Finite Group Databasebeta

← C2×#24917414 #36272224

Subgroups — C2×#24917414 #36272224

Order 21248.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128267C211yesmaximal, characteristic
2C2×#19128182C211yesmaximal, characteristic, complemented
3#24917414C2116yesmaximal, direct product factor
4C2×#19128019C211yesmaximal, characteristic, complemented
5C2×#19128018C211yesmaximal, characteristic, complemented
6C2×#19128028C211yesmaximal, characteristic, complemented
7C2×#19128026C211yesmaximal, characteristic, complemented
8C2×#19128023C211yesmaximal, characteristic, complemented
9C2×#19128022C211yesmaximal, characteristic, complemented
10C2×#19128016C211yesmaximal, characteristic, complemented
11C2×#19127742C211yesmaximal, characteristic, complemented
12C2×#19127738C211yesmaximal, characteristic, complemented
13C2×#19127704C211yesmaximal, characteristic, complemented
14C2×#102×D83C211yesmaximal, characteristic, complemented
15C2×#19127666C211yesmaximal, characteristic, complemented
16C2×#480×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C22×D4×D83C2211yescharacteristic
19C22×#13050573C2211yescharacteristic
20C22×C8×D83C2211yescharacteristic
21#19128267—24no—
22#19128267C2218yes—
23C2×#14581788—21no—
24C2×#14581778—21no—
25C2×#14581767C2211yescharacteristic
26C2×#14581766C2211yescharacteristic
27C2×#14581763C2211yescharacteristic
28C2×#14581762—21no—
29C2×#14581760—21no—
30#19128182—24no—
31#19128182C2218yescomplemented
32C2×#14581757—21no—
33C2×#14581754—21no—
34C2×C4×C22⋊D83—21no—
35C2×C4×C22⋊D83—21no—
36C2×#14581751C2211yescharacteristic, complemented
37C2×#14581750C2211yescharacteristic
38C2×#14581750C2211yescharacteristic
39C2×#14581750C2211yescharacteristic, complemented
40C2×C4⋊C4×D83C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic, complemented
42#19128028C2218yescomplemented
43#19128026C2218yescomplemented
44#19128023C2218yescomplemented
45#19128022C2218yescomplemented
46#19128019C2218yescomplemented
47#19128018C2218yescomplemented
48#19128016C2218yescomplemented
49#19127742C2218yescomplemented
50#19127738C2218yescomplemented
51C2×#14581726C2211yescharacteristic, complemented
52C2×#14581725C2211yescharacteristic, complemented
53C2×#14581724C2211yescharacteristic, complemented
54C2×#14581723C2211yescharacteristic, complemented
55C2×#14581723C2211yescharacteristic, complemented
56C2×#14581723C2211yescharacteristic, complemented
57#19127704C2218yescomplemented
58C2×#14581714C2211yescharacteristic
59C2×#14581714C2211yescharacteristic
60C2×#14581713C2211yescharacteristic
61C2×#14581713C2211yescharacteristic
62C2×#14581712C2211yescharacteristic
63C2×#14581712C2211yescharacteristic
64#102×D83C2218yescomplemented
65#19127666C2218yescomplemented
66C2×C22⋊(C83⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D83)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D83)⋊C8C2211yescharacteristic, complemented
