Finite Group Databasebeta

← #27307548

Subgroups — #27307548

Order 13568.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic53C211yesmaximal, characteristic, complemented
2C2×#16810503C211yesmaximal, characteristic, complemented
3C2×#16810503C211yesmaximal, characteristic, complemented
4C2×#16810503C211yesmaximal, characteristic, complemented
5C2×#16810503C211yesmaximal, characteristic, complemented
6C22×#13133124C211yesmaximal, characteristic, complemented
7#20272968C211yesmaximal, characteristic, complemented
8#20272964C211yesmaximal, characteristic, complemented
9#20272960C211yesmaximal, characteristic, complemented
10#20272956C211yesmaximal, characteristic, complemented
11#20272952C211yesmaximal, characteristic, complemented
12#20272947C211yesmaximal, characteristic, complemented
13#20272938C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic, complemented
15C22×#121×C53C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C2×D4×Dic53—24no—
20C2×D4×Dic53—24no—
21C2×D4×Dic53—24no—
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810503—24no—
34#16810503—24no—
35#16810503—24no—
36#16810503—24no—
37C2×#13133124—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
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C23×D4×C53C2211yescharacteristic
53C23×D4×C53C2211yescharacteristic
54C23×D4×C53C2211yescharacteristic
55C24×C4×C53C2211yescharacteristic
56C2×#121×C53—24no—
57C2×#121×C53—24no—
58C2×#121×C53C418yescomplemented
59C22×C4⋊C4×C53C2211yescharacteristic
60C22×C22⋊C4×C53C2211yescharacteristic
61C22×C22⋊C4×C53C2211yescharacteristic
62C23×Dic53—22no—
63C23×Dic53—22no—
64C23×Dic53—22no—
65C23×Dic53—22no—
66C23×Dic53—22no—
67C23×Dic53—22no—
68C23×Dic53—22no—
69C23×Dic53—22no—
70C23×Dic53—22no—
71C23×Dic53—22no—
72C23×Dic53—22no—
73C23×Dic53—22no—
74C23×Dic53—22no—
75C23×Dic53—22no—
76C23×Dic53—41no—
77C23×Dic53—41no—
78C23×Dic53—41no—
79C23×Dic53—41no—
80C23×Dic53—41no—
81C23×Dic53—41no—
82C23×Dic53D414yescomplemented
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C23×Dic53C2311yescharacteristic
86C23×Dic53C2311yescharacteristic
87C23×Dic53C2311yescharacteristic
88C23×Dic53C2311yescharacteristic
89C23×Dic53C2311yescharacteristic
90C23×Dic53C2311yescharacteristic
91D4×Dic53—232no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53—22no—
94C2×C4⋊Dic53—22no—
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—22no—
109C2×C22⋊Dic53—22no—
110C2×C22⋊Dic53—22no—
111C2×C22⋊Dic53—22no—
112C2×C22⋊Dic53—22no—
113C2×C22⋊Dic53—22no—
114C2×C22⋊Dic53—22no—
115C2×C22⋊Dic53—41no—
116C2×C22⋊Dic53—41no—
117C2×C22⋊Dic53—41no—
118C2×C22⋊Dic53—41no—
119C2×C22⋊Dic53—41no—
120C2×C22⋊Dic53—41no—
121C2×C22⋊Dic53D414yescomplemented
122C2×C4×Dic53—22no—
123C2×C4×Dic53—22no—
124C2×C4×Dic53—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—22no—
134#13133124—22no—
135#13133124—22no—
136#13133124—41no—
137#13133124—41no—
138#13133124D414yescomplemented
139C25×C53C2311yescharacteristic
140C25×C53C2311yescharacteristic
141C25×C53C2311yescharacteristic
142C22×D4×C53—22no—
143C22×D4×C53—22no—
144C22×D4×C53—22no—
145C22×D4×C53—22no—
146C22×D4×C53—22no—
147C22×D4×C53—22no—
148C22×D4×C53—22no—
149C22×D4×C53—22no—
150C22×D4×C53—22no—
151C22×D4×C53—22no—
152C22×D4×C53—22no—
153C22×D4×C53—22no—
154C22×D4×C53—22no—
155C22×D4×C53—22no—
156C22×D4×C53—41no—
157C22×D4×C53—41no—
