Finite Group Databasebeta

← #36275149

Subgroups — #36275149

Order 21248.

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×#19128212C211yesmaximal, characteristic, complemented
2C22×#14581766C211yesmaximal, characteristic, complemented
3#24918279C214yesmaximal, complemented
4#24918270C212yesmaximal, complemented
5#24918263C212yesmaximal, complemented
6#24918230C214yesmaximal, complemented
7#24918221C212yesmaximal, complemented
8#24918214C212yesmaximal, complemented
9#24917404C212yesmaximal, complemented
10#24917388C212yesmaximal, complemented
11#24917082C214yesmaximal, complemented
12#24916717C212yesmaximal, complemented
13#24916693C212yesmaximal, complemented
14C2×#407×C83C211yesmaximal, characteristic, complemented
15C22×#13050590C2211yescharacteristic, complemented
16C23×D332C2211yescharacteristic, complemented
17C23×C22⋊D83—21no—
18C2×#14581820C2214yescomplemented
19#19128212—21no—
20#19128212—21no—
21#19128212—21no—
22#19128212—21no—
23#19128212C2212yes—
24#19128212C2212yescomplemented
25#19128212C2212yescomplemented
26#19128212C2212yescomplemented
27C2×#14581775—21no—
28C2×#14581771C2211yescharacteristic, complemented
29C2×#14581771C2211yescharacteristic, complemented
30C2×#14581766—21no—
31C2×#14581766—21no—
32C2×#14581766—21no—
33C2×#14581766—21no—
34C2×#14581766—21no—
35C2×#14581766—21no—
36C2×#14581766C2212yes—
37C2×#14581766C2212yes—
38C2×#14581766C2212yes—
39C2×#14581766C2212yescomplemented
40C2×#14581766C2212yescomplemented
41C2×#14581766C2212yescomplemented
42C2×#14581766C2211yescharacteristic, complemented
43C2×#14581766C2211yescharacteristic, complemented
44C2×#14581761—21no—
45C2×C4×C22⋊D83—21no—
46C2×C4×C22⋊D83—21no—
47C2×#14581751C2211yescharacteristic, complemented
48C22×C4⋊Dic83C2211yescharacteristic, complemented
49C22×(C2×D83)⋊C4—21no—
50#19128037C2214yescomplemented
51#19128032C2214yescomplemented
52#19128026C2218yescomplemented
53#19128020C2214yescomplemented
54#19128020C2214yescomplemented
55#19128015C2214yescomplemented
56#19128015C2214yescomplemented
57#19127954C2218yescomplemented
58#19127947C2218yescomplemented
59#19127937C2218yescomplemented
60#19127930C2218yescomplemented
61#19127854C2214yescomplemented
62#19127854C2214yescomplemented
63#19127848C2218yescomplemented
64#19127842C2214yescomplemented
65#19127837C2214yescomplemented
66#19127837C2214yescomplemented
67#19127837C2214yescomplemented
68#19127743C2214yescomplemented
69#19127707C2214yescomplemented
70#19127703C2214yescomplemented
71C24×C4×C83C2211yescharacteristic
72C22×M16×C83C2212yescomplemented
73#407×C83C2212yescomplemented
74#407×C83C2212yescomplemented
75#407×C83C2212yescomplemented
76#407×C83C2212yescomplemented
77C2×C22⋊C8×C83C2212yescomplemented
78C2×C22⋊C8×C83C2212yescomplemented
79C24×D83—21no—
80C2×#13050590—21no—
81C2×#13050590—21no—
82C2×#13050590—44no—
83C2×#13050590C2312yes—
84C2×#13050590C2312yescomplemented
85C22×Dic166C2311yescharacteristic, complemented
86C22×D332—21no—
87C22×D332—21no—
88C22×D332—21no—
89C22×D332—44no—
90C22×D332C2312yes—
91C22×D332C2312yes—
92C22×D332C2312yes—
93C22×D332C2311yescharacteristic, complemented
94C22×C22⋊D83—21no—
