Finite Group Databasebeta

← #28254837

Subgroups — #28254837

Order 13568.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811134C211yesmaximal, characteristic, complemented
2C22×#13133191C211yesmaximal, characteristic, complemented
3#20285531C214yesmaximal, complemented
4#20285522C212yesmaximal, complemented
5#20285515C212yesmaximal, complemented
6#20285482C214yesmaximal, complemented
7#20285473C212yesmaximal, complemented
8#20285466C212yesmaximal, complemented
9#20284656C212yesmaximal, complemented
10#20284640C212yesmaximal, complemented
11#20284334C214yesmaximal, complemented
12#20283969C212yesmaximal, complemented
13#20283945C212yesmaximal, complemented
14C2×C53×#407C211yesmaximal, characteristic, complemented
15C22×#11719945C2211yescharacteristic, complemented
16C23×D212C2211yescharacteristic, complemented
17C23×C22⋊D53—21no—
18C2×#13133245C2214yescomplemented
19#16811134—21no—
20#16811134—21no—
21#16811134—21no—
22#16811134—21no—
23#16811134C2212yes—
24#16811134C2212yescomplemented
25#16811134C2212yescomplemented
26#16811134C2212yescomplemented
27C2×#13133200—21no—
28C2×#13133196C2211yescharacteristic, complemented
29C2×#13133196C2211yescharacteristic, complemented
30C2×#13133191—21no—
31C2×#13133191—21no—
32C2×#13133191—21no—
33C2×#13133191—21no—
34C2×#13133191—21no—
35C2×#13133191—21no—
36C2×#13133191C2212yes—
37C2×#13133191C2212yes—
38C2×#13133191C2212yes—
39C2×#13133191C2212yescomplemented
40C2×#13133191C2212yescomplemented
41C2×#13133191C2212yescomplemented
42C2×#13133191C2211yescharacteristic, complemented
43C2×#13133191C2211yescharacteristic, complemented
44C2×#13133186—21no—
45C2×C4×C22⋊D53—21no—
46C2×C4×C22⋊D53—21no—
47C2×#13133176C2211yescharacteristic, complemented
48C22×C4⋊Dic53C2211yescharacteristic, complemented
49C22×#11719921—21no—
50#16810959C2214yescomplemented
51#16810954C2214yescomplemented
52#16810948C2218yescomplemented
53#16810942C2214yescomplemented
54#16810942C2214yescomplemented
55#16810937C2214yescomplemented
56#16810937C2214yescomplemented
57#16810876C2218yescomplemented
58#16810869C2218yescomplemented
59#16810859C2218yescomplemented
60#16810852C2218yescomplemented
61#16810776C2214yescomplemented
62#16810776C2214yescomplemented
63#16810770C2218yescomplemented
64#16810764C2214yescomplemented
65#16810759C2214yescomplemented
66#16810759C2214yescomplemented
67#16810759C2214yescomplemented
68#16810665C2214yescomplemented
69#16810629C2214yescomplemented
70#16810625C2214yescomplemented
71C24×C4×C53C2211yescharacteristic
72C22×M16×C53C2212yescomplemented
73C53×#407C2212yescomplemented
74C53×#407C2212yescomplemented
75C53×#407C2212yescomplemented
76C53×#407C2212yescomplemented
77C2×C22⋊C8×C53C2212yescomplemented
78C2×C22⋊C8×C53C2212yescomplemented
79C24×D53—21no—
80C2×#11719945—21no—
81C2×#11719945—21no—
82C2×#11719945—44no—
83C2×#11719945C2312yes—
84C2×#11719945C2312yescomplemented
85C22×Dic106C2311yescharacteristic, complemented
86C22×D212—21no—
87C22×D212—21no—
88C22×D212—21no—
89C22×D212—44no—
90C22×D212C2312yes—
91C22×D212C2312yes—
92C22×D212C2312yes—
