Finite Group Databasebeta

← C2×#24919501 #36281076

Subgroups — C2×#24919501 #36281076

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×#19128421C211yesmaximal, characteristic, complemented
2C2×#19128347C211yesmaximal, characteristic
3#24919501C2116yesmaximal, direct product factor
4C2×#19128061C211yesmaximal, characteristic, complemented
5C2×#19128043C211yesmaximal, characteristic, complemented
6C2×#19128026C211yesmaximal, characteristic, complemented
7C2×#19127992C211yesmaximal, characteristic, complemented
8C2×#19127959C211yesmaximal, characteristic, complemented
9C2×#19127930C211yesmaximal, characteristic, complemented
10C2×#19127924C211yesmaximal, characteristic, complemented
11C2×#19127865C211yesmaximal, characteristic, complemented
12C2×#19127854C211yesmaximal, characteristic, complemented
13C2×#19127803C211yesmaximal, characteristic, complemented
14C2×#19127707C211yesmaximal, characteristic, complemented
15C2×#19127698C211yesmaximal, characteristic, complemented
16C2×#435×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C23×D332C2211yescharacteristic
19C22×Dic332C2211yescharacteristic, complemented
20C22×#13050579C2211yescharacteristic
21C22×#13050579C2211yescharacteristic
22#19128421—24no—
23#19128421C2218yescomplemented
24#19128347—24no—
25#19128347C2218yes—
26C2×#14581792C2211yescharacteristic, complemented
27C2×#14581785—21no—
28C2×#14581785—21no—
29C2×#14581780C2211yescharacteristic
30C2×#14581779—21no—
31C2×#14581777—21no—
32C2×#14581771C2211yescharacteristic
33C2×#14581771C2211yescharacteristic
34C2×#14581771C2211yescharacteristic, complemented
35C2×#14581766C2211yescharacteristic
36C2×#14581765—21no—
37C2×#14581760—21no—
38C2×C4×Dic166C2211yescharacteristic, complemented
39C2×#14581757—21no—
40C2×C4×D332C2211yescharacteristic
41C2×#14581751C2211yescharacteristic
42C2×#14581751C2211yescharacteristic, complemented
43C2×C22⋊C4×D83—21no—
44#19128061C2218yescomplemented
45#19128043C2218yescomplemented
46#19128026C2218yescomplemented
47#19127992C2218yescomplemented
48#19127959C2218yescomplemented
49#19127930C2218yescomplemented
50#19127924C2218yescomplemented
51#19127865C2218yescomplemented
52#19127854C2218yescomplemented
53#19127803C2218yescomplemented
54C2×#14581726C2211yescharacteristic, complemented
55C2×#14581724C2211yescharacteristic, complemented
56C2×#14581724C2211yescharacteristic, complemented
57#19127707C2218yescomplemented
58#19127698C2218yescomplemented
59C2×#14581717C2211yescharacteristic, complemented
60C2×#14581717C2211yescharacteristic, complemented
61C2×#14581717C2211yescharacteristic, complemented
62C2×#14581717C2211yescharacteristic, complemented
63C2×#14581714C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581714C2211yescharacteristic
68C2×#14581714C2211yescharacteristic
69C22×M16×C83C2211yescharacteristic
70C23×C8×C83C2211yescharacteristic, complemented
71C2×C4×D4×C83C2211yescharacteristic
72#435×C83C2218yescomplemented
73C2×C4⋊C8×C83C2211yescharacteristic, complemented
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×C22⋊C8×C83C2211yescharacteristic, complemented
76C2×#97×C83C2211yescharacteristic, complemented
77C24×D83—21no—
78C2×#13050590—24no—