95C22×C22⋊D83—21no—
96C22×C22⋊D83—21no—
97C22×C22⋊D83—22no—
98C22×C22⋊D83—22no—
99C22×C22⋊D83—22no—
100C22×C22⋊D83—22no—
101C22×C22⋊D83—22no—
102C22×C22⋊D83—22no—
103C22×C22⋊D83—48no—
104C23×Dic83—21no—
105C22×C4×D83—21no—
106#14581820—48no—
107C2×#13050579C2318yescomplemented
108C2×D664C2318yescomplemented
109#14581775—22no—
110#14581775—22no—
111#14581775—22no—
112#14581775—22no—
113#14581771—21no—
114#14581771—21no—
115#14581771—21no—
116#14581771—21no—
117#14581771C2312yes—
118#14581771C2312yes—
119#14581771C2312yescomplemented
120#14581771C2312yescomplemented
121#14581766—22no—
122#14581766—22no—
123#14581766—22no—
124#14581766—22no—
125#14581766—22no—
126#14581766—22no—
127#14581766—22no—
128#14581766—22no—
129#14581766—22no—
130#14581766—22no—
131#14581766—22no—
132#14581766—22no—
133#14581766—21no—
134#14581766—21no—
135#14581766—21no—
136#14581766—21no—
137#14581766C2312yes—
138#14581766C2312yes—
139#14581766C2314yes—
140#14581766C2314yes—
141#14581766C2314yes—
142#14581766C2314yes—
143#14581766C2312yescomplemented
144#14581766C2312yescomplemented
145#14581761—22no—
146#14581761—22no—
147#14581761—22no—
148#14581761—22no—
149C4×C22⋊D83—22no—
150C4×C22⋊D83—22no—
151C4×C22⋊D83—22no—
152C4×C22⋊D83—22no—
153C4×C22⋊D83—22no—
154C4×C22⋊D83—22no—
155C4×C22⋊D83—22no—
156C4×C22⋊D83—22no—
157#14581751—21no—
158#14581751—21no—
159#14581751C2312yes—
160#14581751C2312yescomplemented
161C2×C4⋊Dic83—21no—
162C2×C4⋊Dic83—21no—
163C2×C4⋊Dic83—21no—
164C2×C4⋊Dic83C2312yes—
165C2×C4⋊Dic83C2312yes—
166C2×C4⋊Dic83C2312yes—
167C2×C4⋊Dic83C2311yescharacteristic, complemented
168C2×C4⋊Dic83C2311yescharacteristic, complemented
169C2×Dic83⋊C4—21no—
170C2×Dic83⋊C4—21no—
171C2×C22⋊Dic83—21no—
172C2×C22⋊Dic83—21no—
173C2×C22⋊Dic83—21no—
174C2×(C2×D83)⋊C4—22no—
175C2×(C2×D83)⋊C4—22no—
176C2×(C2×D83)⋊C4—22no—
177C2×(C2×D83)⋊C4—22no—
178C2×(C2×D83)⋊C4—22no—
179C2×(C2×D83)⋊C4—22no—
180C2×(C2×D83)⋊C4—21no—
181C2×(C2×D83)⋊C4—21no—
182C2×C4×Dic83—21no—
183#14581726C2318yescomplemented
184#14581724C2318yescomplemented
185#14581717C2318yescomplemented
186#14581714C2318yescomplemented
187#14581714C2318yescomplemented
188#14581714C2318yescomplemented
189C25×C83D411yescharacteristic
190C23×C4×C83—44no—
191C23×C4×C83D411yescharacteristic
192C23×C4×C83D411yescharacteristic
193C23×C4×C83D411yescharacteristic
194C23×C4×C83D411yescharacteristic
195C23×C4×C83D411yescharacteristic
196C23×C4×C83D411yescharacteristic
197C23×C4×C83D411yescharacteristic
198C23×C4×C83C2311yescharacteristic
199C23×C4×C83C2311yescharacteristic
200C23×C4×C83C2311yescharacteristic
201C23×C4×C83C2311yescharacteristic
202C23×C4×C83C2311yescharacteristic
203C23×C4×C83C2311yescharacteristic
204C23×C4×C83C2311yescharacteristic
205C2×M16×C83—44no—
206C2×M16×C83C2314yes—
207C2×M16×C83C2314yescomplemented
208C22×C8×C83C2314yescomplemented
209C22⋊C8×C83C2314yes—
210C22⋊C8×C83C2314yes—
211C22⋊C8×C83C2314yescomplemented
212C22⋊C8×C83C2314yescomplemented
213C23×D83—21no—
214C23×D83—22no—
215C23×D83—22no—
216C23×D83—22no—
217C23×D83—44no—
218C23×D83—44no—
219C23×D83—44no—
220#13050590—28no—
221#13050590—44no—
222#13050590—44no—
223#13050590—44no—
