Finite Group Databasebeta

← C2×#24918720 #36276597

Subgroups — C2×#24918720 #36276597

Order 21248.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128332C211yesmaximal, characteristic, complemented
2C2×#19128304C211yesmaximal, characteristic
3#24918720C2116yesmaximal, direct product factor
4C2×#19128108C211yesmaximal, characteristic, complemented
5C2×#19128101C211yesmaximal, characteristic, complemented
6C2×#19128064C211yesmaximal, characteristic, complemented
7C2×#19128046C211yesmaximal, characteristic, complemented
8C2×#19128026C211yesmaximal, characteristic, complemented
9C2×#19128022C211yesmaximal, characteristic, complemented
10C2×#19128014C211yesmaximal, characteristic, complemented
11C2×#19128003C211yesmaximal, characteristic, complemented
12C2×#19128000C211yesmaximal, characteristic, complemented
13C2×#19127990C211yesmaximal, characteristic, complemented
14C2×#19127979C211yesmaximal, characteristic, complemented
15C2×#19127759C211yesmaximal, characteristic, complemented
16C2×#481×C83C211yesmaximal, characteristic, complemented
17#19128332—24no—
18#19128332C2218yescomplemented
19#19128304—24no—
20#19128304C2218yes—
21C2×#14581791—21no—
22C2×#14581791C2211yescharacteristic
23C2×#14581791C2211yescharacteristic
24C2×#14581788C2211yescharacteristic
25C2×#14581783—21no—
26C2×#14581783C2211yescharacteristic
27C2×#14581783C2211yescharacteristic
28C2×#14581783C2211yescharacteristic
29C2×#14581776—21no—
30C2×#14581774—21no—
31C2×#14581771—21no—
32C2×#14581771—21no—
33C2×#14581766C2211yescharacteristic
34C2×#14581764—21no—
35C2×#14581763—21no—
36C2×D4×Dic83C2211yescharacteristic
37C2×#14581754C2211yescharacteristic
38C2×#14581751C2211yescharacteristic
39C2×#14581751C2211yescharacteristic
40#19128108C2218yescomplemented
41#19128101C2218yescomplemented
42#19128064C2218yescomplemented
43#19128046C2218yescomplemented
44#19128026C2218yescomplemented
45#19128022C2218yescomplemented
46#19128014C2218yescomplemented
47#19128003C2218yescomplemented
48#19128000C2218yescomplemented
49#19127990C2218yescomplemented
50#19127979C2218yescomplemented
51#19127759C2218yescomplemented
52C2×#14581726C2211yescharacteristic
53C2×#14581725C2211yescharacteristic
54C2×#14581725C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581724C2211yescharacteristic
57C2×#14581723C2211yescharacteristic
58C2×Dic83⋊C8C2211yescharacteristic
59C2×Dic83⋊C8C2211yescharacteristic
60C2×#14581714C2211yescharacteristic
61C2×#14581714C2211yescharacteristic
62C2×#14581713C2211yescharacteristic
63C2×#14581713C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×#14581702C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C2×#121×C83C2211yescharacteristic
70C22×C4⋊C4×C83C2211yescharacteristic
71#481×C83C2218yescomplemented
72C2×#106×C83C2211yescharacteristic
73C2×#106×C83C2211yescharacteristic
74C2×#102×C83C2211yescharacteristic
75C2×#102×C83C2211yescharacteristic
76C2×C22⋊C8×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×D332C2311yescharacteristic
80C22×C22⋊D83—21no—
81C22×C22⋊D83—21no—
82C22×C22⋊D83—21no—
83C23×Dic83—21no—
84C22×C4×D83—21no—
85C22×C83⋊C8C2311yescharacteristic
86C22×C83⋊C8C2311yescharacteristic
87#14581791—28no—
88#14581791—22no—
89#14581791—22no—
90#14581791C2314yes—
91#14581791C2314yes—
92#14581788—22no—
93#14581788C2314yes—
94#14581783—28no—