93C22×D212C2311yescharacteristic, complemented
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C22⋊D53—21no—
97C22×C22⋊D53—22no—
98C22×C22⋊D53—22no—
99C22×C22⋊D53—22no—
100C22×C22⋊D53—22no—
101C22×C22⋊D53—22no—
102C22×C22⋊D53—22no—
103C22×C22⋊D53—48no—
104C23×Dic53—21no—
105C22×C4×D53—21no—
106#13133245—48no—
107C2×#11719913C2318yescomplemented
108C2×D424C2318yescomplemented
109#13133200—22no—
110#13133200—22no—
111#13133200—22no—
112#13133200—22no—
113#13133196—21no—
114#13133196—21no—
115#13133196—21no—
116#13133196—21no—
117#13133196C2312yes—
118#13133196C2312yes—
119#13133196C2312yescomplemented
120#13133196C2312yescomplemented
121#13133191—22no—
122#13133191—22no—
123#13133191—22no—
124#13133191—22no—
125#13133191—22no—
126#13133191—22no—
127#13133191—22no—
128#13133191—22no—
129#13133191—22no—
130#13133191—22no—
131#13133191—22no—
132#13133191—22no—
133#13133191—21no—
134#13133191—21no—
135#13133191—21no—
136#13133191—21no—
137#13133191C2312yes—
138#13133191C2312yes—
139#13133191C2314yes—
140#13133191C2314yes—
141#13133191C2314yes—
142#13133191C2314yes—
143#13133191C2312yescomplemented
144#13133191C2312yescomplemented
145#13133186—22no—
146#13133186—22no—
147#13133186—22no—
148#13133186—22no—
149C4×C22⋊D53—22no—
150C4×C22⋊D53—22no—
151C4×C22⋊D53—22no—
152C4×C22⋊D53—22no—
153C4×C22⋊D53—22no—
154C4×C22⋊D53—22no—
155C4×C22⋊D53—22no—
156C4×C22⋊D53—22no—
157#13133176—21no—
158#13133176—21no—
159#13133176C2312yes—
160#13133176C2312yescomplemented
161C2×C4⋊Dic53—21no—
162C2×C4⋊Dic53—21no—
163C2×C4⋊Dic53—21no—
164C2×C4⋊Dic53C2312yes—
165C2×C4⋊Dic53C2312yes—
166C2×C4⋊Dic53C2312yes—
167C2×C4⋊Dic53C2311yescharacteristic, complemented
168C2×C4⋊Dic53C2311yescharacteristic, complemented
169C2×#11719919—21no—
170C2×#11719919—21no—
171C2×C22⋊Dic53—21no—
172C2×C22⋊Dic53—21no—
173C2×C22⋊Dic53—21no—
174C2×#11719921—22no—
175C2×#11719921—22no—
176C2×#11719921—22no—
177C2×#11719921—22no—
178C2×#11719921—22no—
179C2×#11719921—22no—
180C2×#11719921—21no—
181C2×#11719921—21no—
182C2×C4×Dic53—21no—
183#13133151C2318yescomplemented
184#13133149C2318yescomplemented
185#13133142C2318yescomplemented
186#13133139C2318yescomplemented
187#13133139C2318yescomplemented
188#13133139C2318yescomplemented
189C25×C53D411yescharacteristic
190C23×C4×C53—44no—
191C23×C4×C53D411yescharacteristic
192C23×C4×C53D411yescharacteristic
193C23×C4×C53D411yescharacteristic
194C23×C4×C53D411yescharacteristic
195C23×C4×C53D411yescharacteristic
196C23×C4×C53D411yescharacteristic
197C23×C4×C53D411yescharacteristic
198C23×C4×C53C2311yescharacteristic
199C23×C4×C53C2311yescharacteristic
200C23×C4×C53C2311yescharacteristic
201C23×C4×C53C2311yescharacteristic
202C23×C4×C53C2311yescharacteristic
203C23×C4×C53C2311yescharacteristic
204C23×C4×C53C2311yescharacteristic
205C2×M16×C53—44no—
206C2×M16×C53C2314yes—
207C2×M16×C53C2314yescomplemented
208C22×C8×C53C2314yescomplemented
209C22⋊C8×C53C2314yes—
210C22⋊C8×C53C2314yes—
211C22⋊C8×C53C2314yescomplemented
212C22⋊C8×C53C2314yescomplemented
213C24×C53—24no—
214C24×C53—42no—
215C24×C53—42no—