224C2×Dic166—21no—
225C2×Dic166—42no—
226C2×Dic166C2412yes—
227C2×D332—28no—
228C2×D332—22no—
229C2×D332—22no—
230C2×D332—22no—
231C2×D332—21no—
232C2×D332—44no—
233C2×D332—44no—
234C2×D332—42no—
235C2×D332—44no—
236C2×D332—44no—
237C2×D332—44no—
238C2×D332C2414yes—
239C2×D332C2412yes—
240C2×C22⋊D83—22no—
241C2×C22⋊D83—22no—
242C2×C22⋊D83—22no—
243C2×C22⋊D83—22no—
244C2×C22⋊D83—22no—
245C2×C22⋊D83—22no—
246C2×C22⋊D83—24no—
247C2×C22⋊D83—24no—
248C2×C22⋊D83—24no—
249C2×C22⋊D83—24no—
250C2×C22⋊D83—44no—
251C2×C22⋊D83—48no—
252C2×C22⋊D83—48no—
253C2×C22⋊D83—48no—
254C2×C22⋊D83—48no—
255C2×C22⋊D83—48no—
256C2×C22⋊D83—44no—
257C2×C22⋊D83—44no—
258C2×C22⋊D83—48no—
259C22×Dic83—21no—
260C22×Dic83—22no—
261C22×Dic83—22no—
262C22×Dic83—22no—
263C22×Dic83—21no—
264C22×Dic83—21no—
265C22×Dic83—44no—
266C2×C4×D83—22no—
267C2×C4×D83—22no—
268C2×C4×D83—44no—
269#13050579—48no—
270D664—48no—
271C4⋊Dic83—22no—
272C4⋊Dic83—22no—
273C4⋊Dic83—22no—
274C4⋊Dic83—21no—
275C4⋊Dic83—21no—
276C4⋊Dic83C2414yes—
277C4⋊Dic83C2412yes—
278C4⋊Dic83C2412yes—
279Dic83⋊C4—22no—
280Dic83⋊C4—22no—
281Dic83⋊C4—22no—
282Dic83⋊C4—22no—
283C22⋊Dic83—22no—
284C22⋊Dic83—22no—
285C22⋊Dic83—22no—
286C22⋊Dic83—22no—
287C22⋊Dic83—22no—
288C22⋊Dic83—22no—
289(C2×D83)⋊C4—24no—
290(C2×D83)⋊C4—24no—
291(C2×D83)⋊C4—24no—
292(C2×D83)⋊C4—24no—
293(C2×D83)⋊C4—22no—
294(C2×D83)⋊C4—22no—
295(C2×D83)⋊C4—22no—
296(C2×D83)⋊C4—22no—
297C4×Dic83—22no—
298C4×Dic83—22no—
299C24×C83—24no—
300C24×C83—42no—
301C24×C83—42no—
302C24×C83C2×D411yescharacteristic
303C24×C83C2×D411yescharacteristic
304C24×C83C2×D411yescharacteristic
305C24×C83C2×D411yescharacteristic
306C24×C83C2×D411yescharacteristic
307C24×C83C2×D411yescharacteristic
308C24×C83C2×D411yescharacteristic
309C22×C4×C83—24no—
310C22×C4×C83—24no—
311C22×C4×C83—24no—
312C22×C4×C83—42no—
313C22×C4×C83—42no—
314C22×C4×C83—42no—
315C22×C4×C83—42no—
316C22×C4×C83—42no—
317C22×C4×C83—42no—
318C22×C4×C83—42no—
319C22×C4×C83—42no—
320C22×C4×C83—42no—
321C22×C4×C83—42no—
322C22×C4×C83—42no—
323C22×C4×C83C2×D411yescharacteristic
324C22×C4×C83C2×D411yescharacteristic
325C22×C4×C83C2×D411yescharacteristic
326C22×C4×C83C2×D411yescharacteristic
327C22×C4×C83C2×D411yescharacteristic
328C22×C4×C83C2×D411yescharacteristic
329C22×C4×C83C2×D411yescharacteristic
330C22×C4×C83C2×D411yescharacteristic
331C22×C4×C83C2×D411yescharacteristic
332C22×C4×C83C2×D411yescharacteristic
333C22×C4×C83C2×D411yescharacteristic
334C22×C4×C83C2×D411yescharacteristic
335C22×C4×C83C2×D411yescharacteristic
336C22×C4×C83C2×D411yescharacteristic
337C22×C4×C83C2×D411yescharacteristic
338C22×C4×C83C2×D411yescharacteristic
339C22×C4×C83C2×D411yescharacteristic
340C22×C4×C83C2×D411yescharacteristic
341C22×C4×C83C2×D411yescharacteristic
342C22×C4×C83C2×D411yescharacteristic
343C22×C4×C83C2×D411yescharacteristic
344C22×C4×C83C2411yescharacteristic
345C22×C4×C83C2411yescharacteristic
346C22×C4×C83C2411yescharacteristic
347C22×C4×C83C2411yescharacteristic
348C22×C4×C83C2411yescharacteristic
349C22×C4×C83C2411yescharacteristic
350C22×C4×C83C2411yescharacteristic
351M16×C83—28no—
352M16×C83—44no—
353C2×C8×C83—44no—
354C2×C8×C83C2418yes—