79C2×#13050590—22no—
80C2×#13050590—42no—
81C2×#13050590C2314yes—
82C22×Dic166—21no—
83C22×Dic166C2311yescharacteristic
84C22×Dic166C2311yescharacteristic
85C22×D332—24no—
86C22×D332—22no—
87C22×D332—21no—
88C22×D332—42no—
89C22×D332C2311yescharacteristic
90C22×D332C2314yes—
91C22×D332C2311yescharacteristic
92C22×C22⋊D83—21no—
93C22×C22⋊D83—21no—
94C22×C4×D83—21no—
95C22×C4×D83—21no—
96C2×Dic332—42no—
97C2×Dic332C2314yescomplemented
98C2×#13050579—24no—
99C2×#13050579—42no—
100C2×#13050579C2314yes—
101C2×#13050579C2314yes—
102#14581792—22no—
103#14581792C2314yescomplemented
104#14581785—28no—
105#14581785—28no—
106#14581780—22no—
107#14581780C2314yes—
108#14581779—28no—
109#14581777—28no—
110#14581771—22no—
111#14581771—22no—
112#14581771—22no—
113#14581771C2314yes—
114#14581771C2314yes—
115#14581771C2314yescomplemented
116#14581766—22no—
117#14581766C2314yes—
118#14581765—28no—
119#14581760—28no—
120C4×Dic166—22no—
121C4×Dic166C2314yescomplemented
122#14581757—28no—
123C4×D332—22no—
124C4×D332C2314yes—
125#14581751—22no—
126#14581751—22no—
127#14581751C2314yes—
128#14581751C2314yescomplemented
129C2×C4⋊Dic83—21no—
130C2×C4⋊Dic83C2311yescharacteristic
131C2×C4⋊Dic83C2311yescharacteristic
132C2×C4⋊Dic83C2311yescharacteristic
133C2×C4⋊Dic83C2311yescharacteristic
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4—21no—
137C2×Dic83⋊C4—21no—
138C2×C22⋊Dic83—21no—
139C2×C22⋊Dic83—21no—
140C2×C22⋊Dic83—21no—
141C2×C22⋊Dic83—21no—
142C2×C22⋊Dic83—21no—
143C2×(C2×D83)⋊C4—21no—
144C2×(C2×D83)⋊C4—21no—
145C2×(C2×D83)⋊C4—21no—
146C2×(C2×D83)⋊C4—21no—
147C22⋊C4×D83—28no—
148C2×C4×Dic83—21no—
149C2×C4×Dic83—21no—
150C2×C4×Dic83—21no—
151#14581726C2314yescomplemented
152#14581724C2314yescomplemented
153#14581724C2314yescomplemented
154#14581717C2314yescomplemented
155#14581717C2314yescomplemented
156#14581717C2314yescomplemented
157#14581717C2314yescomplemented
158#14581714C2314yes—
159#14581714C2314yes—
160#14581714C2314yes—
161#14581714C2314yes—
162#14581714C2314yes—
163#14581714C2314yes—
164C22×D4×C83D411yescharacteristic
165C23×C4×C83C2311yescharacteristic
166C23×C4×C83C2311yescharacteristic
167C2×M16×C83—42no—
168C2×M16×C83C2314yes—
169C22×C8×C83—42no—
170C22×C8×C83C2311yescharacteristic
171C22×C8×C83C2311yescharacteristic
172C22×C8×C83C2311yescharacteristic
173C22×C8×C83C2311yescharacteristic
174C22×C8×C83C2314yescomplemented
175C4×D4×C83D414yes—
176C4×D4×C83C2314yes—
177C2×C4⋊C4×C83D411yescharacteristic
178C2×C22⋊C4×C83D411yescharacteristic
179C2×C22⋊C4×C83D411yescharacteristic
180C2×C42×C83C2311yescharacteristic
181C4⋊C8×C83C2314yescomplemented
182C22⋊C8×C83C2314yes—
183C22⋊C8×C83C2314yescomplemented
184#97×C83C2314yescomplemented
185C23×D83—21no—
186C23×D83—21no—
187C23×D83—24no—
188C23×D83—44no—
189C23×D83—44no—
190C23×D83—82no—
191#13050590—28no—
192#13050590—44no—
193#13050590—48no—
194C2×Dic166—22no—
195C2×Dic166—22no—
196C2×Dic166—22no—
197C2×Dic166—22no—
198C2×Dic166—21no—
199C2×Dic166—21no—
200C2×Dic166—24no—
201C2×Dic166—44no—
202C2×Dic166C2412yes—
203C2×Dic166C2412yes—
204C2×D332—21no—
205C2×D332—22no—
206C2×D332—22no—
207C2×D332—22no—
208C2×D332—28no—
209C2×D332—24no—
210C2×D332—21no—