216C24×C53C2×D411yescharacteristic
217C24×C53C2×D411yescharacteristic
218C24×C53C2×D411yescharacteristic
219C24×C53C2×D411yescharacteristic
220C24×C53C2×D411yescharacteristic
221C24×C53C2×D411yescharacteristic
222C24×C53C2×D411yescharacteristic
223C23×D53—21no—
224C23×D53—22no—
225C23×D53—22no—
226C23×D53—22no—
227C23×D53—44no—
228C23×D53—44no—
229C23×D53—44no—
230C22×C4×C53—24no—
231C22×C4×C53—24no—
232C22×C4×C53—24no—
233C22×C4×C53—42no—
234C22×C4×C53—42no—
235C22×C4×C53—42no—
236C22×C4×C53—42no—
237C22×C4×C53—42no—
238C22×C4×C53—42no—
239C22×C4×C53—42no—
240C22×C4×C53—42no—
241C22×C4×C53—42no—
242C22×C4×C53—42no—
243C22×C4×C53—42no—
244C22×C4×C53C2×D411yescharacteristic
245C22×C4×C53C2×D411yescharacteristic
246C22×C4×C53C2×D411yescharacteristic
247C22×C4×C53C2×D411yescharacteristic
248C22×C4×C53C2×D411yescharacteristic
249C22×C4×C53C2×D411yescharacteristic
250C22×C4×C53C2×D411yescharacteristic
251C22×C4×C53C2×D411yescharacteristic
252C22×C4×C53C2×D411yescharacteristic
253C22×C4×C53C2×D411yescharacteristic
254C22×C4×C53C2×D411yescharacteristic
255C22×C4×C53C2×D411yescharacteristic
256C22×C4×C53C2×D411yescharacteristic
257C22×C4×C53C2×D411yescharacteristic
258C22×C4×C53C2×D411yescharacteristic
259C22×C4×C53C2×D411yescharacteristic
260C22×C4×C53C2×D411yescharacteristic
261C22×C4×C53C2×D411yescharacteristic
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2411yescharacteristic
266C22×C4×C53C2411yescharacteristic
267C22×C4×C53C2411yescharacteristic
268C22×C4×C53C2411yescharacteristic
269C22×C4×C53C2411yescharacteristic
270C22×C4×C53C2411yescharacteristic
271C22×C4×C53C2411yescharacteristic
272C2×C22⋊D53—22no—
273C2×C22⋊D53—22no—
274C2×C22⋊D53—22no—
275C2×C22⋊D53—22no—
276C2×C22⋊D53—22no—
277C2×C22⋊D53—22no—
278C2×C22⋊D53—24no—
279C2×C22⋊D53—24no—
280C2×C22⋊D53—24no—
281C2×C22⋊D53—24no—
282C2×C22⋊D53—44no—
283C2×C22⋊D53—48no—
284C2×C22⋊D53—48no—
285C2×C22⋊D53—48no—
286C2×C22⋊D53—48no—
287C2×C22⋊D53—48no—
288C2×C22⋊D53—44no—
289C2×C22⋊D53—44no—
290C2×C22⋊D53—48no—
291C22×Dic53—21no—
292C22×Dic53—21no—
293C22×Dic53—22no—
294C22×Dic53—22no—
295C22×Dic53—22no—
296C22×Dic53—21no—
297C22×Dic53—44no—
298#11719945—28no—
299#11719945—44no—
300#11719945—44no—
301#11719945—44no—
302C2×D212—28no—
303C2×D212—22no—
304C2×D212—22no—
305C2×D212—22no—
306C2×D212—21no—
307C2×D212—44no—
308C2×D212—44no—
309C2×D212—42no—
310C2×D212—44no—
311C2×D212—44no—
312C2×D212—44no—
313C2×D212C2414yes—
314C2×D212C2412yes—
315C2×C4×D53—22no—
316C2×C4×D53—22no—
317C2×C4×D53—44no—
318C2×Dic106—21no—
319C2×Dic106—42no—
320C2×Dic106C2412yes—
321M16×C53—28no—
322M16×C53—44no—
323C2×C8×C53—44no—
324C2×C8×C53C2418yes—
325C22⋊Dic53—22no—
326C22⋊Dic53—22no—
327C22⋊Dic53—22no—
328C22⋊Dic53—22no—
329C22⋊Dic53—22no—
330C22⋊Dic53—22no—
331#11719921—24no—
332#11719921—24no—
333#11719921—24no—
334#11719921—24no—
335#11719921—22no—
336#11719921—22no—
337#11719921—22no—
338#11719921—22no—
339C4⋊Dic53—22no—
340C4⋊Dic53—22no—
341C4⋊Dic53—22no—
342C4⋊Dic53—21no—
343C4⋊Dic53—21no—
344C4⋊Dic53C2412yes—
345C4⋊Dic53C2412yes—
346C4⋊Dic53C2414yes—