95#14581783—22no—
96#14581783—22no—
97#14581783—22no—
98#14581783C2314yes—
99#14581783C2314yes—
100#14581783C2314yes—
101#14581776—28no—
102#14581774—28no—
103#14581771—28no—
104#14581771—28no—
105#14581766—22no—
106#14581766C2314yes—
107#14581764—28no—
108#14581763—28no—
109D4×Dic83—22no—
110D4×Dic83C2314yes—
111#14581754—22no—
112#14581754C2314yes—
113#14581751—22no—
114#14581751D414yes—
115#14581751C2314yes—
116#14581751C2314yes—
117C2×C4⋊Dic83—21no—
118C2×C4⋊Dic83—21no—
119C2×C4⋊Dic83—21no—
120C2×C4⋊Dic83D411yescharacteristic
121C2×C4⋊Dic83D411yescharacteristic
122C2×C4⋊Dic83C2311yescharacteristic
123C2×C4⋊Dic83C2311yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×C22⋊Dic83—21no—
131C2×C22⋊Dic83—21no—
132C2×C22⋊Dic83D411yescharacteristic
133C2×C22⋊Dic83D411yescharacteristic
134C2×(C2×D83)⋊C4—21no—
135C2×(C2×D83)⋊C4—21no—
136C2×C4×Dic83—21no—
137C2×C4×Dic83C2311yescharacteristic
138C2×C4×Dic83C2311yescharacteristic
139#14581726C2314yes—
140#14581725C2314yes—
141#14581725C2314yes—
142#14581725C2314yes—
143#14581724C2314yes—
144#14581723C2314yes—
145Dic83⋊C8C2314yes—
146Dic83⋊C8C2314yes—
147#14581714C2314yes—
148#14581714C2314yes—
149#14581713C2314yes—
150#14581713C2314yes—
151#14581712C2314yes—
152#14581712C2314yes—
153C22⋊(C83⋊C8)C2314yes—
154#14581702C2314yes—
155C8×Dic83C2314yes—
156C22×D4×C83—21no—
157C22×D4×C83C2311yescharacteristic
158C23×C4×C83—21no—
159C23×C4×C83C2311yescharacteristic
160C22×C8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162#121×C83—22no—
163#121×C83C2314yes—
164C2×C4⋊C4×C83—22no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83C2314yes—
167C2×C4⋊C4×C83C2311yescharacteristic
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C22⋊C4×C83—21no—
171#106×C83C2314yes—
172#106×C83C2314yes—
173#102×C83C2314yes—
174#102×C83C2314yes—
175C22⋊C8×C83C2314yes—
176C23×D83—21no—
177C2×Dic166—24no—
178C2×Dic166—24no—
179C2×Dic166—82no—
180C2×Dic166—82no—
181C2×D332—22no—
182C2×D332—22no—
183C2×D332—21no—
184C2×D332C2412yes—
185C2×C22⋊D83—24no—
186C2×C22⋊D83—24no—
187C2×C22⋊D83—24no—
188C2×C22⋊D83—82no—
189C2×C22⋊D83—82no—
190C2×C22⋊D83—82no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—24no—
195C22×Dic83—82no—
196C22×Dic83C2×D411yescharacteristic
197C22×Dic83C2×D411yescharacteristic
198C22×Dic83C2×D411yescharacteristic
199C22×Dic83C2×D411yescharacteristic
200C2×C4×D83—24no—
201C2×C4×D83—82no—
202C2×C83⋊C8—22no—
203C2×C83⋊C8—22no—
204C2×C83⋊C8C2412yes—
205C2×C83⋊C8C2412yes—
206C4⋊Dic83—21no—
207C4⋊Dic83—21no—
208C4⋊Dic83—21no—
209C4⋊Dic83—24no—
210C4⋊Dic83—24no—
211C4⋊Dic83—24no—
212C4⋊Dic83C2×D414yes—
213C4⋊Dic83C2×D414yes—
214C4⋊Dic83C2412yes—
215C4⋊Dic83C2412yes—
216C4⋊Dic83C2412yes—
217Dic83⋊C4—24no—
218Dic83⋊C4—24no—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222C22⋊Dic83—24no—
223C22⋊Dic83—24no—
224C22⋊Dic83C2×D414yes—
225C22⋊Dic83C2×D414yes—
226(C2×D83)⋊C4—24no—
227(C2×D83)⋊C4—24no—
228C4×Dic83—24no—
229C4×Dic83C2×D412yes—
230C4×Dic83C2×D412yes—
231C4×Dic83C2412yes—
232C4×Dic83C2412yes—
233C24×C83—21no—
234C24×C83C2×D411yescharacteristic
235C2×D4×C83—24no—
236C2×D4×C83—21no—
237C2×D4×C83—22no—
238C2×D4×C83—22no—
239C2×D4×C83—82no—
240C2×D4×C83C2412yes—
241C22×C4×C83—22no—
242C22×C4×C83—22no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—24no—
247C22×C4×C83—82no—
