋊C4C4×D5314yes—
722C2×C22⋊C4D21214yes—
723C2×C22⋊C4C22⋊D5314yes—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—41no—
729C2×C42—41no—
730C2×C42—534no—
731C2×C42—1062no—
732C2×C42—1062no—
733C2×C42—1062no—
734C2×C42—1062no—
735C2×C42—2121no—
736#95—22no—
737#95—22no—
738#95—534no—
739#95—1062no—
740#95—1062no—
741#95—1062no—
742#95—1062no—
743#95—1062no—
744#95—1062no—
745#95—1062no—
746#95—1062no—
747#95—1062no—
748#95—1062no—
749#95—1062no—
750#95—2121no—
751#95—2121no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—532no—
765C24—1061no—
766C24—1061no—
767C24—1061no—
768C24—1061no—
769C24—1061no—
770C24—1061no—
771C24—1061no—
772C24—1061no—
773C24—1061no—
774C24—1061no—
775C24—1061no—
776C24—1061no—
777C24—1061no—
778C24—1061no—
779C24C2×C4×D5312yes—
780C24C2×D21212yes—
781C24C2×C22⋊D5312yes—
782C24C23×D5311yescharacteristic
783C2×Q8—1068no—
784C2×Q8—1068no—
785C2×Q8—2124no—
786C2×Q8—2124no—
787C2×Q8—2124no—
788C2×Q8—2124no—
789C2×Q8—2124no—
790C2×D4—1068no—
791C2×D4—1068no—
792C2×D4—2124no—
793C2×D4—2124no—
794C2×D4—2124no—
795C2×D4—2124no—
796C2×D4—2124no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—28no—
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—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—532no—
835C22×C4—532no—
836C22×C4—532no—
837C22×C4—532no—
838C22×C4—532no—
839C22×C4—532no—
840C22×C4—532no—
841C22×C4—1061no—
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—1061no—
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×C4C2×C4×D5312yes—
884C22×C4C2×C4×D5312yes—
885C22×C4C2×D21212yes—
886C22×C4C2×D21212yes—
887C22×C4#1171994512yes—
888C22×C4#1171994512yes—
889C22×C4#1171994512yes—
890C22×C4#1171994512yes—
891C22×C4D4×D5312yes—
892C22×C4#1171994712yes—
893C22×C4C2×C22⋊D5312yes—
894C22×C4C2×C22⋊D5312yes—
895C4⋊C4—2124no—
896C22⋊C4—28no—
897C22⋊C4—1068no—
898C22⋊C4—1068no—
899C22⋊C4—1068no—
900C22⋊C4—2124no—
901C22⋊C4—2124no—
902C22⋊C4—2124no—
903C22⋊C4—2124no—
904C22⋊C4—2124no—
905C22⋊C4—2124no—
906C22⋊C4#11719921116yescomplemented
907C42—44no—
908C42—44no—
909C42—1068no—
910C42—2124no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—1062no—
946C23—1062no—
947C23—1062no—
948C23—1062no—
949C23—1062no—
950C23—1062no—
951C23—1062no—
952C23—2121no—
953C23—2121no—
954C23—2121no—
955C23—2121no—
956C23—2121no—
957C23—2121no—
958C23—2121no—
959C23—2121no—
960C23—2121no—
961C23—2121no—
962C23—2121no—
963C23—2121no—
964C23—2121no—
965C23—2121no—
966C23—2121no—
967C23—2121no—
968C23—2121no—
969C23—2121no—
970C23—2121no—
971C23—2121no—
972C23—2121no—
973C23—2121no—
974C23—2121no—
975C23—2121no—
976C23—2121no—
977C23—2121no—
978C23—2121no—
979C23—2121no—
980C23C2×#1171992114yes—
981C23C22×C4×D5311yescharacteristic
982C23C2×D4×D5311yescharacteristic
983C23C22×C22⋊D5311yescharacteristic
984C23C22×D21211yescharacteristic
985C23#41×D5311yescharacteristic
986C23#41×D5311yescharacteristic
987C23C2×#1171994711yescharacteristic
988C23C2×#1171994511yescharacteristic
989C23C2×#1171994511yescharacteristic
990C23C2×#1171994511yescharacteristic
991C23C2×#1171994511yescharacteristic
992C23#1313326211yescharacteristic
993C23#1313326211yescharacteristic
994C23#1313326311yescharacteristic
995C23#1313326411yescharacteristic
996Q8—21216no—
997D4—21216no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
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—416no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—534no—
1039C2×C4—1062no—
1040C2×C4—1062no—
1041C2×C4—1062no—
1042C2×C4—1062no—
1043C2×C4—1062no—
1044C2×C4—1062no—
1045C2×C4—1062no—
1046C2×C4—1062no—
1047C2×C4—1062no—
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—2121no—
1058C2×C4—2121no—
1059C2×C4—2121no—
