Finite Group Databasebeta

← C2×#24919677 #36281215

Subgroups — C2×#24919677 #36281215

Order 21248.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128390C211yesmaximal, characteristic, complemented
2C2×#19128342C211yesmaximal, characteristic
3#24919677C2116yesmaximal, direct product factor
4C2×#19128057C211yesmaximal, characteristic, complemented
5C2×#19128021C211yesmaximal, characteristic, complemented
6C2×#19128004C211yesmaximal, characteristic, complemented
7C2×#19127957C211yesmaximal, characteristic, complemented
8C2×#19127948C211yesmaximal, characteristic, complemented
9C2×#19127926C211yesmaximal, characteristic, complemented
10C2×#19127866C211yesmaximal, characteristic, complemented
11C2×#19127854C211yesmaximal, characteristic, complemented
12C2×#19127788C211yesmaximal, characteristic, complemented
13C2×#19127776C211yesmaximal, characteristic, complemented
14C2×#19127701C211yesmaximal, characteristic, complemented
15C2×#19127705C211yesmaximal, characteristic, complemented
16C2×#485×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C23×D332C2211yescharacteristic
19C22×#13050580C2211yescharacteristic, complemented
20C22×#13050579C2211yescharacteristic
21C22×#13050579C2211yescharacteristic
22C22×#13050574C2211yescharacteristic
23C22×#13050573C2211yescharacteristic, complemented
24#19128390—24no—
25#19128390C2218yescomplemented
26#19128342—24no—
27#19128342C2218yes—
28C2×#14581785—21no—
29C2×#14581784—21no—
30C2×#14581783C2211yescharacteristic, complemented
31C2×#14581781C2211yescharacteristic
32C2×#14581777—21no—
33C2×#14581774—21no—
34C2×#14581772C2211yescharacteristic, complemented
35C2×#14581771C2211yescharacteristic
36C2×#14581767—21no—
37C2×#14581767C2211yescharacteristic
38C2×#14581762—21no—
39C2×#14581757C2211yescharacteristic, complemented
40C2×#14581754C2211yescharacteristic
41C2×C4×C22⋊D83C2211yescharacteristic
42C2×#14581749—21no—
43C2×C4⋊C4×D83C2211yescharacteristic, complemented
44C2×C22⋊C4×D83—21no—
45#19128057C2218yescomplemented
46#19128021C2218yescomplemented
47#19128004C2218yescomplemented
48#19127957C2218yescomplemented
49#19127948C2218yescomplemented
50#19127926C2218yescomplemented
51#19127866C2218yescomplemented
52#19127854C2218yescomplemented
53#19127788C2218yescomplemented
54#19127776C2218yescomplemented
55C2×#14581723C2211yescharacteristic, complemented
56C2×Dic83⋊C8C2211yescharacteristic, complemented
57#19127705C2218yescomplemented
58#19127701C2218yescomplemented
59C2×#14581716C2211yescharacteristic, complemented
60C2×#14581715C2211yescharacteristic, complemented
61C2×#14581714C2211yescharacteristic
62C2×#14581714C2211yescharacteristic
63C2×#14581712C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×#14581712C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic83C2211yescharacteristic, complemented
69C2×C22⋊Q8×C83C2211yescharacteristic
70C2×#117×C83C2211yescharacteristic