158C22×D4×C53C2×C414yes—
159C22×D4×C53C2×C414yescomplemented
160C22×D4×C53C2×C414yescomplemented
161C22×D4×C53D414yes—
162C22×D4×C53D414yes—
163C23×C4×C53—22no—
164C23×C4×C53—22no—
165C23×C4×C53—22no—
166C23×C4×C53—22no—
167C23×C4×C53—41no—
168C23×C4×C53—41no—
169C23×C4×C53C2×C414yescomplemented
170C23×C4×C53C2311yescharacteristic
171C23×C4×C53C2311yescharacteristic
172C23×C4×C53C2311yescharacteristic
173C23×C4×C53C2311yescharacteristic
174#121×C53—232no—
175C2×C4⋊C4×C53—22no—
176C2×C4⋊C4×C53—22no—
177C2×C4⋊C4×C53C2×C414yescomplemented
178C2×C22⋊C4×C53—22no—
179C2×C22⋊C4×C53—22no—
180C2×C22⋊C4×C53—22no—
181C2×C22⋊C4×C53—22no—
182C2×C22⋊C4×C53C2×C414yescomplemented
183C2×C22⋊C4×C53C2×C414yescomplemented
184C24×C53—21no—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53—21no—
189C24×C53—21no—
190C24×C53—21no—
191C24×C53—21no—
192C24×C53—21no—
193C24×C53—21no—
194C24×C53—21no—
195C24×C53—21no—
196C24×C53—21no—
197C24×C53—21no—
198C24×C53—21no—
199C24×C53—21no—
200C24×C53—21no—
201C24×C53—21no—
202C24×C53—21no—
203C24×C53—21no—
204C24×C53—21no—
205C24×C53—21no—
206C24×C53—21no—
207C24×C53—21no—
208C24×C53—21no—
209C24×C53—21no—
210C24×C53—21no—
211C24×C53—21no—
212C24×C53—21no—
213C24×C53—21no—
214C24×C53—21no—
215C24×C53—21no—
216C24×C53—21no—
217C24×C53—21no—
218C24×C53C22×C412yes—
219C24×C53C22×C412yes—
220C24×C53C22×C412yes—
221C24×C53C2×D412yes—
222C24×C53C2×D412yes—
223C24×C53C2×D412yes—
224C24×C53C2×D412yes—
225C24×C53C2×D412yes—
226C24×C53C2×D412yes—
227C24×C53#4112yes—
228C24×C53#4112yes—
229C24×C53C2411yescharacteristic
230C2×D4×C53—28no—
231C2×D4×C53—28no—
232C2×D4×C53—28no—
233C2×D4×C53—28no—
234C2×D4×C53—28no—
235C2×D4×C53—28no—
236C2×D4×C53—28no—
237C2×D4×C53—28no—
238C2×D4×C53—28no—
239C2×D4×C53—28no—
240C2×D4×C53—28no—
241C2×D4×C53—44no—
242C2×D4×C53—44no—
243C2×D4×C53—44no—
244C2×D4×C53—44no—
245C2×D4×C53—44no—
246C2×D4×C53—44no—
247C2×D4×C53—44no—
248C2×D4×C53—44no—
249C2×D4×C53—44no—
250C2×D4×C53C22⋊C4116yescomplemented
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53—21no—
255C22×C4×C53—21no—
256C22×C4×C53—21no—
257C22×C4×C53—21no—
258C22×C4×C53—21no—
259C22×C4×C53—28no—
260C22×C4×C53—21no—
261C22×C4×C53—21no—
262C22×C4×C53—21no—
263C22×C4×C53—21no—
264C22×C4×C53—21no—
265C22×C4×C53—21no—
266C22×C4×C53—21no—
267C22×C4×C53—21no—
268C22×C4×C53—21no—
269C22×C4×C53—21no—
270C22×C4×C53—21no—
271C22×C4×C53—21no—
272C22×C4×C53—28no—
273C22×C4×C53—44no—
274C22×C4×C53—44no—
275C22×C4×C53—44no—
276C22×C4×C53—44no—
277C22×C4×C53—44no—
278C22×C4×C53C22×C412yes—
279C22×C4×C53C22×C412yes—
280C22×C4×C53C22×C412yes—
281C22×C4×C53C22×C412yes—
282C22×C4×C53C2×D412yes—
283C22×C4×C53C2×D412yes—
284C22×C4×C53C2×D412yes—
285C22×C4×C53#4112yes—
286C22×Dic53—21no—
287C22×Dic53—21no—
288C22×Dic53—21no—
289C22×Dic53—21no—
290C22×Dic53—28no—
291C22×Dic53—28no—
292C22×Dic53—28no—
293C22×Dic53—21no—
294C22×Dic53—21no—
295C22×Dic53—21no—
296C22×Dic53—21no—
297C22×Dic53—21no—
298C22×Dic53—21no—
299C22×Dic53—21no—
300C22×Dic53—21no—
301C22×Dic53—21no—
302C22×Dic53—21no—
303C22×Dic53—21no—
304C22×Dic53—21no—
305C22×Dic53—21no—
306C22×Dic53—21no—
307C22×Dic53—21no—
308C22×Dic53—21no—
309C22×Dic53—21no—
310C22×Dic53—21no—
311C22×Dic53—21no—
312C22×Dic53—21no—
313C22×Dic53—21no—
314C22×Dic53—21no—
315C22×Dic53—21no—
316C22×Dic53—21no—
317C22×Dic53—21no—
318C22×Dic53—21no—
319C22×Dic53—21no—
