Finite Group Databasebeta

← C2×#24918252 #36274965

Subgroups — C2×#24918252 #36274965

Order 21248.

2394 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128214C211yesmaximal, characteristic, complemented
2C2×#19128211C211yesmaximal, characteristic, complemented
3#24918252C2116yesmaximal, direct product factor
4C2×#19128045C211yesmaximal, characteristic, complemented
5C2×#19128040C211yesmaximal, characteristic, complemented
6C2×#19128027C211yesmaximal, characteristic, complemented
7C2×#19128024C211yesmaximal, characteristic, complemented
8C2×#19127940C211yesmaximal, characteristic, complemented
9C2×#19127935C211yesmaximal, characteristic, complemented
10C2×#19127930C211yesmaximal, characteristic, complemented
11C2×#19127866C211yesmaximal, characteristic, complemented
12C2×#19127860C211yesmaximal, characteristic, complemented
13C2×#19127847C211yesmaximal, characteristic, complemented
14C2×#19127845C211yesmaximal, characteristic, complemented
15C22×(C2×D83)⋊C8C211yesmaximal, characteristic, complemented
16C2×#465×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×#13050589C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C22×#13050580C2211yescharacteristic, complemented
21C22×#13050579C2211yescharacteristic, complemented
22C22×#13050575C2211yescharacteristic, complemented
23C23×C83⋊C8C2211yescharacteristic
24#19128214—24no—
25#19128214C2218yescomplemented
26#19128211—24no—
27#19128211C2218yescomplemented
28C2×#14581777—21no—
29C2×#14581774—21no—
30C2×#14581772C2211yescharacteristic
31C2×#14581771C2211yescharacteristic
32C2×#14581768C2211yescharacteristic
33C2×#14581767C2211yescharacteristic
34C2×#14581766C2211yescharacteristic
35C2×#14581763C2211yescharacteristic
36C2×#14581762—21no—
37C2×#14581760—21no—
38C2×D4×Dic83—21no—
39C2×#14581754—21no—
40C2×(C22⋊D83)⋊C4—21no—
41C2×(C22⋊D83)⋊C4—21no—
42C2×#14581750C2211yescharacteristic
43C2×#14581750C2211yescharacteristic
44#19128045C2218yescomplemented
45#19128040C2218yescomplemented
46#19128027C2218yescomplemented
47#19128024C2218yescomplemented
48#19127940C2218yescomplemented
49#19127935C2218yescomplemented
50#19127930C2218yescomplemented
51#19127866C2218yescomplemented
52#19127860C2218yescomplemented
53#19127847C2218yescomplemented
54#19127845C2218yescomplemented
55C2×#14581725C2211yescharacteristic, complemented
56C2×#14581725C2211yescharacteristic, complemented
57C2×#14581724C2211yescharacteristic, complemented
58C2×#14581717C2211yescharacteristic, complemented
59C2×#14581716C2211yescharacteristic, complemented
60C2×#14581715C2211yescharacteristic, complemented
61C2×#14581714C2211yescharacteristic, complemented
62C2×#14581713C2211yescharacteristic, complemented