69C2×#121×C83C2211yescharacteristic
70C22×C4⋊C4×C83C2211yescharacteristic, complemented
71#480×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic, complemented
73C2×#107×C83C2211yescharacteristic, complemented
74C2×#102×C83C2211yescharacteristic
75C2×#102×C83C2211yescharacteristic
76C2×C22⋊C8×C83C2211yescharacteristic, complemented
77C24×D83—21no—
78C2×#13050590—24no—
79C2×#13050590—24no—
80C2×#13050590D414yes—
81C2×#13050590C2314yes—
82C22×Dic166D411yescharacteristic
83C22×D332—21no—
84C22×D332D411yescharacteristic
85C22×D332C2311yescharacteristic
86C22×C22⋊D83—21no—
87C22×C22⋊D83—21no—
88C22×C22⋊D83—21no—
89C22×C22⋊D83D411yescharacteristic
90C22×C22⋊D83D411yescharacteristic
91C2×D4×D83—22no—
92C2×D4×D83—24no—
93C2×D4×D83—24no—
94C2×D4×D83C2314yes—
95C22×C4×D83—21no—
96C22×C4×D83—21no—
97C22×C4×D83C2311yescharacteristic
98C22×C4×D83C2311yescharacteristic
99C2×#13050573—24no—
100C2×#13050573C2314yes—
101C22×C83⋊C8C2311yescharacteristic
102C22×C83⋊C8C2311yescharacteristic
103C2×C8×D83—24no—
104C2×C8×D83C2314yes—
105#14581788—28no—
106#14581778—28no—
107#14581767—22no—
108#14581767C2314yes—
109#14581766—22no—
110#14581766C2314yes—
111#14581763—22no—
112#14581763C2314yes—
113#14581762—28no—
114#14581760—28no—
115#14581757—28no—
116#14581754—28no—
117C4×C22⋊D83—28no—
118C4×C22⋊D83—28no—
119#14581751—22no—
120#14581751C2314yescomplemented
121#14581750—22no—
122#14581750—22no—
123#14581750—22no—
124#14581750C2314yes—
125#14581750C2314yes—
126#14581750C2314yescomplemented
127C2×C4⋊Dic83C2311yescharacteristic
128C2×C4⋊Dic83C2311yescharacteristic
129C2×C4⋊Dic83C2311yescharacteristic
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C4⋊C4×D83—22no—
133C4⋊C4×D83—22no—
134C4⋊C4×D83C2314yes—
135C4⋊C4×D83C2314yescomplemented
136C2×C22⋊Dic83—21no—
137C2×C22⋊Dic83—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×C4×Dic83—21no—
144C2×C4×Dic83—21no—
145C2×C4×Dic83—21no—
146C2×C4×Dic83—21no—
147#14581726C2314yescomplemented
148#14581725C2314yescomplemented
149#14581724C2314yescomplemented
150#14581723C2314yescomplemented
151#14581723C2314yescomplemented
152#14581723C2314yescomplemented
153#14581714C2314yes—
154#14581714C2314yes—
155#14581713C2314yes—
156#14581713C2314yes—
157#14581712C2314yes—
158#14581712C2314yes—
159C22⋊(C83⋊C8)C2314yescomplemented
160(C2×D83)⋊C8C2314yescomplemented
161(C2×D83)⋊C8C2314yescomplemented
162C22×D4×C83—21no—
163C22×D4×C83C2311yescharacteristic
164C23×C4×C83—21no—
165C23×C4×C83C2311yescharacteristic
166C22×C8×C83C2311yescharacteristic
167C22×C8×C83C2311yescharacteristic
168#121×C83—22no—
169#121×C83C2314yes—
170C2×C4⋊C4×C83—21no—
171C2×C4⋊C4×C83—22no—
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C4⋊C4×C83C2314yescomplemented
176C2×C22⋊C4×C83—21no—
177#107×C83C2314yescomplemented
178#107×C83C2314yescomplemented
179#102×C83C2314yes—
180#102×C83C2314yes—
181C22⋊C8×C83C2314yescomplemented
