Finite Group Databasebeta

← #28254835

Subgroups — #28254835

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
2#20285529C214yesmaximal, complemented
3#20285521C212yesmaximal, complemented
4#20285512C212yesmaximal, complemented
5#20285480C214yesmaximal, complemented
6#20285472C212yesmaximal, complemented
7#20285463C212yesmaximal, complemented
8#20284651C212yesmaximal, complemented
9#20284638C212yesmaximal, complemented
10#20284330C214yesmaximal, complemented
11#20283965C212yesmaximal, complemented
12#20283942C212yesmaximal, complemented
13C2×#16810587C211yesmaximal, characteristic, complemented
14C22×#121×C53C211yesmaximal, characteristic, complemented
15C22×#11719945C2211yescharacteristic, complemented
16C2×#13133243C2214yescomplemented
17C22×#11719917C2212yescomplemented
18#16811134—21no—
19#16811134—21no—
20#16811134—21no—
21#16811134—21no—
22#16811134C2212yes—
23#16811134C2212yescomplemented
24#16811134C2212yescomplemented
25#16811134C2212yescomplemented
26C2×#13133200—21no—
27C2×#13133196C2211yescharacteristic, complemented
28C2×#13133196C2211yescharacteristic, complemented
29C2×#13133191C2211yescharacteristic, complemented
30C2×#13133191C2211yescharacteristic, complemented
31C2×#13133186—21no—
32C2×C4×C22⋊D53—21no—
33C2×C4×C22⋊D53—21no—
34C2×#13133176C2211yescharacteristic, complemented
35#16810958C2214yescomplemented
36#16810953C2214yescomplemented
37#16810944C2218yescomplemented
38#16810941C2214yescomplemented
39#16810939C2214yescomplemented
40#16810936C2214yescomplemented
41#16810934C2214yescomplemented
42#16810874C2218yescomplemented
43#16810867C2218yescomplemented
44#16810857C2218yescomplemented
45#16810850C2218yescomplemented
46#16810774C2214yescomplemented
47#16810774C2214yescomplemented
48#16810766C2218yescomplemented
49#16810761C2214yescomplemented
50#16810757C2214yescomplemented
51#16810757C2214yescomplemented
52#16810756C2214yescomplemented
53#16810663C2214yescomplemented
54#16810628C2214yescomplemented
55#16810622C2214yescomplemented
56#16810587C2212yescomplemented
57#16810587C2212yescomplemented
58#16810587C2212yescomplemented
59#16810587C2212yescomplemented
60C2×C22⋊#88322C2212yescomplemented
61C2×C22⋊#88322C2212yescomplemented
62C23×D4×C53—21no—
63C23×D4×C53C2211yescharacteristic, complemented
64C24×C4×C53C2211yescharacteristic
65C2×#121×C53—21no—
66C2×#121×C53—21no—
67C2×#121×C53—21no—
68C2×#121×C53—21no—
69C2×#121×C53—21no—
70C2×#121×C53—21no—
71C2×#121×C53C2212yes—
72C2×#121×C53C2212yes—
73C2×#121×C53C2212yes—
74C2×#121×C53C2212yescomplemented
75C2×#121×C53C2212yescomplemented
76C2×#121×C53C2212yescomplemented
77C22×C4⋊C4×C53C2211yescharacteristic, complemented
78C22×C22⋊C4×C53—21no—
79C2×#11719945—21no—
80C2×#11719945—21no—
81C2×#11719945—44no—
82C2×#11719945C2312yes—
83C2×#11719945C2312yescomplemented
84C22×Dic106C2311yescharacteristic, complemented
85C22×D212C2311yescharacteristic, complemented
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C4×D53—21no—
90#13133243—48no—
91C2×#11719923C2318yescomplemented
92C2×#11719922C2318yescomplemented