63C2×#14581712C2211yescharacteristic, complemented
64C2×(C2×D83)⋊C8C2211yescharacteristic
65C2×(C2×D83)⋊C8C2211yescharacteristic
66C2×(C2×D83)⋊C8C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×(C2×D83)⋊C8C2218yescomplemented
69C22×SD16×C83C2211yescharacteristic, complemented
70C23×C8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×#121×C83C2211yescharacteristic
73#465×C83C2218yescomplemented
74C2×#106×C83C2211yescharacteristic, complemented
75C2×#103×C83C2211yescharacteristic, complemented
76C2×#102×C83C2211yescharacteristic, complemented
77C24×D83D411yescharacteristic
78C2×#13050591—22no—
79C2×#13050591—42no—
80C2×#13050591—42no—
81C2×#13050591C2314yes—
82C2×#13050589—22no—
83C2×#13050589—42no—
84C2×#13050589—42no—
85C2×#13050589C2314yes—
86C22×Dic166C2311yescharacteristic
87C22×D332—21no—
88C22×D332—21no—
89C22×D332C2311yescharacteristic
90C22×C22⋊D83—21no—
91C22×C22⋊D83—21no—
92C22×C22⋊D83—21no—
93C23×Dic83—21no—
94C23×Dic83D411yescharacteristic
95C22×C4×D83—21no—
96C22×C4×D83—42no—
97C22×C4×D83—42no—
98C22×C4×D83D411yescharacteristic
99C22×C4×D83D411yescharacteristic
100C22×C4×D83D414yes—
101C22×C4×D83C2311yescharacteristic
102C22×C4×D83C2311yescharacteristic
103C22×C4×D83C2314yes—
104C2×#13050580—42no—
105C2×#13050580C2314yescomplemented
106C2×#13050579—42no—
107C2×#13050579C2314yescomplemented
108C2×#13050575—42no—
109C2×#13050575C2314yescomplemented
110C22×C83⋊C8—42no—
111C22×C83⋊C8C2311yescharacteristic
112C22×C83⋊C8C2311yescharacteristic
113C22×C83⋊C8C2314yes—
114#14581777—28no—
115#14581774—28no—
116#14581772—22no—
117#14581772C2314yes—
118#14581771—22no—
119#14581771C2314yes—
120#14581768—22no—
121#14581768C2314yes—
122#14581767—22no—
123#14581767C2314yes—
124#14581766—22no—
125#14581766C2314yes—
126#14581763—22no—
127#14581763C2314yes—
128#14581762—28no—
129#14581760—28no—
130D4×Dic83—28no—
131#14581754—28no—
132(C22⋊D83)⋊C4—28no—
133(C22⋊D83)⋊C4—28no—
134#14581750—22no—
135#14581750—22no—
136#14581750C2314yes—
137#14581750C2314yes—
138C2×C4⋊Dic83—21no—
139C2×C4⋊Dic83C2311yescharacteristic
140C2×C4⋊Dic83C2311yescharacteristic
141C2×Dic83⋊C4—21no—
142C2×Dic83⋊C4—21no—
143C2×C22⋊Dic83—21no—
144C2×C22⋊Dic83—21no—
145C2×(C2×D83)⋊C4—21no—
146C2×(C2×D83)⋊C4—21no—
147C2×(C2×D83)⋊C4—21no—
148C2×(C2×D83)⋊C4—21no—
149C2×(C2×D83)⋊C4—21no—
150C2×(C2×D83)⋊C4—21no—
151C2×C4×Dic83—21no—
152C2×C4×Dic83—21no—
153#14581725C2314yescomplemented
154#14581725C2314yescomplemented
155#14581724C2314yescomplemented
156#14581717C2314yescomplemented
157#14581716C2314yescomplemented
158#14581715C2314yescomplemented
159#14581714C2314yescomplemented
160#14581713C2314yescomplemented
161#14581712C2314yescomplemented