320C22×Dic53—21no—
321C22×Dic53—21no—
322C22×Dic53—21no—
323C22×Dic53—28no—
324C22×Dic53—21no—
325C22×Dic53—21no—
326C22×Dic53—21no—
327C22×Dic53—21no—
328C22×Dic53—21no—
329C22×Dic53—21no—
330C22×Dic53—21no—
331C22×Dic53—21no—
332C22×Dic53—21no—
333C22×Dic53—21no—
334C22×Dic53—21no—
335C22×Dic53—21no—
336C22×Dic53—21no—
337C22×Dic53—21no—
338C22×Dic53—44no—
339C22×Dic53—44no—
340C22×Dic53—44no—
341C22×Dic53—44no—
342C22×Dic53—44no—
343C22×Dic53—44no—
344C22×Dic53—44no—
345C22×Dic53—44no—
346C22×Dic53—44no—
347C22×Dic53—44no—
348C22×Dic53—44no—
349C22×Dic53—44no—
350C22×Dic53—44no—
351C22×Dic53—44no—
352C22×Dic53—44no—
353C22×Dic53—44no—
354C22×Dic53—44no—
355C22×Dic53C2×D412yes—
356C22×Dic53C2×D412yes—
357C22×Dic53C2×D412yes—
358C22×Dic53C2×D412yes—
359C22×Dic53C2×D412yes—
360C22×Dic53C2×D412yes—
361C22×Dic53#4112yes—
362C22×Dic53#4112yes—
363C4⋊C4×C53—28no—
364C22⋊C4×C53—28no—
365C22⋊C4×C53—28no—
366C22⋊Dic53—28no—
367C22⋊Dic53—28no—
368C22⋊Dic53—44no—
369C22⋊Dic53—44no—
370C22⋊Dic53—44no—
371C22⋊Dic53—44no—
372C22⋊Dic53—44no—
373C22⋊Dic53—44no—
374C22⋊Dic53—44no—
375C4⋊Dic53—28no—
376C4×Dic53—28no—
377C23×C53—22no—
378C23×C53—22no—
379C23×C53—22no—
380C23×C53—22no—
381C23×C53—22no—
382C23×C53—22no—
383C23×C53—22no—
384C23×C53—22no—
385C23×C53—22no—
386C23×C53—22no—
387C23×C53—22no—
388C23×C53—22no—
389C23×C53—22no—
390C23×C53—22no—
391C23×C53—22no—
392C23×C53—22no—
393C23×C53—22no—
394C23×C53—22no—
395C23×C53—22no—
396C23×C53—22no—
397C23×C53—22no—
398C23×C53—22no—
399C23×C53—22no—
400C23×C53—22no—
401C23×C53—22no—
402C23×C53—22no—
403C23×C53—22no—
404C23×C53—22no—
405C23×C53—22no—
406C23×C53—22no—
407C23×C53—22no—
408C23×C53—22no—
409C23×C53—22no—
410C23×C53—22no—
411C23×C53—22no—
412C23×C53—22no—
413C23×C53—22no—
414C23×C53—22no—
415C23×C53—22no—
416C23×C53—22no—
417C23×C53—22no—
418C23×C53—22no—
419C23×C53—22no—
420C23×C53—22no—
421C23×C53—22no—
422C23×C53—22no—
423C23×C53—22no—
424C23×C53—22no—
425C23×C53—22no—
426C23×C53—22no—
427C23×C53—22no—
428C23×C53—22no—
429C23×C53—22no—
430C23×C53—41no—
431C23×C53—41no—
432C23×C53—41no—
433C23×C53—41no—
434C23×C53—41no—
435C23×C53—41no—
436C23×C53—41no—
437C23×C53—41no—
438C23×C53—41no—
439C23×C53—41no—
440C23×C53—41no—
441C23×C53—41no—
442C23×C53—41no—
443C23×C53—41no—
444C23×C53—41no—
445C23×C53—41no—
446C23×C53—41no—
447C23×C53—41no—
448C23×C53—41no—
449C23×C53—41no—
450C23×C53—41no—
451C23×C53—41no—
452C23×C53—41no—
453C23×C53—41no—
454C23×C53—41no—
455C23×C53—41no—
456C23×C53—41no—
457C23×C53—41no—
458C23×C53—41no—
459C23×C53—41no—
460C23×C53—41no—
461C23×C53—41no—
462C23×C53—41no—
463C23×C53—41no—
464C23×C53—41no—
465C23×C53—41no—
466C23×C53—41no—
467C23×C53—41no—
468C23×C53—41no—
469C23×C53—41no—
470C23×C53—41no—
471C23×C53—41no—
472C23×C53—41no—
473C23×C53—41no—
474C23×C53C2×C22⋊C414yes—
475C23×C53C2×C22⋊C414yes—
476C23×C53C4×D414yes—
477C23×C53C4×D414yes—
478C23×C53#12014yes—
479C23×C53#12114yes—
480C23×C53#12114yes—
481C23×C53#12314yes—
482C23×C53C23×C411yescharacteristic
483C23×C53C22×D411yescharacteristic
484C23×C53C22×D411yescharacteristic
485C23×C53C22×D411yescharacteristic
486C23×C53C22×D411yescharacteristic
487C23×C53C22×D411yescharacteristic
488C23×C53C2×#4111yescharacteristic
489C23×C53C2×#4111yescharacteristic
490C23×C53C2×#4111yescharacteristic
491C23×C53C2×#4111yescharacteristic
492C23×C53C2×#4111yescharacteristic