93C2×#11719917—44no—
94C2×#11719917C2314yes—
95C2×#11719917C2314yescomplemented
96C22×#88322C2314yescomplemented
97#13133200—22no—
98#13133200—22no—
99#13133200—22no—
100#13133200—22no—
101#13133196—21no—
102#13133196—21no—
103#13133196—21no—
104#13133196—21no—
105#13133196C2312yes—
106#13133196C2312yes—
107#13133196C2312yescomplemented
108#13133196C2312yescomplemented
109#13133191—21no—
110#13133191—21no—
111#13133191—21no—
112#13133191—21no—
113#13133191C2312yes—
114#13133191C2312yes—
115#13133191C2312yescomplemented
116#13133191C2312yescomplemented
117#13133186—22no—
118#13133186—22no—
119#13133186—22no—
120#13133186—22no—
121C4×C22⋊D53—22no—
122C4×C22⋊D53—22no—
123C4×C22⋊D53—22no—
124C4×C22⋊D53—22no—
125C4×C22⋊D53—22no—
126C4×C22⋊D53—22no—
127C4×C22⋊D53—22no—
128C4×C22⋊D53—22no—
129#13133176—21no—
130#13133176—21no—
131#13133176C2312yes—
132#13133176C2312yescomplemented
133C2×C4⋊Dic53C2311yescharacteristic, complemented
134C2×C4⋊Dic53C2311yescharacteristic, complemented
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143#13133150C2318yescomplemented
144#13133148C2318yescomplemented
145#13133140C2318yescomplemented
146#13133138C2318yescomplemented
147#13133138C2318yescomplemented
148#13133137C2318yescomplemented
149C22⋊#88322C2314yes—
150C22⋊#88322C2314yes—
151C22⋊#88322C2314yescomplemented
152C22⋊#88322C2314yescomplemented
153C25×C53—21no—
154C25×C53D411yescharacteristic
155C22×D4×C53—22no—
156C22×D4×C53—22no—
157C22×D4×C53—22no—
158C22×D4×C53—22no—
159C22×D4×C53—22no—
160C22×D4×C53—22no—
161C22×D4×C53—21no—
162C22×D4×C53—21no—
163C22×D4×C53—21no—
164C22×D4×C53—44no—
165C22×D4×C53—48no—
166C22×D4×C53C2312yes—
167C22×D4×C53C2312yes—
168C22×D4×C53C2312yes—
169C23×C4×C53—21no—
170C23×C4×C53—44no—
171C23×C4×C53D411yescharacteristic
172C23×C4×C53D411yescharacteristic
173C23×C4×C53D411yescharacteristic
174C23×C4×C53D411yescharacteristic
175C23×C4×C53D411yescharacteristic
176C23×C4×C53D411yescharacteristic
177C23×C4×C53D411yescharacteristic
178C23×C4×C53C2311yescharacteristic
179C23×C4×C53C2311yescharacteristic
180C23×C4×C53C2311yescharacteristic
181C23×C4×C53C2311yescharacteristic
182C23×C4×C53C2311yescharacteristic
183C23×C4×C53C2311yescharacteristic
184C23×C4×C53C2311yescharacteristic
185#121×C53—22no—
186#121×C53—22no—
187#121×C53—22no—
188#121×C53—22no—
189#121×C53—22no—
190#121×C53—22no—
191#121×C53—22no—
192#121×C53—22no—
193#121×C53—22no—
194#121×C53—22no—
195#121×C53—22no—
196#121×C53—22no—
197#121×C53C2314yes—
198#121×C53C2314yes—
199#121×C53C2314yes—
200#121×C53C2314yes—
201C2×C4⋊C4×C53—21no—
202C2×C4⋊C4×C53—21no—
203C2×C4⋊C4×C53—21no—
204C2×C4⋊C4×C53C2312yes—
205C2×C4⋊C4×C53C2312yes—
206C2×C4⋊C4×C53C2312yes—
207C2×C22⋊C4×C53—22no—
208C2×C22⋊C4×C53—22no—
209C2×C22⋊C4×C53—22no—
210C2×C22⋊C4×C53—22no—
211C2×C22⋊C4×C53—22no—
212C2×C22⋊C4×C53—22no—
213C24×C53—24no—
214C24×C53—22no—
215C24×C53—22no—
216C24×C53—22no—
217C24×C53—42no—
218C24×C53—42no—
219C24×C53—44no—
220C24×C53—44no—
221C24×C53—44no—
222C24×C53C2×D411yescharacteristic
223C24×C53C2×D411yescharacteristic