162(C2×D83)⋊C8C2314yes—
163(C2×D83)⋊C8C2314yes—
164(C2×D83)⋊C8C2314yes—
165(C2×D83)⋊C8C2314yes—
166C22×Q8×C83C2311yescharacteristic
167C22×D4×C83—21no—
168C22×D4×C83C2311yescharacteristic
169C23×C4×C83C2311yescharacteristic
170C2×SD16×C83—42no—
171C2×SD16×C83C2314yescomplemented
172C22×C8×C83—42no—
173C22×C8×C83C2311yescharacteristic
174C22×C8×C83C2311yescharacteristic
175C22×C8×C83C2314yes—
176C22⋊Q8×C83—22no—
177C22⋊Q8×C83C2314yes—
178#121×C83—22no—
179#121×C83C2314yes—
180C2×C4⋊C4×C83—21no—
181C2×C4⋊C4×C83C2311yescharacteristic
182C2×C4⋊C4×C83C2311yescharacteristic
183C2×C22⋊C4×C83—21no—
184C2×C22⋊C4×C83—21no—
185#106×C83C2314yescomplemented
186#103×C83C2314yescomplemented
187#102×C83C2314yescomplemented
188C23×D83—24no—
189C23×D83—21no—
190C23×D83—42no—
191C23×D83—42no—
192C23×D83C2×D411yescharacteristic
193C23×D83C2×D411yescharacteristic
194C23×D83C2×D414yes—
195#13050591—44no—
196#13050591—44no—
197#13050591—48no—
198#13050589—44no—
199#13050589—44no—
200#13050589—48no—
201C2×Dic166—22no—
202C2×Dic166—22no—
203C2×Dic166—21no—
204C2×Dic166C2412yes—
205C2×D332—22no—
206C2×D332—22no—
207C2×D332—24no—
208C2×D332—24no—
209C2×D332—21no—
210C2×D332—44no—
211C2×D332—44no—
212C2×D332C2412yes—
213C2×C22⋊D83—24no—
214C2×C22⋊D83—24no—
215C2×C22⋊D83—24no—
216C2×C22⋊D83—44no—
217C2×C22⋊D83—44no—
218C2×C22⋊D83—44no—
219C22×Dic83—21no—
220C22×Dic83—21no—
221C22×Dic83—21no—
222C22×Dic83—24no—
223C22×Dic83—42no—
224C22×Dic83—44no—
225C22×Dic83C2×D411yescharacteristic
226C22×Dic83C2×D411yescharacteristic
227C22×Dic83C2×D414yes—
228C2×C4×D83—22no—
229C2×C4×D83—22no—
230C2×C4×D83—22no—
231C2×C4×D83—22no—
232C2×C4×D83—24no—
233C2×C4×D83—48no—
234C2×C4×D83—44no—
235C2×C4×D83—44no—
236C2×C4×D83—42no—
237C2×C4×D83—42no—
238C2×C4×D83—44no—
239C2×C4×D83C2×D412yes—
240C2×C4×D83C2×D412yes—
241C2×C4×D83C2×D414yes—
242C2×C4×D83C2×D414yes—
243C2×C4×D83C2412yes—
244C2×C4×D83C2412yes—
245#13050580—44no—
246#13050579—44no—
247#13050575—44no—
248C2×C83⋊C8—22no—
249C2×C83⋊C8—22no—
250C2×C83⋊C8—44no—
251C2×C83⋊C8C2412yes—
252C2×C83⋊C8C2412yes—
253C4⋊Dic83—21no—
254C4⋊Dic83—21no—
255C4⋊Dic83—24no—
256C4⋊Dic83C2412yes—
257C4⋊Dic83C2412yes—
258Dic83⋊C4—24no—
259Dic83⋊C4—24no—
260C22⋊Dic83—24no—
261C22⋊Dic83—24no—
262(C2×D83)⋊C4—24no—
263(C2×D83)⋊C4—24no—
264(C2×D83)⋊C4—24no—
265(C2×D83)⋊C4—24no—
266(C2×D83)⋊C4—24no—
267(C2×D83)⋊C4—24no—
268C4×Dic83—24no—
269C4×Dic83—24no—
270C24×C83—21no—
271C24×C83C2×D411yescharacteristic
272C2×Q8×C83—21no—
273C2×Q8×C83—22no—
274C2×Q8×C83—22no—
275C2×Q8×C83C2412yes—
276C2×D4×C83—24no—
277C2×D4×C83—21no—
278C2×D4×C83—22no—
279C2×D4×C83—22no—
280C2×D4×C83—44no—
281C2×D4×C83C2412yes—
282C22×C4×C83—22no—
