Finite Group Databasebeta

← #27308528

Subgroups — #27308528

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133200C211yesmaximal, characteristic
2C2×#16810523C211yesmaximal, characteristic
3C2×#16810507C211yesmaximal, characteristic, complemented
4C2×C4×#11719919C211yesmaximal, characteristic, complemented
5#20272966C211yesmaximal, characteristic, complemented
6#20272959C211yesmaximal, characteristic, complemented
7#20272958C211yesmaximal, characteristic, complemented
8#20272954C211yesmaximal, characteristic
9#20272953C211yesmaximal, characteristic, complemented
10#20272953C211yesmaximal, characteristic, complemented
11#20272952C211yesmaximal, characteristic, complemented
12#20272951C211yesmaximal, characteristic, complemented
13#20272946C211yesmaximal, characteristic, complemented
14#20272938C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C2×#13133200—24no—
18C2×#13133200—24no—
19C2×#13133200C418yescomplemented
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35#16810523—24no—
36#16810507—24no—
37C4×#11719919—24no—
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×C22⋊D53—22no—
60C22×C22⋊D53—22no—
61C22×C22⋊D53—22no—
62C22×C22⋊D53—22no—
63C22×C22⋊D53—41no—
64C22×C22⋊D53—41no—
65C22×C22⋊D53C2×C414yes—
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73#13133200—232no—
74C2×#11719919—22no—
75C2×#11719919—22no—
76C2×#11719919—22no—
77C2×#11719919—22no—
78C2×#11719919—22no—
79C2×#11719919—22no—
80C2×#11719919—22no—
81C2×#11719919—41no—
82C2×#11719919C2×C414yes—
83C2×#11719919C2×C414yes—
84C2×#11719919D414yes—
85C2×#11719919D414yes—
86C2×C22⋊Dic53—22no—
87C2×C22⋊Dic53—22no—
88C2×C22⋊Dic53—22no—
89C2×C22⋊Dic53—22no—
90C2×C22⋊Dic53—22no—
91C2×C22⋊Dic53—22no—
92C2×C22⋊Dic53—41no—
93C2×C22⋊Dic53—41no—
94C2×C22⋊Dic53C2×C414yes—
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—22no—
106C2×#11719921—22no—
107C2×#11719921—41no—
108C2×#11719921—41no—
109C2×#11719921—41no—
110C2×#11719921—41no—
111C2×#11719921C2×C414yes—
112C2×#11719921C2×C414yes—
113C2×C4×Dic53—22no—
114C2×C4×Dic53—22no—
115C2×C4×Dic53—22no—
116C2×C4×Dic53—22no—
117C2×C4×Dic53—22no—
118C2×C4×Dic53—41no—
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—41no—
128#13133124—41no—
129#13133124—41no—
130#13133124—41no—
131C25×C53C2311yescharacteristic
132C23×C4×C53—22no—
133C23×C4×C53—22no—
134C23×C4×C53—22no—
135C23×C4×C53—22no—
136C23×C4×C53—41no—
137C23×C4×C53—41no—
138C23×C4×C53C2×C414yes—
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×C53—22no—
149C2×C22⋊C4×C53—22no—
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×C53#4112yes—
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—28no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
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—28no—
224C22×C4×C53—44no—
225C22×C4×C53—44no—
226C22×C4×C53—44no—
227C22×C4×C53—44no—
228C22×C4×C53—44no—
229C22×C4×C53C22×C412yes—
230C22×C4×C53C22×C412yes—
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2×D412yes—
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×Dic53C22×C412yes—
287C22×Dic53C22×C412yes—
288C22×Dic53C22×C412yes—
289C22×Dic53C2×D412yes—
290C22×Dic53C2×D412yes—
291C22×Dic53C2×D412yes—
292C22×Dic53C2×D412yes—
293C22×Dic53#4112yes—
294C22×Dic53#4112yes—
295C22⋊C4×C53—28no—
296C22⋊C4×C53—28no—
297C42×C53—44no—
298C42×C53—44no—
299C22⋊Dic53—28no—