224C24×C53C2×D411yescharacteristic
225C24×C53C2×D411yescharacteristic
226C24×C53C2×D411yescharacteristic
227C24×C53C2×D411yescharacteristic
228C24×C53C2×D411yescharacteristic
229C23×D53—21no—
230C2×D4×C53—24no—
231C2×D4×C53—24no—
232C2×D4×C53—24no—
233C2×D4×C53—24no—
234C2×D4×C53—22no—
235C2×D4×C53—22no—
236C2×D4×C53—22no—
237C2×D4×C53—28no—
238C2×D4×C53—44no—
239C2×D4×C53—44no—
240C2×D4×C53—44no—
241C2×D4×C53—44no—
242C2×D4×C53—44no—
243C2×D4×C53—48no—
244C2×D4×C53—48no—
245C2×D4×C53—48no—
246C2×D4×C53—48no—
247C2×D4×C53—48no—
248C2×D4×C53—48no—
249C2×D4×C53C2414yes—
250C22×C4×C53—24no—
251C22×C4×C53—24no—
252C22×C4×C53—24no—
253C22×C4×C53—22no—
254C22×C4×C53—22no—
255C22×C4×C53—22no—
256C22×C4×C53—42no—
257C22×C4×C53—42no—
258C22×C4×C53—42no—
259C22×C4×C53—42no—
260C22×C4×C53—42no—
261C22×C4×C53—42no—
262C22×C4×C53—42no—
263C22×C4×C53—42no—
264C22×C4×C53—42no—
265C22×C4×C53—42no—
266C22×C4×C53—42no—
267C22×C4×C53—44no—
268C22×C4×C53C2×D411yescharacteristic
269C22×C4×C53C2×D411yescharacteristic
270C22×C4×C53C2×D411yescharacteristic
271C22×C4×C53C2×D411yescharacteristic
272C22×C4×C53C2×D411yescharacteristic
273C22×C4×C53C2×D411yescharacteristic
274C22×C4×C53C2×D411yescharacteristic
275C22×C4×C53C2×D411yescharacteristic
276C22×C4×C53C2×D411yescharacteristic
277C22×C4×C53C2×D411yescharacteristic
278C22×C4×C53C2×D411yescharacteristic
279C22×C4×C53C2×D411yescharacteristic
280C22×C4×C53C2×D411yescharacteristic
281C22×C4×C53C2×D411yescharacteristic
282C22×C4×C53C2×D411yescharacteristic
283C22×C4×C53C2×D411yescharacteristic
284C22×C4×C53C2×D411yescharacteristic
285C22×C4×C53C2×D411yescharacteristic
286C22×C4×C53C2×D411yescharacteristic
287C22×C4×C53C2×D411yescharacteristic
288C22×C4×C53C2×D411yescharacteristic
289C22×C4×C53C2411yescharacteristic
290C22×C4×C53C2411yescharacteristic
291C22×C4×C53C2411yescharacteristic
292C22×C4×C53C2411yescharacteristic
293C22×C4×C53C2411yescharacteristic
294C22×C4×C53C2411yescharacteristic
295C22×C4×C53C2411yescharacteristic
296C2×C22⋊D53—22no—
297C2×C22⋊D53—22no—
298C2×C22⋊D53—22no—
299C2×C22⋊D53—22no—
300C2×C22⋊D53—22no—
301C2×C22⋊D53—22no—
302C2×C22⋊D53—44no—
303C2×C22⋊D53—44no—
304C2×C22⋊D53—44no—
305C22×Dic53—21no—
306C22×Dic53—21no—
307C22×Dic53—21no—
308#11719945—28no—
309#11719945—44no—
310#11719945—44no—
311#11719945—44no—
312C2×D212—21no—
313C2×D212—42no—
314C2×D212C2412yes—
315C2×C4×D53—22no—
316C2×C4×D53—22no—
317C2×C4×D53—44no—
318C2×Dic106—21no—
319C2×Dic106—42no—
320C2×Dic106C2412yes—
321C4⋊C4×C53—22no—
322C4⋊C4×C53—22no—
323C4⋊C4×C53—22no—
324C4⋊C4×C53C2414yes—
325C22⋊C4×C53—24no—
326C22⋊C4×C53—24no—
327C22⋊C4×C53—24no—
328C22⋊C4×C53—24no—
329C22⋊Dic53—22no—
330C22⋊Dic53—22no—
331C22⋊Dic53—22no—
332C22⋊Dic53—22no—
333C22⋊Dic53—22no—
334C22⋊Dic53—22no—
335#11719923—48no—
336#11719922—48no—
337#11719921—22no—
338#11719921—22no—
339#11719921—22no—
340#11719921—22no—
341C4⋊Dic53—21no—
342C4⋊Dic53—21no—
343C4⋊Dic53C2412yes—
344C4⋊Dic53C2412yes—
345#11719919—22no—
346#11719919—22no—
347#11719919—22no—
348#11719919—22no—
349C4×Dic53—22no—
350C4×Dic53—22no—
