Finite Group Databasebeta

← C2×#24919504 #36281079

Subgroups — C2×#24919504 #36281079

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×#19128424C211yesmaximal, characteristic, complemented
2C2×#19128346C211yesmaximal, characteristic
3#24919504C2116yesmaximal, direct product factor
4C2×#19128061C211yesmaximal, characteristic, complemented
5C2×#19128044C211yesmaximal, characteristic, complemented
6C2×#19128028C211yesmaximal, characteristic, complemented
7C2×#19127991C211yesmaximal, characteristic, complemented
8C2×#19127958C211yesmaximal, characteristic, complemented
9C2×#19127933C211yesmaximal, characteristic, complemented
10C2×#19127923C211yesmaximal, characteristic, complemented
11C2×#19127860C211yesmaximal, characteristic, complemented
12C2×#19127850C211yesmaximal, characteristic, complemented
13C2×#19127774C211yesmaximal, characteristic, complemented
14C2×#19127704C211yesmaximal, characteristic, complemented
15C2×#19127694C211yesmaximal, characteristic, complemented
16C2×#440×C83C211yesmaximal, characteristic, complemented
17C22×#13050589C2211yescharacteristic
18C22×D4×D83C2211yescharacteristic
19C22×#13050580C2211yescharacteristic, complemented
20C22×#13050577C2211yescharacteristic
21C22×#13050573C2211yescharacteristic
22C22×C8×D83C2211yescharacteristic, complemented
23#19128424—24no—
24#19128424C2218yescomplemented
25#19128346—24no—
26#19128346C2218yes—
27C2×#14581792C2211yescharacteristic, complemented
28C2×#14581787—21no—
29C2×#14581787—21no—
30C2×#14581780—21no—
31C2×#14581780C2211yescharacteristic
32C2×#14581776—21no—
33C2×#14581772C2211yescharacteristic
34C2×#14581768C2211yescharacteristic
35C2×#14581768C2211yescharacteristic, complemented
36C2×#14581767C2211yescharacteristic
37C2×#14581766—21no—
38C2×#14581762—21no—
39C2×C4×Dic166—21no—
40C2×C4×D332C2211yescharacteristic
41C2×#14581750C2211yescharacteristic
42C2×#14581750C2211yescharacteristic, complemented
43C22×(C2×D83)⋊C4—21no—
44#19128061C2218yescomplemented
45#19128044C2218yescomplemented
46#19128028C2218yescomplemented
47#19127991C2218yescomplemented
48#19127958C2218yescomplemented
49#19127933C2218yescomplemented
50#19127923C2218yescomplemented
51#19127860C2218yescomplemented
52#19127850C2218yescomplemented
53#19127774C2218yescomplemented
54C2×#14581723C2211yescharacteristic, complemented
55C2×#14581723C2211yescharacteristic, complemented
56C2×C4⋊(C83⋊C8)C2211yescharacteristic, complemented
57#19127704C2218yescomplemented
58#19127694C2218yescomplemented
59C2×#14581717C2211yescharacteristic, complemented
60C2×#14581717C2211yescharacteristic, complemented
61C2×#14581715C2211yescharacteristic, complemented
62C2×#14581714C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65C2×#14581713C2211yescharacteristic
66C2×#14581712C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×(C2×D83)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C83C2211yescharacteristic