182C23×D83—21no—
183C23×D83—24no—
184C23×D83—44no—
185C23×D83—82no—
186C23×D83—82no—
187C23×D83C2×D411yescharacteristic
188C23×D83C2×D411yescharacteristic
189#13050590—216no—
190#13050590—28no—
191#13050590—28no—
192C2×Dic166—24no—
193C2×Dic166C2×D414yes—
194C2×D332—24no—
195C2×D332—22no—
196C2×D332—22no—
197C2×D332—21no—
198C2×D332—24no—
199C2×D332—82no—
200C2×D332C2×D414yes—
201C2×D332C2412yes—
202C2×C22⋊D83—24no—
203C2×C22⋊D83—24no—
204C2×C22⋊D83—24no—
205C2×C22⋊D83—24no—
206C2×C22⋊D83—24no—
207C2×C22⋊D83—44no—
208C2×C22⋊D83—82no—
209C2×C22⋊D83—82no—
210C2×C22⋊D83C2×D414yes—
211C2×C22⋊D83C2×D414yes—
212D4×D83—28no—
213D4×D83—28no—
214D4×D83—48no—
215C22×Dic83—21no—
216C22×Dic83—21no—
217C22×Dic83—21no—
218C22×Dic83C2×D411yescharacteristic
219C22×Dic83C2×D411yescharacteristic
220C2×C4×D83—22no—
221C2×C4×D83—22no—
222C2×C4×D83—24no—
223C2×C4×D83—24no—
224C2×C4×D83—82no—
225C2×C4×D83—82no—
226C2×C4×D83C2×D412yes—
227C2×C4×D83C2×D412yes—
228C2×C4×D83#4114yes—
229C2×C4×D83#4114yes—
230C2×C4×D83C2412yes—
231C2×C4×D83C2412yes—
232#13050573—28no—
233C2×C83⋊C8—22no—
234C2×C83⋊C8—22no—
235C2×C83⋊C8C2412yes—
236C2×C83⋊C8C2412yes—
237C8×D83—28no—
238C4⋊Dic83—21no—
239C4⋊Dic83—21no—
240C4⋊Dic83—21no—
241C4⋊Dic83C2412yes—
242C4⋊Dic83C2412yes—
243C4⋊Dic83C2412yes—
244Dic83⋊C4—24no—
245Dic83⋊C4—24no—
246C22⋊Dic83—24no—
247C22⋊Dic83—24no—
248(C2×D83)⋊C4—24no—
249(C2×D83)⋊C4—24no—
250(C2×D83)⋊C4—24no—
251(C2×D83)⋊C4—24no—
252(C2×D83)⋊C4—24no—
253C4×Dic83—24no—
254C4×Dic83—24no—
255C4×Dic83—24no—
256C4×Dic83—24no—
257C24×C83—21no—
258C24×C83C2×D411yescharacteristic
259C2×D4×C83—24no—
260C2×D4×C83—21no—
261C2×D4×C83—22no—
262C2×D4×C83—22no—
263C2×D4×C83—82no—
264C2×D4×C83C2412yes—
265C22×C4×C83—22no—
266C22×C4×C83—22no—
267C22×C4×C83—21no—
268C22×C4×C83—21no—
269C22×C4×C83—21no—
270C22×C4×C83—24no—
271C22×C4×C83—82no—
272C22×C4×C83C2×D412yes—
273C22×C4×C83C2×D411yescharacteristic
274C22×C4×C83C2412yes—
275C22×C4×C83C2411yescharacteristic
276C2×C8×C83—22no—
277C2×C8×C83—22no—
278C2×C8×C83C2412yes—
279C2×C8×C83C2412yes—
280C4⋊C4×C83—21no—
281C4⋊C4×C83—21no—
282C4⋊C4×C83—21no—
283C4⋊C4×C83—24no—
284C4⋊C4×C83C2412yes—
285C4⋊C4×C83C2412yes—
286C4⋊C4×C83C2412yes—
287C22⋊C4×C83—24no—
288C23×C83—22no—
289C23×C83—22no—
290C23×C83—22no—
291C23×C83—22no—
292C23×C83—42no—
293C23×C83—42no—
294C23×C83—42no—
295C23×C83C22×D412yes—
296C23×C83C22×D411yescharacteristic
297C22×D83—22no—
298C22×D83—22no—
299C22×D83—22no—
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—42no—
304C22×D83—42no—
305C22×D83—42no—
306C22×D83—48no—
307C22×D83—84no—
308C22×D83—84no—
309C22×D83—816no—
310C22×D83#12314yes—
311C22×D83C22×D412yes—
312C22×D83C22×D412yes—
313D4×C83—22no—
314D4×C83—22no—
315D4×C83—42no—
316D4×C83—84no—
317C2×C4×C83—22no—
318C2×C4×C83—24no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—42no—
325C2×C4×C83—42no—
326C2×C4×C83—42no—