351#11719917—28no—
352#11719917—44no—
353C2×#88322—44no—
354C2×#88322C2418yes—
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—24no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—416no—
377C23×C53—44no—
378C23×C53—44no—
379C23×C53—44no—
380C23×C53—44no—
381C23×C53—44no—
382C23×C53—44no—
383C23×C53—44no—
384C23×C53—44no—
385C23×C53—44no—
386C23×C53—816no—
387C23×C53AGL(1,ℤ/8)14yescomplemented
388C23×C53C22×D411yescharacteristic
389C23×C53C22×D411yescharacteristic
390C23×C53C22×D411yescharacteristic
391C23×C53C22×D411yescharacteristic
392C23×C53C22×D411yescharacteristic
393C23×C53C22×D411yescharacteristic
394C23×C53C22×D411yescharacteristic
395C22×D53—22no—
396C22×D53—42no—
397C22×D53—42no—
398C22×D53—42no—
399D4×C53—28no—
400D4×C53—44no—
401D4×C53—44no—
402D4×C53—48no—
403D4×C53—48no—
404D4×C53—48no—
405D4×C53—48no—
406D4×C53—44no—
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—24no—
423C2×C4×C53—41no—
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—44no—
436C2×C4×C53—44no—
437C2×C4×C53—44no—
438C2×C4×C53C22×D411yescharacteristic
439C2×C4×C53C22×D411yescharacteristic
440C2×C4×C53C22×D411yescharacteristic
441C2×C4×C53C22×D411yescharacteristic
442C2×C4×C53C22×D411yescharacteristic
443C2×C4×C53C22×D411yescharacteristic
444C2×C4×C53C22×D411yescharacteristic
445C2×C4×C53H(5,𝔽2)14yes—
446C2×C4×C53C2511yescharacteristic
447C22⋊D53—44no—
448C22⋊D53—44no—
449C22⋊D53—44no—
450C22⋊D53—44no—
451C22⋊D53—44no—
452C22⋊D53—44no—
453C2×Dic53—22no—
454C2×Dic53—22no—
455C2×Dic53—22no—
456C2×Dic53—42no—
457C2×Dic53—42no—
458C2×Dic53—42no—
459D212—24no—
460D212—42no—
461C4×D53—44no—
462C4×D53—44no—
463Dic106—24no—
464Dic106—42no—
465#88322—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—44no—
491C22×C53—44no—
492C22×C53—44no—
493C22×C53—88no—
494C22×C53—88no—
495C22×C53—88no—
496C22×C53#53412yes—
497C22×C53C2×AGL(1,ℤ/8)12yes—
498C22×C53C2×AGL(1,ℤ/8)12yes—
499C22×C53C2×AGL(1,ℤ/8)12yes—
500C22×C53#57512yes—
501C22×C53C23×D411yescharacteristic
502C2×D53—42no—
503C2×D53—42no—
504C2×D53—42no—
505C2×D53—84no—
506C4×C53—21no—
507C4×C53—21no—
508C4×C53—21no—
509C4×C53—21no—
510C4×C53—21no—
511C4×C53—21no—
512C4×C53—44no—
513C4×C53#53412yes—
514C4×C53C2×H(5,𝔽2)12yes—
515Dic53—42no—
516Dic53—42no—
517Dic53—42no—
518C2×#525—531no—
519C22×#121D5311yescharacteristic, complemented
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×#407—531no—
532C2×C53—22no—
533C2×C53—22no—
534C2×C53—22no—
535C2×C53—22no—
536C2×C53—22no—
537C2×C53—41no—
538C2×C53—41no—
539C2×C53—84no—
540C2×C53C2×#53411yescharacteristic
541C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C53C2×#57511yescharacteristic
543D53—82no—
544C22×#41—531no—
545C23×D4—21no—
546C23×D4C2×D5311yescharacteristic, complemented
547C24×C4C2×D5311yescharacteristic
548C2×AGL(1,ℤ/8)—534no—
549C22×M16—532no—
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—21no—
562C2×#121—21no—
563C2×#121—21no—
564C2×#121—21no—
565C2×#121—21no—
566C2×#121—21no—
567C2×#121—531no—
568C2×#121—531no—
569C2×#121C2×D5312yes—
570C2×#121C2×D5312yes—