70C2×C4×Q8×C83C2211yescharacteristic, complemented
71C2×C4×D4×C83C2211yescharacteristic
72#440×C83C2218yescomplemented
73C2×#107×C83C2211yescharacteristic, complemented
74C2×#103×C83C2211yescharacteristic, complemented
75C2×#102×C83C2211yescharacteristic
76C2×#97×C83C2211yescharacteristic, complemented
77C24×D83—21no—
78C2×#13050589—22no—
79C2×#13050589—24no—
80C2×#13050589—42no—
81C2×#13050589C2314yes—
82C22×Dic166—21no—
83C22×Dic166C2311yescharacteristic
84C22×D332—21no—
85C22×D332D411yescharacteristic
86C22×D332C2311yescharacteristic
87C22×C22⋊D83—21no—
88C22×C22⋊D83—21no—
89C2×D4×D83—22no—
90C2×D4×D83—24no—
91C2×D4×D83—42no—
92C2×D4×D83C2314yes—
93C23×Dic83—21no—
94C22×C4×D83C2311yescharacteristic
95C22×C4×D83C2311yescharacteristic
96C2×#13050580—42no—
97C2×#13050580C2314yescomplemented
98C2×#13050577—42no—
99C2×#13050577C2314yes—
100C2×#13050573—42no—
101C2×#13050573C2314yes—
102C22×C83⋊C8C2311yescharacteristic
103C22×C83⋊C8C2311yescharacteristic
104C2×C8×D83—42no—
105C2×C8×D83C2314yescomplemented
106#14581792—22no—
107#14581792C2314yescomplemented
108#14581787—28no—
109#14581787—28no—
110#14581780—28no—
111#14581780—22no—
112#14581780C2314yes—
113#14581776—28no—
114#14581772—22no—
115#14581772C2314yes—
116#14581768—22no—
117#14581768—22no—
118#14581768C2314yes—
119#14581768C2314yescomplemented
120#14581767—22no—
121#14581767C2314yes—
122#14581766—28no—
123#14581762—28no—
124C4×Dic166—28no—
125C4×D332D414yes—
126C4×D332C2314yes—
127#14581750—22no—
128#14581750—22no—
129#14581750C2314yes—
130#14581750C2314yescomplemented
131C2×C4⋊Dic83—21no—
132C2×C4⋊Dic83—21no—
133C2×C4⋊Dic83D411yescharacteristic
134C2×C4⋊Dic83C2311yescharacteristic
135C2×C4⋊Dic83C2311yescharacteristic
136C2×Dic83⋊C4—21no—
137C2×Dic83⋊C4—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×(C2×D83)⋊C4—21no—
144C2×(C2×D83)⋊C4—28no—
145C2×(C2×D83)⋊C4—21no—
146C2×(C2×D83)⋊C4—21no—
147C2×(C2×D83)⋊C4D411yescharacteristic
148C2×(C2×D83)⋊C4D411yescharacteristic
149C2×C4×Dic83—21no—
150C2×C4×Dic83—21no—
151#14581723C2314yescomplemented
152#14581723C2314yescomplemented
153C4⋊(C83⋊C8)C2314yescomplemented
154#14581717C2314yescomplemented
155#14581717C2314yescomplemented
156#14581715C2314yescomplemented
157#14581714C2314yes—
158#14581714C2314yes—
159#14581713C2314yes—
160#14581713C2314yes—
161#14581712C2314yes—
162(C2×D83)⋊C8C2314yes—
163(C2×D83)⋊C8C2314yescomplemented
164C22×Q8×C83C2311yescharacteristic
165C22×D4×C83C2311yescharacteristic
166C23×C4×C83—21no—
167C2×SD16×C83—24no—
168C2×SD16×C83C2314yes—
169C22×C8×C83C2311yescharacteristic
170C22×C8×C83C2311yescharacteristic
171C4×Q8×C83—22no—
172C4×Q8×C83C2314yescomplemented
173C4×D4×C83—22no—
174C4×D4×C83C2314yes—
175C2×C4⋊C4×C83—21no—
176C2×C4⋊C4×C83C2311yescharacteristic
