Finite Group Databasebeta

← C2×#24920149 #36284017

Subgroups — C2×#24920149 #36284017

Order 21248.

1830 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128427C211yesmaximal, characteristic, complemented
2C2×#19128423C211yesmaximal, characteristic
3#24920149C2116yesmaximal, direct product factor
4C2×#19128057C211yesmaximal, characteristic
5C2×#19128056C211yesmaximal, characteristic
6C2×#19128050C211yesmaximal, characteristic, complemented
7C2×#19128008C211yesmaximal, characteristic, complemented
8C2×#19128007C211yesmaximal, characteristic, complemented
9C2×#19127980C211yesmaximal, characteristic
10C2×#19127925C211yesmaximal, characteristic
11C2×#19127923C211yesmaximal, characteristic
12C2×#19127909C211yesmaximal, characteristic, complemented
13C2×C8×Dic166C211yesmaximal, characteristic, complemented
14C2×#19127793C211yesmaximal, characteristic, complemented
15C2×#19127786C211yesmaximal, characteristic
16C2×C4×Q16×C83C211yesmaximal, characteristic, complemented
17C22×#13050580C2211yescharacteristic
18C22×#13050577C2211yescharacteristic
19#19128427—24no—
20#19128427C2218yescomplemented
21#19128423—24no—
22#19128423C2218yes—
23C2×#14581791—21no—
24C2×#14581791C2211yescharacteristic
25C2×#14581790C2211yescharacteristic
26C2×#14581787—21no—
27C2×#14581786—21no—
28C2×#14581784—21no—
29C2×#14581784C2211yescharacteristic
30C2×#14581783—21no—
31C2×#14581783C2211yescharacteristic
32C2×#14581781C2211yescharacteristic
33C2×#14581780C2211yescharacteristic
34C2×#14581770—21no—
35C2×Q8×Dic83C2211yescharacteristic
36C2×Q8×Dic83C2211yescharacteristic
37C2×C4×Dic166—21no—
38C2×C4×Dic166C2211yescharacteristic
39C2×#14581757C2211yescharacteristic
40C2×#14581754C2211yescharacteristic
41C2×#14581749—21no—
42#19128057C2218yes—
43#19128056C2218yes—
44#19128050C2218yescomplemented
45#19128008C2218yescomplemented
46#19128007C2218yescomplemented
47#19127980C2218yes—
48#19127925C2218yes—
49#19127923C2218yes—
50#19127909C2218yescomplemented
51C8×Dic166C2218yescomplemented
52#19127793C2218yescomplemented
53#19127786C2218yes—
54C2×#14581725C2211yescharacteristic
55C2×#14581723C2211yescharacteristic
56C2×C4⋊(C83⋊C8)C2211yescharacteristic
57C2×Dic83⋊C8C2211yescharacteristic
58C2×Dic83⋊C8C2211yescharacteristic
59C2×#14581717C2211yescharacteristic
60C2×#14581717C2211yescharacteristic
61C2×#14581716C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581715C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581712C2211yescharacteristic
67C2×C8×Dic83C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C22×Q16×C83C2211yescharacteristic
70C2×C4×Q8×C83C2211yescharacteristic
71C2×C4×Q8×C83C2211yescharacteristic
72C4×Q16×C83C2218yescomplemented
73C2×#107×C83C2211yescharacteristic
74C2×#103×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×C4×C8×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166D411yescharacteristic
79C22×Dic166C2311yescharacteristic
80C22×D332C2311yescharacteristic
81C22×C4×D83—21no—
82C2×#13050580—24no—
83C2×#13050580C2314yes—
84C2×#13050577—24no—
85C2×#13050577C2314yes—
86C22×C83⋊C8C2311yescharacteristic
87C22×C83⋊C8C2311yescharacteristic
88#14581791—28no—