300C22⋊Dic53—44no—
301C22⋊Dic53—44no—
302#11719921—28no—
303#11719921—28no—
304#11719921—44no—
305#11719921—44no—
306#11719921—44no—
307#11719921—44no—
308#11719919—28no—
309#11719919—28no—
310#11719919—44no—
311#11719919C22⋊C4116yescomplemented
312C4×Dic53—28no—
313C4×Dic53—44no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53—22no—
317C23×C53—22no—
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—41no—
333C23×C53—41no—
334C23×C53—41no—
335C23×C53—41no—
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×C53C4×D414yes—
349C23×C53C23×C411yescharacteristic
350C23×C53C22×D411yescharacteristic
351C23×C53C22×D411yescharacteristic
352C23×C53C22×D411yescharacteristic
353C23×C53C2×#4111yescharacteristic
354C23×C53C2×#4111yescharacteristic
355C23×C53C2×#4111yescharacteristic
356C23×C53C2×#4111yescharacteristic
357C23×C53C2×#4111yescharacteristic
358C23×C53C2×#4111yescharacteristic
359C23×C53C2×#4111yescharacteristic
360C23×C53H(5,𝔽2)11yescharacteristic
361C23×C53H(5,𝔽2)11yescharacteristic
362C23×C53H(5,𝔽2)11yescharacteristic
363C23×C532−1+411yescharacteristic
364C22×D53—22no—
365C22×D53—22no—
366C22×D53—22no—
367C22×D53—22no—
368C22×D53—22no—
369C22×D53—22no—
370C22×D53—22no—
371C22×D53—41no—
372C22×D53—41no—
373C22×D53—41no—
374C22×D53—41no—
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—
399C2×C4×C53—22no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
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—416no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—41no—
427C2×C4×C53—41no—
428C2×C4×C53—41no—
429C2×C4×C53—41no—
430C2×C4×C53—41no—
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×C53C2×C22⋊C414yes—
441C2×C4×C53#12314yescomplemented
442C22⋊D53—416no—
443C2×Dic53—22no—
444C2×Dic53—22no—
445C2×Dic53—22no—
446C2×Dic53—22no—
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—41no—
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×Dic53C2×C22⋊C414yes—
491C2×Dic53C2×C22⋊C414yes—
492#14095—531nomaximal, Sylow
493C22×C53—24no—
494C22×C53—24no—
495C22×C53—24no—
496C22×C53—42no—
497C22×C53—42no—
498C22×C53—42no—
499C22×C53—42no—
500C22×C53—42no—
501C22×C53—42no—
502C22×C53—42no—
503C22×C53—42no—
504C22×C53—42no—
505C22×C53—42no—
506C22×C53—42no—
507C22×C53—42no—
508C22×C53C22×C22⋊C411yescharacteristic
509C22×C53C2×C4×D411yescharacteristic
510C22×C53C4×#4111yescharacteristic
511C22×C53C4×#4111yescharacteristic
512C22×C53C4×#4111yescharacteristic
513C22×C53#51811yescharacteristic
514C22×C53#52011yescharacteristic
515C22×C53C2×#12311yescharacteristic
516C22×C53#52511yescharacteristic
517C22×C53#52511yescharacteristic
518C22×C53#52511yescharacteristic
519C22×C53#52911yescharacteristic
520C22×C53#52911yescharacteristic
521C22×C53#53211yescharacteristic
522C22×C53#53211yescharacteristic
523C22×C53#53811yescharacteristic
524C22×C53#53911yescharacteristic
525C22×C53#54011yescharacteristic
526C22×C53#54211yescharacteristic
527C22×C53D4211yescharacteristic
528C22×C53D4211yescharacteristic
529C22×C53#54611yescharacteristic
530C22×C53#54611yescharacteristic
531C22×C53#54611yescharacteristic
532C22×C53#54711yescharacteristic
533C22×C53#54811yescharacteristic
534C22×C53#54811yescharacteristic
535C22×C53#55011yescharacteristic
536C22×C53#55011yescharacteristic
537C22×C53#55111yescharacteristic
538C22×C53#55111yescharacteristic
539C22×C53#55211yescharacteristic