248C22×C4×C83C2×D412yes—
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2412yes—
251C22×C4×C83C2411yescharacteristic
252C2×C8×C83—22no—
253C2×C8×C83—22no—
254C2×C8×C83C2412yes—
255C2×C8×C83C2412yes—
256C4⋊C4×C83—24no—
257C4⋊C4×C83—21no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83C2412yes—
261C4⋊C4×C83C2412yes—
262C4⋊C4×C83C2412yes—
263C22⋊C4×C83—24no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—42no—
269C23×C83—42no—
270C23×C83—42no—
271C23×C83C22×D412yes—
272C23×C83C22×D411yescharacteristic
273C22×D83—22no—
274C22×D83—42no—
275C22×D83—42no—
276C22×D83—42no—
277D4×C83—22no—
278D4×C83—22no—
279D4×C83—42no—
280D4×C83—84no—
281C2×C4×C83—22no—
282C2×C4×C83—24no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—42no—
289C2×C4×C83—42no—
290C2×C4×C83—42no—
291C2×C4×C83—84no—
292C2×C4×C83C22×D412yes—
293C2×C4×C83C22×D411yescharacteristic
294C2×C4×C832−1+412yes—
295C2×C4×C832−1+412yes—
296C2×C4×C83C2511yescharacteristic
297C22⋊D83—84no—
298C22⋊D83—84no—
299C22⋊D83—84no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—42no—
308C2×Dic83—42no—
309C2×Dic83—42no—
310C2×Dic83—84no—
311C2×Dic83C22×D412yes—
312C2×Dic83C22×D412yes—
313C2×Dic83C22×D412yes—
314C2×Dic83C22×D412yes—
315D332—22no—
316D332—22no—
317D332—42no—
318C4×D83—84no—
319Dic166—84no—
320Dic166—84no—
321C8×C83—22no—
322C8×C83—22no—
323C83⋊C8—22no—
324C83⋊C8—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—44no—
329C22×C83—42no—
330C22×C83—42no—
331C22×C83—42no—
332C22×C83—84no—
333C22×C83#53612yes—
334C22×C83#57612yes—
335C22×C83#57712yes—
336C22×C83C23×D411yescharacteristic
337C2×D83—42no—
338C2×D83—42no—
339C2×D83—42no—
340C2×D83—84no—
341C4×C83—22no—
342C4×C83—42no—
343C4×C83—42no—
344C4×C83—42no—
345C4×C83#53612yes—
346C4×C83C2×2−1+411yescharacteristic
347C4×C83C2×2−1+411yescharacteristic
348Dic83—22no—
349Dic83—22no—
350Dic83—22no—
351Dic83—22no—
352Dic83—42no—
353Dic83—42no—
354Dic83—42no—
355C2×#3241—831nomaximal, Sylow
356C2×C83—42no—
357C2×C83—82no—
358C2×C83#324114yescomplemented
359C2×C83C2×#53611yescharacteristic
360C2×C83C2×#57611yescharacteristic
361C2×C83C2×#57711yescharacteristic
362D83—82no—
363C2×#544—831no—
364C2×#540—831no—
365#3241—8316no—
366C2×#501—831no—
367C2×#499—831no—
368C2×#490—831no—
369C2×#486—831no—
370C2×#481D8311yescharacteristic, complemented
371C2×#482—831no—
372C2×#482—831no—
373C2×#480—831no—
374C2×#478—831no—
375C2×#478—831no—
376C2×#476—831no—
377C2×#474—831no—
378C2×#433—831no—
379C83C2×#324111yescharacteristic, complemented, Sylow
380#544—838no—
381#544—1664no—
382#540—838no—
383#540—1664no—
384C2×C4⋊Q8—831no—
385C2×C4⋊Q8—831no—
386C2×C4⋊Q8—1661no—
387C2×#127—831no—
388C2×#125—831no—
389C2×#125—831no—
390C2×#125—831no—
391C2×#125—1661no—
392C2×#123—1661no—
393C2×#123—1661no—
394C2×C22⋊Q8—1661no—
395C2×C22⋊Q8—1661no—
396C2×#121—831no—
397C2×#121—1661no—
398C2×#121—1661no—
399C2×#121C2×D8311yescharacteristic
400C2×C4×D4—831no—
401C2×C4×D4—831no—
402C2×#117—831no—
403C2×#117—831no—
404C22×C4⋊C4C2×D8311yescharacteristic
405#501—838no—
406#499—838no—
407#490—838no—
408#486—838no—
409#482—838no—
410#482—838no—
411#481C2×D8318yescomplemented
412#480—838no—
413#478—838no—
414#478—838no—
415#476—838no—
416#474—838no—
417#433—838no—
418C2×#107—831no—
419C2×#107—831no—
420C2×#107—831no—
421C2×#107—831no—