571C2×#121C2×D5312yes—
572C2×#121C2×D5312yescomplemented
573C2×#121C2×D5312yescomplemented
574C2×#121C2×D5312yescomplemented
575C2×#120—1061no—
576C2×C4×D4—1061no—
577C2×C4×D4—1061no—
578C2×#117—531no—
579C22×C4⋊C4C2×D5311yescharacteristic, complemented
580C22×C22⋊C4—21no—
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#407—532no—
603#407—532no—
604#407—532no—
605#407—532no—
606C2×C22⋊C8—532no—
607C2×C22⋊C8—532no—
608C53#6075011yescharacteristic, complemented, Sylow
609C25—21no—
610C25C22⋊D5311yescharacteristic
611C2×#41—532no—
612C2×#41—532no—
613C2×#41—1061no—
614C2×#41—1061no—
615C2×#41—2124no—
616C22×Q8—531no—
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—21no—
626C22×D4—44no—
627C22×D4—48no—
628C22×D4—531no—
629C22×D4—1061no—
630C22×D4—1061no—
631C22×D4—1061no—
632C22×D4C22×D5312yes—
633C22×D4C22×D5312yes—
634C22×D4C22×D5312yes—
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1061no—
638C23×C4C22⋊D5311yescharacteristic
639C23×C4C22⋊D5311yescharacteristic
640C23×C4C22⋊D5311yescharacteristic
641C23×C4C22⋊D5311yescharacteristic
642C23×C4C22⋊D5311yescharacteristic
643C23×C4C22⋊D5311yescharacteristic
644C23×C4C22⋊D5311yescharacteristic
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—534no—
656C2×M16—534no—
657C2×M16—2124no—
658C22×C8—534no—
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—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—22no—
682#121—22no—
683#121—532no—
684#121—532no—
685#121—532no—
686#121—532no—
687#121—1061no—
688#121—1061no—
689#121—1061no—
690#121—1061no—
691#121C22×D5314yes—
692#121C22×D5314yes—
693#121C22×D5314yes—
694#121C22×D5314yes—
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—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—531no—
715C2×C4⋊C4—531no—
716C2×C4⋊C4—1061no—
717C2×C4⋊C4—1061no—
718C2×C4⋊C4C22×D5312yes—
719C2×C4⋊C4C22×D5312yes—
720C2×C4⋊C4C22×D5312yes—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—1061no—
728C2×C22⋊C4—1061no—
729C2×C22⋊C4—1061no—
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⋊C8—534no—
740C22⋊C8—534no—
741C22⋊C8—534no—
742C22⋊C8—534no—
743C24—24no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—42no—
748C24—42no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24—1061no—
753C24C2×C22⋊D5311yescharacteristic
754C24C2×C22⋊D5311yescharacteristic
755C24C2×C22⋊D5311yescharacteristic
756C24C2×C22⋊D5311yescharacteristic
757C24C2×C22⋊D5311yescharacteristic
758C24C2×C22⋊D5311yescharacteristic
759C24C2×C22⋊D5311yescharacteristic
760#41—1068no—
761#41—2124no—
762#41—2124no—
763#41—2124no—
764C2×Q8—532no—
765C2×Q8—1061no—
766C2×Q8—2122no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—532no—
787C2×D4—1062no—
788C2×D4—1062no—
789C2×D4—1062no—
790C2×D4—1062no—
791C2×D4—1062no—
792C2×D4—1062no—
793C2×D4—1061no—
794C2×D4—2122no—
795C2×D4—2124no—
796C2×D4—2124no—
797C2×D4—2124no—
798C2×D4C23×D5314yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
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—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—1061no—
818C22×C4—1061no—