283C22×C4×C83—22no—
284C22×C4×C83—21no—
285C22×C4×C83—21no—
286C22×C4×C83—21no—
287C22×C4×C83C2×D412yes—
288C22×C4×C83C2×D411yescharacteristic
289C22×C4×C83C2412yes—
290C22×C4×C83C2411yescharacteristic
291SD16×C83—44no—
292C2×C8×C83—22no—
293C2×C8×C83—22no—
294C2×C8×C83—44no—
295C2×C8×C83C2412yes—
296C2×C8×C83C2412yes—
297C4⋊C4×C83—21no—
298C4⋊C4×C83—21no—
299C4⋊C4×C83—24no—
300C4⋊C4×C83C2412yes—
301C4⋊C4×C83C2412yes—
302C22⋊C4×C83—24no—
303C22⋊C4×C83—24no—
304C23×C83—22no—
305C23×C83—22no—
306C23×C83—22no—
307C23×C83—42no—
308C23×C83—42no—
309C23×C83—42no—
310C23×C83#13514yes—
311C23×C83C22×D412yes—
312C23×C83C22×D411yescharacteristic
313C22×D83—22no—
314C22×D83—22no—
315C22×D83—28no—
316C22×D83—22no—
317C22×D83—22no—
318C22×D83—22no—
319C22×D83—22no—
320C22×D83—22no—
321C22×D83—44no—
322C22×D83—44no—
323C22×D83—416no—
324C22×D83—42no—
325C22×D83—42no—
326C22×D83—42no—
327C22×D83C22×D412yes—
328C22×D83C22×D412yes—
329Q8×C83—22no—
330Q8×C83—22no—
331Q8×C83—42no—
332D4×C83—22no—
333D4×C83—22no—
334D4×C83—48no—
335D4×C83—42no—
336C2×C4×C83—22no—
337C2×C4×C83—24no—
338C2×C4×C83—22no—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—22no—
342C2×C4×C83—22no—
343C2×C4×C83—42no—
344C2×C4×C83—42no—
345C2×C4×C83—42no—
346C2×C4×C83C22×D412yes—
347C2×C4×C83C22×D411yescharacteristic
348C2×C4×C83H(5,𝔽2)12yes—
349C2×C4×C83H(5,𝔽2)12yes—
350C2×C4×C83C2511yescharacteristic
351C22⋊D83—48no—
352C22⋊D83—48no—
353C22⋊D83—48no—
354C2×Dic83—22no—
355C2×Dic83—22no—
356C2×Dic83—22no—
357C2×Dic83—22no—
358C2×Dic83—22no—
359C2×Dic83—44no—
360C2×Dic83—48no—
361C2×Dic83—42no—
362C2×Dic83—42no—
363C2×Dic83—42no—
364C2×Dic83C22×D412yes—
365C2×Dic83C22×D412yes—
366D332—22no—
367D332—22no—
368D332—48no—
369D332—48no—
370D332—42no—
371C4×D83—24no—
372C4×D83—24no—
373C4×D83—22no—
374C4×D83—22no—
375C4×D83—22no—
376C4×D83—22no—
377C4×D83—44no—
378C4×D83—44no—
379C4×D83—48no—
380Dic166—22no—
381Dic166—22no—
382Dic166—42no—
383C8×C83—22no—
384C8×C83—22no—
385C83⋊C8—22no—
386C83⋊C8—22no—
387C22×C83—22no—
388C22×C83—28no—
389C22×C83—22no—
390C22×C83—42no—
391C22×C83—42no—
392C22×C83—42no—
393C22×C83—84no—
394C22×C83#53412yes—
395C22×C83C2×#13514yes—
396C22×C83C2×#13512yes—
397C22×C83#57512yes—
398C22×C83C23×D411yescharacteristic
399C2×D83—22no—
400C2×D83—22no—
401C2×D83—22no—
402C2×D83—22no—
403C2×D83—22no—
404C2×D83—22no—
405C2×D83—416no—
406C2×D83—44no—
407C2×D83—44no—
408C2×D83—42no—
409C2×D83—42no—
410C2×D83—42no—
411C2×D83—84no—
412C4×C83—22no—
413C4×C83—42no—
414C4×C83—42no—
415C4×C83—42no—
416C4×C83#53412yes—
417C4×C83C2×H(5,𝔽2)11yescharacteristic
418C4×C83C2×H(5,𝔽2)11yescharacteristic
419Dic83—22no—
420Dic83—22no—
421Dic83—42no—