355C23×C83—22no—
356C23×C83—22no—
357C23×C83—22no—
358C23×C83—22no—
359C23×C83—22no—
360C23×C83—22no—
361C23×C83—22no—
362C23×C83—22no—
363C23×C83—22no—
364C23×C83—22no—
365C23×C83—22no—
366C23×C83—22no—
367C23×C83—41no—
368C23×C83—41no—
369C23×C83—41no—
370C23×C83—41no—
371C23×C83—41no—
372C23×C83—41no—
373C23×C83—41no—
374C23×C83—41no—
375C23×C83—416no—
376C23×C83AGL(1,ℤ/8)14yescomplemented
377C23×C83C22×D411yescharacteristic
378C23×C83C22×D411yescharacteristic
379C23×C83C22×D411yescharacteristic
380C23×C83C22×D411yescharacteristic
381C23×C83C22×D411yescharacteristic
382C23×C83C22×D411yescharacteristic
383C23×C83C22×D411yescharacteristic
384C22×D83—22no—
385C22×D83—24no—
386C22×D83—42no—
387C22×D83—44no—
388C22×D83—44no—
389C22×D83—42no—
390C22×D83—44no—
391C22×D83—44no—
392C22×D83—44no—
393C22×D83—44no—
394C22×D83—44no—
395C22×D83—44no—
396C22×D83—42no—
397C22×D83—44no—
398C22×D83—816no—
399C2×C4×C83—22no—
400C2×C4×C83—22no—
401C2×C4×C83—22no—
402C2×C4×C83—22no—
403C2×C4×C83—22no—
404C2×C4×C83—22no—
405C2×C4×C83—22no—
406C2×C4×C83—22no—
407C2×C4×C83—22no—
408C2×C4×C83—22no—
409C2×C4×C83—22no—
410C2×C4×C83—22no—
411C2×C4×C83—22no—
412C2×C4×C83—22no—
413C2×C4×C83—22no—
414C2×C4×C83—41no—
415C2×C4×C83—41no—
416C2×C4×C83—41no—
417C2×C4×C83—41no—
418C2×C4×C83—41no—
419C2×C4×C83—41no—
420C2×C4×C83—41no—
421C2×C4×C83—41no—
422C2×C4×C83—41no—
423C2×C4×C83—41no—
424C2×C4×C83—41no—
425C2×C4×C83—41no—
426C2×C4×C83C22×D411yescharacteristic
427C2×C4×C83C22×D411yescharacteristic
428C2×C4×C83C22×D411yescharacteristic
429C2×C4×C83C22×D411yescharacteristic
430C2×C4×C83C22×D411yescharacteristic
431C2×C4×C83C22×D411yescharacteristic
432C2×C4×C83C22×D411yescharacteristic
433C2×C4×C83H(5,𝔽2)14yes—
434C2×C4×C83C2511yescharacteristic
435C22⋊D83—44no—
436C22⋊D83—48no—
437C22⋊D83—48no—
438C22⋊D83—44no—
439C22⋊D83—44no—
440C22⋊D83—44no—
441C22⋊D83—44no—
442C22⋊D83—48no—
443C22⋊D83—48no—
444C22⋊D83—44no—
445C2×Dic83—22no—
446C2×Dic83—22no—
447C2×Dic83—24no—
448C2×Dic83—22no—
449C2×Dic83—42no—
450C2×Dic83—44no—
451C2×Dic83—44no—
452C2×Dic83—42no—
453C2×Dic83—44no—
454C2×Dic83—42no—
455D332—24no—
456D332—28no—
457D332—44no—
458D332—44no—
459D332—42no—
460D332—44no—
461C4×D83—44no—
462C4×D83—44no—
463Dic166—24no—
464Dic166—42no—
465C8×C83—28no—
466C22×C83—28no—
467C22×C83—21no—
468C22×C83—21no—
469C22×C83—21no—
470C22×C83—21no—
471C22×C83—21no—
472C22×C83—21no—
473C22×C83—21no—
474C22×C83—21no—
475C22×C83—21no—
476C22×C83—21no—
477C22×C83—21no—
478C22×C83—21no—
479C22×C83—21no—
480C22×C83—21no—
481C22×C83—21no—
482C22×C83—21no—
483C22×C83—44no—
484C22×C83—44no—
485C22×C83—44no—
486C22×C83—44no—
487C22×C83—44no—
488C22×C83—44no—
489C22×C83#53412yes—
490C22×C83C2×AGL(1,ℤ/8)12yes—
491C22×C83C2×AGL(1,ℤ/8)12yes—
492C22×C83C2×AGL(1,ℤ/8)12yes—
493C22×C83#57512yes—
494C22×C83C23×D411yescharacteristic
495C2×D83—42no—
496C2×D83—44no—
497C2×D83—44no—
498C2×D83—42no—
499C2×D83—42no—
500C2×D83—44no—
501C2×D83—84no—
502C2×D83—88no—
503C2×D83—88no—
504C2×D83—88no—
505C4×C83—21no—
506C4×C83—21no—
507C4×C83—21no—
508C4×C83—21no—
509C4×C83—21no—
510C4×C83—21no—
511C4×C83#53412yes—
512C4×C83C2×H(5,𝔽2)12yes—