71#485×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic, complemented
73C2×#106×C83C2211yescharacteristic, complemented
74C2×#103×C83C2211yescharacteristic, complemented
75C2×#103×C83C2211yescharacteristic, complemented
76C2×C22⋊C8×C83C2211yescharacteristic
77C24×D83—21no—
78C2×#13050591—22no—
79C2×#13050591—24no—
80C2×#13050591—42no—
81C2×#13050591C2314yes—
82C22×Dic166C2311yescharacteristic
83C22×D332—24no—
84C22×D332—21no—
85C22×D332—21no—
86C22×D332—22no—
87C22×D332—21no—
88C22×D332—42no—
89C22×D332C2311yescharacteristic
90C22×D332C2314yes—
91C22×D332C2311yescharacteristic
92C22×C22⋊D83D411yescharacteristic
93C22×C4×D83—21no—
94C22×C4×D83—21no—
95C22×C4×D83—21no—
96C22×C4×D83C2311yescharacteristic
97C2×#13050580—42no—
98C2×#13050580C2314yescomplemented
99C2×#13050579—24no—
100C2×#13050579—42no—
101C2×#13050579C2314yes—
102C2×#13050579C2314yes—
103C2×#13050574—42no—
104C2×#13050574C2314yes—
105C2×#13050573—42no—
106C2×#13050573C2314yescomplemented
107C22×C83⋊C8C2311yescharacteristic
108C22×C83⋊C8C2311yescharacteristic
109#14581785—28no—
110#14581784—28no—
111#14581783—22no—
112#14581783C2314yescomplemented
113#14581781—22no—
114#14581781C2314yes—
115#14581777—28no—
116#14581774—28no—
117#14581772—22no—
118#14581772C2314yescomplemented
119#14581771—22no—
120#14581771C2314yes—
121#14581767—22no—
122#14581767—28no—
123#14581767C2314yes—
124#14581762—28no—
125#14581757—22no—
126#14581757C2314yescomplemented
127#14581754—22no—
128#14581754C2314yes—
129C4×C22⋊D83D414yes—
130C4×C22⋊D83C2314yes—
131#14581749—28no—
132C2×C4⋊Dic83—21no—
133C2×C4⋊Dic83—21no—
134C2×C4⋊Dic83C2311yescharacteristic
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4—21no—
137C2×Dic83⋊C4—21no—
138C2×Dic83⋊C4—21no—
139C2×Dic83⋊C4D411yescharacteristic
140C4⋊C4×D83—22no—
141C4⋊C4×D83C2314yescomplemented
142C2×C22⋊Dic83—21no—
143C2×C22⋊Dic83D411yescharacteristic
144C2×(C2×D83)⋊C4—21no—
145C2×(C2×D83)⋊C4—21no—
146C2×(C2×D83)⋊C4—21no—
147C2×(C2×D83)⋊C4—21no—
148C2×(C2×D83)⋊C4—21no—
149C2×(C2×D83)⋊C4D411yescharacteristic
150C22⋊C4×D83—28no—
151C2×C4×Dic83—21no—
152C2×C4×Dic83C2311yescharacteristic
153#14581723C2314yescomplemented
154Dic83⋊C8C2314yescomplemented
155#14581716C2314yescomplemented
156#14581715C2314yescomplemented
157#14581714C2314yes—
158#14581714C2314yes—
159#14581712C2314yes—
160#14581712C2314yes—
161#14581712C2314yes—
162#14581712C2314yes—
163(C2×D83)⋊C8C2314yescomplemented
164C8×Dic83C2314yescomplemented
165C22×Q8×C83C2311yescharacteristic
166C23×C4×C83C2311yescharacteristic
167C22×C8×C83C2311yescharacteristic
168C22×C8×C83C2311yescharacteristic
169C22⋊Q8×C83—22no—
170C22⋊Q8×C83C2314yes—
171#117×C83—22no—
172#117×C83C2314yes—
173C2×C4⋊C4×C83—21no—
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C4⋊C4×C83C2311yescharacteristic
176C2×C4⋊C4×C83C2311yescharacteristic
177C2×C22⋊C4×C83—21no—
178C2×C22⋊C4×C83—21no—