422Dic83—42no—
423Dic83—42no—
424C2×#3191—831nomaximal, Sylow
425C2×C83—24no—
426C2×C83—82no—
427C2×C83#319114yescomplemented
428C2×C83C2×#53411yescharacteristic
429C2×C83C22×#13511yescharacteristic
430C2×C83C2×#57511yescharacteristic
431D83—42no—
432D83—42no—
433D83—82no—
434C2×#525—831no—
435C2×#525—831no—
436#3191—8316no—
437C2×#485—831no—
438C2×#485—831no—
439C2×#482—831no—
440C2×#482—831no—
441C2×#467—831no—
442C2×#466—831no—
443C2×#465—831no—
444C2×#465D8311yescharacteristic, complemented
445C2×#452—831no—
446C2×#452—831no—
447C2×#449—831no—
448C2×#449—831no—
449C22×C22⋊C8—831no—
450C83C2×#319111yescharacteristic, complemented, Sylow
451C22×#41—831no—
452C22×#41—831no—
453C24×C4—831no—
454C22×Q16—831no—
455C22×SD16—831no—
456C22×SD16C2×D8311yescharacteristic, complemented
457C22×D8—831no—
458C23×C8—831no—
459C23×C8C2×D8311yescharacteristic
460#525—838no—
461#525—838no—
462#525—1664no—
463#525—1664no—
464C2×#123—1661no—
465C2×#123—1661no—
466C2×C22⋊Q8—831no—
467C2×C22⋊Q8—831no—
468C2×C22⋊Q8—831no—
469C2×C22⋊Q8C2×D8311yescharacteristic
470C2×#121—831no—
471C2×#121—831no—
472C2×#121—831no—
473C2×#121C2×D8311yescharacteristic
474C2×#120—1661no—
475C2×#120—1661no—
476C2×C4×D4—1661no—
477C2×C4×D4—1661no—
478C2×C4×D4—1661no—
479C2×C4×D4—1661no—
480C2×#117—831no—
481C2×#117—831no—
482#485—838no—
483#485—838no—
484#482—838no—
485#482—838no—
486#467—838no—
487#466—838no—
488#465—838no—
489#465C2×D8318yescomplemented
490#452—838no—
491#452—838no—
492#449—838no—
493#449—838no—
494C2×#107—831no—
495C2×#107—831no—
496C2×#106—831no—
497C2×#106C2×D8311yescharacteristic, complemented
498C2×#103—831no—
499C2×#103—831no—
500C2×#103—831no—
501C2×#103C2×D8311yescharacteristic, complemented
502C2×#102—831no—
503C2×#102—831no—
504C2×#102—831no—
505C2×#102C2×D8311yescharacteristic, complemented
506C2×C22⋊C8—831no—
507C2×C22⋊C8—831no—
508C2×C22⋊C8—831no—
509C2×C22⋊C8—831no—
510C2×C22⋊C8—838no—
511C25—831no—
512C2×#41—3322no—
513C2×#41—3322no—
514C2×#41—3322no—
515C2×#41—3322no—
516C2×#41—834no—
517C2×#41—834no—
518C2×#41—1662no—
519C2×#41—1662no—
520C22×Q8—831no—
521C22×Q8C22×D8311yescharacteristic
522C22×D4—21no—
523C22×D4—831no—
524C22×D4—1661no—
525C22×D4—1661no—
526C22×D4—1661no—
527C22×D4—1661no—
528C22×D4—1661no—
529C22×D4C22×D8311yescharacteristic
530C23×C4—3322no—
531C23×C4—3322no—
532C23×C4—831no—
533C23×C4—831no—
534C23×C4—831no—
535C23×C4—834no—
536C23×C4—834no—
537C23×C4—831no—
538C23×C4—831no—
539C23×C4—1661no—
540C23×C4—1661no—
541C23×C4C22×D8311yescharacteristic
542C2×Q16—3322no—
543C2×Q16—834no—
544C2×SD16—42no—
545C2×SD16—3322no—
546C2×SD16—834no—
547C2×SD16C22×D8314yescomplemented
548C2×D8—3322no—
549C2×D8—834no—