347#11719919—22no—
348#11719919—22no—
349#11719919—22no—
350#11719919—22no—
351C4×Dic53—22no—
352C4×Dic53—22no—
353D424—48no—
354#11719913—48no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—22no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
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—416no—
376C23×C53AGL(1,ℤ/8)14yescomplemented
377C23×C53C22×D411yescharacteristic
378C23×C53C22×D411yescharacteristic
379C23×C53C22×D411yescharacteristic
380C23×C53C22×D411yescharacteristic
381C23×C53C22×D411yescharacteristic
382C23×C53C22×D411yescharacteristic
383C23×C53C22×D411yescharacteristic
384C22×D53—22no—
385C22×D53—24no—
386C22×D53—42no—
387C22×D53—44no—
388C22×D53—44no—
389C22×D53—44no—
390C22×D53—44no—
391C22×D53—42no—
392C22×D53—44no—
393C22×D53—44no—
394C22×D53—44no—
395C22×D53—44no—
396C22×D53—42no—
397C22×D53—44no—
398C22×D53—816no—
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—41no—
415C2×C4×C53—41no—
416C2×C4×C53—41no—
417C2×C4×C53—41no—
418C2×C4×C53—41no—
419C2×C4×C53—41no—
420C2×C4×C53—41no—
421C2×C4×C53—41no—
422C2×C4×C53—41no—
423C2×C4×C53—41no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53C22×D411yescharacteristic
427C2×C4×C53C22×D411yescharacteristic
428C2×C4×C53C22×D411yescharacteristic
429C2×C4×C53C22×D411yescharacteristic
430C2×C4×C53C22×D411yescharacteristic
431C2×C4×C53C22×D411yescharacteristic
432C2×C4×C53C22×D411yescharacteristic
433C2×C4×C53H(5,𝔽2)14yes—
434C2×C4×C53C2511yescharacteristic
435C22⋊D53—44no—
436C22⋊D53—44no—
437C22⋊D53—48no—
438C22⋊D53—48no—
439C22⋊D53—44no—
440C22⋊D53—44no—
441C22⋊D53—44no—
442C22⋊D53—48no—
443C22⋊D53—48no—
444C22⋊D53—44no—
445C2×Dic53—22no—
446C2×Dic53—24no—
447C2×Dic53—22no—
448C2×Dic53—22no—
449C2×Dic53—42no—
450C2×Dic53—44no—
451C2×Dic53—44no—
452C2×Dic53—42no—
453C2×Dic53—44no—
454C2×Dic53—42no—
455D212—28no—
456D212—24no—
457D212—44no—
458D212—44no—
459D212—42no—
460D212—44no—
461C4×D53—44no—
462C4×D53—44no—
463Dic106—24no—
464Dic106—42no—
465C8×C53—28no—
466#60750—531nomaximal, Sylow
467C22×C53—28no—
468C22×C53—21no—
469C22×C53—21no—
470C22×C53—21no—
471C22×C53—21no—
472C22×C53—21no—
473C22×C53—21no—
474C22×C53—21no—
475C22×C53—21no—
476C22×C53—21no—
477C22×C53—21no—
478C22×C53—21no—
479C22×C53—21no—
480C22×C53—21no—
481C22×C53—21no—
482C22×C53—21no—
483C22×C53—21no—
484C22×C53—44no—
485C22×C53—44no—
486C22×C53—44no—
487C22×C53—44no—
488C22×C53—44no—
489C22×C53—44no—
490C22×C53#53412yes—
491C22×C53C2×AGL(1,ℤ/8)12yes—
492C22×C53C2×AGL(1,ℤ/8)12yes—
493C22×C53C2×AGL(1,ℤ/8)12yes—
494C22×C53#57512yes—
495C22×C53C23×D411yescharacteristic
496C2×D53—42no—
497C2×D53—44no—
498C2×D53—44no—
499C2×D53—42no—
500C2×D53—42no—
501C2×D53—44no—
502C2×D53—84no—
503C2×D53—88no—
504C2×D53—88no—
505C2×D53—88no—
506C4×C53—21no—
507C4×C53—21no—
508C4×C53—21no—
509C4×C53—21no—
510C4×C53—21no—
511C4×C53—21no—
512C4×C53#53412yes—
513C4×C53C2×H(5,𝔽2)12yes—
514Dic53—42no—
515Dic53—44no—
516Dic53—42no—
517Dic53—42no—
518C2×#525—531no—
519C22×#121—531no—
520#3194—534no—
521#3193—532no—
522#3192—532no—
523#3188—534no—
524#3187—532no—