540C22×C53#55311yescharacteristic
541C22×C53#55311yescharacteristic
542C22×C53#55911yescharacteristic
543C2×D53—42no—
544C2×D53—42no—
545C2×D53—42no—
546C2×D53—42no—
547C2×D53—42no—
548C2×D53—42no—
549C2×D53—42no—
550C2×D53—81no—
551C2×D53—81no—
552C2×D53—81no—
553C2×D53—81no—
554C2×D53—81no—
555C2×D53—81no—
556C2×D53—81no—
557C2×D53—81no—
558C4×C53—24no—
559C4×C53—24no—
560C4×C53—42no—
561C4×C53—42no—
562C4×C53—42no—
563C4×C53—42no—
564Dic53—24no—
565Dic53—24no—
566Dic53—42no—
567Dic53—42no—
568Dic53—42no—
569Dic53—81no—
570Dic53—81no—
571C22×#123—531no—
572C2×#390—531no—
573C2×#387—531no—
574C2×C4×C4⋊C4—531no—
575C2×C4×C22⋊C4D5311yescharacteristic, complemented
576#1441—531no—
577#1439—531no—
578#1439—531no—
579#1438—531no—
580#1437—531no—
581#1437—531no—
582#1437—531no—
583#1437—531no—
584#1436—531no—
585C22⋊#95—531no—
586C2×C53—44no—
587C2×C53#229711yescharacteristic
588C2×C53C4×#12311yescharacteristic
589C2×C53#233511yescharacteristic
590C2×C53D4×C22⋊C411yescharacteristic
591C2×C53#234111yescharacteristic
592C2×C53#235911yescharacteristic
593C2×C53#237411yescharacteristic
594C2×C53#244311yescharacteristic
595C2×C53#244511yescharacteristic
596C2×C53#245611yescharacteristic
597C2×C53#245811yescharacteristic
598C2×C53#246111yescharacteristic
599C2×C53#247111yescharacteristic
600C2×C53#255411yescharacteristic
601C2×C53#255811yescharacteristic
602D53—82no—
603C23×D4—531no—
604C24×C4C2×D5311yescharacteristic
605C2×#123—538no—
606C2×#123—1064no—
607C2×#123—1064no—
608C22×C4⋊C4—531no—
609C22×C4⋊C4—531no—
610C22×C4⋊C4—531no—
611C22×C4⋊C4—531no—
612C22×C22⋊C4—531no—
613C22×C22⋊C4—531no—
614C22×C22⋊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⋊C4C2×D5311yescharacteristic
622C22×C22⋊C4C2×D5311yescharacteristic
623C22×C42—531no—
624C22×C42—531no—
625C22×C42C2×D5311yescharacteristic
626C22×C42C2×D5311yescharacteristic
627#390—1064no—
628#387—1064no—
629C4×C4⋊C4—1064no—
630C4×C22⋊C4—24no—
631C2×#95—531no—
632C2×#95—531no—
633C2×#95—531no—
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×#95C2×D5311yescharacteristic
644C2×#95C2×D5311yescharacteristic
645C53#1409511yescharacteristic, complemented, Sylow
646C25—531no—
647C25C22×D5311yescharacteristic
648C22×D4—534no—
649C22×D4—1062no—
650C22×D4—1062no—
651C22×D4—1062no—
652C22×D4—1062no—
653C22×D4—2121no—
654C22×D4—2121no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4—531no—
662C23×C4—531no—
663C23×C4—531no—
664C23×C4—531no—
665C23×C4—531no—
666C23×C4—531no—
667C23×C4—531no—
668C23×C4C4×D5314yes—
669C23×C4C22×D5311yescharacteristic
670C23×C4C22×D5311yescharacteristic
671C23×C4C22×D5311yescharacteristic
672C23×C4C22×D5311yescharacteristic
673C23×C4C22×D5311yescharacteristic
674C23×C4C22×D5311yescharacteristic
675#123—10632no—
676C2×C4⋊C4—534no—
677C2×C4⋊C4—534no—
678C2×C4⋊C4—534no—
679C2×C4⋊C4—534no—
680C2×C4⋊C4—1062no—
681C2×C4⋊C4—1062no—
682C2×C4⋊C4—1062no—
683C2×C4⋊C4—1062no—
684C2×C4⋊C4—1062no—
685C2×C4⋊C4—1062no—
686C2×C4⋊C4—1062no—
687C2×C4⋊C4—2121no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—534no—
694C2×C22⋊C4—534no—
695C2×C22⋊C4—534no—
696C2×C22⋊C4—1062no—
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—2121no—
715C2×C22⋊C4—2121no—
716C2×C22⋊C4—2121no—
717C2×C22⋊C4—2121no—
718C2×C22⋊C4—2121no—
719C2×C22⋊C4—2121no—
720C2×C22⋊C4C22⋊D5314yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—41no—