550C22×C8—42no—
551C22×C8—3322no—
552C22×C8—834no—
553C22×C8—831no—
554C22×C8—831no—
555C22×C8C22×D8311yescharacteristic
556C22×C8C22×D8311yescharacteristic
557C22×C8C22×D8314yes—
558#123—1668no—
559#123—1668no—
560C22⋊Q8—22no—
561C22⋊Q8—834no—
562C22⋊Q8—834no—
563C22⋊Q8—834no—
564C22⋊Q8—1662no—
565C22⋊Q8—1662no—
566C22⋊Q8—1662no—
567C22⋊Q8C22×D8314yes—
568#121—22no—
569#121—834no—
570#121—834no—
571#121—834no—
572#121—1662no—
573#121—1662no—
574#121—1662no—
575#121C22×D8314yes—
576#120—1668no—
577#120—1668no—
578C4×D4—1668no—
579C4×D4—1668no—
580C4×D4—1668no—
581C4×D4—1668no—
582#117—834no—
583#117—834no—
584#117—1662no—
585#117—1662no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—831no—
588C2×C4⋊C4—831no—
589C2×C4⋊C4—1661no—
590C2×C4⋊C4—1661no—
591C2×C4⋊C4—1661no—
592C2×C4⋊C4C22×D8311yescharacteristic
593C2×C4⋊C4C22×D8311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—1661no—
597C2×C22⋊C4—1661no—
598C2×C22⋊C4—1661no—
599C2×C22⋊C4—1661no—
600C2×C22⋊C4—1661no—
601C2×C22⋊C4—1661no—
602C2×C22⋊C4—1661no—
603C2×C22⋊C4—1661no—
604C2×C42—1661no—
605C2×C42—1661no—
606#107—834no—
607#107—834no—
608#106—834no—
609#106C22×D8314yescomplemented
610#103—834no—
611#103—834no—
612#103—834no—
613#103C22×D8314yescomplemented
614#102—834no—
615#102—834no—
616#102—834no—
617#102C22×D8314yescomplemented
618C22⋊C8—834no—
619C22⋊C8—834no—
620C22⋊C8—834no—
621C22⋊C8—834no—
622C24—21no—
623C24—3322no—
624C24—3322no—
625C24—834no—
626C24—831no—
627C24—831no—
628C24—1661no—
629C24—1664no—
630C24D4×D8311yescharacteristic
631#41—3324no—
632#41—3324no—
633#41—3328no—
634#41—3328no—
635#41—3324no—
636#41—3324no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—832no—
641C2×Q8—1662no—
642C2×Q8—1662no—
643C2×Q8—1661no—
644C2×Q8C23×D8312yes—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—44no—
650C2×D4—3324no—
651C2×D4—3324no—
652C2×D4—3324no—
653C2×D4—3324no—
654C2×D4—3324no—
655C2×D4—832no—
656C2×D4—1664no—
657C2×D4—1664no—
658C2×D4—1664no—
659C2×D4—1664no—
660C2×D4—1664no—
661C2×D4—1661no—
662C2×D4—1662no—
663C2×D4—1662no—
664C2×D4C23×D8312yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—3322no—
671C22×C4—3322no—
672C22×C4—3328no—
673C22×C4—3324no—
674C22×C4—3324no—
675C22×C4—3324no—
676C22×C4—3324no—
677C22×C4—3322no—
678C22×C4—834no—
679C22×C4—834no—
680C22×C4—834no—
681C22×C4—831no—
682C22×C4—831no—
683C22×C4—832no—
684C22×C4—832no—
685C22×C4—832no—
686C22×C4—832no—
687C22×C4—1664no—
688C22×C4—1664no—
689C22×C4—1661no—
690C22×C4—1661no—
691C22×C4—1661no—
692C22×C4—1662no—
693C22×C4—1662no—
694C22×C4—1662no—
695C22×C4—1662no—
696C22×C4D4×D8312yes—
697C22×C4D4×D8311yescharacteristic
698C22×C4C23×D8312yes—