525#3186—532no—
526#3094—532no—
527#3092—532no—
528#3055—534no—
529#3006—532no—
530#3003—532no—
531C2×#407D5311yescharacteristic, complemented
532C2×C53—22no—
533C2×C53—22no—
534C2×C53—22no—
535C2×C53—22no—
536C2×C53—22no—
537C2×C53—41no—
538C2×C53—41no—
539C2×C53C2×#53411yescharacteristic
540C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
541C2×C53C2×#57511yescharacteristic
542D53—82no—
543D53—84no—
544C22×#41—531no—
545C23×D4—531no—
546C23×D4—1061no—
547C24×C4C2×D5311yescharacteristic
548C2×AGL(1,ℤ/8)—534no—
549C22×M16C2×D5312yescomplemented
550#525—532no—
551#525—532no—
552#525—532no—
553#525—532no—
554#525—1061no—
555#525—1061no—
556#525—1061no—
557#525—1061no—
558C2×#123—1061no—
559C2×C22⋊Q8—531no—
560C2×C22⋊Q8—531no—
561C2×#121—532no—
562C2×#121—532no—
563C2×#121—532no—
564C2×#121—532no—
565C2×#121—532no—
566C2×#121—532no—
567C2×#121—531no—
568C2×#121—531no—
569C2×#121—1061no—
570C2×#121—1061no—
571C2×#121—1061no—
572C2×#121—1061no—
573C2×#121—1061no—
574C2×#121—1061no—
575C2×#120—1061no—
576C2×C4×D4—1061no—
577C2×C4×D4—1061no—
578C2×#117—531no—
579C22×C4⋊C4—531no—
580C22×C22⋊C4—1061no—
581#484—534no—
582#483—534no—
583#482—538no—
584#481—534no—
585#481—534no—
586#480—534no—
587#480—534no—
588#469—538no—
589#468—538no—
590#466—538no—
591#465—538no—
592#450—534no—
593#450—534no—
594#449—538no—
595#448—534no—
596#447—534no—
597#447—534no—
598#447—534no—
599#428—534no—
600#418—534no—
601#417—534no—
602#407C2×D5312yescomplemented
603#407C2×D5312yescomplemented
604#407C2×D5312yescomplemented
605#407C2×D5312yescomplemented
606C2×C22⋊C8C2×D5312yescomplemented
607C2×C22⋊C8C2×D5312yescomplemented
608C53#6075011yescharacteristic, complemented, Sylow
609C25—1061no—
610C25D21211yescharacteristic
611C2×#41—532no—
612C2×#41—532no—
613C2×#41—1061no—
614C2×#41—1061no—
615C2×#41—2124no—
616C22×Q8—531no—
617C22×D4—532no—
618C22×D4—532no—
619C22×D4—532no—
620C22×D4—531no—
621C22×D4—1061no—
622C22×D4—1061no—
623C22×D4—1061no—
624C22×D4—1062no—
625C22×D4—1062no—
626C22×D4—1062no—
627C22×D4—1062no—
628C22×D4—1062no—
629C22×D4—1062no—
630C22×D4—1061no—
631C22×D4—1061no—
632C22×D4—1061no—
633C22×D4—2124no—
634C22×D4—2128no—
635C23×C4—44no—
636C23×C4—1061no—
637C23×C4—1061no—
638C23×C4D21211yescharacteristic
639C23×C4D21211yescharacteristic
640C23×C4D21211yescharacteristic
641C23×C4D21211yescharacteristic
642C23×C4D21211yescharacteristic
643C23×C4D21211yescharacteristic
644C23×C4D21211yescharacteristic
645C23×C4C22×D5311yescharacteristic
646C23×C4C22×D5311yescharacteristic
647C23×C4C22×D5311yescharacteristic
648C23×C4C22×D5311yescharacteristic
649C23×C4C22×D5311yescharacteristic
650C23×C4C22×D5311yescharacteristic
651C23×C4C22×D5311yescharacteristic
652AGL(1,ℤ/8)—2128no—
653C2×SD16—538no—
654C2×D8—538no—
655C2×M16—44no—
656C2×M16C22×D5314yes—
657C2×M16C22×D5314yescomplemented
658C22×C8C22×D5314yescomplemented
659#123—1062no—
660#123—1062no—
661#123—1062no—
662#123—1062no—
663C22⋊Q8—532no—
664C22⋊Q8—532no—
665C22⋊Q8—532no—
666C22⋊Q8—532no—
667C22⋊Q8—1061no—
668C22⋊Q8—1061no—
669C22⋊Q8—1061no—