493C23×C53H(5,𝔽2)11yescharacteristic
494C23×C53H(5,𝔽2)11yescharacteristic
495C23×C53H(5,𝔽2)11yescharacteristic
496C23×C532−1+411yescharacteristic
497D4×C53—232no—
498D4×C53—416no—
499D4×C53—416no—
500C2×C4×C53—22no—
501C2×C4×C53—22no—
502C2×C4×C53—22no—
503C2×C4×C53—22no—
504C2×C4×C53—22no—
505C2×C4×C53—22no—
506C2×C4×C53—22no—
507C2×C4×C53—22no—
508C2×C4×C53—22no—
509C2×C4×C53—22no—
510C2×C4×C53—22no—
511C2×C4×C53—22no—
512C2×C4×C53—22no—
513C2×C4×C53—22no—
514C2×C4×C53—22no—
515C2×C4×C53—22no—
516C2×C4×C53—22no—
517C2×C4×C53—22no—
518C2×C4×C53—416no—
519C2×C4×C53—41no—
520C2×C4×C53—41no—
521C2×C4×C53—41no—
522C2×C4×C53—41no—
523C2×C4×C53—41no—
524C2×C4×C53—41no—
525C2×C4×C53—41no—
526C2×C4×C53—41no—
527C2×C4×C53C2×C22⋊C414yes—
528C2×C4×C53C4×D414yescomplemented
529C2×Dic53—22no—
530C2×Dic53—22no—
531C2×Dic53—22no—
532C2×Dic53—22no—
533C2×Dic53—22no—
534C2×Dic53—22no—
535C2×Dic53—22no—
536C2×Dic53—22no—
537C2×Dic53—22no—
538C2×Dic53—22no—
539C2×Dic53—22no—
540C2×Dic53—22no—
541C2×Dic53—22no—
542C2×Dic53—22no—
543C2×Dic53—22no—
544C2×Dic53—22no—
545C2×Dic53—22no—
546C2×Dic53—22no—
547C2×Dic53—22no—
548C2×Dic53—22no—
549C2×Dic53—22no—
550C2×Dic53—416no—
551C2×Dic53—416no—
552C2×Dic53—416no—
553C2×Dic53—41no—
554C2×Dic53—41no—
555C2×Dic53—41no—
556C2×Dic53—41no—
557C2×Dic53—41no—
558C2×Dic53—41no—
559C2×Dic53—41no—
560C2×Dic53—41no—
561C2×Dic53—41no—
562C2×Dic53—41no—
563C2×Dic53—41no—
564C2×Dic53—41no—
565C2×Dic53—41no—
566C2×Dic53—41no—
567C2×Dic53—41no—
568C2×Dic53—41no—
569C2×Dic53—41no—
570C2×Dic53—41no—
571C2×Dic53—41no—
572C2×Dic53—41no—
573C2×Dic53—41no—
574C2×Dic53—41no—
575C2×Dic53—41no—
576C2×Dic53—41no—
577C2×Dic53—41no—
578C2×Dic53—41no—
579C2×Dic53—41no—
580C2×Dic53—41no—
581C2×Dic53—41no—
582C2×Dic53—41no—
583C2×Dic53—41no—
584C2×Dic53—41no—
585C2×Dic53—41no—
586C2×Dic53—41no—
587C2×Dic53#12114yescomplemented
588#14023—531nomaximal, Sylow
589C22×C53—24no—
590C22×C53—24no—
591C22×C53—24no—
592C22×C53—24no—
593C22×C53—24no—
594C22×C53—24no—
595C22×C53—24no—
596C22×C53—24no—
597C22×C53—24no—
598C22×C53—24no—
599C22×C53—24no—
600C22×C53—24no—
601C22×C53—24no—
602C22×C53—24no—
603C22×C53—24no—
604C22×C53—24no—
605C22×C53—24no—
606C22×C53—42no—
607C22×C53—42no—
608C22×C53—42no—
609C22×C53—42no—
610C22×C53—42no—
611C22×C53—42no—
612C22×C53—42no—
613C22×C53—42no—
614C22×C53—42no—
615C22×C53—42no—
616C22×C53—42no—
617C22×C53—42no—
618C22×C53—42no—
619C22×C53—42no—
620C22×C53—42no—
621C22×C53—42no—
622C22×C53—42no—
623C22×C53—42no—
624C22×C53—42no—
625C22×C53—81no—
626C22×C53—81no—
627C22×C53—81no—
628C22×C53—81no—
629C22×C53—81no—
630C22×C53—81no—
631C22×C53—81no—
632C22×C53—81no—
633C22×C53#38618yescomplemented
634C22×C53C22×C22⋊C411yescharacteristic
635C22×C53C2×C4×D411yescharacteristic
636C22×C53C2×C4×D411yescharacteristic
637C22×C53C2×C4×D411yescharacteristic
638C22×C53C4×#4111yescharacteristic
639C22×C53#51811yescharacteristic
640C22×C53#52011yescharacteristic
641C22×C53C2×#12011yescharacteristic
642C22×C53C2×#12111yescharacteristic
643C22×C53C2×#12111yescharacteristic
644C22×C53C2×#12111yescharacteristic
645C22×C53C2×#12311yescharacteristic
646C22×C53#52511yescharacteristic
647C22×C53#52911yescharacteristic
648C22×C53#53211yescharacteristic
649C22×C53#53411yescharacteristic
650C22×C53#53711yescharacteristic
651C22×C53#53811yescharacteristic