211C2×D332—44no—
212C2×D332—48no—
213C2×D332—44no—
214C2×D332#4114yes—
215C2×D332C2412yes—
216C2×D332C2412yes—
217C2×C22⋊D83—24no—
218C2×C22⋊D83—24no—
219C2×C22⋊D83—44no—
220C2×C22⋊D83—82no—
221C22×Dic83—21no—
222C22×Dic83—21no—
223C22×Dic83—21no—
224C22×Dic83—21no—
225C22×Dic83—21no—
226C22×Dic83—21no—
227C2×C4×D83—24no—
228C2×C4×D83—24no—
229C2×C4×D83—44no—
230C2×C4×D83—82no—
231Dic332—44no—
232#13050579—28no—
233#13050579—44no—
234C4⋊Dic83—21no—
235C4⋊Dic83—21no—
236C4⋊Dic83—21no—
237C4⋊Dic83—24no—
238C4⋊Dic83—21no—
239C4⋊Dic83C2412yes—
240C4⋊Dic83C2412yes—
241C4⋊Dic83C2412yes—
242C4⋊Dic83C2412yes—
243Dic83⋊C4—24no—
244Dic83⋊C4—24no—
245Dic83⋊C4—24no—
246Dic83⋊C4—24no—
247C22⋊Dic83—24no—
248C22⋊Dic83—24no—
249C22⋊Dic83—24no—
250C22⋊Dic83—24no—
251C22⋊Dic83—24no—
252(C2×D83)⋊C4—24no—
253(C2×D83)⋊C4—24no—
254(C2×D83)⋊C4—24no—
255(C2×D83)⋊C4—24no—
256C4×Dic83—24no—
257C4×Dic83—24no—
258C4×Dic83—24no—
259C24×C83C2×D411yescharacteristic
260C24×C83C2×D411yescharacteristic
261C2×D4×C83—42no—
262C2×D4×C83C2×D414yes—
263C22×C4×C83—22no—
264C22×C4×C83—22no—
265C22×C4×C83—22no—
266C22×C4×C83—22no—
267C22×C4×C83C2×D412yes—
268C22×C4×C83C2×D412yes—
269C22×C4×C83C2×D411yescharacteristic
270C22×C4×C83C2×D411yescharacteristic
271C22×C4×C83C2×D411yescharacteristic
272C22×C4×C83C2×D411yescharacteristic
273C22×C4×C83C2412yes—
274C22×C4×C83C2412yes—
275C22×C4×C83C2411yescharacteristic
276M16×C83—44no—
277C2×C8×C83—22no—
278C2×C8×C83—22no—
279C2×C8×C83—22no—
280C2×C8×C83—22no—
281C2×C8×C83—44no—
282C2×C8×C83C2412yes—
283C2×C8×C83C2412yes—
284C2×C8×C83C2412yes—
285C2×C8×C83C2412yes—
286C4⋊C4×C83C2×D414yes—
287C22⋊C4×C83C2×D414yes—
288C22⋊C4×C83C2×D414yes—
289C42×C83C2×D412yes—
290C42×C83C2412yes—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83C22×D412yes—
298C23×C83C22×D412yes—
299C23×C83C22×D411yescharacteristic
300C22×D83—24no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—48no—
304C22×D83—42no—
305C22×D83—42no—
306C22×D83—48no—
307C22×D83—42no—
308C22×D83—42no—
309C22×D83—42no—
310C22×D83—84no—
311C22×D83—816no—
312D4×C83—44no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—24no—
318C2×C4×C83—24no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83C22×D412yes—
324C2×C4×C83C22×D412yes—
325C2×C4×C83C22×D412yes—
326C2×C4×C83C22×D412yes—
327C2×C4×C83C22×D411yescharacteristic
328C2×C4×C83C2×#4112yes—
329C2×C4×C83H(5,𝔽2)12yes—
330C2×C4×C83C2511yescharacteristic
331C22⋊D83—48no—
332C22⋊D83—84no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—42no—
340C2×Dic83—42no—
341C2×Dic83—42no—
342C2×Dic83—42no—
343C2×Dic83—42no—
344C2×Dic83—42no—
345D332—24no—
346D332—22no—
347D332—22no—
348D332—22no—
349D332—48no—
350D332—42no—
351D332C2×#4114yes—
352C4×D83—48no—
353C4×D83—84no—
354Dic166—22no—
355Dic166—22no—
356Dic166—22no—
357Dic166—22no—
358Dic166—48no—
359Dic166—42no—
360Dic166—42no—
361C8×C83—22no—
362C8×C83—22no—
363C8×C83—22no—
364C8×C83—22no—
365C22×C83—22no—
366C22×C83—22no—
367C22×C83—22no—
368C22×C83—22no—
369C22×C83—22no—
370C22×C83—22no—
371C22×C83—44no—
372C22×C83—44no—
373C22×C83#54612yes—
374C22×C83#57512yes—
375C22×C83#57712yes—
376C22×C83C23×D411yescharacteristic
377C2×D83—24no—
