Finite Group Databasebeta

← C2×#24920206 #36284130

Subgroups — C2×#24920206 #36284130

Order 21248.

1842 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128431C211yesmaximal, characteristic, complemented
2C2×#19128423C211yesmaximal, characteristic
3#24920206C2116yesmaximal, direct product factor
4C2×#19128063C211yesmaximal, characteristic
5C2×#19128062C211yesmaximal, characteristic
6C2×#19128050C211yesmaximal, characteristic, complemented
7C2×#19127985C211yesmaximal, characteristic, complemented
8C2×#19127990C211yesmaximal, characteristic
9C2×#19127926C211yesmaximal, characteristic
10C2×#19127924C211yesmaximal, characteristic
11C2×#19127910C211yesmaximal, characteristic, complemented
12C2×#19127830C211yesmaximal, characteristic, complemented
13C2×#19127807C211yesmaximal, characteristic, complemented
14C2×#19127806C211yesmaximal, characteristic, complemented
15C2×#19127788C211yesmaximal, characteristic
16C2×#475×C83C211yesmaximal, characteristic, complemented
17C22×Dic332C2211yescharacteristic
18C22×#13050580C2211yescharacteristic
19C22×#13050579C2211yescharacteristic
20#19128431—24no—
21#19128431C2218yescomplemented
22#19128423—24no—
23#19128423C2218yes—
24C2×#14581791—21no—
25C2×#14581791C2211yescharacteristic
26C2×#14581791C2211yescharacteristic
27C2×#14581790—21no—
28C2×#14581790—21no—
29C2×#14581790C2211yescharacteristic
30C2×#14581787—21no—
31C2×#14581786—21no—
32C2×#14581781C2211yescharacteristic
33C2×#14581780C2211yescharacteristic
34C2×#14581770—21no—
35C2×C4×Dic166C2211yescharacteristic
36C2×C4×Dic166C2211yescharacteristic
37C2×#14581757—21no—
38C2×#14581757C2211yescharacteristic
39C2×#14581757C2211yescharacteristic
40C2×#14581757C2211yescharacteristic
41C2×#14581754C2211yescharacteristic
42C2×#14581749—21no—
43#19128063C2218yes—
44#19128062C2218yes—
45#19128050C2218yescomplemented
46#19127990C2218yes—
47#19127985C2218yescomplemented
48#19127926C2218yes—
49#19127924C2218yes—
50#19127910C2218yescomplemented
51#19127830C2218yescomplemented
52#19127807C2218yescomplemented
53#19127806C2218yescomplemented
54#19127788C2218yes—
55C2×#14581723C2211yescharacteristic
56C2×Dic83⋊C8C2211yescharacteristic
57C2×Dic83⋊C8C2211yescharacteristic
58C2×#14581717C2211yescharacteristic
59C2×#14581716C2211yescharacteristic
60C2×#14581715C2211yescharacteristic
61C2×#14581715C2211yescharacteristic
62C2×#14581715C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×#14581703C2211yescharacteristic
67C2×#14581702C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C2×C4⋊Q8×C83C2211yescharacteristic
70C2×C4×Q8×C83C2211yescharacteristic
71#475×C83C2218yescomplemented
72C2×#106×C83C2211yescharacteristic
73C2×#106×C83C2211yescharacteristic
74C2×C4⋊C8×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#103×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×Dic166D411yescharacteristic
80C22×Dic166C2311yescharacteristic
81C22×Dic166C2311yescharacteristic
82C22×D332C2311yescharacteristic
83C22×C4×D83—21no—
84C2×Dic332—24no—
85C2×Dic332C2314yes—
86C2×#13050580—24no—
87C2×#13050580C2314yes—
88C2×#13050579—24no—
89C2×#13050579C2314yes—
90C22×C83⋊C8C2311yescharacteristic