327C2×C4×C83—84no—
328C2×C4×C83C22×D412yes—
329C2×C4×C83C22×D411yescharacteristic
330C2×C4×C83C2×#4112yes—
331C2×C4×C83C2×#4112yes—
332C2×C4×C83C2511yescharacteristic
333C22⋊D83—28no—
334C22⋊D83—28no—
335C22⋊D83—48no—
336C22⋊D83—84no—
337C22⋊D83—84no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—42no—
343C2×Dic83—42no—
344C2×Dic83—42no—
345C2×Dic83#12314yes—
346C2×Dic83C22×D412yes—
347C2×Dic83C22×D412yes—
348D332—28no—
349D332—22no—
350D332—22no—
351D332—42no—
352D332—84no—
353C4×D83—24no—
354C4×D83—22no—
355C4×D83—22no—
356C4×D83—84no—
357C4×D83—84no—
358C4×D83#12318yes—
359C4×D83C2×#4114yes—
360C4×D83C2×#4114yes—
361Dic166—28no—
362C8×C83—22no—
363C8×C83—22no—
364C83⋊C8—22no—
365C83⋊C8—22no—
366C22×C83—22no—
367C22×C83—22no—
368C22×C83—22no—
369C22×C83—44no—
370C22×C83—42no—
371C22×C83—42no—
372C22×C83—42no—
373C22×C83—84no—
374C22×C83C2×#12312yes—
375C22×C83#57612yes—
376C22×C83#57712yes—
377C22×C83C23×D411yescharacteristic
378C2×D83—28no—
379C2×D83—22no—
380C2×D83—22no—
381C2×D83—22no—
382C2×D83—22no—
383C2×D83—22no—
384C2×D83—44no—
385C2×D83—42no—
386C2×D83—42no—
387C2×D83—42no—
388C2×D83—816no—
389C2×D83—84no—
390C2×D83C2×#12314yes—
391C4×C83—22no—
392C4×C83—42no—
393C4×C83—42no—
394C4×C83—42no—
395C4×C83C2×#12312yes—
396C4×C83C22×#4111yescharacteristic
397C4×C83C22×#4111yescharacteristic
398Dic83—22no—
399Dic83—42no—
400Dic83—42no—
401Dic83—42no—
402Dic83C2×#12314yes—
403C2×#3096—831nomaximal, Sylow
404C2×C83—42no—
405C2×C83—82no—
406C2×C83#309614yescomplemented
407C2×C83C22×#12311yescharacteristic
408C2×C83C2×#57611yescharacteristic
409C2×C83C2×#57711yescharacteristic
410D83—24no—
411D83—42no—
412D83—82no—
413C2×#535—831no—
414C2×#520—831no—
415#3096—8316no—
416C2×#481—831no—
417C2×#481—831no—
418C2×#482—831no—
419C2×#482—831no—
420C2×#482—831no—
421C2×#482—831no—
422C2×#480—831no—
423C2×#480D8311yescharacteristic, complemented
424C2×#428—831no—
425C2×#427—831no—
426C2×#418—831no—
427C22×#102—831no—
428C2×#408—831no—
429C83C2×#309611yescharacteristic, complemented, Sylow
430C22×#41—831no—
431C23×D4—831no—
432C22×M16—831no—
433C23×C8—831no—
434#535—838no—
435#535—1664no—
436C2×#127—1661no—
437C2×#124—1661no—
438C2×#121—831no—
439C2×#121—831no—
440C2×#121—831no—
441C2×#121C2×D8311yescharacteristic
442C2×#120—1661no—
443C2×#120—1661no—
444#520—838no—
445#520—1664no—
446C2×C4×Q8—1661no—
447C2×C4×D4—1661no—
448C2×C4×D4—1661no—
449C2×C4×D4—1661no—
450C2×#117—831no—
451C2×#117—831no—
452C2×#117—831no—
453C2×#117—831no—
454C22×C4⋊C4—831no—
455C22×C4⋊C4—831no—
456C22×C4⋊C4C2×D8311yescharacteristic, complemented
457#482—838no—
458#482—838no—
459#482—838no—
460#482—838no—
461#481—838no—
462#481—838no—
463#480—838no—
464#480C2×D8318yescomplemented
465#428—838no—
466#427—838no—
467C2×#107—831no—
468C2×#107—831no—
469C2×#107C2×D8311yescharacteristic, complemented
470C2×#107C2×D8311yescharacteristic, complemented