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—22no—
388C4×C83—22no—
389C4×C83—22no—
390C4×C83#54612yes—
391C4×C83C22×#4111yescharacteristic
392C4×C83C2×H(5,𝔽2)11yescharacteristic
393Dic83—42no—
394Dic83—42no—
395Dic83—42no—
396Dic83—42no—
397Dic83—42no—
398Dic83—42no—
399C2×#3311—831nomaximal, Sylow
400C2×C83—42no—
401C2×C83—42no—
402C2×C83#331114yescomplemented
403C2×C83C2×#54611yescharacteristic
404C2×C83C2×#57511yescharacteristic
405C2×C83C2×#57711yescharacteristic
406D83—44no—
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×#440—831no—
421C2×#435D8311yescharacteristic, complemented
422C2×#418—831no—
423C2×#416—831no—
424C83C2×#331111yescharacteristic, complemented, Sylow
425C22×#41—831no—
426C23×D4—831no—
427C22×Q16—831no—
428C22×SD16—831no—
429C22×SD16—831no—
430C22×M16C2×D8311yescharacteristic
431C23×C8C2×D8311yescharacteristic, complemented
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—831no—
449C2×C4×Q8—1661no—
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#440—838no—
465#435C2×D8318yescomplemented
466C2×#107—831no—
467C2×#106—831no—
468C2×#106—831no—
469C2×C4⋊C8C2×D8311yescharacteristic, complemented
470#418—838no—
471#416—838no—
472C2×#103—831no—
473C2×#103—831no—
474C2×#103—831no—
475C2×#103—831no—
476C2×#102—831no—
477C2×#102—831no—
478C2×#102—831no—
479C2×#102—831no—
480C2×#102—831no—
481C2×#102—831no—
482C2×C22⋊C8C2×D8311yescharacteristic
483C2×C22⋊C8C2×D8311yescharacteristic, complemented
484C2×#97C2×D8311yescharacteristic, complemented
485C25—1661no—
486C2×#41—3322no—
487C2×#41—834no—
488C2×#41—1664no—
489C2×#41—1662no—
490C22×Q8—831no—
491C22×Q8—831no—
492C22×Q8—1661no—
493C22×D4—3322no—
494C22×D4—834no—
495C22×D4—831no—
496C22×D4—831no—
497C22×D4—1664no—
498C22×D4—1661no—
499C22×D4—1661no—
500C22×D4—1661no—
501C22×D4—1662no—
502C22×D4D33211yescharacteristic
503C23×C4—1661no—
504C23×C4—1661no—
505C23×C4C22×D8311yescharacteristic
506C23×C4C22×D8311yescharacteristic
507C2×Q16—3322no—
508C2×Q16—834no—
509C2×SD16—3322no—
510C2×SD16—834no—
511C2×SD16—834no—
512C2×SD16—1664no—
513C2×M16—42no—
514C2×M16C22×D8314yes—
515C22×C8—42no—
516C22×C8C22×D8311yescharacteristic
517C22×C8C22×D8311yescharacteristic
518C22×C8C22×D8311yescharacteristic
519C22×C8C22×D8311yescharacteristic
520C22×C8C22×D8314yescomplemented
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—1662no—
537#121—1668no—
538#120—1668no—
539C4×Q8—834no—
540C4×Q8—1668no—
541C4×Q8—1662no—
542C4×D4—834no—
543C4×D4—1662no—
544C4×D4D33214yes—
545C4×D4C22×D8314yes—
546#117—834no—
547#117—834no—
548#117—1662no—
549#117—1662no—
550C2×C4⋊C4—831no—
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⋊C4—1661no—
559C2×C4⋊C4D33211yescharacteristic
560C2×C22⋊C4—1661no—
561C2×C22⋊C4—1661no—
562C2×C22⋊C4—1661no—
563C2×C22⋊C4—1661no—
564C2×C22⋊C4—1661no—
565C2×C22⋊C4—1661no—
566C2×C22⋊C4—1661no—
567C2×C22⋊C4—1661no—
568C2×C22⋊C4—1661no—
569C2×C22⋊C4—1668no—
570C2×C22⋊C4D33211yescharacteristic
571C2×C22⋊C4D33211yescharacteristic
572C2×C42—1661no—
573C2×C42—1661no—
574C2×C42—1661no—
575C2×C42C22×D8311yescharacteristic
576#107—834no—
577#106—834no—
578#106—834no—
579C4⋊C8C22×D8314yescomplemented
580#103—834no—
581#103—834no—
582#103—834no—