699C22×C4C23×D8311yescharacteristic
700Q16—3324no—
701SD16—44no—
702SD16—3324no—
703D8—3324no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—44no—
707C2×C8—3324no—
708C2×C8—832no—
709C2×C8—832no—
710C2×C8—1662no—
711C2×C8—1662no—
712C2×C8C23×D8312yes—
713C2×C8C23×D8312yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—832no—
718C4⋊C4—832no—
719C4⋊C4—1664no—
720C4⋊C4—1664no—
721C4⋊C4—1661no—
722C4⋊C4—1661no—
723C4⋊C4—1664no—
724C4⋊C4C23×D8312yes—
725C4⋊C4C23×D8312yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—1664no—
729C22⋊C4—1664no—
730C22⋊C4—1664no—
731C22⋊C4—1664no—
732C22⋊C4—1664no—
733C22⋊C4—1664no—
734C22⋊C4—1664no—
735C22⋊C4—1664no—
736C42—1664no—
737C42—1664no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—33216no—
745C23—3324no—
746C23—3324no—
747C23—3322no—
748C23—3322no—
749C23—3322no—
750C23—832no—
751C23—832no—
752C23—1662no—
753C23—1668no—
754C23—1662no—
755C23—1662no—
756C23—1662no—
757C23—1662no—
758C23—1662no—
759C23—1662no—
760C23#1458181314yes—
761C23C2×D4×D8312yes—
762C23C2×D4×D8311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—3322no—
767Q8—1662no—
768Q8—1662no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—3328no—
774D4—3328no—
775D4—3328no—
776D4—3328no—
777D4—3328no—
778D4—3322no—
779D4—1662no—
780D4—1662no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—3324no—
792C2×C4—3324no—
793C2×C4—3328no—
794C2×C4—3322no—
795C2×C4—3322no—
796C2×C4—3322no—
797C2×C4—3328no—
798C2×C4—3324no—
799C2×C4—832no—
800C2×C4—832no—
801C2×C4—1662no—
802C2×C4—1662no—
803C2×C4—1662no—
804C2×C4—1662no—
805C2×C4—1662no—
806C2×C4—1664no—
807C2×C4—1664no—
808C2×C4—1662no—
809C2×C4—1662no—
810C2×C4—1662no—
811C2×C4—1662no—
812C2×C4C2×D4×D8312yes—
813C2×C4C2×D4×D8311yescharacteristic
814C2×C4#1458183712yes—
815C2×C4#1458183812yes—
816C2×C4C24×D8311yescharacteristic
817C8—22no—
818C8—22no—
819C8—1662no—
820C8—1662no—
821C22—22no—
822C22—22no—
823C22—28no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—84no—
828C22—33216no—
829C22—3324no—
830C22—3324no—
831C22—3322no—
832C22—3322no—
833C22—3322no—
834C22—6644no—
835C22—1662no—
836C22—1662no—
837C22—1662no—
838C22—1662no—
839C22—1662no—
840C22—1662no—
841C22#1912825912yes—
842C22C2×#1458181314yes—
843C22C2×#1458181312yes—
844C22#1912849812yes—
845C22C22×D4×D8311yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—3322no—
851C4—3322no—
852C4—3322no—
853C4—1662no—
854C4—1662no—
855C4#1912825912yes—
856C4C2×#1458183711yescharacteristic
857C4C2×#1458183811yescharacteristic
858C2—24no—
859C2—82no—
860C2—3322no—
861C2—3322no—
862C2—6642no—
863C2#2491825214yesdirect product factor
864C2C2×#1912825911yescharacteristic