177C2×C4⋊C4×C83C2311yescharacteristic
178C2×C22⋊C4×C83—21no—
179C2×C42×C83—21no—
180C2×C42×C83C2311yescharacteristic
181#107×C83C2314yescomplemented
182#103×C83C2314yescomplemented
183#102×C83C2314yes—
184#97×C83C2314yescomplemented
185C23×D83—21no—
186C23×D83—24no—
187C23×D83—44no—
188C23×D83—44no—
189C23×D83—82no—
190C23×D83C2×D411yescharacteristic
191C23×D83C2×D411yescharacteristic
192#13050589—28no—
193#13050589—44no—
194#13050589—48no—
195C2×Dic166—22no—
196C2×Dic166—22no—
197C2×Dic166—21no—
198C2×Dic166—24no—
199C2×Dic166—44no—
200C2×Dic166C2412yes—
201C2×D332—22no—
202C2×D332—22no—
203C2×D332—21no—
204C2×D332—24no—
205C2×D332—42no—
206C2×D332—82no—
207C2×D332C2×D414yes—
208C2×D332C2412yes—
209C2×C22⋊D83—24no—
210C2×C22⋊D83—24no—
211C2×C22⋊D83—44no—
212C2×C22⋊D83—44no—
213D4×D83—28no—
214D4×D83—44no—
215D4×D83—48no—
216C22×Dic83—21no—
217C22×Dic83—21no—
218C22×Dic83—21no—
219C22×Dic83—24no—
220C22×Dic83—44no—
221C22×Dic83C2×D411yescharacteristic
222C22×Dic83C2×D411yescharacteristic
223C2×C4×D83—22no—
224C2×C4×D83—22no—
225C2×C4×D83—22no—
226C2×C4×D83—22no—
227C2×C4×D83C2×D412yes—
228C2×C4×D83C2×D412yes—
229C2×C4×D83C2412yes—
230C2×C4×D83C2412yes—
231#13050580—44no—
232#13050577—44no—
233#13050573—44no—
234C2×C83⋊C8—22no—
235C2×C83⋊C8—22no—
236C2×C83⋊C8C2412yes—
237C2×C83⋊C8C2412yes—
238C8×D83—44no—
239C4⋊Dic83—21no—
240C4⋊Dic83—21no—
241C4⋊Dic83—24no—
242C4⋊Dic83—24no—
243C4⋊Dic83C2×D414yes—
244C4⋊Dic83C2412yes—
245C4⋊Dic83C2412yes—
246Dic83⋊C4—24no—
247Dic83⋊C4—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—
253(C2×D83)⋊C4—24no—
254(C2×D83)⋊C4—24no—
255(C2×D83)⋊C4—24no—
256(C2×D83)⋊C4C2×D414yes—
257(C2×D83)⋊C4C2×D414yes—
258C4×Dic83—24no—
259C4×Dic83—24no—
260C24×C83—21no—
261C2×Q8×C83—21no—
262C2×Q8×C83—22no—
263C2×Q8×C83—22no—
264C2×Q8×C83C2412yes—
265C2×D4×C83—21no—
266C2×D4×C83—22no—
267C2×D4×C83#4114yes—
268C2×D4×C83C2412yes—
269C22×C4×C83—21no—
270C22×C4×C83—21no—
271C22×C4×C83—21no—
272C22×C4×C83—24no—
273C22×C4×C83—82no—
274C22×C4×C83C2×D411yescharacteristic
275C22×C4×C83C2×D411yescharacteristic
276C22×C4×C83C2411yescharacteristic
277SD16×C83—28no—
278C2×C8×C83—22no—
279C2×C8×C83—22no—
280C2×C8×C83C2412yes—
281C2×C8×C83C2412yes—
282C4⋊C4×C83—21no—
283C4⋊C4×C83—24no—
284C4⋊C4×C83—21no—
285C4⋊C4×C83C2412yes—
286C4⋊C4×C83C2412yes—
287C22⋊C4×C83—24no—
288C42×C83—24no—
289C42×C83C2×D412yes—
290C42×C83C2412yes—
291C23×C83—24no—
292C23×C83—22no—
293C23×C83—42no—
294C23×C83—42no—
295C23×C83C22×D411yescharacteristic
296C22×D83—22no—
297C22×D83—22no—
298C22×D83—22no—
299C22×D83—22no—
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—48no—
304C22×D83—48no—
305C22×D83—42no—
306C22×D83—42no—
307C22×D83—42no—
308C22×D83—84no—
309C22×D83—816no—
310C22×D83C22×D412yes—
311C22×D83C22×D412yes—
312Q8×C83—22no—
313Q8×C83—22no—
314Q8×C83—42no—
315D4×C83—24no—