670C22⋊Q8—1061no—
671#121—534no—
672#121—534no—
673#121—534no—
674#121—534no—
675#121—532no—
676#121—532no—
677#121—532no—
678#121—532no—
679#121—1062no—
680#121—1062no—
681#121—1062no—
682#121—1062no—
683#121—1062no—
684#121—1062no—
685#121—1062no—
686#121—1062no—
687#121—1062no—
688#121—1062no—
689#121—1062no—
690#121—1062no—
691#121—1061no—
692#121—1061no—
693#121—1061no—
694#121—1061no—
695#120—1062no—
696#120—1062no—
697#120—1062no—
698#120—1062no—
699C4×D4—1062no—
700C4×D4—1062no—
701C4×D4—1062no—
702C4×D4—1062no—
703C4×D4—1062no—
704C4×D4—1062no—
705C4×D4—1062no—
706C4×D4—1062no—
707#117—532no—
708#117—532no—
709#117—1061no—
710#117—1061no—
711C2×C4⋊C4—532no—
712C2×C4⋊C4—532no—
713C2×C4⋊C4—532no—
714C2×C4⋊C4—531no—
715C2×C4⋊C4—531no—
716C2×C4⋊C4—1061no—
717C2×C4⋊C4—1061no—
718C2×C4⋊C4—1061no—
719C2×C4⋊C4—1061no—
720C2×C4⋊C4—1061no—
721C2×C22⋊C4—1061no—
722C2×C22⋊C4—1061no—
723C2×C22⋊C4—1061no—
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—1061no—
731C2×C22⋊C4—1061no—
732C2×C42—1061no—
733#107—538no—
734#106—538no—
735#103—538no—
736#102—538no—
737#102—538no—
738#102—538no—
739C22⋊C8C22×D5314yes—
740C22⋊C8C22×D5314yes—
741C22⋊C8C22×D5314yescomplemented
742C22⋊C8C22×D5314yescomplemented
743C24—24no—
744C24—42no—
745C24—42no—
746C24—1061no—
747C24—1062no—
748C24—1062no—
749C24—1062no—
750C24—2124no—
751C24—2124no—
752C24—2124no—
753C24C2×D21211yescharacteristic
754C24C2×D21211yescharacteristic
755C24C2×D21211yescharacteristic
756C24C2×D21211yescharacteristic
757C24C2×D21211yescharacteristic
758C24C2×D21211yescharacteristic
759C24C2×D21211yescharacteristic
760#41—1068no—
761#41—2124no—
762#41—2124no—
763#41—2124no—
764C2×Q8—532no—
765C2×Q8—1061no—
766C2×Q8—2122no—
767C2×D4—532no—
768C2×D4—534no—
769C2×D4—1062no—
770C2×D4—1062no—
771C2×D4—1062no—
772C2×D4—1062no—
773C2×D4—1062no—
774C2×D4—1062no—
775C2×D4—1064no—
776C2×D4—1064no—
777C2×D4—1064no—
778C2×D4—1064no—
779C2×D4—1062no—
780C2×D4—1062no—
781C2×D4—1062no—
782C2×D4—1061no—
783C2×D4—1068no—
784C2×D4—2124no—
785C2×D4—2124no—
786C2×D4—2122no—
787C2×D4—2124no—
788C2×D4—2124no—
789C2×D4—2124no—
790C2×D4—2124no—
791C2×D4—2128no—
792C2×D4—2128no—
793C2×D4—2128no—
794C2×D4—2128no—
795C2×D4—2128no—
796C2×D4—2124no—
797C2×D4—2124no—
798C2×D4—2128no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—1061no—
814C22×C4—1061no—
815C22×C4—1062no—
816C22×C4—1062no—
817C22×C4—1062no—
818C22×C4—1061no—
819C22×C4—1062no—
820C22×C4—1062no—
821C22×C4—2124no—
822C22×C4—2124no—
823C22×C4C2×D21211yescharacteristic
824C22×C4C2×D21211yescharacteristic
825C22×C4C2×D21211yescharacteristic
826C22×C4C2×D21211yescharacteristic
827C22×C4C2×D21211yescharacteristic
828C22×C4C2×D21211yescharacteristic
829C22×C4C2×D21211yescharacteristic
830C22×C4C2×D21211yescharacteristic
831C22×C4C2×D21211yescharacteristic
832C22×C4C2×D21211yescharacteristic
833C22×C4C2×D21211yescharacteristic
834C22×C4C2×D21211yescharacteristic
835C22×C4C2×D21211yescharacteristic
836C22×C4C2×D21211yescharacteristic
837C22×C4C2×D21211yescharacteristic
838C22×C4C2×D21211yescharacteristic