652C22×C53#53911yescharacteristic
653C22×C53D4211yescharacteristic
654C22×C53D4211yescharacteristic
655C22×C53D4211yescharacteristic
656C22×C53#54611yescharacteristic
657C22×C53#54611yescharacteristic
658C22×C53#54611yescharacteristic
659C22×C53#54611yescharacteristic
660C22×C53#54611yescharacteristic
661C22×C53#54611yescharacteristic
662C22×C53#54711yescharacteristic
663C22×C53#54711yescharacteristic
664C22×C53#54711yescharacteristic
665C22×C53#54811yescharacteristic
666C22×C53#55311yescharacteristic
667C22×C53#55311yescharacteristic
668C22×C53#55311yescharacteristic
669C4×C53—24no—
670C4×C53—24no—
671C4×C53—42no—
672C4×C53—42no—
673Dic53—24no—
674Dic53—42no—
675Dic53—42no—
676Dic53—42no—
677Dic53—42no—
678Dic53—42no—
679Dic53—81no—
680Dic53—81no—
681C22×#121D5311yescharacteristic
682C22×C4×D4—531no—
683C2×#386—531no—
684C2×#386—531no—
685C2×#386—531no—
686C2×#386—531no—
687C22×#95—531no—
688#1441—531no—
689#1440—531no—
690#1439—531no—
691#1438—531no—
692#1437—531no—
693#1436—531no—
694C22⋊#95—531no—
695C22⋊#95—531no—
696C2×C53—28no—
697C2×C53—44no—
698C2×C53—82no—
699C2×C53C2×#38611yescharacteristic
700C2×C53C4×#12111yescharacteristic
701C2×C53#232511yescharacteristic
702C2×C53D4×C22⋊C411yescharacteristic
703C2×C53#233911yescharacteristic
704C2×C53#236111yescharacteristic
705C2×C53#236411yescharacteristic
706C2×C53#241011yescharacteristic
707C2×C53#241611yescharacteristic
708C2×C53#242411yescharacteristic
709C2×C53#242511yescharacteristic
710C2×C53#243011yescharacteristic
711C2×C53#244311yescharacteristic
712C2×C53#244411yescharacteristic
713C2×C53#254311yescharacteristic
714C23×D4C2×D5311yescharacteristic
715C23×D4C2×D5311yescharacteristic
716C23×D4C2×D5311yescharacteristic
717C24×C4—531no—
718C24×C4—531no—
719C24×C4—531no—
720C24×C4C2×D5311yescharacteristic
721C2×#121—24no—
722C2×#121—24no—
723C2×#121Dic5318yescomplemented
724C2×C4×D4—1064no—
725C2×C4×D4—1064no—
726C2×C4×D4—1064no—
727C22×C4⋊C4—531no—
728C22×C4⋊C4C2×D5311yescharacteristic
729C22×C22⋊C4—531no—
730C22×C22⋊C4—531no—
731C22×C22⋊C4—531no—
732C22×C22⋊C4—531no—
733C22×C22⋊C4—531no—
734C22×C22⋊C4—531no—
735C22×C22⋊C4—531no—
736C22×C22⋊C4—531no—
737C22×C22⋊C4—531no—
738C22×C22⋊C4C2×D5311yescharacteristic
739C22×C22⋊C4C2×D5311yescharacteristic
740C22×C42—531no—
741#386—1064no—
742#386—1064no—
743#386—1064no—
744#386—1064no—
745C2×#95—531no—
746C2×#95—531no—
747C2×#95—531no—
748C2×#95—531no—
749C2×#95—531no—
750C2×#95—531no—
751C2×#95—531no—
752C2×#95—531no—
753C2×#95—531no—
754C2×#95—531no—
755C2×#95—531no—
756C2×#95—531no—
757C2×#95—531no—
758C2×#95—531no—
759C2×#95—1064no—
760C53#1402311yescharacteristic, complemented, Sylow
761C25C22×D5311yescharacteristic
762C25C22×D5311yescharacteristic
763C25C22×D5311yescharacteristic
764C22×D4—22no—
765C22×D4—22no—
766C22×D4—22no—
767C22×D4—22no—
768C22×D4—22no—
769C22×D4—22no—
770C22×D4—22no—
771C22×D4—22no—
772C22×D4—22no—
773C22×D4—22no—
774C22×D4—22no—
775C22×D4—22no—
776C22×D4—22no—
777C22×D4—22no—
778C22×D4—41no—
779C22×D4—41no—
780C22×D4C2×Dic5314yes—
781C22×D4C2×Dic5314yescomplemented
782C22×D4C2×Dic5314yescomplemented
783C22×D4C22⋊D5314yes—
784C22×D4C22⋊D5314yes—
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—22no—
789C23×C4—41no—
790C23×C4—41no—
791C23×C4—531no—
792C23×C4—531no—
793C23×C4—531no—
794C23×C4—531no—
795C23×C4—531no—
796C23×C4—531no—
797C23×C4—534no—