316D4×C83—22no—
317D4×C83C2×#4114yes—
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—84no—
327C2×C4×C83C22×D412yes—
328C2×C4×C83C22×D412yes—
329C2×C4×C83C22×D411yescharacteristic
330C2×C4×C83C2×#4112yes—
331C2×C4×C83H(5,𝔽2)12yes—
332C2×C4×C83C2511yescharacteristic
333C22⋊D83—48no—
334C22⋊D83—48no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—48no—
341C2×Dic83—42no—
342C2×Dic83—42no—
343C2×Dic83—42no—
344C2×Dic83C22×D412yes—
345C2×Dic83C22×D412yes—
346D332—22no—
347D332—22no—
348D332—44no—
349D332—42no—
350D332—84no—
351C4×D83—24no—
352C4×D83—24no—
353C4×D83—22no—
354C4×D83—22no—
355C4×D83—22no—
356C4×D83—22no—
357Dic166—22no—
358Dic166—22no—
359Dic166—48no—
360Dic166—42no—
361C8×C83—22no—
362C8×C83—22no—
363C83⋊C8—22no—
364C83⋊C8—22no—
365C22×C83—24no—
366C22×C83—48no—
367C22×C83—42no—
368C22×C83—42no—
369C22×C83#54612yes—
370C22×C83#57512yes—
371C22×C83#57712yes—
372C22×C83C23×D411yescharacteristic
373C2×D83—22no—
374C2×D83—22no—
375C2×D83—22no—
376C2×D83—22no—
377C2×D83—22no—
378C2×D83—22no—
379C2×D83—44no—
380C2×D83—44no—
381C2×D83—42no—
382C2×D83—42no—
383C2×D83—42no—
384C2×D83—816no—
385C2×D83—84no—
386C4×C83—22no—
387C4×C83—22no—
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—42no—
397Dic83—42no—
398Dic83—42no—
399C2×#3311—831nomaximal, Sylow
400C2×C83—44no—
401C2×C83#331114yescomplemented
402C2×C83C2×#54611yescharacteristic
403C2×C83C2×#57511yescharacteristic
404C2×C83C2×#57711yescharacteristic
405D83—42no—
406D83—42no—
407D83—82no—
408C2×#556—831no—
409C2×#546—831no—
410#3311—8316no—
411C2×#489—831no—
412C2×#485—831no—
413C2×#482—831no—
414C2×#476—831no—
415C2×#470—831no—
416C2×#465—831no—
417C2×#464—831no—
418C2×#452—831no—
419C2×#450—831no—
420C2×#440D8311yescharacteristic, complemented
421C2×#435—831no—
422C2×#418—831no—
423C2×#416—831no—
424C83C2×#331111yescharacteristic, complemented, Sylow
425C22×#41—831no—
426C23×D4—831no—
427C22×Q16—831no—
428C22×SD16—831no—
429C22×SD16C2×D8311yescharacteristic
430C22×M16—831no—
431C23×C8—831no—
432#556—838no—
433#556—1664no—
434#546—838no—
435#546—1664no—
436C2×C4⋊Q8—831no—
437C2×#126—1661no—
438C2×#126—1661no—
439C2×#124—831no—
440C2×#124—1661no—
441C2×#123—1661no—
442C2×C22⋊Q8—831no—
443C2×C22⋊Q8—831no—
444C2×C22⋊Q8—831no—
445C2×#121—831no—
446C2×#121—1661no—
447C2×#120—1661no—
448C2×C4×Q8—1661no—
449C2×C4×Q8C2×D8311yescharacteristic, complemented
450C2×C4×D4—831no—
451C2×C4×D4C2×D8311yescharacteristic
452C2×#117—831no—
453C2×#117—831no—
454C22×C22⋊C4—1661no—
455#489—838no—
456#485—838no—
457#482—838no—
458#476—838no—
459#470—838no—
460#465—838no—
461#464—838no—
462#452—838no—
463#450—838no—
464#440C2×D8318yescomplemented
465#435—838no—
466C2×#107C2×D8311yescharacteristic, complemented
467C2×#106—831no—
468C2×#106—831no—
469C2×C4⋊C8—831no—
470#418—838no—
471#416—838no—
472C2×#103—831no—