89#14581791—22no—
90#14581791C2314yes—
91#14581790—22no—
92#14581790C2314yes—
93#14581787—28no—
94#14581786—28no—
95#14581784—28no—
96#14581784—22no—
97#14581784C2314yes—
98#14581783—28no—
99#14581783—22no—
100#14581783C2314yes—
101#14581781—22no—
102#14581781C2314yes—
103#14581780—22no—
104#14581780C2314yes—
105#14581770—28no—
106Q8×Dic83—22no—
107Q8×Dic83—22no—
108Q8×Dic83C2314yes—
109Q8×Dic83C2314yes—
110C4×Dic166—28no—
111C4×Dic166D414yes—
112C4×Dic166C2314yes—
113#14581757—22no—
114#14581757C2314yes—
115#14581754—22no—
116#14581754C2314yes—
117#14581749—28no—
118C2×C4⋊Dic83—21no—
119C2×C4⋊Dic83—21no—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83D411yescharacteristic
122C2×C4⋊Dic83C2311yescharacteristic
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⋊C4D411yescharacteristic
132C2×Dic83⋊C4D411yescharacteristic
133C2×(C2×D83)⋊C4—21no—
134C2×(C2×D83)⋊C4—21no—
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×C4×Dic83—21no—
139C2×C4×Dic83—21no—
140C2×C4×Dic83—21no—
141C2×C4×Dic83C2311yescharacteristic
142C2×C4×Dic83C2311yescharacteristic
143#14581725C2314yes—
144#14581723C2314yes—
145C4⋊(C83⋊C8)C2314yes—
146Dic83⋊C8C2314yes—
147Dic83⋊C8C2314yes—
148#14581717C2314yes—
149#14581717C2314yes—
150#14581716C2314yes—
151#14581716C2314yes—
152#14581715C2314yes—
153#14581714C2314yes—
154#14581714C2314yes—
155#14581712C2314yes—
156C8×Dic83C2314yes—
157C8×Dic83C2314yes—
158C22×Q8×C83C2311yescharacteristic
159C22×Q8×C83C2311yescharacteristic
160C2×Q16×C83—24no—
161C2×Q16×C83C2314yes—
162C22×C8×C83C2311yescharacteristic
163C22×C8×C83C2311yescharacteristic
164C4×Q8×C83—22no—
165C4×Q8×C83—22no—
166C4×Q8×C83C2314yes—
167C4×Q8×C83C2314yes—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C42×C83—21no—
173C2×C42×C83—21no—
174C2×C42×C83C2311yescharacteristic
175#107×C83C2314yes—
176#103×C83C2314yes—
177#103×C83C2314yes—
178C4×C8×C83C2314yes—
179C23×D83—21no—
180C2×Dic166—24no—
181C2×Dic166—22no—
182C2×Dic166—22no—
183C2×Dic166—21no—
184C2×Dic166—24no—
185C2×Dic166—44no—
186C2×Dic166C2×D414yes—
187C2×Dic166C2412yes—
188C2×D332—22no—
189C2×D332—22no—
190C2×D332—21no—
191C2×D332C2412yes—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83C2×D411yescharacteristic
196C22×Dic83C2×D411yescharacteristic
197C22×Dic83C2×D411yescharacteristic
198C22×Dic83C2×D411yescharacteristic
199C2×C4×D83—24no—
200C2×C4×D83—44no—
201#13050580—28no—
202#13050577—28no—
203C2×C83⋊C8—22no—
204C2×C83⋊C8—22no—
205C2×C83⋊C8C2412yes—
206C2×C83⋊C8C2412yes—
207C4⋊Dic83—21no—
208C4⋊Dic83—21no—
209C4⋊Dic83—24no—
210C4⋊Dic83—24no—
211C4⋊Dic83—24no—
212C4⋊Dic83C2×D414yes—
213C4⋊Dic83C2412yes—
214C4⋊Dic83C2412yes—
215Dic83⋊C4—24no—
216Dic83⋊C4—24no—
217Dic83⋊C4—24no—
218Dic83⋊C4—24no—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222Dic83⋊C4C2×D414yes—
223Dic83⋊C4C2×D414yes—
224(C2×D83)⋊C4—24no—
225(C2×D83)⋊C4—24no—
226(C2×D83)⋊C4—24no—
227(C2×D83)⋊C4—24no—
228(C2×D83)⋊C4—24no—
229C4×Dic83—24no—
230C4×Dic83—24no—
231C4×Dic83—24no—
232C4×Dic83C2×D412yes—
233C4×Dic83C2×D412yes—
234C4×Dic83C2412yes—
235C4×Dic83C2412yes—
236C2×Q8×C83—21no—
237C2×Q8×C83—21no—
238C2×Q8×C83—22no—
239C2×Q8×C83—22no—