1060C2×C4—2121no—
1061C2×C4—2121no—
1062C2×C4—2121no—
1063C2×C4—2121no—
1064C2×C4—2121no—
1065C2×C4—2121no—
1066C2×C4—2121no—
1067C2×C4—2121no—
1068C2×C4—2121no—
1069C2×C4—2121no—
1070C2×C4—2121no—
1071C2×C4—2121no—
1072C2×C4—2121no—
1073C2×C4—2121no—
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×C4C2×#1171992114yes—
1088C2×C4C2×#1171992114yes—
1089C2×C4#1313320314yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—4241no—
1106C22—4241no—
1107C22—4241no—
1108C22—4241no—
1109C22—4241no—
1110C22—4241no—
1111C22—4241no—
1112C22—4241no—
1113C22—2122no—
1114C22—2122no—
1115C22—2122no—
1116C22—2122no—
1117C22—2122no—
1118C22—2122no—
1119C22—2122no—
1120C22C22×#1171992111yescharacteristic
1121C22C4×D4×D5311yescharacteristic
1122C22C4×#1171994711yescharacteristic
1123C22C4×#1171994511yescharacteristic
1124C22C4×#1171994511yescharacteristic
1125C22#1681109511yescharacteristic
1126C22#1681110211yescharacteristic
1127C22#1681113411yescharacteristic
1128C22#1681113411yescharacteristic
1129C22C2×#1313320311yescharacteristic
1130C22#1681115111yescharacteristic
1131C22#1681115311yescharacteristic
1132C22#1681117011yescharacteristic
1133C22#1681117311yescharacteristic
1134C22#1681117311yescharacteristic
1135C22#1681120611yescharacteristic
1136C22#1681121111yescharacteristic
1137C22#1681123811yescharacteristic
1138C22#1681124411yescharacteristic
1139C22D4×C22⋊D5311yescharacteristic
1140C22D4×D21211yescharacteristic
1141C22#1681126111yescharacteristic
1142C22#1681126311yescharacteristic
1143C22#1681126711yescharacteristic
1144C22#1681126811yescharacteristic
1145C22#1681126811yescharacteristic
1146C22#1681127211yescharacteristic
1147C22#1681127711yescharacteristic
1148C22#1681128211yescharacteristic
1149C22#1681129911yescharacteristic
1150C22#1681130211yescharacteristic
1151C22#1681133611yescharacteristic
1152C22#1681133811yescharacteristic
1153C22#1681134111yescharacteristic
1154C22#1681135611yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—1064no—
1162C4—4241no—
1163C4—4241no—
1164C4—2122no—
1165C4—2122no—
1166C4—2122no—
1167C4—2122no—
1168C2—44no—
1169C2—4242no—
1170C2#2027720511yescharacteristic
1171C2C4×#1313320311yescharacteristic
1172C2#2027752311yescharacteristic
1173C2D4×#1171992111yescharacteristic
1174C2#2027754011yescharacteristic
1175C2#2027778711yescharacteristic
1176C2#2027782311yescharacteristic
1177C2#2027864611yescharacteristic
1178C2#2027867611yescharacteristic
1179C2#2027883511yescharacteristic
1180C2#2027886511yescharacteristic
1181C2#2027907811yescharacteristic
1182C2#2027941811yescharacteristic
1183C2#2027978411yescharacteristic
1184C2#2027980811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#14098
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16810529C2semidirect
3. C2×#16810516C2semidirect
5. #20272985C2semidirect
6. #20272962C2semidirect
7. #20272961C2semidirect
9. #20272953C2semidirect
10. #20272953C2semidirect
11. #20272951C2semidirect
12. #20272939C2semidirect
13. #20272938C2semidirect
14. C4×#13133124C2semidirect
15. C2×C4×C22⋊C4×C53C2semidirect
20. C2×#13133203C4semidirect
65. C22×Dic106C2×C4semidirect
109. C2×#11719921C2×C4semidirect
110. C2×#11719921C2×C4semidirect
116. C2×C4×Dic53C2×C4semidirect
303. C22⋊C4×C53C22⋊C4semidirect
445. C2×C4×C53#124semidirect
580. C2×C4×C22⋊C4D53semidirect
650. C53#14098semidirect
906. C22⋊C4#11719921semidirect
1089. C2×C4#13133203semidirect

Maximal subgroups

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

subgroupindex
C22×#131332032
C2×#168105292
C2×#168105162
C2×#168105022
#202729852
#202729622
#202729612
#202729542
#202729532
#202729512
#202729392
#202729382
C4×#131331242
C2×C4×C22⋊C4×C532
#1409853