819C22×C4—1061no—
820C22×C4—1062no—
821C22×C4—1062no—
822C22×C4—2124no—
823C22×C4C2×C22⋊D5311yescharacteristic
824C22×C4C2×C22⋊D5311yescharacteristic
825C22×C4C2×C22⋊D5311yescharacteristic
826C22×C4C2×C22⋊D5311yescharacteristic
827C22×C4C2×C22⋊D5311yescharacteristic
828C22×C4C2×C22⋊D5311yescharacteristic
829C22×C4C2×C22⋊D5311yescharacteristic
830C22×C4C2×C22⋊D5311yescharacteristic
831C22×C4C2×C22⋊D5311yescharacteristic
832C22×C4C2×C22⋊D5311yescharacteristic
833C22×C4C2×C22⋊D5311yescharacteristic
834C22×C4C2×C22⋊D5311yescharacteristic
835C22×C4C2×C22⋊D5311yescharacteristic
836C22×C4C2×C22⋊D5311yescharacteristic
837C22×C4C2×C22⋊D5311yescharacteristic
838C22×C4C2×C22⋊D5311yescharacteristic
839C22×C4C2×C22⋊D5311yescharacteristic
840C22×C4C2×C22⋊D5311yescharacteristic
841C22×C4C2×C22⋊D5311yescharacteristic
842C22×C4C2×C22⋊D5311yescharacteristic
843C22×C4C2×C22⋊D5311yescharacteristic
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—1068no—
854M16—2124no—
855C2×C8—538no—
856C2×C8—2124no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—532no—
861C4⋊C4—532no—
862C4⋊C4—1061no—
863C4⋊C4—1061no—
864C4⋊C4—1062no—
865C4⋊C4—1062no—
866C4⋊C4—1062no—
867C4⋊C4—1062no—
868C4⋊C4C23×D5314yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—1062no—
874C22⋊C4—1062no—
875C22⋊C4—1062no—
876C22⋊C4—1062no—
877C22⋊C4—1062no—
878C22⋊C4—1062no—
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—24no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—816no—
917C23—1062no—
918C23—2122no—
919C23—2122no—
920C23—2122no—
921C23#1313324314yescomplemented
922C23C22×C22⋊D5311yescharacteristic
923C23C22×C22⋊D5311yescharacteristic
924C23C22×C22⋊D5311yescharacteristic
925C23C22×C22⋊D5311yescharacteristic
926C23C22×C22⋊D5311yescharacteristic
927C23C22×C22⋊D5311yescharacteristic
928C23C22×C22⋊D5311yescharacteristic
929Q8—1064no—
930Q8—2122no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—1064no—
940D4—2122no—
941D4—2124no—
942D4—2124no—
943D4—2124no—
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—24no—
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—41no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—1062no—
979C2×C4—1062no—
980C2×C4—1062no—
981C2×C4—2124no—
982C2×C4—2122no—
983C2×C4—2122no—
984C2×C4—2122no—
985C2×C4—2124no—
986C2×C4C22×C22⋊D5311yescharacteristic
987C2×C4C22×C22⋊D5311yescharacteristic
988C2×C4C22×C22⋊D5311yescharacteristic
989C2×C4C22×C22⋊D5311yescharacteristic
990C2×C4C22×C22⋊D5311yescharacteristic
991C2×C4C22×C22⋊D5311yescharacteristic
992C2×C4C22×C22⋊D5311yescharacteristic
993C2×C4#1313326214yes—
994C2×C4C24×D5311yescharacteristic
995C8—1068no—
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—44no—
1020C22—44no—
1021C22—44no—
1022C22—88no—
1023C22—88no—
1024C22—88no—
1025C22—4244no—
1026C22—2122no—
1027C22—2122no—
1028C22—2122no—
1029C22#1681118212yes—
1030C22C2×#1313324312yes—
1031C22C2×#1313324312yes—
1032C22C2×#1313324312yes—
1033C22#1681142112yes—
1034C22C23×C22⋊D5311yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—2122no—
1043C4—2122no—
1044C4—2122no—