240C2×Q8×C83—22no—
241C2×Q8×C83#4114yes—
242C2×Q8×C83C2412yes—
243C2×Q8×C83C2412yes—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2411yescharacteristic
251Q16×C83—28no—
252C2×C8×C83—22no—
253C2×C8×C83—22no—
254C2×C8×C83C2412yes—
255C2×C8×C83C2412yes—
256C4⋊C4×C83—24no—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83C2412yes—
261C4⋊C4×C83C2412yes—
262C42×C83—24no—
263C42×C83—24no—
264C42×C83C2×D412yes—
265C42×C83C2412yes—
266C23×C83C22×D411yescharacteristic
267C22×D83—22no—
268C22×D83—42no—
269C22×D83—42no—
270C22×D83—42no—
271Q8×C83—24no—
272Q8×C83—22no—
273Q8×C83—22no—
274Q8×C83—22no—
275Q8×C83—42no—
276Q8×C83C2×#4114yes—
277C2×C4×C83—24no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
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—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—42no—
300C2×Dic83—42no—
301C2×Dic83—42no—
302C2×Dic83#13514yes—
303C2×Dic83C22×D412yes—
304C2×Dic83C22×D412yes—
305C2×Dic83C22×D412yes—
306C2×Dic83C22×D412yes—
307D332—22no—
308D332—22no—
309D332—42no—
310C4×D83—48no—
311Dic166—28no—
312Dic166—22no—
313Dic166—22no—
314Dic166—42no—
315Dic166—48no—
316C8×C83—22no—
317C8×C83—22no—
318C83⋊C8—22no—
319C83⋊C8—22no—
320C22×C83#54812yes—
321C22×C83C2×#13512yes—
322C22×C83#57812yes—
323C22×C83C23×D411yescharacteristic
324C2×D83—42no—
325C2×D83—42no—
326C2×D83—42no—
327C2×D83—84no—
328C4×C83—24no—
329C4×C83—22no—
330C4×C83—22no—
331C4×C83—42no—
332C4×C83—42no—
333C4×C83—42no—
334C4×C83#54812yes—
335C4×C83C22×#4111yescharacteristic
336C4×C83C2×2−1+411yescharacteristic
337Dic83—22no—
338Dic83—22no—
339Dic83—22no—
340Dic83—42no—
341Dic83—42no—
342Dic83—42no—
343Dic83C2×#13514yes—
344C2×#3364—831nomaximal, Sylow
345C2×C83#336414yescomplemented
346C2×C83C2×#54811yescharacteristic
347C2×C83C22×#13511yescharacteristic
348C2×C83C2×#57811yescharacteristic
349D83—82no—
350C2×#557—831no—
351C2×#556—831no—
352#3364—8316no—
353C2×#488—831no—
354C2×#488—831no—
355C2×#487—831no—
356C2×#479—831no—
357C2×#479—831no—
358C2×#474—831no—
359C2×#464—831no—
360C2×#464—831no—
361C2×#462—831no—
362C2×C8×Q8—831no—
363C2×C4×Q16—831no—
364C2×C4×Q16D8311yescharacteristic, complemented
365C2×C4×SD16—831no—
366C83C2×#336411yescharacteristic, complemented, Sylow
367C22×Q16—831no—
368C22×Q16C2×D8311yescharacteristic
369C22×SD16—831no—
370#557—838no—
371#557—1664no—
372#556—838no—
373#556—1664no—
374C2×C4⋊Q8—831no—
375C2×C4⋊Q8—831no—
376C2×C4⋊Q8—1661no—
377C2×#126—1661no—
378C2×#126—1661no—
379C2×#125—831no—
380C2×#125—831no—
381C2×#125—1661no—
382C2×#125—1661no—
383C2×#124—831no—
384C2×#124—831no—
385C2×C22⋊Q8—1661no—
386C2×C4×Q8—831no—
387C2×C4×Q8—831no—
388C2×C4×Q8—831no—
389C2×C4×Q8—831no—
390C2×C4×Q8—1661no—
391C2×C4×Q8C2×D8311yescharacteristic
392C2×C4×Q8C2×D8311yescharacteristic
393C2×C4×D4—831no—
394C2×#117—1661no—
395#488—838no—
396#488—838no—
397#487—838no—
398#479—838no—
399#479—838no—
400#474—838no—
401#464—838no—
402#464—838no—
403#462—838no—
404C8×Q8—838no—
405C4×Q16—838no—
406C4×Q16C2×D8318yescomplemented
407C4×SD16—838no—
408C2×#107—831no—
409C2×#107C2×D8311yescharacteristic
410C2×#106—831no—
411C2×C4⋊C8—831no—
412C2×C4⋊C8—831no—