798C23×C4—531no—
799C23×C4—531no—
800C23×C4—1062no—
801C23×C4—1062no—
802C23×C4—1062no—
803C23×C4—1062no—
804C23×C4—1062no—
805C23×C4—1062no—
806C23×C4—1062no—
807C23×C4—1062no—
808C23×C4—1062no—
809C23×C4—1062no—
810C23×C4—1062no—
811C23×C4—1062no—
812C23×C4—1062no—
813C23×C4—1062no—
814C23×C4—2121no—
815C23×C4—2121no—
816C23×C4—2121no—
817C23×C4—2121no—
818C23×C4—2121no—
819C23×C4—2121no—
820C23×C4C2×Dic5314yescomplemented
821C23×C4C22×D5311yescharacteristic
822C23×C4C22×D5311yescharacteristic
823C23×C4C22×D5311yescharacteristic
824C23×C4C22×D5311yescharacteristic
825#121—232no—
826C4×D4—10632no—
827C2×C4⋊C4—22no—
828C2×C4⋊C4—22no—
829C2×C4⋊C4—1062no—
830C2×C4⋊C4—1062no—
831C2×C4⋊C4—1062no—
832C2×C4⋊C4C2×Dic5314yescomplemented
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—534no—
838C2×C22⋊C4—1062no—
839C2×C22⋊C4—1062no—
840C2×C22⋊C4—1062no—
841C2×C22⋊C4—1062no—
842C2×C22⋊C4—1062no—
843C2×C22⋊C4—1062no—
844C2×C22⋊C4—1062no—
845C2×C22⋊C4—1062no—
846C2×C22⋊C4—1062no—
847C2×C22⋊C4—1062no—
848C2×C22⋊C4—1062no—
849C2×C22⋊C4—1062no—
850C2×C22⋊C4—1062no—
851C2×C22⋊C4—1062no—
852C2×C22⋊C4—1062no—
853C2×C22⋊C4—1062no—
854C2×C22⋊C4—1062no—
855C2×C22⋊C4—1062no—
856C2×C22⋊C4—1062no—
857C2×C22⋊C4—1062no—
858C2×C22⋊C4—2121no—
859C2×C22⋊C4—2121no—
860C2×C22⋊C4—2121no—
861C2×C22⋊C4—2121no—
862C2×C22⋊C4—2121no—
863C2×C22⋊C4—2121no—
864C2×C22⋊C4C2×Dic5314yescomplemented
865C2×C22⋊C4C2×Dic5314yescomplemented
866C2×C42—1062no—
867C2×C42—1062no—
868C2×C42—1062no—
869#95—534no—
870#95—1062no—
871#95—1062no—
872#95—1062no—
873#95—1062no—
874#95—1062no—
875#95—1062no—
876#95—1062no—
877#95—1062no—
878#95—1062no—
879#95—1062no—
880#95—1062no—
881#95—2121no—
882#95—2121no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—21no—
904C24—21no—
905C24—21no—
906C24—21no—
907C24—21no—
908C24—21no—
909C24—21no—
910C24—21no—
911C24—21no—
912C24—21no—
913C24—21no—
914C24—21no—
915C24—21no—
916C24—21no—
917C24D4×D5312yes—
918C24D4×D5312yes—
919C24#1171994712yes—
920C24#1171994712yes—
921C24C22×Dic5312yes—
922C24C22×Dic5312yes—
923C24C22×Dic5312yes—
924C24C2×C22⋊D5312yes—
925C24C2×C22⋊D5312yes—
926C24C2×C22⋊D5312yes—
927C24C2×C22⋊D5312yes—
928C24C23×D5311yescharacteristic
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—28no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4C22⋊Dic53116yescomplemented
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—28no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—28no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—532no—
978C22×C4—532no—
979C22×C4—532no—
980C22×C4—532no—
981C22×C4—532no—
982C22×C4—532no—
983C22×C4—532no—
984C22×C4—532no—
985C22×C4—1068no—
986C22×C4—1061no—
987C22×C4—1061no—
988C22×C4—1061no—
989C22×C4—1061no—
990C22×C4—1068no—
991C22×C4—1068no—
992C22×C4—1068no—
993C22×C4—1061no—
994C22×C4—1061no—
995C22×C4—1061no—
996C22×C4—1061no—
997C22×C4—1061no—
998C22×C4—1061no—
999C22×C4—1061no—
1000C22×C4—1061no—
1001C22×C4—1061no—
1002C22×C4—1061no—
1003C22×C4—1061no—
1004C22×C4—1061no—
1005C22×C4—1061no—
1006C22×C4—1061no—
1007C22×C4—1061no—
1008C22×C4—1061no—
1009C22×C4—1061no—
1010C22×C4—1061no—
1011C22×C4—1061no—
1012C22×C4—1061no—
1013C22×C4—1061no—
1014C22×C4—1061no—
1015C22×C4—1061no—
1016C22×C4—1061no—
1017C22×C4—1061no—
1018C22×C4—1061no—
1019C22×C4—1061no—
1020C22×C4—1061no—
1021C22×C4—1061no—
1022C22×C4—1061no—
1023C22×C4—1061no—