583#103—834no—
584#102—834no—
585#102—834no—
586#102—834no—
587#102—834no—
588#102—834no—
589#102—834no—
590C22⋊C8C22×D8314yes—
591C22⋊C8C22×D8314yescomplemented
592#97C22×D8314yescomplemented
593C24—3324no—
594C24—3324no—
595C24—6642no—
596C24—1661no—
597C24—1664no—
598C24—1661no—
599C24C2×D33211yescharacteristic
600C24C2×D33211yescharacteristic
601#41—3328no—
602#41—3324no—
603#41—1668no—
604C2×Q8—3324no—
605C2×Q8—832no—
606C2×Q8—832no—
607C2×Q8—1662no—
608C2×Q8—1662no—
609C2×Q8—1662no—
610C2×Q8—1662no—
611C2×Q8—1661no—
612C2×Q8—1664no—
613C2×Q8—1661no—
614C2×D4—42no—
615C2×D4—3324no—
616C2×D4—3328no—
617C2×D4—3324no—
618C2×D4—3324no—
619C2×D4—834no—
620C2×D4—832no—
621C2×D4—832no—
622C2×D4—6642no—
623C2×D4—1668no—
624C2×D4—1664no—
625C2×D4—1664no—
626C2×D4—1664no—
627C2×D4—1661no—
628C2×D4—1661no—
629C2×D4—1662no—
630C2×D4—1662no—
631C2×D4—1662no—
632C2×D4C2×D33214yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—3324no—
638C22×C4—6642no—
639C22×C4—1661no—
640C22×C4—1661no—
641C22×C4—1661no—
642C22×C4—1661no—
643C22×C4—1661no—
644C22×C4—1661no—
645C22×C4—1664no—
646C22×C4—1664no—
647C22×C4C2×D33212yes—
648C22×C4C2×D33212yes—
649C22×C4C2×D33211yescharacteristic
650C22×C4C2×D33211yescharacteristic
651C22×C4C2×D33211yescharacteristic
652C22×C4C2×D33211yescharacteristic
653C22×C4C23×D8312yes—
654C22×C4C23×D8312yes—
655C22×C4C23×D8311yescharacteristic
656Q16—3324no—
657SD16—3324no—
658SD16—1668no—
659M16—44no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—44no—
665C2×C8C23×D8312yes—
666C2×C8C23×D8312yes—
667C2×C8C23×D8312yes—
668C2×C8C23×D8312yes—
669C4⋊C4—832no—
670C4⋊C4—832no—
671C4⋊C4—832no—
672C4⋊C4—832no—
673C4⋊C4—1661no—
674C4⋊C4—1661no—
675C4⋊C4—1661no—
676C4⋊C4—1661no—
677C4⋊C4—1664no—
678C4⋊C4—1664no—
679C4⋊C4—1664no—
680C4⋊C4—1664no—
681C4⋊C4—1664no—
682C4⋊C4C2×D33214yes—
683C22⋊C4—1664no—
684C22⋊C4—1664no—
685C22⋊C4—1664no—
686C22⋊C4—1664no—
687C22⋊C4—1664no—
688C22⋊C4—1664no—
689C22⋊C4—1664no—
690C22⋊C4—1664no—
691C22⋊C4—1664no—
692C22⋊C4C2×D33214yes—
693C22⋊C4C2×D33214yes—
694C42—1664no—
695C42—1664no—
696C42—1664no—
697C42C2×D33212yes—
698C42C23×D8312yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—3328no—
706C23—3328no—
707C23—3322no—
708C23—3322no—
709C23—3322no—
710C23—3322no—
711C23—3322no—
712C23—6644no—
713C23—66416no—
714C23—1662no—
715C23—1664no—
716C23—1662no—
717C23C22×D33212yes—
718C23C22×D33212yes—
719C23C22×D33211yescharacteristic
720Q8—3328no—
721Q8—3322no—
722Q8—3322no—
723Q8—1662no—
724Q8—1662no—
725Q8—1662no—
726Q8—1662no—
727D4—44no—
728D4—3328no—
729D4—3328no—
730D4—3322no—
731D4—834no—
732D4—6644no—
733D4—1664no—
734D4—1662no—
735D4—1662no—
736D4—1662no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—3328no—
748C2×C4—3322no—
749C2×C4—3322no—
750C2×C4—3322no—
751C2×C4—3322no—
752C2×C4—3322no—
753C2×C4—3322no—
754C2×C4—6644no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4C22×D33212yes—
762C2×C4C22×D33212yes—
763C2×C4C22×D33212yes—
764C2×C4C22×D33212yes—
765C2×C4C22×D33211yescharacteristic
766C2×C4#41×D8312yes—
767C2×C4#1458183712yes—
768C2×C4C24×D8311yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—3322no—
782C22—3322no—
783C22—3328no—