471C2×#106—831no—
472C2×#106—831no—
473C2×#106—831no—
474C2×#106—831no—
475#418—838no—
476C2×#102—831no—
477C2×#102—831no—
478C2×#102—831no—
479C2×#102—831no—
480C2×#102—831no—
481C2×#102—831no—
482C2×#102—838no—
483C2×#102C2×D8311yescharacteristic
484C2×#102C2×D8311yescharacteristic
485#408—838no—
486C2×C22⋊C8—831no—
487C2×C22⋊C8—831no—
488C2×C22⋊C8—831no—
489C2×C22⋊C8C2×D8311yescharacteristic, complemented
490C25—1661no—
491C2×#41—834no—
492C2×#41—834no—
493C2×#41—1664no—
494C2×#41—1664no—
495C22×Q8—831no—
496C22×D4—21no—
497C22×D4—831no—
498C22×D4—831no—
499C22×D4—834no—
500C22×D4—831no—
501C22×D4—831no—
502C22×D4—1661no—
503C22×D4—1662no—
504C22×D4—1664no—
505C22×D4—1664no—
506C22×D4—1661no—
507C22×D4—1661no—
508C22×D4—1661no—
509C22×D4C22×D8311yescharacteristic
510C23×C4—21no—
511C23×C4—831no—
512C23×C4—831no—
513C23×C4—1661no—
514C23×C4—1661no—
515C23×C4C22×D8311yescharacteristic
516C2×M16—834no—
517C2×M16—1664no—
518C22×C8—831no—
519C22×C8—831no—
520C22×C8—834no—
521C22×C8—1664no—
522C22×C8C22×D8311yescharacteristic
523C22×C8C22×D8311yescharacteristic
524#127—1668no—
525#124—1668no—
526#121—22no—
527#121—834no—
528#121—834no—
529#121—834no—
530#121—1662no—
531#121—1662no—
532#121—1662no—
533#121C22×D8314yes—
534#120—1668no—
535#120—1668no—
536C4×Q8—1668no—
537C4×D4—1668no—
538C4×D4—1668no—
539C4×D4—1668no—
540#117—834no—
541#117—834no—
542#117—834no—
543#117—834no—
544#117—1662no—
545#117—1662no—
546#117—1662no—
547#117—1662no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—831no—
551C2×C4⋊C4—831no—
552C2×C4⋊C4—831no—
553C2×C4⋊C4—834no—
554C2×C4⋊C4—834no—
555C2×C4⋊C4—1662no—
556C2×C4⋊C4—1662no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4—1661no—
559C2×C4⋊C4C22×D8311yescharacteristic
560C2×C4⋊C4C22×D8311yescharacteristic
561C2×C4⋊C4C22×D8311yescharacteristic
562C2×C4⋊C4C22×D8314yescomplemented
563C2×C22⋊C4—21no—
564C2×C22⋊C4—1661no—
565C2×C22⋊C4—1661no—
566C2×C22⋊C4—1661no—
567C2×C22⋊C4—1661no—
568C2×C22⋊C4—1661no—
569C2×C22⋊C4—1661no—
570C2×C22⋊C4—1661no—
571C2×C42—1661no—
572C2×C42—1661no—
573C2×C42—1661no—
574C2×C42—1661no—
575#107—834no—
576#107—834no—
577#107C22×D8314yescomplemented
578#107C22×D8314yescomplemented
579#106—834no—
580#106—834no—
581#106—834no—
582#106—834no—
583#102—834no—
584#102—834no—
585#102—834no—
586#102—834no—
587#102—834no—
588#102—834no—
589#102C22×D8314yes—
590#102C22×D8314yes—
591C22⋊C8—834no—
592C22⋊C8—834no—
593C22⋊C8—834no—
594C22⋊C8C22×D8314yescomplemented
595C24—21no—
596C24—3324no—
597C24—831no—
598C24—831no—
599C24—6642no—
600C24—6642no—
601C24—1664no—
602C24—1661no—
603C24D4×D8311yescharacteristic
604#41—16616no—
605#41—1668no—
606#41—1668no—
607C2×Q8—834no—
608C2×Q8—1664no—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—82no—
614C2×D4—3328no—
615C2×D4—3324no—
616C2×D4—834no—
617C2×D4—834no—
618C2×D4—834no—
619C2×D4—832no—
620C2×D4—6642no—
621C2×D4—6642no—