1045C4#1681118212yes—
1046C4C2×#1313326212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—4242no—
1056C2C2×#1681118211yescharacteristic
1057C2C22×#1313324311yescharacteristic
1058C2C2×#1681142111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC22×#121×C53C2
socleC22×C53C23×D4
hypercenterC22×#121D53
hypocenterC53#60750
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16811134C2semidirect
2. #20285529C2semidirect
3. #20285521C2semidirect
4. #20285512C2semidirect
5. #20285480C2semidirect
6. #20285472C2semidirect
7. #20285463C2semidirect
8. #20284651C2semidirect
9. #20284638C2semidirect
10. #20284330C2semidirect
11. #20283965C2semidirect
12. #20283942C2semidirect
13. C2×#16810587C2semidirect
14. C22×#121×C53C2semidirect
15. C22×#11719945C22semidirect
16. C2×#13133243C22semidirect
17. C22×#11719917C22semidirect
23. #16811134C22semidirect
24. #16811134C22semidirect
25. #16811134C22semidirect
27. C2×#13133196C22semidirect
28. C2×#13133196C22semidirect
29. C2×#13133191C22semidirect
30. C2×#13133191C22semidirect
34. C2×#13133176C22semidirect
35. #16810958C22semidirect
36. #16810953C22semidirect
37. #16810944C22semidirect
38. #16810941C22semidirect
39. #16810939C22semidirect
40. #16810936C22semidirect
41. #16810934C22semidirect
42. #16810874C22semidirect
43. #16810867C22semidirect
44. #16810857C22semidirect
45. #16810850C22semidirect
46. #16810774C22semidirect
47. #16810774C22semidirect
48. #16810766C22semidirect
49. #16810761C22semidirect
50. #16810757C22semidirect
51. #16810757C22semidirect
52. #16810756C22semidirect
53. #16810663C22semidirect
54. #16810628C22semidirect
55. #16810622C22semidirect
56. #16810587C22semidirect
57. #16810587C22semidirect
58. #16810587C22semidirect
59. #16810587C22semidirect
60. C2×C22⋊#88322C22semidirect
61. C2×C22⋊#88322C22semidirect
63. C23×D4×C53C22semidirect
74. C2×#121×C53C22semidirect
75. C2×#121×C53C22semidirect
76. C2×#121×C53C22semidirect
77. C22×C4⋊C4×C53C22semidirect
83. C2×#11719945C23semidirect
84. C22×Dic106C23semidirect
85. C22×D212C23semidirect
91. C2×#11719923C23semidirect
92. C2×#11719922C23semidirect
95. C2×#11719917C23semidirect
96. C22×#88322C23semidirect
107. #13133196C23semidirect
108. #13133196C23semidirect
115. #13133191C23semidirect
116. #13133191C23semidirect
132. #13133176C23semidirect
133. C2×C4⋊Dic53C23semidirect
134. C2×C4⋊Dic53C23semidirect
143. #13133150C23semidirect
144. #13133148C23semidirect
145. #13133140C23semidirect
146. #13133138C23semidirect
147. #13133138C23semidirect
148. #13133137C23semidirect
151. C22⋊#88322C23semidirect
152. C22⋊#88322C23semidirect
387. C23×C53AGL(1,ℤ/8)semidirect
519. C22×#121D53semidirect
546. C23×D4C2×D53semidirect
572. C2×#121C2×D53semidirect
573. C2×#121C2×D53semidirect
574. C2×#121C2×D53semidirect
579. C22×C4⋊C4C2×D53semidirect
608. C53#60750semidirect
921. C23#13133243semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
#202855292
#202855212
#202855122
#202854802
#202854722
#202854632
#202846512
#202846382
#202843302
#202839652
#202839422
C2×#168105872
C22×#121×C532
#6075053