179C2×C42×C83—21no—
180#107×C83C2314yescomplemented
181#106×C83C2314yescomplemented
182#103×C83C2314yescomplemented
183#103×C83C2314yescomplemented
184C22⋊C8×C83C2314yes—
185C23×D83—21no—
186C23×D83—21no—
187C23×D83—24no—
188C23×D83—44no—
189C23×D83—44no—
190C23×D83—82no—
191C23×D83C2×D411yescharacteristic
192#13050591—28no—
193#13050591—44no—
194#13050591—48no—
195C2×Dic166—22no—
196C2×Dic166—22no—
197C2×Dic166—21no—
198C2×Dic166C2412yes—
199C2×D332—21no—
200C2×D332—22no—
201C2×D332—22no—
202C2×D332—22no—
203C2×D332—28no—
204C2×D332—24no—
205C2×D332—24no—
206C2×D332—21no—
207C2×D332—24no—
208C2×D332—44no—
209C2×D332—48no—
210C2×D332—44no—
211C2×D332—44no—
212C2×D332—82no—
213C2×D332#4114yes—
214C2×D332C2412yes—
215C2×D332C2412yes—
216C2×C22⋊D83—42no—
217C2×C22⋊D83C2×D414yes—
218C22×Dic83—21no—
219C22×Dic83—21no—
220C22×Dic83C2×D411yescharacteristic
221C22×Dic83C2×D411yescharacteristic
222C22×Dic83C2×D411yescharacteristic
223C2×C4×D83—22no—
224C2×C4×D83—22no—
225C2×C4×D83—24no—
226C2×C4×D83—24no—
227C2×C4×D83—24no—
228C2×C4×D83—44no—
229C2×C4×D83—44no—
230C2×C4×D83—82no—
231C2×C4×D83C2×D412yes—
232C2×C4×D83C2412yes—
233#13050580—44no—
234#13050579—28no—
235#13050579—44no—
236#13050574—44no—
237#13050573—44no—
238C2×C83⋊C8—22no—
239C2×C83⋊C8—22no—
240C2×C83⋊C8C2412yes—
241C2×C83⋊C8C2412yes—
242C4⋊Dic83—21no—
243C4⋊Dic83—24no—
244C4⋊Dic83—24no—
245C4⋊Dic83C2412yes—
246Dic83⋊C4—24no—
247Dic83⋊C4—24no—
248Dic83⋊C4—24no—
249Dic83⋊C4—24no—
250Dic83⋊C4C2×D414yes—
251C22⋊Dic83—24no—
252C22⋊Dic83C2×D414yes—
253(C2×D83)⋊C4—24no—
254(C2×D83)⋊C4—24no—
255(C2×D83)⋊C4—24no—
256(C2×D83)⋊C4—24no—
257(C2×D83)⋊C4—24no—
258(C2×D83)⋊C4C2×D414yes—
259C4×Dic83—24no—
260C4×Dic83C2×D412yes—
261C4×Dic83C2412yes—
262C24×C83C2×D411yescharacteristic
263C2×Q8×C83—21no—
264C2×Q8×C83—22no—
265C2×Q8×C83—22no—
266C2×Q8×C83C2412yes—
267C22×C4×C83—22no—
268C22×C4×C83—22no—
269C22×C4×C83—21no—
270C22×C4×C83—21no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83C2×D412yes—
274C22×C4×C83C2×D411yescharacteristic
275C22×C4×C83C2412yes—
276C22×C4×C83C2411yescharacteristic
277C2×C8×C83—22no—
278C2×C8×C83—22no—
279C2×C8×C83C2412yes—
280C2×C8×C83C2412yes—
281C4⋊C4×C83—24no—
282C4⋊C4×C83—21no—
283C4⋊C4×C83—21no—
284C4⋊C4×C83—21no—
285C4⋊C4×C83C2412yes—
286C4⋊C4×C83C2412yes—
287C4⋊C4×C83C2412yes—
288C22⋊C4×C83—24no—
289C22⋊C4×C83—24no—
290C42×C83—24no—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83C22×D412yes—
295C23×C83C22×D411yescharacteristic
296C22×D83—22no—
297C22×D83—24no—
298C22×D83—22no—
299C22×D83—22no—
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—48no—
303C22×D83—42no—
304C22×D83—42no—
305C22×D83—48no—
306C22×D83—42no—
307C22×D83—42no—
308C22×D83—42no—
309C22×D83—84no—
310C22×D83—816no—
311C22×D83C22×D412yes—
312Q8×C83—22no—
313Q8×C83—22no—
314Q8×C83—42no—
315C2×C4×C83—22no—
316C2×C4×C83—24no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—42no—