622C2×D4—6642no—
623C2×D4—1664no—
624C2×D4—1664no—
625C2×D4—1668no—
626C2×D4—1668no—
627C2×D4—1664no—
628C2×D4—1664no—
629C2×D4—1664no—
630C2×D4—1664no—
631C2×D4—1664no—
632C2×D4—1661no—
633C2×D4—1662no—
634C2×D4—1662no—
635C2×D4C23×D8312yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—82no—
643C22×C4—831no—
644C22×C4—832no—
645C22×C4—834no—
646C22×C4—834no—
647C22×C4—832no—
648C22×C4—831no—
649C22×C4—832no—
650C22×C4—832no—
651C22×C4—6642no—
652C22×C4—6642no—
653C22×C4—1664no—
654C22×C4—1664no—
655C22×C4—1661no—
656C22×C4—1661no—
657C22×C4—1661no—
658C22×C4—1662no—
659C22×C4—1662no—
660C22×C4D4×D8312yes—
661C22×C4D4×D8311yescharacteristic
662C22×C4C23×D8312yes—
663C22×C4C23×D8311yescharacteristic
664M16—1668no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—832no—
668C2×C8—832no—
669C2×C8—1668no—
670C2×C8—1662no—
671C2×C8—1662no—
672C2×C8C23×D8312yes—
673C2×C8C23×D8312yes—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—832no—
679C4⋊C4—832no—
680C4⋊C4—832no—
681C4⋊C4—1664no—
682C4⋊C4—1664no—
683C4⋊C4—1661no—
684C4⋊C4—1661no—
685C4⋊C4—1661no—
686C4⋊C4C23×D8312yes—
687C4⋊C4C23×D8312yes—
688C4⋊C4C23×D8312yes—
689C22⋊C4—24no—
690C22⋊C4—1664no—
691C22⋊C4—1664no—
692C22⋊C4—1664no—
693C22⋊C4—1664no—
694C22⋊C4—1664no—
695C22⋊C4—1664no—
696C22⋊C4—1664no—
697C42—1664no—
698C42—1664no—
699C42—1664no—
700C42—1664no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—3328no—
709C23—3322no—
710C23—3322no—
711C23—3322no—
712C23—834no—
713C23—832no—
714C23—832no—
715C23—6644no—
716C23—6644no—
717C23—66416no—
718C23—1662no—
719C23—1662no—
720C23—1662no—
721C23—1662no—
722C23—1662no—
723C23—1662no—
724C23C2×D4×D8312yes—
725C23C2×D4×D8311yescharacteristic
726Q8—1668no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—3328no—
732D4—3322no—
733D4—6644no—
734D4—6644no—
735D4—6644no—
736D4—1668no—
737D4—1668no—
738D4—1668no—
739D4—1662no—
740D4—1662no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—3322no—
753C2×C4—3322no—
754C2×C4—3322no—
755C2×C4—834no—
756C2×C4—832no—
757C2×C4—838no—
758C2×C4—834no—
759C2×C4—834no—
760C2×C4—832no—
761C2×C4—6644no—
762C2×C4—6644no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1664no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4C2×D4×D8312yes—
771C2×C4C2×D4×D8311yescharacteristic
772C2×C4#41×D8312yes—
773C2×C4#41×D8312yes—
774C2×C4C24×D8311yescharacteristic
775C8—22no—
776C8—22no—
777C8—1662no—
778C8—1662no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—3324no—
788C22—3322no—
789C22—3322no—
790C22—3322no—
791C22—834no—
792C22—66416no—
793C22—6644no—
794C22—1662no—
795C22—1662no—
796C22—1662no—
797C22—1662no—
798C22—1662no—
799C22—1668no—
800C22#123×D8312yes—
801C22#1912850212yes—
802C22#1912851012yes—
803C22C22×D4×D8311yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—3322no—
809C4—3322no—
810C4—3322no—
811C4—834no—
812C4—1662no—
813C4#123×D8312yes—