413C2×C4⋊C8—831no—
414C2×#103—831no—
415C2×#103—831no—
416C2×#103—831no—
417C2×#103—831no—
418C2×#103—831no—
419C2×#103C2×D8311yescharacteristic
420C2×#103C2×D8311yescharacteristic
421C2×#102—831no—
422C2×#102—831no—
423C2×#102—831no—
424C2×C4×C8—831no—
425C2×C4×C8—831no—
426C2×C4×C8C2×D8311yescharacteristic
427C22×Q8—831no—
428C22×Q8—831no—
429C22×Q8—1661no—
430C22×Q8C22×D8311yescharacteristic
431C22×Q8C22×D8311yescharacteristic
432C22×D4—831no—
433C23×C4—1661no—
434C2×Q16—24no—
435C2×Q16—834no—
436C2×Q16—1664no—
437C2×Q16C22×D8314yes—
438C2×SD16—834no—
439C2×SD16—1664no—
440C22×C8—831no—
441C22×C8—831no—
442C22×C8C22×D8311yescharacteristic
443C22×C8C22×D8311yescharacteristic
444C4⋊Q8—834no—
445C4⋊Q8—834no—
446C4⋊Q8—1662no—
447C4⋊Q8—1662no—
448C4⋊Q8—1668no—
449#126—1668no—
450#126—1668no—
451#125—834no—
452#125—834no—
453#125—1668no—
454#125—1662no—
455#125—1668no—
456#125—1662no—
457#124—834no—
458#124—834no—
459#124—1662no—
460#124—1662no—
461C22⋊Q8—1668no—
462C4×Q8—22no—
463C4×Q8—22no—
464C4×Q8—834no—
465C4×Q8—834no—
466C4×Q8—834no—
467C4×Q8—834no—
468C4×Q8—834no—
469C4×Q8—1668no—
470C4×Q8—1662no—
471C4×Q8—1662no—
472C4×Q8—1662no—
473C4×Q8C22×D8314yes—
474C4×Q8C22×D8314yes—
475C4×D4—834no—
476C4×D4—1662no—
477#117—1668no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—831no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4—831no—
483C2×C4⋊C4—831no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—1661no—
486C2×C4⋊C4—1661no—
487C2×C4⋊C4—1661no—
488C2×C4⋊C4—1661no—
489C2×C4⋊C4—1661no—
490C2×C4⋊C4—1661no—
491C2×C4⋊C4—1661no—
492C2×C4⋊C4—1661no—
493C2×C4⋊C4—1661no—
494C2×C4⋊C4—1661no—
495C2×C4⋊C4C22×D8311yescharacteristic
496C2×C4⋊C4C22×D8311yescharacteristic
497C2×C22⋊C4—1661no—
498C2×C22⋊C4—1661no—
499C2×C22⋊C4—1661no—
500C2×C22⋊C4—1661no—
501C2×C22⋊C4—1661no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—831no—
505C2×C42—831no—
506C2×C42—1661no—
507C2×C42—1661no—
508C2×C42—1661no—
509C2×C42C22×D8311yescharacteristic
510#107—834no—
511#107C22×D8314yes—
512#106—834no—
513C4⋊C8—834no—
514C4⋊C8—834no—
515C4⋊C8—834no—
516#103—834no—
517#103—834no—
518#103—834no—
519#103—834no—
520#103—834no—
521#103C22×D8314yes—
522#103C22×D8314yes—
523#102—834no—
524#102—834no—
525#102—834no—
526C4×C8—834no—
527C4×C8—834no—
528C4×C8C22×D8314yes—
529C24—1661no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—3324no—
536C2×Q8—834no—
537C2×Q8—832no—
538C2×Q8—1664no—
539C2×Q8—1664no—
540C2×Q8—1662no—
541C2×Q8—1662no—
542C2×Q8—1661no—
543C2×Q8#1305059014yes—
544C2×Q8C23×D8312yes—
545C2×Q8C23×D8312yes—
546C2×D4—832no—
547C2×D4—1661no—
548C2×D4—1662no—
549C2×D4—1662no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—3324no—
555C22×C4—831no—
556C22×C4—831no—
557C22×C4—831no—
558C22×C4—831no—
559C22×C4—1664no—
560C22×C4—1661no—
561C22×C4—1661no—
562C22×C4—1661no—
563C22×C4D4×D8311yescharacteristic
564C22×C4D4×D8311yescharacteristic
565C22×C4C23×D8311yescharacteristic
566Q16—28no—
567Q16—1668no—
568SD16—1668no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—832no—
572C2×C8—832no—
573C2×C8—1662no—
574C2×C8—1662no—
575C2×C8C23×D8312yes—