91C22×C83⋊C8C2311yescharacteristic
92#14581791—28no—
93#14581791—22no—
94#14581791—22no—
95#14581791C2314yes—
96#14581791C2314yes—
97#14581790—28no—
98#14581790—28no—
99#14581790—22no—
100#14581790C2314yes—
101#14581787—28no—
102#14581786—28no—
103#14581781—22no—
104#14581781C2314yes—
105#14581780—22no—
106#14581780C2314yes—
107#14581770—28no—
108C4×Dic166—22no—
109C4×Dic166D414yes—
110C4×Dic166C2314yes—
111C4×Dic166C2314yes—
112#14581757—28no—
113#14581757—22no—
114#14581757—22no—
115#14581757—22no—
116#14581757C2314yes—
117#14581757C2314yes—
118#14581757C2314yes—
119#14581754—22no—
120#14581754C2314yes—
121#14581749—28no—
122C2×C4⋊Dic83D411yescharacteristic
123C2×C4⋊Dic83C2311yescharacteristic
124C2×Dic83⋊C4—21no—
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4D411yescharacteristic
133C2×Dic83⋊C4D411yescharacteristic
134C2×(C2×D83)⋊C4—21no—
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×C4×Dic83—21no—
140C2×C4×Dic83—21no—
141C2×C4×Dic83—21no—
142C2×C4×Dic83—21no—
143C2×C4×Dic83C2311yescharacteristic
144C2×C4×Dic83C2311yescharacteristic
145#14581723C2314yes—
146Dic83⋊C8C2314yes—
147Dic83⋊C8C2314yes—
148#14581717C2314yes—
149#14581716C2314yes—
150#14581715C2314yes—
151#14581715C2314yes—
152#14581715C2314yes—
153#14581714C2314yes—
154#14581712C2314yes—
155#14581712C2314yes—
156#14581703C2314yes—
157#14581702C2314yes—
158C8×Dic83C2314yes—
159C22×Q8×C83—21no—
160C22×Q8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163C4⋊Q8×C83—22no—
164C4⋊Q8×C83C2314yes—
165C4×Q8×C83—22no—
166C4×Q8×C83C2314yes—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C42×C83—21no—
173C2×C42×C83C2311yescharacteristic
174#106×C83C2314yes—
175#106×C83C2314yes—
176C4⋊C8×C83C2314yes—
177#103×C83C2314yes—
178#103×C83C2314yes—
179C23×D83—21no—
180C2×Dic166—21no—
181C2×Dic166—22no—
182C2×Dic166—24no—
183C2×Dic166—22no—
184C2×Dic166—22no—
185C2×Dic166—21no—
186C2×Dic166—24no—
187C2×Dic166—24no—
188C2×Dic166—82no—
189C2×Dic166—82no—
190C2×Dic166C2×D414yes—
191C2×Dic166#4114yes—
192C2×Dic166C2412yes—
193C2×Dic166C2412yes—
194C2×D332—22no—
195C2×D332—22no—
196C2×D332—21no—
197C2×D332C2412yes—
198C22×Dic83—21no—
199C22×Dic83—21no—
200C22×Dic83—21no—
201C22×Dic83C2×D411yescharacteristic
202C22×Dic83C2×D411yescharacteristic
203C22×Dic83C2×D411yescharacteristic
204C22×Dic83C2×D411yescharacteristic
205C2×C4×D83—24no—
206C2×C4×D83—44no—
207Dic332—28no—
208#13050580—28no—
209#13050579—28no—
210C2×C83⋊C8—22no—
211C2×C83⋊C8—22no—
212C2×C83⋊C8C2412yes—
213C2×C83⋊C8C2412yes—
214C4⋊Dic83—21no—
215C4⋊Dic83C2×D414yes—
216C4⋊Dic83C2412yes—
217Dic83⋊C4—24no—
218Dic83⋊C4—24no—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4C2×D414yes—
226Dic83⋊C4C2×D414yes—
227(C2×D83)⋊C4—24no—
228(C2×D83)⋊C4—24no—
229(C2×D83)⋊C4—24no—
230(C2×D83)⋊C4—24no—
231(C2×D83)⋊C4—24no—
232C4×Dic83—24no—
233C4×Dic83—24no—
234C4×Dic83—24no—
235C4×Dic83—24no—
236C4×Dic83C2×D412yes—
237C4×Dic83C2×D412yes—
238C4×Dic83C2412yes—
239C4×Dic83C2412yes—
240C2×Q8×C83—21no—
241C2×Q8×C83—24no—
242C2×Q8×C83—22no—
243C2×Q8×C83—22no—
244C2×Q8×C83—82no—
245C2×Q8×C83C2412yes—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2411yescharacteristic