473C2×#103—831no—
474C2×#103—831no—
475C2×#103C2×D8311yescharacteristic, complemented
476C2×#102—831no—
477C2×#102—831no—
478C2×#102—831no—
479C2×#102—831no—
480C2×#102—831no—
481C2×#102C2×D8311yescharacteristic
482C2×C22⋊C8—831no—
483C2×C22⋊C8—831no—
484C2×#97C2×D8311yescharacteristic, complemented
485C25—1661no—
486C2×#41—3322no—
487C2×#41—834no—
488C2×#41—1664no—
489C2×#41—1662no—
490C22×Q8—831no—
491C22×Q8—1661no—
492C22×Q8C22×D8311yescharacteristic
493C22×D4—3322no—
494C22×D4—834no—
495C22×D4—831no—
496C22×D4—831no—
497C22×D4—1661no—
498C22×D4—1662no—
499C22×D4—1661no—
500C22×D4—1661no—
501C22×D4—1664no—
502C22×D4C22×D8311yescharacteristic
503C23×C4—21no—
504C23×C4—831no—
505C23×C4—831no—
506C23×C4—1661no—
507C2×Q16—3322no—
508C2×Q16—834no—
509C2×SD16—24no—
510C2×SD16—3322no—
511C2×SD16—834no—
512C2×SD16C22×D8314yes—
513C2×M16—3322no—
514C2×M16—834no—
515C22×C8—3322no—
516C22×C8—834no—
517C22×C8—831no—
518C22×C8—831no—
519C22×C8C22×D8311yescharacteristic
520C22×C8C22×D8311yescharacteristic
521C4⋊Q8—834no—
522C4⋊Q8—1662no—
523#126—1668no—
524#126—1668no—
525#124—834no—
526#124—1668no—
527#124—1662no—
528#123—1668no—
529C22⋊Q8—834no—
530C22⋊Q8—834no—
531C22⋊Q8—834no—
532C22⋊Q8—1662no—
533C22⋊Q8—1662no—
534C22⋊Q8—1662no—
535#121—834no—
536#121—1668no—
537#121—1662no—
538#120—1668no—
539C4×Q8—22no—
540C4×Q8—1668no—
541C4×Q8C22×D8314yescomplemented
542C4×D4—22no—
543C4×D4—834no—
544C4×D4—834no—
545C4×D4C22×D8314yes—
546#117—834no—
547#117—834no—
548#117—1662no—
549#117—1662no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—831no—
552C2×C4⋊C4—831no—
553C2×C4⋊C4—831no—
554C2×C4⋊C4—1661no—
555C2×C4⋊C4—1661no—
556C2×C4⋊C4—1661no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4C22×D8311yescharacteristic
559C2×C4⋊C4C22×D8311yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—831no—
562C2×C22⋊C4—831no—
563C2×C22⋊C4—1668no—
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×C22⋊C4—1661no—
572C2×C42—21no—
573C2×C42—1661no—
574C2×C42—1661no—
575C2×C42C22×D8311yescharacteristic
576#107C22×D8314yescomplemented
577#106—834no—
578#106—834no—
579C4⋊C8—834no—
580#103—834no—
581#103—834no—
582#103—834no—
583#103C22×D8314yescomplemented
584#102—834no—
585#102—834no—
586#102—834no—
587#102—834no—
588#102—834no—
589#102C22×D8314yes—
590C22⋊C8—834no—
591C22⋊C8—834no—
592#97C22×D8314yescomplemented
593C24—21no—
594C24—3324no—
595C24—3324no—
596C24—831no—
597C24—831no—
598C24—6642no—
599C24—1664no—
600C24—1661no—
601#41—3328no—
602#41—3324no—
603#41—1668no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—3324no—
608C2×Q8—832no—
609C2×Q8—1662no—
610C2×Q8—1662no—
611C2×Q8—1664no—
612C2×Q8—1661no—
613C2×Q8C23×D8312yes—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—3322no—
617C2×D4—3324no—
618C2×D4—3328no—
619C2×D4—3324no—
620C2×D4—3324no—
621C2×D4—834no—