513Dic83—42no—
514Dic83—44no—
515Dic83—42no—
516Dic83—42no—
517#60750—831nomaximal, Sylow
518C2×C83—22no—
519C2×C83—22no—
520C2×C83—22no—
521C2×C83—22no—
522C2×C83—22no—
523C2×C83—41no—
524C2×C83—41no—
525C2×C83C2×#53411yescharacteristic
526C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
527C2×C83C2×#57511yescharacteristic
528D83—82no—
529D83—84no—
530C2×#525—831no—
531C22×#121—831no—
532#3194—834no—
533#3193—832no—
534#3192—832no—
535#3188—834no—
536#3187—832no—
537#3186—832no—
538#3094—832no—
539#3092—832no—
540#3055—834no—
541#3006—832no—
542#3003—832no—
543C2×#407D8311yescharacteristic, complemented
544C83#6075011yescharacteristic, complemented, Sylow
545C22×#41—831no—
546C23×D4—831no—
547C23×D4—1661no—
548C24×C4C2×D8311yescharacteristic
549C2×AGL(1,ℤ/8)—834no—
550C22×M16C2×D8312yescomplemented
551#525—832no—
552#525—832no—
553#525—832no—
554#525—832no—
555#525—1661no—
556#525—1661no—
557#525—1661no—
558#525—1661no—
559C2×#123—1661no—
560C2×C22⋊Q8—831no—
561C2×C22⋊Q8—831no—
562C2×#121—832no—
563C2×#121—832no—
564C2×#121—832no—
565C2×#121—832no—
566C2×#121—832no—
567C2×#121—832no—
568C2×#121—831no—
569C2×#121—831no—
570C2×#121—1661no—
571C2×#121—1661no—
572C2×#121—1661no—
573C2×#121—1661no—
574C2×#121—1661no—
575C2×#121—1661no—
576C2×#120—1661no—
577C2×C4×D4—1661no—
578C2×C4×D4—1661no—
579C2×#117—831no—
580C22×C4⋊C4—831no—
581C22×C22⋊C4—1661no—
582#484—834no—
583#483—834no—
584#482—838no—
585#481—834no—
586#481—834no—
587#480—834no—
588#480—834no—
589#469—838no—
590#468—838no—
591#466—838no—
592#465—838no—
593#450—834no—
594#450—834no—
595#449—838no—
596#448—834no—
597#447—834no—
598#447—834no—
599#447—834no—
600#428—834no—
601#418—834no—
602#417—834no—
603#407C2×D8312yescomplemented
604#407C2×D8312yescomplemented
605#407C2×D8312yescomplemented
606#407C2×D8312yescomplemented
607C2×C22⋊C8C2×D8312yescomplemented
608C2×C22⋊C8C2×D8312yescomplemented
609C25—1661no—
610C25D33211yescharacteristic
611C2×#41—3324no—
612C2×#41—832no—
613C2×#41—832no—
614C2×#41—1661no—
615C2×#41—1661no—
616C22×Q8—831no—
617C22×D4—3324no—
618C22×D4—3328no—
619C22×D4—832no—
620C22×D4—832no—
621C22×D4—831no—
622C22×D4—832no—
623C22×D4—1661no—
624C22×D4—1661no—
625C22×D4—1661no—
626C22×D4—1662no—
627C22×D4—1662no—
628C22×D4—1662no—
629C22×D4—1662no—
630C22×D4—1662no—
631C22×D4—1662no—
632C22×D4—1661no—
633C22×D4—1661no—
634C22×D4—1661no—
635C23×C4—44no—
636C23×C4—1661no—
637C23×C4—1661no—
638C23×C4D33211yescharacteristic
639C23×C4D33211yescharacteristic
640C23×C4D33211yescharacteristic
641C23×C4D33211yescharacteristic
642C23×C4D33211yescharacteristic
643C23×C4D33211yescharacteristic
644C23×C4D33211yescharacteristic
645C23×C4C22×D8311yescharacteristic
646C23×C4C22×D8311yescharacteristic
647C23×C4C22×D8311yescharacteristic
648C23×C4C22×D8311yescharacteristic
649C23×C4C22×D8311yescharacteristic
650C23×C4C22×D8311yescharacteristic
651C23×C4C22×D8311yescharacteristic
652AGL(1,ℤ/8)—3328no—
653C2×SD16—838no—
654C2×D8—838no—
655C2×M16—44no—
656C2×M16C22×D8314yes—
657C2×M16C22×D8314yescomplemented
658C22×C8C22×D8314yescomplemented
659#123—1662no—
660#123—1662no—
661#123—1662no—
662#123—1662no—