324C2×C4×C83—42no—
325C2×C4×C83—42no—
326C2×C4×C83—42no—
327C2×C4×C83C22×D412yes—
328C2×C4×C83C22×D411yescharacteristic
329C2×C4×C83C2×#4112yes—
330C2×C4×C83H(5,𝔽2)12yes—
331C2×C4×C83C2511yescharacteristic
332C22⋊D83—44no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—42no—
339C2×Dic83—42no—
340C2×Dic83C22×D412yes—
341C2×Dic83C22×D412yes—
342C2×Dic83C22×D412yes—
343D332—24no—
344D332—22no—
345D332—22no—
346D332—22no—
347D332—48no—
348D332—48no—
349D332—42no—
350D332—84no—
351D332C2×#4114yes—
352C4×D83—24no—
353C4×D83—22no—
354C4×D83—22no—
355C4×D83—48no—
356C4×D83—48no—
357C4×D83—84no—
358Dic166—22no—
359Dic166—22no—
360Dic166—42no—
361C8×C83—22no—
362C8×C83—22no—
363C83⋊C8—22no—
364C83⋊C8—22no—
365C22×C83—22no—
366C22×C83—22no—
367C22×C83—22no—
368C22×C83—44no—
369C22×C83#54612yes—
370C22×C83#57512yes—
371C22×C83#57712yes—
372C22×C83C23×D411yescharacteristic
373C2×D83—22no—
374C2×D83—24no—
375C2×D83—22no—
376C2×D83—22no—
377C2×D83—44no—
378C2×D83—48no—
379C2×D83—42no—
380C2×D83—42no—
381C2×D83—42no—
382C2×D83—42no—
383C2×D83—42no—
384C2×D83—816no—
385C2×D83—84no—
386C4×C83—22no—
387C4×C83—42no—
388C4×C83—42no—
389C4×C83—42no—
390C4×C83—42no—
391C4×C83#54612yes—
392C4×C83C22×#4111yescharacteristic
393C4×C83C2×H(5,𝔽2)11yescharacteristic
394Dic83—22no—
395Dic83—22no—
396Dic83—22no—
397Dic83—42no—
398Dic83—42no—
399C2×#3323—831nomaximal, Sylow
400C2×C83—42no—
401C2×C83#332314yescomplemented
402C2×C83C2×#54611yescharacteristic
403C2×C83C2×#57511yescharacteristic
404C2×C83C2×#57711yescharacteristic
405D83—42no—
406D83—44no—
407D83—82no—
408C2×#552—831no—
409C2×#546—831no—
410#3323—8316no—
411C2×#488—831no—
412C2×#481—831no—
413C2×#485D8311yescharacteristic, complemented
414C2×#478—831no—
415C2×#470—831no—
416C2×#468—831no—
417C2×#464—831no—
418C2×#452—831no—
419C2×#450—831no—
420C2×C4×SD16—831no—
421C2×#436—831no—
422C2×#417—831no—
423C2×#418—831no—
424C83C2×#332311yescharacteristic, complemented, Sylow
425C22×#41—831no—
426C23×D4—831no—
427C22×Q16—831no—
428C22×SD16—831no—
429C22×SD16—831no—
430C22×M16—831no—
431C22×M16—831no—
432#552—838no—
433#552—1664no—
434#546—838no—
435#546—1664no—
436C2×#126—1661no—
437C2×#125—831no—
438C2×#125—1661no—
439C2×#124—831no—
440C2×#123—1661no—
441C2×#123—1661no—
442C2×C22⋊Q8—831no—
443C2×C22⋊Q8—831no—
444C2×C22⋊Q8C2×D8311yescharacteristic
445C2×#121—831no—
446C2×#121—1661no—
447C2×#120—1661no—
448C2×C4×Q8—831no—
449C2×C4×D4—831no—
450C2×C4×D4—831no—
451C2×#117—1661no—
452C2×#117C2×D8311yescharacteristic
453C22×C4⋊C4—831no—
454C22×C22⋊C4—1661no—
455#488—838no—
456#485C2×D8318yescomplemented
457#481—838no—
458#478—838no—
459#470—838no—
460#468—838no—
461#464—838no—
462#452—838no—
463#450—838no—
464C4×SD16—838no—
465#436—838no—
466C2×#107C2×D8311yescharacteristic, complemented
467C2×#106—831no—
468C2×#106C2×D8311yescharacteristic, complemented