726C2×C42—41no—
727C2×C42—1062no—
728C2×C42—1062no—
729C2×C42—1062no—
730C2×C42—1062no—
731C2×C42—1062no—
732C2×C42—2121no—
733#95—22no—
734#95—22no—
735#95—1062no—
736#95—1062no—
737#95—1062no—
738#95—1062no—
739#95—1062no—
740#95—1062no—
741#95—1062no—
742#95—1062no—
743#95—2121no—
744#95—2121no—
745#95—2121no—
746#95—2121no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—532no—
760C24—1061no—
761C24—1061no—
762C24—1061no—
763C24—1061no—
764C24—1061no—
765C24—1061no—
766C24—1061no—
767C24—1061no—
768C24—1061no—
769C24—1061no—
770C24—1061no—
771C24—1061no—
772C24—1061no—
773C24—1061no—
774C24C2×C4×D5312yes—
775C24#1171994512yes—
776C24C2×C22⋊D5312yes—
777C24C23×D5311yescharacteristic
778C2×D4—1068no—
779C2×D4—1068no—
780C2×D4—2124no—
781C2×D4—2124no—
782C2×D4—2124no—
783C2×D4—2124no—
784C2×D4—2124no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—28no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
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—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—28no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—532no—
825C22×C4—532no—
826C22×C4—532no—
827C22×C4—532no—
828C22×C4—532no—
829C22×C4—532no—
830C22×C4—532no—
831C22×C4—532no—
832C22×C4—532no—
833C22×C4—1061no—
834C22×C4—1061no—
835C22×C4—1061no—
836C22×C4—1061no—
837C22×C4—1061no—
838C22×C4—1061no—
839C22×C4—1061no—
840C22×C4—1061no—
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×C4C2×C4×D5312yes—
874C22×C4C2×C4×D5312yes—
875C22×C4#1171994512yes—
876C22×C4#1171994512yes—
877C22×C4#1171994512yes—
878C22×C4#1171994512yes—
879C22×C4D4×D5312yes—
880C22×C4D4×D5312yes—
881C22×C4C2×C22⋊D5312yes—
882C22×C4C2×C22⋊D5312yes—
883C4⋊C4—5316no—
884C4⋊C4—1068no—
885C4⋊C4—1068no—
886C4⋊C4—2124no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—1068no—
890C22⋊C4—1068no—
891C22⋊C4—1068no—
892C22⋊C4—2124no—
893C22⋊C4—2124no—
894C22⋊C4—2124no—
895C22⋊C4—2124no—
896C22⋊C4—2124no—
897C22⋊C4—2124no—
898C42—44no—
899C42—44no—
900C42—1068no—
901C42—2124no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—1062no—
937C23—1062no—
938C23—1062no—
939C23—1062no—
940C23—1062no—
941C23—1062no—
942C23—1062no—
943C23—2121no—
944C23—2121no—
945C23—2121no—
946C23—2121no—
947C23—2121no—
948C23—2121no—
949C23—2121no—
950C23—2121no—
951C23—2121no—
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—
971C23C4×C22⋊D5314yes—
972C23C22×C4×D5311yescharacteristic
973C23C2×D4×D5311yescharacteristic
974C23C2×D4×D5311yescharacteristic
975C23C22×C22⋊D5311yescharacteristic
976C23#41×D5311yescharacteristic
977C23#41×D5311yescharacteristic
978C23C2×#1171994511yescharacteristic
979C23C2×#1171994511yescharacteristic
980C23C2×#1171994511yescharacteristic
981C23C2×#1171994511yescharacteristic
982C23C2×#1171994511yescharacteristic
983C23#1313326211yescharacteristic
984C23#1313326211yescharacteristic
985C23#1313326311yescharacteristic
986C23#1313326411yescharacteristic
987D4—21216no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
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—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—534no—
1030C2×C4—534no—
1031C2×C4—1062no—
1032C2×C4—1062no—
1033C2×C4—1062no—
1034C2×C4—1062no—
1035C2×C4—1062no—
1036C2×C4—1062no—
1037C2×C4—1062no—
1038C2×C4—1062no—
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—2121no—