576C2×C8C23×D8312yes—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—834no—
582C4⋊C4—834no—
583C4⋊C4—834no—
584C4⋊C4—832no—
585C4⋊C4—832no—
586C4⋊C4—1664no—
587C4⋊C4—1664no—
588C4⋊C4—1664no—
589C4⋊C4—1664no—
590C4⋊C4—1664no—
591C4⋊C4—1664no—
592C4⋊C4—1664no—
593C4⋊C4—1664no—
594C4⋊C4—1661no—
595C4⋊C4—1661no—
596C4⋊C4—1664no—
597C4⋊C4—1664no—
598C4⋊C4C23×D8312yes—
599C4⋊C4C23×D8312yes—
600C22⋊C4—1664no—
601C22⋊C4—1664no—
602C22⋊C4—1664no—
603C22⋊C4—1664no—
604C22⋊C4—1664no—
605C42—24no—
606C42—24no—
607C42—832no—
608C42—832no—
609C42—832no—
610C42—832no—
611C42—1664no—
612C42—1664no—
613C42—1664no—
614C42D4×D8312yes—
615C42C23×D8312yes—
616C23—3322no—
617C23—3322no—
618C23—3322no—
619C23—1662no—
620C23C2×D4×D8311yescharacteristic
621Q8—24no—
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—42no—
626Q8—3328no—
627Q8—3322no—
628Q8—1668no—
629Q8—1662no—
630Q8—1662no—
631Q8C2×#1305059014yes—
632D4—3322no—
633D4—1662no—
634D4—1662no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—3328no—
646C2×C4—3322no—
647C2×C4—3322no—
648C2×C4—3322no—
649C2×C4—834no—
650C2×C4—832no—
651C2×C4—832no—
652C2×C4—832no—
653C2×C4—832no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4—1662no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4C2×D4×D8312yes—
661C2×C4C2×D4×D8312yes—
662C2×C4C2×D4×D8311yescharacteristic
663C2×C4C2×#1305059012yes—
664C2×C4#1458183912yes—
665C2×C4C24×D8311yescharacteristic
666C8—22no—
667C8—22no—
668C8—1662no—
669C8—1662no—
670C22—3322no—
671C22—3322no—
672C22—3322no—
673C22—6644no—
674C22#1912836012yes—
675C22#135×D8312yes—
676C22#1912851412yes—
677C22C22×D4×D8311yescharacteristic
678C4—22no—
679C4—24no—
680C4—22no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—3322no—
685C4—3322no—
686C4—3322no—
687C4—834no—
688C4—1662no—
689C4—1662no—
690C4—1662no—
691C4#1912836012yes—
692C4C22×#1305059011yescharacteristic
693C4C2×#1458183911yescharacteristic
694C2—6642no—
695C2#2492014914yesdirect product factor
696C2C2×#1912836011yescharacteristic
697C2C2×#135×D8311yescharacteristic
698C2C2×#1912851411yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×C4×Q16×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenterC2×C4×Q16D83
hypocenterC83C2×#3364
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#19128427C2semidirect
3. #24920149C2direct (N × H)
6. C2×#19128050C2semidirect
7. C2×#19128008C2semidirect
8. C2×#19128007C2semidirect
12. C2×#19127909C2semidirect
13. C2×C8×Dic166C2semidirect
14. C2×#19127793C2semidirect
16. C2×C4×Q16×C83C2semidirect
20. #19128427C22semidirect
44. #19128050C22semidirect
45. #19128008C22semidirect
46. #19128007C22semidirect
50. #19127909C22semidirect
51. C8×Dic166C22semidirect
52. #19127793C22semidirect
72. C4×Q16×C83C22semidirect
345. C2×C83#3364semidirect
364. C2×C4×Q16D83semidirect
366. C83C2×#3364semidirect
406. C4×Q16C2×D83semidirect
695. C2#24920149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284272
C2×#191284232
#249201492
C2×#191280572
C2×#191280562
C2×#191280502
C2×#191280082
C2×#191280072
C2×#191279802
C2×#191279252
C2×#191279232
C2×#191279092
C2×C8×Dic1662
C2×#191277932
C2×#191277862
C2×C4×Q16×C832
C2×#336483