622C2×D4—832no—
623C2×D4—6642no—
624C2×D4—1664no—
625C2×D4—1664no—
626C2×D4—1664no—
627C2×D4—1668no—
628C2×D4—1661no—
629C2×D4—1662no—
630C2×D4—1662no—
631C2×D4#1305059014yes—
632C2×D4C23×D8312yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—82no—
638C22×C4—3324no—
639C22×C4—831no—
640C22×C4—831no—
641C22×C4—832no—
642C22×C4—832no—
643C22×C4—832no—
644C22×C4—832no—
645C22×C4—1664no—
646C22×C4—1661no—
647C22×C4—1661no—
648C22×C4—1661no—
649C22×C4—1662no—
650C22×C4—1662no—
651C22×C4—1662no—
652C22×C4—1662no—
653C22×C4D4×D8311yescharacteristic
654C22×C4D4×D8311yescharacteristic
655C22×C4C23×D8311yescharacteristic
656Q16—3324no—
657SD16—28no—
658SD16—3324no—
659M16—3324no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—3324no—
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—834no—
673C4⋊C4—832no—
674C4⋊C4—832no—
675C4⋊C4—1664no—
676C4⋊C4—1664no—
677C4⋊C4—1664no—
678C4⋊C4—1661no—
679C4⋊C4—1661no—
680C4⋊C4—1664no—
681C4⋊C4C23×D8312yes—
682C4⋊C4C23×D8312yes—
683C22⋊C4—24no—
684C22⋊C4—834no—
685C22⋊C4—834no—
686C22⋊C4—1664no—
687C22⋊C4—1664no—
688C22⋊C4—1664no—
689C22⋊C4—1664no—
690C22⋊C4—1664no—
691C22⋊C4—1664no—
692C22⋊C4—1664no—
693C22⋊C4—1664no—
694C42—24no—
695C42—1664no—
696C42—1664no—
697C42D4×D8312yes—
698C42C23×D8312yes—
699C23—24no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—3328no—
704C23—3328no—
705C23—3322no—
706C23—3322no—
707C23—3322no—
708C23—832no—
709C23—832no—
710C23—66416no—
711C23—6644no—
712C23—1662no—
713C23—1662no—
714C23—1662no—
715C23—1662no—
716C23—1662no—
717C23—1662no—
718C23—1662no—
719C23C2×D4×D8311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—3328no—
724Q8—3322no—
725Q8—1662no—
726Q8—1662no—
727D4—24no—
728D4—22no—
729D4—3324no—
730D4—3328no—
731D4—3328no—
732D4—3322no—
733D4—6644no—
734D4—1662no—
735D4—1662no—
736D4C2×#1305059014yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—84no—
746C2×C4—3322no—
747C2×C4—3322no—
748C2×C4—3322no—
749C2×C4—3328no—
750C2×C4—832no—
751C2×C4—832no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1664no—
758C2×C4—1664no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4C2×D4×D8312yes—
764C2×C4C2×D4×D8312yes—
765C2×C4C2×D4×D8311yescharacteristic
766C2×C4C2×#1305059012yes—
767C2×C4#1458183812yes—
768C2×C4C24×D8311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1662no—
772C8—1662no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—3324no—
778C22—3324no—
779C22—3322no—
780C22—3322no—
781C22—3322no—
782C22—66416no—
783C22—6644no—
784C22—1662no—
785C22—1662no—
786C22—1662no—
787C22—1662no—
788C22—1662no—
789C22—1662no—
790C22#1912834712yes—
791C22#1912850012yes—
792C22#1912851112yes—
793C22C22×D4×D8311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—3322no—
800C4—3322no—
801C4—3322no—
802C4—1662no—
803C4—1662no—
804C4#1912834712yes—
805C4C22×#1305059011yescharacteristic