469C2×C4⋊C8—831no—
470#418—838no—
471#417—838no—
472C2×#103—831no—
473C2×#103—831no—
474C2×#103C2×D8311yescharacteristic, complemented
475C2×#103C2×D8311yescharacteristic, complemented
476C2×#102—831no—
477C2×#102—831no—
478C2×#102—831no—
479C2×#102—831no—
480C2×#102—831no—
481C2×#102—831no—
482C2×C22⋊C8—831no—
483C2×C22⋊C8C2×D8311yescharacteristic
484C2×C4×C8—831no—
485C25—1661no—
486C2×#41—3322no—
487C2×#41—834no—
488C2×#41—1664no—
489C2×#41—1662no—
490C22×Q8—831no—
491C22×Q8C22×D8311yescharacteristic
492C22×D4—3322no—
493C22×D4—831no—
494C22×D4—834no—
495C22×D4—831no—
496C22×D4—831no—
497C22×D4—1661no—
498C22×D4—1664no—
499C22×D4—1661no—
500C22×D4—1661no—
501C22×D4—1662no—
502C23×C4—831no—
503C23×C4—1661no—
504C23×C4—1661no—
505C23×C4—1661no—
506C23×C4C22×D8311yescharacteristic
507C2×Q16—3322no—
508C2×Q16—834no—
509C2×SD16—3322no—
510C2×SD16—834no—
511C2×SD16—834no—
512C2×SD16—1664no—
513C2×M16—3322no—
514C2×M16—3322no—
515C2×M16—834no—
516C2×M16—834no—
517C22×C8—831no—
518C22×C8—831no—
519C22×C8C22×D8311yescharacteristic
520C22×C8C22×D8311yescharacteristic
521#126—1668no—
522#125—834no—
523#125—1668no—
524#125—1662no—
525#124—834no—
526#124—1662no—
527#123—1668no—
528#123—1668no—
529C22⋊Q8—22no—
530C22⋊Q8—834no—
531C22⋊Q8—834no—
532C22⋊Q8—1662no—
533C22⋊Q8—1662no—
534C22⋊Q8C22×D8314yes—
535#121—834no—
536#121—1668no—
537#121—1662no—
538#120—1668no—
539C4×Q8—834no—
540C4×Q8—1662no—
541C4×D4—834no—
542C4×D4—834no—
543C4×D4—834no—
544C4×D4—1662no—
545#117—22no—
546#117—1668no—
547#117C22×D8314yes—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—831no—
550C2×C4⋊C4—831no—
551C2×C4⋊C4—834no—
552C2×C4⋊C4—1662no—
553C2×C4⋊C4—1661no—
554C2×C4⋊C4—1661no—
555C2×C4⋊C4—1661no—
556C2×C4⋊C4—1661no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4—1661no—
559C2×C4⋊C4C22×D8311yescharacteristic
560C2×C4⋊C4C22×D8311yescharacteristic
561C2×C4⋊C4C22×D8311yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—831no—
565C2×C22⋊C4—831no—
566C2×C22⋊C4—1668no—
567C2×C22⋊C4—1661no—
568C2×C22⋊C4—1661no—
569C2×C22⋊C4—1661no—
570C2×C22⋊C4—1661no—
571C2×C22⋊C4—1661no—
572C2×C22⋊C4—1661no—
573C2×C42—21no—
574C2×C42—831no—
575C2×C42—1661no—
576#107C22×D8314yescomplemented
577#106—834no—
578#106C22×D8314yescomplemented
579C4⋊C8—834no—
580#103—834no—
581#103—834no—
582#103C22×D8314yescomplemented
583#103C22×D8314yescomplemented
584#102—834no—
585#102—834no—
586#102—834no—
587#102—834no—
588#102—834no—
589#102—834no—
590C22⋊C8—834no—
591C22⋊C8C22×D8314yes—
592C4×C8—834no—
593C24—3324no—
594C24—3324no—
595C24—831no—
596C24—6642no—
597C24—1661no—
598C24—1664no—
599C24—1661no—
600C24D4×D8311yescharacteristic
601#41—3324no—
602#41—3328no—
603#41—1668no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—832no—
608C2×Q8—1662no—
609C2×Q8—1662no—
610C2×Q8—1661no—
611C2×Q8C23×D8312yes—
612C2×D4—3324no—
613C2×D4—3328no—
614C2×D4—3324no—
615C2×D4—3324no—