865C2C22×#1458181311yescharacteristic
866C2C2×#1912849811yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#465×C83C2
socleC23×C83C22×D4
hypercenterC2×#465D83
hypocenterC83C2×#3191
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#19128214C2semidirect
2. C2×#19128211C2semidirect
3. #24918252C2direct (N × H)
4. C2×#19128045C2semidirect
5. C2×#19128040C2semidirect
6. C2×#19128027C2semidirect
7. C2×#19128024C2semidirect
8. C2×#19127940C2semidirect
9. C2×#19127935C2semidirect
10. C2×#19127930C2semidirect
11. C2×#19127866C2semidirect
12. C2×#19127860C2semidirect
13. C2×#19127847C2semidirect
14. C2×#19127845C2semidirect
15. C22×(C2×D83)⋊C8C2semidirect
16. C2×#465×C83C2semidirect
20. C22×#13050580C22semidirect
21. C22×#13050579C22semidirect
22. C22×#13050575C22semidirect
25. #19128214C22semidirect
27. #19128211C22semidirect
44. #19128045C22semidirect
45. #19128040C22semidirect
46. #19128027C22semidirect
47. #19128024C22semidirect
48. #19127940C22semidirect
49. #19127935C22semidirect
50. #19127930C22semidirect
51. #19127866C22semidirect
52. #19127860C22semidirect
53. #19127847C22semidirect
54. #19127845C22semidirect
55. C2×#14581725C22semidirect
56. C2×#14581725C22semidirect
57. C2×#14581724C22semidirect
58. C2×#14581717C22semidirect
59. C2×#14581716C22semidirect
60. C2×#14581715C22semidirect
61. C2×#14581714C22semidirect
62. C2×#14581713C22semidirect
63. C2×#14581712C22semidirect
68. C2×(C2×D83)⋊C8C22semidirect
69. C22×SD16×C83C22semidirect
73. #465×C83C22semidirect
74. C2×#106×C83C22semidirect
75. C2×#103×C83C22semidirect
76. C2×#102×C83C22semidirect
105. C2×#13050580C23semidirect
107. C2×#13050579C23semidirect
109. C2×#13050575C23semidirect
153. #14581725C23semidirect
154. #14581725C23semidirect
155. #14581724C23semidirect
156. #14581717C23semidirect
157. #14581716C23semidirect
158. #14581715C23semidirect
159. #14581714C23semidirect
160. #14581713C23semidirect
161. #14581712C23semidirect
171. C2×SD16×C83C23semidirect
185. #106×C83C23semidirect
186. #103×C83C23semidirect
187. #102×C83C23semidirect
427. C2×C83#3191semidirect
444. C2×#465D83semidirect
450. C83C2×#3191semidirect
456. C22×SD16C2×D83semidirect
489. #465C2×D83semidirect
497. C2×#106C2×D83semidirect
501. C2×#103C2×D83semidirect
505. C2×#102C2×D83semidirect
547. C2×SD16C22×D83semidirect
609. #106C22×D83semidirect
613. #103C22×D83semidirect
617. #102C22×D83semidirect
863. C2#24918252direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282142
C2×#191282112
#249182522
C2×#191280452
C2×#191280402
C2×#191280272
C2×#191280242
C2×#191279402
C2×#191279352
C2×#191279302
C2×#191278662
C2×#191278602
C2×#191278472
C2×#191278452
C22×(C2×D83)⋊C82
C2×#465×C832
C2×#319183