663C22⋊Q8—832no—
664C22⋊Q8—832no—
665C22⋊Q8—832no—
666C22⋊Q8—832no—
667C22⋊Q8—1661no—
668C22⋊Q8—1661no—
669C22⋊Q8—1661no—
670C22⋊Q8—1661no—
671#121—834no—
672#121—834no—
673#121—834no—
674#121—834no—
675#121—832no—
676#121—832no—
677#121—832no—
678#121—832no—
679#121—1662no—
680#121—1662no—
681#121—1662no—
682#121—1662no—
683#121—1662no—
684#121—1662no—
685#121—1662no—
686#121—1662no—
687#121—1662no—
688#121—1662no—
689#121—1662no—
690#121—1662no—
691#121—1661no—
692#121—1661no—
693#121—1661no—
694#121—1661no—
695#120—1662no—
696#120—1662no—
697#120—1662no—
698#120—1662no—
699C4×D4—1662no—
700C4×D4—1662no—
701C4×D4—1662no—
702C4×D4—1662no—
703C4×D4—1662no—
704C4×D4—1662no—
705C4×D4—1662no—
706C4×D4—1662no—
707#117—832no—
708#117—832no—
709#117—1661no—
710#117—1661no—
711C2×C4⋊C4—832no—
712C2×C4⋊C4—832no—
713C2×C4⋊C4—832no—
714C2×C4⋊C4—831no—
715C2×C4⋊C4—831no—
716C2×C4⋊C4—1661no—
717C2×C4⋊C4—1661no—
718C2×C4⋊C4—1661no—
719C2×C4⋊C4—1661no—
720C2×C4⋊C4—1661no—
721C2×C22⋊C4—1661no—
722C2×C22⋊C4—1661no—
723C2×C22⋊C4—1661no—
724C2×C22⋊C4—1662no—
725C2×C22⋊C4—1662no—
726C2×C22⋊C4—1662no—
727C2×C22⋊C4—1662no—
728C2×C22⋊C4—1662no—
729C2×C22⋊C4—1662no—
730C2×C22⋊C4—1661no—
731C2×C22⋊C4—1661no—
732C2×C42—1661no—
733#107—838no—
734#106—838no—
735#103—838no—
736#102—838no—
737#102—838no—
738#102—838no—
739C22⋊C8C22×D8314yes—
740C22⋊C8C22×D8314yes—
741C22⋊C8C22×D8314yescomplemented
742C22⋊C8C22×D8314yescomplemented
743C24—24no—
744C24—42no—
745C24—42no—
746C24—3324no—
747C24—3324no—
748C24—3324no—
749C24—1661no—
750C24—1662no—
751C24—1662no—
752C24—1662no—
753C24C2×D33211yescharacteristic
754C24C2×D33211yescharacteristic
755C24C2×D33211yescharacteristic
756C24C2×D33211yescharacteristic
757C24C2×D33211yescharacteristic
758C24C2×D33211yescharacteristic
759C24C2×D33211yescharacteristic
760#41—3324no—
761#41—3324no—
762#41—3324no—
763#41—1668no—
764C2×Q8—3322no—
765C2×Q8—832no—
766C2×Q8—1661no—
767C2×D4—3324no—
768C2×D4—3324no—
769C2×D4—3324no—
770C2×D4—3324no—
771C2×D4—3324no—
772C2×D4—3322no—
773C2×D4—3328no—
774C2×D4—3328no—
775C2×D4—3328no—
776C2×D4—3328no—
777C2×D4—3328no—
778C2×D4—3324no—
779C2×D4—3324no—
780C2×D4—3328no—
781C2×D4—3324no—
782C2×D4—832no—
783C2×D4—834no—
784C2×D4—1662no—
785C2×D4—1662no—
786C2×D4—1662no—
787C2×D4—1662no—
788C2×D4—1662no—
789C2×D4—1662no—
790C2×D4—1664no—
791C2×D4—1664no—
792C2×D4—1664no—
793C2×D4—1664no—
794C2×D4—1662no—
795C2×D4—1662no—
796C2×D4—1662no—
797C2×D4—1661no—
798C2×D4—1668no—
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—3324no—
814C22×C4—3324no—
815C22×C4—1661no—
816C22×C4—1661no—
817C22×C4—1662no—
818C22×C4—1662no—
819C22×C4—1662no—
820C22×C4—1661no—
821C22×C4—1662no—
822C22×C4—1662no—
823C22×C4C2×D33211yescharacteristic
824C22×C4C2×D33211yescharacteristic
825C22×C4C2×D33211yescharacteristic
826C22×C4C2×D33211yescharacteristic
827C22×C4C2×D33211yescharacteristic
828C22×C4C2×D33211yescharacteristic
829C22×C4C2×D33211yescharacteristic
830C22×C4C2×D33211yescharacteristic
831C22×C4C2×D33211yescharacteristic
832C22×C4C2×D33211yescharacteristic
833C22×C4C2×D33211yescharacteristic
834C22×C4C2×D33211yescharacteristic
835C22×C4C2×D33211yescharacteristic