253C2×C8×C83—22no—
254C2×C8×C83—22no—
255C2×C8×C83C2412yes—
256C2×C8×C83C2412yes—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—24no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—21no—
262C4⋊C4×C83C2412yes—
263C4⋊C4×C83C2412yes—
264C4⋊C4×C83C2412yes—
265C42×C83—24no—
266C42×C83C2×D412yes—
267C42×C83C2412yes—
268C23×C83C22×D411yescharacteristic
269C22×D83—22no—
270C22×D83—42no—
271C22×D83—42no—
272C22×D83—42no—
273Q8×C83—22no—
274Q8×C83—22no—
275Q8×C83—42no—
276Q8×C83—84no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—42no—
284C2×C4×C83—42no—
285C2×C4×C83—42no—
286C2×C4×C83—42no—
287C2×C4×C83C22×D412yes—
288C2×C4×C83C22×D412yes—
289C2×C4×C83C22×D411yescharacteristic
290C2×C4×C83C2×#4112yes—
291C2×C4×C832−1+412yes—
292C2×C4×C83C2511yescharacteristic
293C2×Dic83—24no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—42no—
301C2×Dic83—42no—
302C2×Dic83#13714yes—
303C2×Dic83C22×D412yes—
304C2×Dic83C22×D412yes—
305C2×Dic83C22×D412yes—
306C2×Dic83C22×D412yes—
307D332—22no—
308D332—22no—
309D332—42no—
310C4×D83—48no—
311Dic166—24no—
312Dic166—22no—
313Dic166—28no—
314Dic166—22no—
315Dic166—22no—
316Dic166—42no—
317Dic166—84no—
318Dic166—84no—
319Dic166C2×#4114yes—
320C8×C83—22no—
321C8×C83—22no—
322C83⋊C8—22no—
323C83⋊C8—22no—
324C22×C83#54812yes—
325C22×C83C2×#13712yes—
326C22×C83#57712yes—
327C22×C83C23×D411yescharacteristic
328C2×D83—42no—
329C2×D83—42no—
330C2×D83—42no—
331C2×D83—84no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—42no—
335C4×C83—42no—
336C4×C83—42no—
337C4×C83—42no—
338C4×C83#54812yes—
339C4×C83C22×#4111yescharacteristic
340C4×C83C2×2−1+411yescharacteristic
341Dic83—24no—
342Dic83—22no—
343Dic83—22no—
344Dic83—22no—
345Dic83—42no—
346Dic83—42no—
347Dic83C2×#13714yes—
348C2×#3369—831nomaximal, Sylow
349C2×C83#336914yescomplemented
350C2×C83C2×#54811yescharacteristic
351C2×C83C22×#13711yescharacteristic
352C2×C83C2×#57711yescharacteristic
353D83—82no—
354C2×Q82—831no—
355C2×#556—831no—
356#3369—8316no—
357C2×#489—831no—
358C2×#489—831no—
359C2×#487—831no—
360C2×#475—831no—
361C2×#475D8311yescharacteristic, complemented
362C2×#476—831no—
363C2×#464—831no—
364C2×#464—831no—
365C2×#462—831no—
366C2×#446—831no—
367C2×#441—831no—
368C2×#441—831no—
369C2×C4×SD16—831no—
370C83C2×#336911yescharacteristic, complemented, Sylow
371C22×Q16—831no—
372C22×Q16—831no—
373C22×SD16—831no—
374Q82—838no—
375Q82—1664no—
376#556—838no—
377#556—1664no—
378C2×C4⋊Q8—831no—
379C2×C4⋊Q8—831no—
380C2×C4⋊Q8—831no—
381C2×C4⋊Q8—1661no—
382C2×C4⋊Q8—1661no—
383C2×C4⋊Q8—1661no—
384C2×C4⋊Q8C2×D8311yescharacteristic
385C2×#126—1661no—
386C2×#126—1661no—
387C2×#124—831no—
388C2×#124—831no—
389C2×C22⋊Q8—1661no—
390C2×C4×Q8—831no—
391C2×C4×Q8—831no—
392C2×C4×Q8—831no—
393C2×C4×Q8—831no—
394C2×C4×Q8—831no—
395C2×C4×Q8—1661no—
396C2×C4×Q8C2×D8311yescharacteristic
397C2×C4×D4—831no—
398C2×#117—1661no—
399#489—838no—
400#489—838no—
401#487—838no—
402#476—838no—
403#475—838no—
404#475C2×D8318yescomplemented
405#464—838no—
406#464—838no—
407#462—838no—
408#446—838no—
409#441—838no—
410#441—838no—
411C4×SD16—838no—
412C2×#106—831no—