839C22×C4C2×D21211yescharacteristic
840C22×C4C2×D21211yescharacteristic
841C22×C4C2×D21211yescharacteristic
842C22×C4C2×D21211yescharacteristic
843C22×C4C2×D21211yescharacteristic
844C22×C4C23×D5311yescharacteristic
845C22×C4C23×D5311yescharacteristic
846C22×C4C23×D5311yescharacteristic
847C22×C4C23×D5311yescharacteristic
848C22×C4C23×D5311yescharacteristic
849C22×C4C23×D5311yescharacteristic
850C22×C4C23×D5311yescharacteristic
851SD16—2128no—
852D8—2128no—
853M16—28no—
854M16—44no—
855C2×C8—44no—
856C2×C8C23×D5318yes—
857C4⋊C4—532no—
858C4⋊C4—532no—
859C4⋊C4—534no—
860C4⋊C4—1062no—
861C4⋊C4—1062no—
862C4⋊C4—1062no—
863C4⋊C4—1061no—
864C4⋊C4—1061no—
865C4⋊C4—1062no—
866C4⋊C4—1062no—
867C4⋊C4—1062no—
868C4⋊C4—1062no—
869C22⋊C4—1062no—
870C22⋊C4—1062no—
871C22⋊C4—1062no—
872C22⋊C4—1062no—
873C22⋊C4—1062no—
874C22⋊C4—1062no—
875C22⋊C4—1064no—
876C22⋊C4—1064no—
877C22⋊C4—1064no—
878C22⋊C4—1064no—
879C22⋊C4—1062no—
880C22⋊C4—1062no—
881C22⋊C4—1062no—
882C22⋊C4—1062no—
883C42—1062no—
884C42—1062no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—416no—
906C23—1062no—
907C23—1064no—
908C23—42416no—
909C23—2122no—
910C23—2124no—
911C23—2124no—
912C23—2124no—
913C23—2124no—
914C23—2122no—
915C23—2124no—
916C23—2124no—
917C23—2124no—
918C23—2122no—
919C23—2124no—
920C23—2124no—
921C23#1313324514yescomplemented
922C23C22×D21211yescharacteristic
923C23C22×D21211yescharacteristic
924C23C22×D21211yescharacteristic
925C23C22×D21211yescharacteristic
926C23C22×D21211yescharacteristic
927C23C22×D21211yescharacteristic
928C23C22×D21211yescharacteristic
929Q8—1064no—
930Q8—2122no—
931D4—1064no—
932D4—1068no—
933D4—2124no—
934D4—2124no—
935D4—2122no—
936D4—2124no—
937D4—2128no—
938D4—2128no—
939D4—2124no—
940D4—2124no—
941D4—2124no—
942D4—2128no—
943D4—2128no—
944D4—2124no—
945D4—2124no—
946D4—2124no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—1062no—
975C2×C4—1062no—
976C2×C4—1064no—
977C2×C4—1062no—
978C2×C4—2124no—
979C2×C4—2124no—
980C2×C4—2124no—
981C2×C4—2122no—
982C2×C4—2122no—
983C2×C4—2124no—
984C2×C4—2122no—
985C2×C4—2124no—
986C2×C4C22×D21211yescharacteristic
987C2×C4C22×D21211yescharacteristic
988C2×C4C22×D21211yescharacteristic
989C2×C4C22×D21211yescharacteristic
990C2×C4C22×D21211yescharacteristic
991C2×C4C22×D21211yescharacteristic
992C2×C4C22×D21211yescharacteristic
993C2×C4#1313326214yes—
994C2×C4C24×D5311yescharacteristic
995C8—28no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—4248no—
1020C22—4248no—
1021C22—4248no—
1022C22—4244no—
1023C22—2122no—
1024C22—2124no—
1025C22—2124no—
1026C22—2122no—
1027C22—2122no—
1028C22—2124no—
1029C22#1681118512yes—
1030C22C2×#1313324512yes—
1031C22C2×#1313324512yes—
1032C22C2×#1313324512yes—
1033C22#1681142312yes—
1034C22C23×D21211yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—2122no—
1042C4—2124no—
1043C4—2122no—
1044C4—2122no—
1045C4#1681118512yes—
1046C4C2×#1313326212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—4244no—
1055C2—4242no—
1056C2C2×#1681118511yescharacteristic
1057C2C22×#1313324511yescharacteristic