616C2×D4—3322no—
617C2×D4—834no—
618C2×D4—834no—
619C2×D4—832no—
620C2×D4—832no—
621C2×D4—6642no—
622C2×D4—1664no—
623C2×D4—1668no—
624C2×D4—1664no—
625C2×D4—1664no—
626C2×D4—1661no—
627C2×D4—1661no—
628C2×D4—1662no—
629C2×D4—1662no—
630C2×D4—1662no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—3324no—
638C22×C4—3324no—
639C22×C4—831no—
640C22×C4—831no—
641C22×C4—831no—
642C22×C4—832no—
643C22×C4—832no—
644C22×C4—6642no—
645C22×C4—1664no—
646C22×C4—1664no—
647C22×C4—1664no—
648C22×C4—1661no—
649C22×C4—1661no—
650C22×C4—1662no—
651C22×C4—1662no—
652C22×C4D4×D8312yes—
653C22×C4D4×D8311yescharacteristic
654C22×C4C23×D8312yes—
655C22×C4C23×D8311yescharacteristic
656Q16—3324no—
657SD16—3324no—
658SD16—1668no—
659M16—3324no—
660M16—3324no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—832no—
664C2×C8—832no—
665C2×C8—1662no—
666C2×C8—1662no—
667C2×C8C23×D8312yes—
668C2×C8C23×D8312yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—834no—
674C4⋊C4—832no—
675C4⋊C4—1664no—
676C4⋊C4—1664no—
677C4⋊C4—1664no—
678C4⋊C4—1664no—
679C4⋊C4—1664no—
680C4⋊C4—1661no—
681C4⋊C4—1664no—
682C4⋊C4C23×D8312yes—
683C4⋊C4C23×D8312yes—
684C4⋊C4C23×D8312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—834no—
688C22⋊C4—834no—
689C22⋊C4—1664no—
690C22⋊C4—1664no—
691C22⋊C4—1664no—
692C22⋊C4—1664no—
693C22⋊C4—1664no—
694C22⋊C4—1664no—
695C42—24no—
696C42—832no—
697C42—832no—
698C42—1664no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—3328no—
703C23—3328no—
704C23—3322no—
705C23—3322no—
706C23—3322no—
707C23—3322no—
708C23—3322no—
709C23—832no—
710C23—6644no—
711C23—66416no—
712C23—1662no—
713C23—1664no—
714C23—1662no—
715C23—1662no—
716C23—1662no—
717C23—1662no—
718C23C2×D4×D8312yes—
719C23C2×D4×D8311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—3322no—
724Q8—1662no—
725Q8—1662no—
726D4—3328no—
727D4—3328no—
728D4—3324no—
729D4—3322no—
730D4—834no—
731D4—6644no—
732D4—1664no—
733D4—1662no—
734D4—1662no—
735D4—1662no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—3328no—
749C2×C4—3328no—
750C2×C4—3322no—
751C2×C4—3322no—
752C2×C4—832no—
753C2×C4—832no—
754C2×C4—832no—
755C2×C4—6644no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1664no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4C2×D4×D8312yes—
765C2×C4C2×D4×D8311yescharacteristic
766C2×C4#41×D8312yes—
767C2×C4#1458183812yes—
768C2×C4C24×D8311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1662no—
772C8—1662no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—3322no—
778C22—3322no—
779C22—3328no—
780C22—3324no—
781C22—3322no—
782C22—3322no—
783C22—3322no—
784C22—66416no—
785C22—6644no—
786C22—1664no—
787C22—1662no—
788C22—1662no—
789C22—1662no—
790C22#1912834312yes—
791C22#1912850012yes—
792C22#1912850812yes—
793C22C22×D4×D8311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—3322no—
800C4—3322no—
801C4—1662no—
802C4—1662no—