1053C2×C4—2121no—
1054C2×C4—2121no—
1055C2×C4—2121no—
1056C2×C4—2121no—
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×C4C22⋊C4×D5314yes—
1079C2×C4#1313320014yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—4241no—
1096C22—4241no—
1097C22—4241no—
1098C22—4241no—
1099C22—4241no—
1100C22—4241no—
1101C22—4241no—
1102C22—4241no—
1103C22—2122no—
1104C22—2122no—
1105C22—2122no—
1106C22—2122no—
1107C22—2122no—
1108C22—2122no—
1109C22—2122no—
1110C22C2×C22⋊C4×D5311yescharacteristic
1111C22C2×C4×C22⋊D5311yescharacteristic
1112C22#1681109111yescharacteristic
1113C22C4×#1171994511yescharacteristic
1114C22C4×#1171994511yescharacteristic
1115C22#1681109611yescharacteristic
1116C22#1681110311yescharacteristic
1117C22C2×#1313320011yescharacteristic
1118C22#1681113211yescharacteristic
1119C22#1681113211yescharacteristic
1120C22#1681113411yescharacteristic
1121C22#1681115711yescharacteristic
1122C22#1681115711yescharacteristic
1123C22#1681117011yescharacteristic
1124C22#1681117011yescharacteristic
1125C22#1681120611yescharacteristic
1126C22#1681121511yescharacteristic
1127C22#1681122411yescharacteristic
1128C22#1681123811yescharacteristic
1129C22D4×C22⋊D5311yescharacteristic
1130C22D4×C22⋊D5311yescharacteristic
1131C22#1681126111yescharacteristic
1132C22#1681126311yescharacteristic
1133C22#1681126311yescharacteristic
1134C22#1681127211yescharacteristic
1135C22#1681128211yescharacteristic
1136C22#1681128211yescharacteristic
1137C22#1681129411yescharacteristic
1138C22#1681129411yescharacteristic
1139C22#1681129711yescharacteristic
1140C22#1681130211yescharacteristic
1141C22#1681130611yescharacteristic
1142C22#1681132211yescharacteristic
1143C22#1681132311yescharacteristic
1144C22#1681135611yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—1064no—
1152C4—1064no—
1153C4—4241no—
1154C4—4241no—
1155C4—2122no—
1156C4—2122no—
1157C4—2122no—
1158C2—44no—
1159C2—4242no—
1160C2#2027720111yescharacteristic
1161C2C4×#1313320011yescharacteristic
1162C2#2027750511yescharacteristic
1163C2C22⋊C4×C22⋊D5311yescharacteristic
1164C2#2027755511yescharacteristic
1165C2#2027770711yescharacteristic
1166C2#2027784611yescharacteristic
1167C2#2027844411yescharacteristic
1168C2#2027847411yescharacteristic
1169C2#2027860711yescharacteristic
1170C2#2027863711yescharacteristic
1171C2#2027867611yescharacteristic
1172C2#2027882611yescharacteristic
1173C2#2027977511yescharacteristic
1174C2#2027982911yescharacteristic
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#14095
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16810507C2semidirect
4. C2×C4×#11719919C2semidirect
5. #20272966C2semidirect
6. #20272959C2semidirect
7. #20272958C2semidirect
9. #20272953C2semidirect
10. #20272953C2semidirect
11. #20272952C2semidirect
12. #20272951C2semidirect
13. #20272946C2semidirect
14. #20272938C2semidirect
15. C2×C4×C22⋊C4×C53C2semidirect
19. C2×#13133200C4semidirect
311. #11719919C22⋊C4semidirect
441. C2×C4×C53#123semidirect
575. C2×C4×C22⋊C4D53semidirect
645. C53#14095semidirect
1079. C2×C4#13133200semidirect

Maximal subgroups

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

subgroupindex
C22×#131332002
C2×#168105232
C2×#168105072
C2×C4×#117199192
#202729662
#202729592
#202729582
#202729542
#202729532
#202729522
#202729512
#202729462
#202729382
C2×C4×C22⋊C4×C532
#1409553