814C4C2×#41×D8311yescharacteristic
815C4C2×#41×D8311yescharacteristic
816C2—42no—
817C2—82no—
818C2—3322no—
819C2—6642no—
820C2—1664no—
821C2#2491741414yesdirect product factor
822C2C2×#123×D8311yescharacteristic
823C2C2×#1912850211yescharacteristic
824C2C2×#1912851011yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#480×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128267C2
hypercenterC2×#480D83
hypocenterC83C2×#3096
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#19128182C2semidirect
3. #24917414C2direct (N × H)
4. C2×#19128019C2semidirect
5. C2×#19128018C2semidirect
6. C2×#19128028C2semidirect
7. C2×#19128026C2semidirect
8. C2×#19128023C2semidirect
9. C2×#19128022C2semidirect
10. C2×#19128016C2semidirect
11. C2×#19127742C2semidirect
12. C2×#19127738C2semidirect
13. C2×#19127704C2semidirect
14. C2×#102×D83C2semidirect
15. C2×#19127666C2semidirect
16. C2×#480×C83C2semidirect
31. #19128182C22semidirect
36. C2×#14581751C22semidirect
39. C2×#14581750C22semidirect
41. C2×C4⋊C4×D83C22semidirect
42. #19128028C22semidirect
43. #19128026C22semidirect
44. #19128023C22semidirect
45. #19128022C22semidirect
46. #19128019C22semidirect
47. #19128018C22semidirect
48. #19128016C22semidirect
49. #19127742C22semidirect
50. #19127738C22semidirect
51. C2×#14581726C22semidirect
52. C2×#14581725C22semidirect
53. C2×#14581724C22semidirect
54. C2×#14581723C22semidirect
55. C2×#14581723C22semidirect
56. C2×#14581723C22semidirect
57. #19127704C22semidirect
64. #102×D83C22semidirect
65. #19127666C22semidirect
66. C2×C22⋊(C83⋊C8)C22semidirect
67. C2×(C2×D83)⋊C8C22semidirect
68. C2×(C2×D83)⋊C8C22semidirect
70. C22×C4⋊C4×C83C22semidirect
71. #480×C83C22semidirect
72. C2×#107×C83C22semidirect
73. C2×#107×C83C22semidirect
76. C2×C22⋊C8×C83C22semidirect
120. #14581751C23semidirect
126. #14581750C23semidirect
135. C4⋊C4×D83C23semidirect
147. #14581726C23semidirect
148. #14581725C23semidirect
149. #14581724C23semidirect
150. #14581723C23semidirect
151. #14581723C23semidirect
152. #14581723C23semidirect
159. C22⋊(C83⋊C8)C23semidirect
160. (C2×D83)⋊C8C23semidirect
161. (C2×D83)⋊C8C23semidirect
175. C2×C4⋊C4×C83C23semidirect
177. #107×C83C23semidirect
178. #107×C83C23semidirect
181. C22⋊C8×C83C23semidirect
406. C2×C83#3096semidirect
423. C2×#480D83semidirect
429. C83C2×#3096semidirect
456. C22×C4⋊C4C2×D83semidirect
464. #480C2×D83semidirect
469. C2×#107C2×D83semidirect
470. C2×#107C2×D83semidirect
489. C2×C22⋊C8C2×D83semidirect
562. C2×C4⋊C4C22×D83semidirect
577. #107C22×D83semidirect
578. #107C22×D83semidirect
594. C22⋊C8C22×D83semidirect
821. C2#24917414direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282672
C2×#191281822
#249174142
C2×#191280192
C2×#191280182
C2×#191280282
C2×#191280262
C2×#191280232
C2×#191280222
C2×#191280162
C2×#191277422
C2×#191277382
C2×#191277042
C2×#102×D832
C2×#191276662
C2×#480×C832
C2×#309683