836C22×C4C2×D33211yescharacteristic
837C22×C4C2×D33211yescharacteristic
838C22×C4C2×D33211yescharacteristic
839C22×C4C2×D33211yescharacteristic
840C22×C4C2×D33211yescharacteristic
841C22×C4C2×D33211yescharacteristic
842C22×C4C2×D33211yescharacteristic
843C22×C4C2×D33211yescharacteristic
844C22×C4C23×D8311yescharacteristic
845C22×C4C23×D8311yescharacteristic
846C22×C4C23×D8311yescharacteristic
847C22×C4C23×D8311yescharacteristic
848C22×C4C23×D8311yescharacteristic
849C22×C4C23×D8311yescharacteristic
850C22×C4C23×D8311yescharacteristic
851SD16—3328no—
852D8—3328no—
853M16—28no—
854M16—44no—
855C2×C8—44no—
856C2×C8C23×D8318yes—
857C4⋊C4—832no—
858C4⋊C4—832no—
859C4⋊C4—834no—
860C4⋊C4—1662no—
861C4⋊C4—1662no—
862C4⋊C4—1662no—
863C4⋊C4—1661no—
864C4⋊C4—1661no—
865C4⋊C4—1662no—
866C4⋊C4—1662no—
867C4⋊C4—1662no—
868C4⋊C4—1662no—
869C22⋊C4—1662no—
870C22⋊C4—1662no—
871C22⋊C4—1662no—
872C22⋊C4—1662no—
873C22⋊C4—1662no—
874C22⋊C4—1662no—
875C22⋊C4—1664no—
876C22⋊C4—1664no—
877C22⋊C4—1664no—
878C22⋊C4—1664no—
879C22⋊C4—1662no—
880C22⋊C4—1662no—
881C22⋊C4—1662no—
882C22⋊C4—1662no—
883C42—1662no—
884C42—1662no—
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—3322no—
907C23—3324no—
908C23—3324no—
909C23—3324no—
910C23—3324no—
911C23—3322no—
912C23—3324no—
913C23—3324no—
914C23—3324no—
915C23—3322no—
916C23—3324no—
917C23—3324no—
918C23—66416no—
919C23—1662no—
920C23—1664no—
921C23#1458182014yescomplemented
922C23C22×D33211yescharacteristic
923C23C22×D33211yescharacteristic
924C23C22×D33211yescharacteristic
925C23C22×D33211yescharacteristic
926C23C22×D33211yescharacteristic
927C23C22×D33211yescharacteristic
928C23C22×D33211yescharacteristic
929Q8—3322no—
930Q8—1664no—
931D4—3324no—
932D4—3324no—
933D4—3322no—
934D4—3328no—
935D4—3328no—
936D4—3324no—
937D4—3324no—
938D4—3328no—
939D4—3328no—
940D4—3324no—
941D4—3324no—
942D4—3324no—
943D4—3324no—
944D4—3324no—
945D4—1664no—
946D4—1668no—
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—3324no—
975C2×C4—3324no—
976C2×C4—3324no—
977C2×C4—3322no—
978C2×C4—3322no—
979C2×C4—3324no—
980C2×C4—3322no—
981C2×C4—3324no—
982C2×C4—1662no—
983C2×C4—1662no—
984C2×C4—1664no—
985C2×C4—1662no—
986C2×C4C22×D33211yescharacteristic
987C2×C4C22×D33211yescharacteristic
988C2×C4C22×D33211yescharacteristic
989C2×C4C22×D33211yescharacteristic
990C2×C4C22×D33211yescharacteristic
991C2×C4C22×D33211yescharacteristic
992C2×C4C22×D33211yescharacteristic
993C2×C4#1458183714yes—
994C2×C4C24×D8311yescharacteristic
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—3324no—
1020C22—3322no—
1021C22—3322no—
1022C22—3324no—
1023C22—3322no—
1024C22—3324no—
1025C22—6648no—
1026C22—6648no—
1027C22—6648no—
1028C22—6644no—
1029C22#1912826312yes—
1030C22C2×#1458182012yes—
1031C22C2×#1458182012yes—
1032C22C2×#1458182012yes—
1033C22#1912850112yes—
1034C22C23×D33211yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—3324no—
1042C4—3322no—
1043C4—3322no—
1044C4—3322no—
1045C4#1912826312yes—
1046C4C2×#1458183712yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—6644no—
1055C2—6642no—
1056C2C2×#1912826311yescharacteristic
1057C2C22×#1458182011yescharacteristic