422C2×#106—831no—
423C2×#106—831no—
424C2×#106C2×D8311yescharacteristic
425C2×#106C2×D8311yescharacteristic
426C2×C4⋊C8—831no—
427C2×C4⋊C8—831no—
428C2×#102—831no—
429C2×#102—831no—
430C2×#102—831no—
431C2×#102—831no—
432C2×#102—831no—
433C2×#102—831no—
434C2×#102C2×D8311yescharacteristic
435C2×#102C2×D8311yescharacteristic
436C2×C22⋊C8—831no—
437C2×C22⋊C8C2×D8311yescharacteristic
438C2×#97—831no—
439C2×C4×C8—831no—
440C22×Q8—1661no—
441C22×Q8—1661no—
442C22×D4—21no—
443C22×D4—831no—
444C22×D4—1661no—
445C22×D4—1661no—
446C22×D4—1661no—
447C22×D4C22×D8311yescharacteristic
448C23×C4—21no—
449C23×C4—1661no—
450C23×C4—1661no—
451C23×C4C22×D8311yescharacteristic
452C22×C8—831no—
453C22×C8—831no—
454C22×C8C22×D8311yescharacteristic
455C22×C8C22×D8311yescharacteristic
456C4⋊Q8—834no—
457C4⋊Q8—834no—
458C4⋊Q8—1662no—
459C4⋊Q8—1662no—
460C4⋊Q8—1668no—
461#127—834no—
462#127—1662no—
463#125—834no—
464#125—834no—
465#125—834no—
466#125—1662no—
467#125—1662no—
468#125—1662no—
469#125—1668no—
470#123—1668no—
471#123—1668no—
472C22⋊Q8—1668no—
473C22⋊Q8—1668no—
474#121—22no—
475#121—834no—
476#121—1668no—
477#121—1668no—
478#121—1662no—
479#121C22×D8314yes—
480C4×D4—834no—
481C4×D4—834no—
482C4×D4—1662no—
483C4×D4—1662no—
484#117—834no—
485#117—834no—
486#117—834no—
487#117—1662no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—831no—
491C2×C4⋊C4—831no—
492C2×C4⋊C4—831no—
493C2×C4⋊C4—831no—
494C2×C4⋊C4—831no—
495C2×C4⋊C4—1661no—
496C2×C4⋊C4—1661no—
497C2×C4⋊C4—1661no—
498C2×C4⋊C4—1661no—
499C2×C4⋊C4—1661no—
500C2×C4⋊C4—1661no—
501C2×C4⋊C4—1661no—
502C2×C4⋊C4—1661no—
503C2×C4⋊C4C22×D8311yescharacteristic
504C2×C4⋊C4C22×D8311yescharacteristic
505C2×C4⋊C4C22×D8314yes—
506C2×C4⋊C4C22×D8311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—831no—
509C2×C22⋊C4—831no—
510C2×C22⋊C4—1661no—
511C2×C22⋊C4—1661no—
512C2×C22⋊C4—1661no—
513C2×C22⋊C4—1661no—
514C2×C42—831no—
515C2×C42—831no—
516C2×C42—1661no—
517#107—834no—
518#107—834no—
519#107—834no—
520#107—834no—
521#106—834no—
522#106—834no—
523#106C22×D8314yes—
524#106C22×D8314yes—
525C4⋊C8—834no—
526C4⋊C8—834no—
527#102—834no—
528#102—834no—
529#102—834no—
530#102—834no—
531#102—834no—
532#102—834no—
533#102C22×D8314yes—
534#102C22×D8314yes—
535C22⋊C8—834no—
536C22⋊C8C22×D8314yes—
537#97—834no—
538C4×C8—834no—
539C24—21no—
540C24—1661no—
541C24D4×D8311yescharacteristic
542C2×Q8—6642no—
543C2×Q8—6642no—
544C2×Q8—1664no—
545C2×Q8—1664no—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—82no—
551C2×D4—832no—
552C2×D4—6642no—
553C2×D4—6642no—
554C2×D4—6642no—
555C2×D4—1664no—
556C2×D4—1664no—
557C2×D4—1664no—
558C2×D4—1661no—
559C2×D4—1662no—
560C2×D4—1662no—
561C2×D4C23×D8312yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—831no—
570C22×C4—831no—
571C22×C4—831no—
572C22×C4—831no—
573C22×C4—6642no—
574C22×C4—6642no—
575C22×C4—1664no—
576C22×C4—1661no—
577C22×C4—1661no—
578C22×C4—1661no—
579C22×C4—1664no—
580C22×C4D4×D8312yes—
581C22×C4D4×D8311yescharacteristic
582C22×C4C23×D8312yes—
583C22×C4C23×D8311yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—832no—
587C2×C8—832no—
588C2×C8—1662no—
589C2×C8—1662no—
590C2×C8C23×D8312yes—
591C2×C8C23×D8312yes—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—834no—
597C4⋊C4—834no—
598C4⋊C4—832no—
599C4⋊C4—832no—
600C4⋊C4—832no—
601C4⋊C4—1664no—