806C4C2×#1458183811yescharacteristic
807C2—44no—
808C2—3322no—
809C2—3322no—
810C2—6642no—
811C2#2491950414yesdirect product factor
812C2C2×#1912834711yescharacteristic
813C2C2×#1912850011yescharacteristic
814C2C2×#1912851111yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#440×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128346C2
hypercenterC2×#440D83
hypocenterC83C2×#3311
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#19128424C2semidirect
3. #24919504C2direct (N × H)
4. C2×#19128061C2semidirect
5. C2×#19128044C2semidirect
6. C2×#19128028C2semidirect
7. C2×#19127991C2semidirect
8. C2×#19127958C2semidirect
9. C2×#19127933C2semidirect
10. C2×#19127923C2semidirect
11. C2×#19127860C2semidirect
12. C2×#19127850C2semidirect
13. C2×#19127774C2semidirect
14. C2×#19127704C2semidirect
15. C2×#19127694C2semidirect
16. C2×#440×C83C2semidirect
19. C22×#13050580C22semidirect
22. C22×C8×D83C22semidirect
24. #19128424C22semidirect
27. C2×#14581792C22semidirect
35. C2×#14581768C22semidirect
42. C2×#14581750C22semidirect
44. #19128061C22semidirect
45. #19128044C22semidirect
46. #19128028C22semidirect
47. #19127991C22semidirect
48. #19127958C22semidirect
49. #19127933C22semidirect
50. #19127923C22semidirect
51. #19127860C22semidirect
52. #19127850C22semidirect
53. #19127774C22semidirect
54. C2×#14581723C22semidirect
55. C2×#14581723C22semidirect
56. C2×C4⋊(C83⋊C8)C22semidirect
57. #19127704C22semidirect
58. #19127694C22semidirect
59. C2×#14581717C22semidirect
60. C2×#14581717C22semidirect
61. C2×#14581715C22semidirect
68. C2×(C2×D83)⋊C8C22semidirect
70. C2×C4×Q8×C83C22semidirect
72. #440×C83C22semidirect
73. C2×#107×C83C22semidirect
74. C2×#103×C83C22semidirect
76. C2×#97×C83C22semidirect
97. C2×#13050580C23semidirect
105. C2×C8×D83C23semidirect
107. #14581792C23semidirect
119. #14581768C23semidirect
130. #14581750C23semidirect
151. #14581723C23semidirect
152. #14581723C23semidirect
153. C4⋊(C83⋊C8)C23semidirect
154. #14581717C23semidirect
155. #14581717C23semidirect
156. #14581715C23semidirect
163. (C2×D83)⋊C8C23semidirect
172. C4×Q8×C83C23semidirect
181. #107×C83C23semidirect
182. #103×C83C23semidirect
184. #97×C83C23semidirect
401. C2×C83#3311semidirect
420. C2×#440D83semidirect
424. C83C2×#3311semidirect
449. C2×C4×Q8C2×D83semidirect
464. #440C2×D83semidirect
466. C2×#107C2×D83semidirect
475. C2×#103C2×D83semidirect
484. C2×#97C2×D83semidirect
541. C4×Q8C22×D83semidirect
576. #107C22×D83semidirect
583. #103C22×D83semidirect
592. #97C22×D83semidirect
811. C2#24919504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284242
C2×#191283462
#249195042
C2×#191280612
C2×#191280442
C2×#191280282
C2×#191279912
C2×#191279582
C2×#191279332
C2×#191279232
C2×#191278602
C2×#191278502
C2×#191277742
C2×#191277042
C2×#191276942
C2×#440×C832
C2×#331183