413C2×#106C2×D8311yescharacteristic
414C2×#106C2×D8311yescharacteristic
415C2×C4⋊C8—831no—
416C2×C4⋊C8—831no—
417C2×C4⋊C8C2×D8311yescharacteristic
418C2×#103—831no—
419C2×#103—831no—
420C2×#103—831no—
421C2×#103—831no—
422C2×#103—831no—
423C2×#103C2×D8311yescharacteristic
424C2×#103C2×D8311yescharacteristic
425C2×#102—831no—
426C2×#102—831no—
427C2×#102—831no—
428C2×#97—831no—
429C2×#97—831no—
430C2×C4×C8—831no—
431C22×Q8—21no—
432C22×Q8—831no—
433C22×Q8—831no—
434C22×Q8—831no—
435C22×Q8—1661no—
436C22×Q8—1661no—
437C22×Q8C22×D8311yescharacteristic
438C22×D4—831no—
439C23×C4—1661no—
440C2×Q16—834no—
441C2×Q16—834no—
442C2×Q16—1664no—
443C2×Q16—1664no—
444C2×SD16—834no—
445C2×SD16—1664no—
446C22×C8—831no—
447C22×C8—831no—
448C22×C8C22×D8311yescharacteristic
449C22×C8C22×D8311yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8—834no—
452C4⋊Q8—834no—
453C4⋊Q8—834no—
454C4⋊Q8—1662no—
455C4⋊Q8—1662no—
456C4⋊Q8—1662no—
457C4⋊Q8—1668no—
458C4⋊Q8—1668no—
459C4⋊Q8—1668no—
460C4⋊Q8C22×D8314yes—
461#126—1668no—
462#126—1668no—
463#124—834no—
464#124—834no—
465#124—1662no—
466#124—1662no—
467C22⋊Q8—1668no—
468C4×Q8—22no—
469C4×Q8—834no—
470C4×Q8—834no—
471C4×Q8—834no—
472C4×Q8—834no—
473C4×Q8—834no—
474C4×Q8—834no—
475C4×Q8—1662no—
476C4×Q8—1662no—
477C4×Q8—1662no—
478C4×Q8—1668no—
479C4×Q8—1662no—
480C4×Q8C22×D8314yes—
481C4×D4—834no—
482C4×D4—1662no—
483#117—1668no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—831no—
490C2×C4⋊C4—1661no—
491C2×C4⋊C4—1661no—
492C2×C4⋊C4—1661no—
493C2×C4⋊C4—1661no—
494C2×C4⋊C4—1661no—
495C2×C4⋊C4—1661no—
496C2×C4⋊C4—1661no—
497C2×C4⋊C4—1661no—
498C2×C4⋊C4C22×D8311yescharacteristic
499C2×C4⋊C4C22×D8311yescharacteristic
500C2×C4⋊C4C22×D8311yescharacteristic
501C2×C22⋊C4—1661no—
502C2×C22⋊C4—1661no—
503C2×C22⋊C4—1661no—
504C2×C22⋊C4—1661no—
505C2×C22⋊C4—1661no—
506C2×C42—21no—
507C2×C42—831no—
508C2×C42—831no—
509C2×C42—1661no—
510C2×C42—1661no—
511C2×C42—1661no—
512C2×C42—1661no—
513C2×C42C22×D8311yescharacteristic
514#106—834no—
515#106C22×D8314yes—
516#106C22×D8314yes—
517C4⋊C8—834no—
518C4⋊C8—834no—
519C4⋊C8C22×D8314yes—
520#103—834no—
521#103—834no—
522#103—834no—
523#103—834no—
524#103—834no—
525#103C22×D8314yes—
526#103C22×D8314yes—
527#102—834no—
528#102—834no—
529#102—834no—
530#97—834no—
531#97—834no—
532C4×C8—834no—
533C24—1661no—
534C2×Q8—21no—
535C2×Q8—24no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—82no—
539C2×Q8—834no—
540C2×Q8—834no—
541C2×Q8—832no—
542C2×Q8—832no—
543C2×Q8—6642no—
544C2×Q8—6642no—
545C2×Q8—1664no—
546C2×Q8—1664no—
547C2×Q8—1664no—
548C2×Q8—1662no—
549C2×Q8—1662no—
550C2×Q8—1661no—
551C2×Q8—1661no—
552C2×Q8—1662no—
553C2×Q8C23×D8312yes—
554C2×D4—832no—
555C2×D4—1661no—
556C2×D4—1662no—
557C2×D4—1662no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—3324no—
563C22×C4—831no—
564C22×C4—831no—
565C22×C4—831no—
566C22×C4—831no—
567C22×C4—1664no—
568C22×C4—1661no—
569C22×C4—1661no—
570C22×C4—1661no—
571C22×C4D4×D8311yescharacteristic
572C22×C4D4×D8311yescharacteristic
573C22×C4C23×D8311yescharacteristic
574Q16—1668no—
575Q16—1668no—
576SD16—1668no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—832no—