1024C22×C4—1061no—
1025C22×C4—1061no—
1026C22×C4—1061no—
1027C22×C4—1061no—
1028C22×C4—1061no—
1029C22×C4—1061no—
1030C22×C4—1061no—
1031C22×C4—1061no—
1032C22×C4—1061no—
1033C22×C4—1061no—
1034C22×C4—1061no—
1035C22×C4—1061no—
1036C22×C4—1061no—
1037C22×C4—2124no—
1038C22×C4—2124no—
1039C22×C4—2124no—
1040C22×C4—2124no—
1041C22×C4—2124no—
1042C22×C4—2124no—
1043C22×C4—2124no—
1044C22×C4—2124no—
1045C22×C4—2124no—
1046C22×C4—2124no—
1047C22×C4—2124no—
1048C22×C4—2124no—
1049C22×C4—2124no—
1050C22×C4—2124no—
1051C22×C4—2124no—
1052C22×C4—2124no—
1053C22×C4—2124no—
1054C22×C4D4×D5312yes—
1055C22×C4#1171994712yes—
1056C22×C4C22×Dic5312yes—
1057C22×C4C22×Dic5312yes—
1058C22×C4C22×Dic5312yes—
1059C22×C4C22×Dic5312yes—
1060C22×C4C2×C22⋊D5312yes—
1061C22×C4C2×C22⋊D5312yes—
1062C4⋊C4—28no—
1063C4⋊C4—1068no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—1068no—
1067C22⋊C4—1068no—
1068C22⋊C4—2124no—
1069C22⋊C4—2124no—
1070C22⋊C4—2124no—
1071C22⋊C4—2124no—
1072C22⋊C4—2124no—
1073C22⋊C4—2124no—
1074C22⋊C4—2124no—
1075C42—1068no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23C2×C22⋊Dic5314yes—
1174C23C2×C22⋊Dic5314yes—
1175C23D4×Dic5314yes—
1176C23D4×Dic5314yes—
1177C23#1313318514yes—
1178C23#1313318914yes—
1179C23#1313318914yes—
1180C23#1313319814yes—
1181C23C23×Dic5311yescharacteristic
1182C23C2×D4×D5311yescharacteristic
1183C23C2×D4×D5311yescharacteristic
1184C23C2×D4×D5311yescharacteristic
1185C23C22×C22⋊D5311yescharacteristic
1186C23C22×C22⋊D5311yescharacteristic
1187C23#41×D5311yescharacteristic
1188C23#41×D5311yescharacteristic
1189C23C2×#1171994711yescharacteristic
1190C23C2×#1171994711yescharacteristic
1191C23C2×#1171994711yescharacteristic
1192C23#1313326211yescharacteristic
1193C23#1313326211yescharacteristic
1194C23#1313326311yescharacteristic
1195C23#1313326411yescharacteristic
1196D4—232no—
1197D4—416no—
1198D4—416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—416no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—534no—
1227C2×C4—1062no—
1228C2×C4—1062no—
1229C2×C4—1062no—
1230C2×C4—1062no—
1231C2×C4—1062no—
1232C2×C4—1062no—
1233C2×C4—1062no—
1234C2×C4—1062no—
1235C2×C4—1062no—
1236C2×C4—1062no—
1237C2×C4—1062no—
1238C2×C4—1062no—
1239C2×C4—1062no—
1240C2×C4—1062no—
1241C2×C4—1062no—
1242C2×C4—1062no—
1243C2×C4—1062no—
1244C2×C4—1062no—
1245C2×C4—1062no—
1246C2×C4—1062no—
1247C2×C4—1062no—
1248C2×C4—21216no—
1249C2×C4—21216no—
1250C2×C4—2121no—
1251C2×C4—2121no—
1252C2×C4—2121no—
1253C2×C4—2121no—
1254C2×C4—2121no—
1255C2×C4—2121no—
1256C2×C4—2121no—
1257C2×C4—2121no—
1258C2×C4—2121no—
1259C2×C4—2121no—
1260C2×C4—2121no—
1261C2×C4—2121no—
1262C2×C4—2121no—
1263C2×C4—2121no—
1264C2×C4—21216no—
1265C2×C4—2121no—
1266C2×C4—2121no—
1267C2×C4—2121no—
1268C2×C4—2121no—
1269C2×C4—2121no—
1270C2×C4—2121no—
1271C2×C4—2121no—
1272C2×C4—2121no—
1273C2×C4—2121no—
1274C2×C4—2121no—
1275C2×C4—2121no—
1276C2×C4—2121no—
1277C2×C4—2121no—
1278C2×C4—2121no—
1279C2×C4—2121no—
1280C2×C4—2121no—
1281C2×C4—2121no—
1282C2×C4—2121no—
1283C2×C4—2121no—
1284C2×C4—2121no—
1285C2×C4C2×C22⋊Dic5314yes—
1286C2×C4D4×Dic5314yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22#1681050318yescomplemented
1332C22C22×C22⋊Dic5311yescharacteristic
1333C22C2×D4×Dic5311yescharacteristic
1334C22C2×D4×Dic5311yescharacteristic
1335C22C2×D4×Dic5311yescharacteristic