803C4—1662no—
804C4#1912834312yes—
805C4C2×#41×D8311yescharacteristic
806C4C2×#1458183811yescharacteristic
807C2—42no—
808C2—3324no—
809C2—3322no—
810C2—6642no—
811C2#2491967714yesdirect product factor
812C2C2×#1912834311yescharacteristic
813C2C2×#1912850011yescharacteristic
814C2C2×#1912850811yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#485×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128342C2
hypercenterC2×#485D83
hypocenterC83C2×#3323
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#19128390C2semidirect
3. #24919677C2direct (N × H)
4. C2×#19128057C2semidirect
5. C2×#19128021C2semidirect
6. C2×#19128004C2semidirect
7. C2×#19127957C2semidirect
8. C2×#19127948C2semidirect
9. C2×#19127926C2semidirect
10. C2×#19127866C2semidirect
11. C2×#19127854C2semidirect
12. C2×#19127788C2semidirect
13. C2×#19127776C2semidirect
14. C2×#19127701C2semidirect
15. C2×#19127705C2semidirect
16. C2×#485×C83C2semidirect
19. C22×#13050580C22semidirect
23. C22×#13050573C22semidirect
25. #19128390C22semidirect
30. C2×#14581783C22semidirect
34. C2×#14581772C22semidirect
39. C2×#14581757C22semidirect
43. C2×C4⋊C4×D83C22semidirect
45. #19128057C22semidirect
46. #19128021C22semidirect
47. #19128004C22semidirect
48. #19127957C22semidirect
49. #19127948C22semidirect
50. #19127926C22semidirect
51. #19127866C22semidirect
52. #19127854C22semidirect
53. #19127788C22semidirect
54. #19127776C22semidirect
55. C2×#14581723C22semidirect
56. C2×Dic83⋊C8C22semidirect
57. #19127705C22semidirect
58. #19127701C22semidirect
59. C2×#14581716C22semidirect
60. C2×#14581715C22semidirect
67. C2×(C2×D83)⋊C8C22semidirect
68. C2×C8×Dic83C22semidirect
71. #485×C83C22semidirect
72. C2×#107×C83C22semidirect
73. C2×#106×C83C22semidirect
74. C2×#103×C83C22semidirect
75. C2×#103×C83C22semidirect
98. C2×#13050580C23semidirect
106. C2×#13050573C23semidirect
112. #14581783C23semidirect
118. #14581772C23semidirect
126. #14581757C23semidirect
141. C4⋊C4×D83C23semidirect
153. #14581723C23semidirect
154. Dic83⋊C8C23semidirect
155. #14581716C23semidirect
156. #14581715C23semidirect
163. (C2×D83)⋊C8C23semidirect
164. C8×Dic83C23semidirect
180. #107×C83C23semidirect
181. #106×C83C23semidirect
182. #103×C83C23semidirect
183. #103×C83C23semidirect
401. C2×C83#3323semidirect
413. C2×#485D83semidirect
424. C83C2×#3323semidirect
456. #485C2×D83semidirect
466. C2×#107C2×D83semidirect
468. C2×#106C2×D83semidirect
474. C2×#103C2×D83semidirect
475. C2×#103C2×D83semidirect
576. #107C22×D83semidirect
578. #106C22×D83semidirect
582. #103C22×D83semidirect
583. #103C22×D83semidirect
811. C2#24919677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283902
C2×#191283422
#249196772
C2×#191280572
C2×#191280212
C2×#191280042
C2×#191279572
C2×#191279482
C2×#191279262
C2×#191278662
C2×#191278542
C2×#191277882
C2×#191277762
C2×#191277012
C2×#191277052
C2×#485×C832
C2×#332383