580C2×C8—832no—
581C2×C8—1662no—
582C2×C8—1662no—
583C2×C8C23×D8312yes—
584C2×C8C23×D8312yes—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—834no—
591C4⋊C4—834no—
592C4⋊C4—834no—
593C4⋊C4—832no—
594C4⋊C4—1664no—
595C4⋊C4—1664no—
596C4⋊C4—1664no—
597C4⋊C4—1664no—
598C4⋊C4—1664no—
599C4⋊C4—1664no—
600C4⋊C4—1664no—
601C4⋊C4—1661no—
602C4⋊C4—1664no—
603C4⋊C4C23×D8312yes—
604C4⋊C4C23×D8312yes—
605C4⋊C4C23×D8312yes—
606C22⋊C4—1664no—
607C22⋊C4—1664no—
608C22⋊C4—1664no—
609C22⋊C4—1664no—
610C22⋊C4—1664no—
611C42—24no—
612C42—832no—
613C42—832no—
614C42—832no—
615C42—832no—
616C42—1664no—
617C42—1664no—
618C42—1664no—
619C42—1664no—
620C42D4×D8312yes—
621C42C23×D8312yes—
622C23—3322no—
623C23—3322no—
624C23—3322no—
625C23—1662no—
626C23C2×D4×D8311yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—42no—
630Q8—84no—
631Q8—3322no—
632Q8—834no—
633Q8—6644no—
634Q8—6644no—
635Q8—1668no—
636Q8—1662no—
637Q8—1662no—
638Q8—1664no—
639Q8—1662no—
640D4—3322no—
641D4—1662no—
642D4—1662no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—3328no—
654C2×C4—3322no—
655C2×C4—3322no—
656C2×C4—834no—
657C2×C4—832no—
658C2×C4—832no—
659C2×C4—832no—
660C2×C4—832no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1664no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4C2×D4×D8312yes—
669C2×C4C2×D4×D8312yes—
670C2×C4C2×D4×D8311yescharacteristic
671C2×C4#41×D8312yes—
672C2×C4#1458184012yes—
673C2×C4C24×D8311yescharacteristic
674C8—22no—
675C8—22no—
676C8—1662no—
677C8—1662no—
678C22—3322no—
679C22—3322no—
680C22—3322no—
681C22—6644no—
682C22#1912836112yes—
683C22#137×D8312yes—
684C22#1912850712yes—
685C22C22×D4×D8311yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—3322no—
693C4—3322no—
694C4—834no—
695C4—1662no—
696C4—1664no—
697C4—1662no—
698C4—1662no—
699C4#1912836112yes—
700C4C2×#41×D8311yescharacteristic
701C4C2×#1458184011yescharacteristic
702C2—6642no—
703C2#2492020614yesdirect product factor
704C2C2×#1912836111yescharacteristic
705C2C2×#137×D8311yescharacteristic
706C2C2×#1912850711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#475×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenterC2×#475D83
hypocenterC83C2×#3369
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#19128431C2semidirect
3. #24920206C2direct (N × H)
6. C2×#19128050C2semidirect
7. C2×#19127985C2semidirect
11. C2×#19127910C2semidirect
12. C2×#19127830C2semidirect
13. C2×#19127807C2semidirect
14. C2×#19127806C2semidirect
16. C2×#475×C83C2semidirect
21. #19128431C22semidirect
45. #19128050C22semidirect
47. #19127985C22semidirect
50. #19127910C22semidirect
51. #19127830C22semidirect
52. #19127807C22semidirect
53. #19127806C22semidirect
71. #475×C83C22semidirect
349. C2×C83#3369semidirect
361. C2×#475D83semidirect
370. C83C2×#3369semidirect
404. #475C2×D83semidirect
703. C2#24920206direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284312
C2×#191284232
#249202062
C2×#191280632
C2×#191280622
C2×#191280502
C2×#191279852
C2×#191279902
C2×#191279262
C2×#191279242
C2×#191279102
C2×#191278302
C2×#191278072
C2×#191278062
C2×#191277882
C2×#475×C832
C2×#336983