784C22—3322no—
785C22—3322no—
786C22—3322no—
787C22—66416no—
788C22—6644no—
789C22—1664no—
790C22#1912834612yes—
791C22#1912850112yes—
792C22#1912851312yes—
793C22C23×D33211yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—3322no—
799C4—3322no—
800C4—3322no—
801C4—3322no—
802C4—3322no—
803C4—3322no—
804C4#1912834612yes—
805C4C2×#41×D8311yescharacteristic
806C4C2×#1458183711yescharacteristic
807C2—42no—
808C2—42no—
809C2—3324no—
810C2—6642no—
811C2#2491950114yesdirect product factor
812C2C2×#1912834611yescharacteristic
813C2C2×#1912850111yescharacteristic
814C2C2×#1912851311yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#435×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128347C2
hypercenterC2×#435D83
hypocenterC83C2×#3311
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#19128421C2semidirect
3. #24919501C2direct (N × H)
4. C2×#19128061C2semidirect
5. C2×#19128043C2semidirect
6. C2×#19128026C2semidirect
7. C2×#19127992C2semidirect
8. C2×#19127959C2semidirect
9. C2×#19127930C2semidirect
10. C2×#19127924C2semidirect
11. C2×#19127865C2semidirect
12. C2×#19127854C2semidirect
13. C2×#19127803C2semidirect
14. C2×#19127707C2semidirect
15. C2×#19127698C2semidirect
16. C2×#435×C83C2semidirect
19. C22×Dic332C22semidirect
23. #19128421C22semidirect
26. C2×#14581792C22semidirect
34. C2×#14581771C22semidirect
38. C2×C4×Dic166C22semidirect
42. C2×#14581751C22semidirect
44. #19128061C22semidirect
45. #19128043C22semidirect
46. #19128026C22semidirect
47. #19127992C22semidirect
48. #19127959C22semidirect
49. #19127930C22semidirect
50. #19127924C22semidirect
51. #19127865C22semidirect
52. #19127854C22semidirect
53. #19127803C22semidirect
54. C2×#14581726C22semidirect
55. C2×#14581724C22semidirect
56. C2×#14581724C22semidirect
57. #19127707C22semidirect
58. #19127698C22semidirect
59. C2×#14581717C22semidirect
60. C2×#14581717C22semidirect
61. C2×#14581717C22semidirect
62. C2×#14581717C22semidirect
70. C23×C8×C83C22semidirect
72. #435×C83C22semidirect
73. C2×C4⋊C8×C83C22semidirect
75. C2×C22⋊C8×C83C22semidirect
76. C2×#97×C83C22semidirect
97. C2×Dic332C23semidirect
103. #14581792C23semidirect
115. #14581771C23semidirect
121. C4×Dic166C23semidirect
128. #14581751C23semidirect
151. #14581726C23semidirect
152. #14581724C23semidirect
153. #14581724C23semidirect
154. #14581717C23semidirect
155. #14581717C23semidirect
156. #14581717C23semidirect
157. #14581717C23semidirect
174. C22×C8×C83C23semidirect
181. C4⋊C8×C83C23semidirect
183. C22⋊C8×C83C23semidirect
184. #97×C83C23semidirect
402. C2×C83#3311semidirect
421. C2×#435D83semidirect
424. C83C2×#3311semidirect
431. C23×C8C2×D83semidirect
465. #435C2×D83semidirect
469. C2×C4⋊C8C2×D83semidirect
483. C2×C22⋊C8C2×D83semidirect
484. C2×#97C2×D83semidirect
520. C22×C8C22×D83semidirect
579. C4⋊C8C22×D83semidirect
591. C22⋊C8C22×D83semidirect
592. #97C22×D83semidirect
811. C2#24919501direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284212
C2×#191283472
#249195012
C2×#191280612
C2×#191280432
C2×#191280262
C2×#191279922
C2×#191279592
C2×#191279302
C2×#191279242
C2×#191278652
C2×#191278542
C2×#191278032
C2×#191277072
C2×#191276982
C2×#435×C832
C2×#331183