1058C2C2×#1681142311yescharacteristic
subgroupG/H
centerC22C23×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#407C2
socleC22×C53C23×D4
hypercenterC2×#407D53
hypocenterC53#60750
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#16811134C2semidirect
2. C22×#13133191C2semidirect
3. #20285531C2semidirect
4. #20285522C2semidirect
5. #20285515C2semidirect
6. #20285482C2semidirect
7. #20285473C2semidirect
8. #20285466C2semidirect
9. #20284656C2semidirect
10. #20284640C2semidirect
11. #20284334C2semidirect
12. #20283969C2semidirect
13. #20283945C2semidirect
14. C2×C53×#407C2semidirect
15. C22×#11719945C22semidirect
16. C23×D212C22semidirect
18. C2×#13133245C22semidirect
24. #16811134C22semidirect
25. #16811134C22semidirect
26. #16811134C22semidirect
28. C2×#13133196C22semidirect
29. C2×#13133196C22semidirect
39. C2×#13133191C22semidirect
40. C2×#13133191C22semidirect
41. C2×#13133191C22semidirect
42. C2×#13133191C22semidirect
43. C2×#13133191C22semidirect
47. C2×#13133176C22semidirect
48. C22×C4⋊Dic53C22semidirect
50. #16810959C22semidirect
51. #16810954C22semidirect
52. #16810948C22semidirect
53. #16810942C22semidirect
54. #16810942C22semidirect
55. #16810937C22semidirect
56. #16810937C22semidirect
57. #16810876C22semidirect
58. #16810869C22semidirect
59. #16810859C22semidirect
60. #16810852C22semidirect
61. #16810776C22semidirect
62. #16810776C22semidirect
63. #16810770C22semidirect
64. #16810764C22semidirect
65. #16810759C22semidirect
66. #16810759C22semidirect
67. #16810759C22semidirect
68. #16810665C22semidirect
69. #16810629C22semidirect
70. #16810625C22semidirect
72. C22×M16×C53C22semidirect
73. C53×#407C22semidirect
74. C53×#407C22semidirect
75. C53×#407C22semidirect
76. C53×#407C22semidirect
77. C2×C22⋊C8×C53C22semidirect
78. C2×C22⋊C8×C53C22semidirect
84. C2×#11719945C23semidirect
85. C22×Dic106C23semidirect
93. C22×D212C23semidirect
107. C2×#11719913C23semidirect
108. C2×D424C23semidirect
119. #13133196C23semidirect
120. #13133196C23semidirect
143. #13133191C23semidirect
144. #13133191C23semidirect
160. #13133176C23semidirect
167. C2×C4⋊Dic53C23semidirect
168. C2×C4⋊Dic53C23semidirect
183. #13133151C23semidirect
184. #13133149C23semidirect
185. #13133142C23semidirect
186. #13133139C23semidirect
187. #13133139C23semidirect
188. #13133139C23semidirect
207. C2×M16×C53C23semidirect
208. C22×C8×C53C23semidirect
211. C22⋊C8×C53C23semidirect
212. C22⋊C8×C53C23semidirect
376. C23×C53AGL(1,ℤ/8)semidirect
531. C2×#407D53semidirect
549. C22×M16C2×D53semidirect
602. #407C2×D53semidirect
603. #407C2×D53semidirect
604. #407C2×D53semidirect
605. #407C2×D53semidirect
606. C2×C22⋊C8C2×D53semidirect
607. C2×C22⋊C8C2×D53semidirect
608. C53#60750semidirect
657. C2×M16C22×D53semidirect
658. C22×C8C22×D53semidirect
741. C22⋊C8C22×D53semidirect
742. C22⋊C8C22×D53semidirect
921. C23#13133245semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
C22×#131331912
#202855312
#202855222
#202855152
#202854822
#202854732
#202854662
#202846562
#202846402
#202843342
#202839692
#202839452
C2×C53×#4072
#6075053