1058C2C2×#1912850111yescharacteristic
subgroupG/H
centerC22C23×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#407×C83C2
socleC22×C83C23×D4
hypercenterC2×#407D83
hypocenterC83#60750
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#19128212C2semidirect
2. C22×#14581766C2semidirect
3. #24918279C2semidirect
4. #24918270C2semidirect
5. #24918263C2semidirect
6. #24918230C2semidirect
7. #24918221C2semidirect
8. #24918214C2semidirect
9. #24917404C2semidirect
10. #24917388C2semidirect
11. #24917082C2semidirect
12. #24916717C2semidirect
13. #24916693C2semidirect
14. C2×#407×C83C2semidirect
15. C22×#13050590C22semidirect
16. C23×D332C22semidirect
18. C2×#14581820C22semidirect
24. #19128212C22semidirect
25. #19128212C22semidirect
26. #19128212C22semidirect
28. C2×#14581771C22semidirect
29. C2×#14581771C22semidirect
39. C2×#14581766C22semidirect
40. C2×#14581766C22semidirect
41. C2×#14581766C22semidirect
42. C2×#14581766C22semidirect
43. C2×#14581766C22semidirect
47. C2×#14581751C22semidirect
48. C22×C4⋊Dic83C22semidirect
50. #19128037C22semidirect
51. #19128032C22semidirect
52. #19128026C22semidirect
53. #19128020C22semidirect
54. #19128020C22semidirect
55. #19128015C22semidirect
56. #19128015C22semidirect
57. #19127954C22semidirect
58. #19127947C22semidirect
59. #19127937C22semidirect
60. #19127930C22semidirect
61. #19127854C22semidirect
62. #19127854C22semidirect
63. #19127848C22semidirect
64. #19127842C22semidirect
65. #19127837C22semidirect
66. #19127837C22semidirect
67. #19127837C22semidirect
68. #19127743C22semidirect
69. #19127707C22semidirect
70. #19127703C22semidirect
72. C22×M16×C83C22semidirect
73. #407×C83C22semidirect
74. #407×C83C22semidirect
75. #407×C83C22semidirect
76. #407×C83C22semidirect
77. C2×C22⋊C8×C83C22semidirect
78. C2×C22⋊C8×C83C22semidirect
84. C2×#13050590C23semidirect
85. C22×Dic166C23semidirect
93. C22×D332C23semidirect
107. C2×#13050579C23semidirect
108. C2×D664C23semidirect
119. #14581771C23semidirect
120. #14581771C23semidirect
143. #14581766C23semidirect
144. #14581766C23semidirect
160. #14581751C23semidirect
167. C2×C4⋊Dic83C23semidirect
168. C2×C4⋊Dic83C23semidirect
183. #14581726C23semidirect
184. #14581724C23semidirect
185. #14581717C23semidirect
186. #14581714C23semidirect
187. #14581714C23semidirect
188. #14581714C23semidirect
207. C2×M16×C83C23semidirect
208. C22×C8×C83C23semidirect
211. C22⋊C8×C83C23semidirect
212. C22⋊C8×C83C23semidirect
376. C23×C83AGL(1,ℤ/8)semidirect
543. C2×#407D83semidirect
544. C83#60750semidirect
550. C22×M16C2×D83semidirect
603. #407C2×D83semidirect
604. #407C2×D83semidirect
605. #407C2×D83semidirect
606. #407C2×D83semidirect
607. C2×C22⋊C8C2×D83semidirect
608. C2×C22⋊C8C2×D83semidirect
657. C2×M16C22×D83semidirect
658. C22×C8C22×D83semidirect
741. C22⋊C8C22×D83semidirect
742. C22⋊C8C22×D83semidirect
921. C23#14581820semidirect

Maximal subgroups

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

subgroupindex
C2×#191282122
C22×#145817662
#249182792
#249182702
#249182632
#249182302
#249182212
#249182142
#249174042
#249173882
#249170822
#249167172
#249166932
C2×#407×C832
#6075083