602C4⋊C4—1664no—
603C4⋊C4—1664no—
604C4⋊C4—1664no—
605C4⋊C4—1664no—
606C4⋊C4—1664no—
607C4⋊C4—1664no—
608C4⋊C4—1664no—
609C4⋊C4—1661no—
610C4⋊C4—1661no—
611C4⋊C4—1661no—
612C4⋊C4C23×D8312yes—
613C4⋊C4C23×D8312yes—
614C4⋊C4C23×D8312yes—
615C22⋊C4—24no—
616C22⋊C4—834no—
617C22⋊C4—834no—
618C22⋊C4—1664no—
619C22⋊C4—1664no—
620C22⋊C4—1664no—
621C22⋊C4—1664no—
622C42—832no—
623C42—832no—
624C42—832no—
625C42—832no—
626C42—1664no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—3322no—
635C23—3322no—
636C23—3322no—
637C23—1662no—
638C23C2×D4×D8312yes—
639C23C2×D4×D8311yescharacteristic
640Q8—6644no—
641Q8—6644no—
642D4—22no—
643D4—22no—
644D4—42no—
645D4—84no—
646D4—3322no—
647D4—6644no—
648D4—6644no—
649D4—6644no—
650D4—1662no—
651D4—1662no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—3322no—
664C2×C4—3322no—
665C2×C4—3322no—
666C2×C4—832no—
667C2×C4—832no—
668C2×C4—832no—
669C2×C4—832no—
670C2×C4—6644no—
671C2×C4—6644no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4—1662no—
678C2×C4—1662no—
679C2×C4C2×D4×D8312yes—
680C2×C4C2×D4×D8311yescharacteristic
681C2×C4#1458183912yes—
682C2×C4#1458183912yes—
683C2×C4C24×D8311yescharacteristic
684C8—22no—
685C8—22no—
686C8—1662no—
687C8—1662no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—84no—
696C22—3322no—
697C22—3322no—
698C22—3322no—
699C22—6644no—
700C22#1912827312yes—
701C22#1912850512yes—
702C22#1912850712yes—
703C22C22×D4×D8311yescharacteristic
704C4—22no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—3322no—
709C4—3322no—
710C4—3322no—
711C4—1662no—
712C4—1662no—
713C4—1662no—
714C4—1662no—
715C4#1912827312yes—
716C4C2×#1458183911yescharacteristic
717C4C2×#1458183911yescharacteristic
718C2—42no—
719C2—82no—
720C2—6642no—
721C2#2491872014yesdirect product factor
722C2C2×#1912827311yescharacteristic
723C2C2×#1912850511yescharacteristic
724C2C2×#1912850711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#481×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128304C2
hypercenterC2×#481D83
hypocenterC83C2×#3241
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#19128332C2semidirect
3. #24918720C2direct (N × H)
4. C2×#19128108C2semidirect
5. C2×#19128101C2semidirect
6. C2×#19128064C2semidirect
7. C2×#19128046C2semidirect
8. C2×#19128026C2semidirect
9. C2×#19128022C2semidirect
10. C2×#19128014C2semidirect
11. C2×#19128003C2semidirect
12. C2×#19128000C2semidirect
13. C2×#19127990C2semidirect
14. C2×#19127979C2semidirect
15. C2×#19127759C2semidirect
16. C2×#481×C83C2semidirect
18. #19128332C22semidirect
40. #19128108C22semidirect
41. #19128101C22semidirect
42. #19128064C22semidirect
43. #19128046C22semidirect
44. #19128026C22semidirect
45. #19128022C22semidirect
46. #19128014C22semidirect
47. #19128003C22semidirect
48. #19128000C22semidirect
49. #19127990C22semidirect
50. #19127979C22semidirect
51. #19127759C22semidirect
71. #481×C83C22semidirect
358. C2×C83#3241semidirect
370. C2×#481D83semidirect
379. C83C2×#3241semidirect
411. #481C2×D83semidirect
721. C2#24918720direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283322
C2×#191283042
#249187202
C2×#191281082
C2×#191281012
C2×#191280642
C2×#191280462
C2×#191280262
C2×#191280222
C2×#191280142
C2×#191280032
C2×#191280002
C2×#191279902
C2×#191279792
C2×#191277592
C2×#481×C832
C2×#324183