1336C22#41×Dic5311yescharacteristic
1337C22#1681109811yescharacteristic
1338C22#1681110611yescharacteristic
1339C22C2×#1313318511yescharacteristic
1340C22#121×D5311yescharacteristic
1341C22C2×#1313318911yescharacteristic
1342C22C2×#1313318911yescharacteristic
1343C22C2×#1313319811yescharacteristic
1344C22#1681113311yescharacteristic
1345C22#1681115411yescharacteristic
1346C22#1681116811yescharacteristic
1347C22#1681118111yescharacteristic
1348C22#1681120011yescharacteristic
1349C22#1681121011yescharacteristic
1350C22#1681121811yescharacteristic
1351C22D4×C22⋊D5311yescharacteristic
1352C22D4×C22⋊D5311yescharacteristic
1353C22#1681125711yescharacteristic
1354C22#1681126111yescharacteristic
1355C22#1681126111yescharacteristic
1356C22#1681126211yescharacteristic
1357C22#1681126211yescharacteristic
1358C22#1681126711yescharacteristic
1359C22#1681126711yescharacteristic
1360C22#1681127211yescharacteristic
1361C22#1681127211yescharacteristic
1362C22#1681127311yescharacteristic
1363C22#1681127911yescharacteristic
1364C22#1681131611yescharacteristic
1365C22#1681131611yescharacteristic
1366C22#1681132511yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—1064no—
1372C4—4241no—
1373C4—4241no—
1374C4—2122no—
1375C4—2122no—
1376C4—2122no—
1377C4—2122no—
1378C4—2122no—
1379C2—28no—
1380C2—44no—
1381C2—82no—
1382C2C2×#1681050311yescharacteristic
1383C2#121×Dic5311yescharacteristic
1384C2#2027742011yescharacteristic
1385C2D4×C22⋊Dic5311yescharacteristic
1386C2#2027754511yescharacteristic
1387C2#2027773511yescharacteristic
1388C2#2027776711yescharacteristic
1389C2#2027808611yescharacteristic
1390C2#2027815211yescharacteristic
1391C2#2027825711yescharacteristic
1392C2#2027827211yescharacteristic
1393C2#2027832111yescharacteristic
1394C2#2027844611yescharacteristic
1395C2#2027846111yescharacteristic
1396C2#2027967311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
Fitting, prime radicalC22×#121×C53C2
socle, cosocleC24×C53C24
hypercenterC22×#121D53
hypocenterC53#14023
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic53C2semidirect
2. C2×#16810503C2semidirect
3. C2×#16810503C2semidirect
4. C2×#16810503C2semidirect
5. C2×#16810503C2semidirect
6. C22×#13133124C2semidirect
7. #20272968C2semidirect
8. #20272964C2semidirect
9. #20272960C2semidirect
10. #20272956C2semidirect
11. #20272952C2semidirect
12. #20272947C2semidirect
13. #20272938C2semidirect
14. #20272937C2semidirect
58. C2×#121×C53C4semidirect
82. C23×Dic53D4semidirect
121. C2×C22⋊Dic53D4semidirect
138. #13133124D4semidirect
159. C22×D4×C53C2×C4semidirect
160. C22×D4×C53C2×C4semidirect
169. C23×C4×C53C2×C4semidirect
177. C2×C4⋊C4×C53C2×C4semidirect
182. C2×C22⋊C4×C53C2×C4semidirect
183. C2×C22⋊C4×C53C2×C4semidirect
250. C2×D4×C53C22⋊C4semidirect
528. C2×C4×C53C4×D4semidirect
587. C2×Dic53#121semidirect
633. C22×C53#386semidirect
723. C2×#121Dic53semidirect
760. C53#14023semidirect
781. C22×D4C2×Dic53semidirect
782. C22×D4C2×Dic53semidirect
820. C23×C4C2×Dic53semidirect
832. C2×C4⋊C4C2×Dic53semidirect
864. C2×C22⋊C4C2×Dic53semidirect
865. C2×C22⋊C4C2×Dic53semidirect
949. C2×D4C22⋊Dic53semidirect
1286. C2×C4D4×Dic53semidirect
1331. C22#16810503semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic532
C2×#168105032
C22×#131331242
#202729682
#202729642
#202729602
#202729562
#202729522
#202729472
#202729382
#202729372
C22×#121×C532
#1402353