Finite Group Databasebeta

← C2×#24918626 #36276429

Subgroups — C2×#24918626 #36276429

Order 21248.

1822 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128230C211yesmaximal, characteristic
2C2×#125×D83C211yesmaximal, characteristic, complemented
3#24918626C2116yesmaximal, direct product factor
4C2×#19128103C211yesmaximal, characteristic, complemented
5C2×#19128100C211yesmaximal, characteristic, complemented
6C2×#19128055C211yesmaximal, characteristic, complemented
7C2×#19128035C211yesmaximal, characteristic, complemented
8C2×#19128018C211yesmaximal, characteristic
9C2×#19128030C211yesmaximal, characteristic, complemented
10C2×#19128013C211yesmaximal, characteristic
11C2×#19128010C211yesmaximal, characteristic, complemented
12C2×#19128006C211yesmaximal, characteristic, complemented
13C2×#19128003C211yesmaximal, characteristic, complemented
14C2×#19127999C211yesmaximal, characteristic, complemented
15C2×#19127752C211yesmaximal, characteristic, complemented
16C2×#488×C83C211yesmaximal, characteristic, complemented
17#19128230—24no—
18#19128230C2218yes—
19C2×#14581785—21no—
20C2×#14581784C2211yescharacteristic
21C2×#14581784C2211yescharacteristic
22C2×#14581783C2211yescharacteristic
23C2×#14581783C2211yescharacteristic
24C2×#14581782—21no—
25C2×#14581782—21no—
26#125×D83—24no—
27#125×D83C2218yescomplemented
28C2×#14581774—21no—
29C2×#14581768C2211yescharacteristic
30C2×#14581763C2211yescharacteristic
31C2×Q8×Dic83C2211yescharacteristic
32C2×D4×Dic83C2211yescharacteristic
33C2×(C22⋊D83)⋊C4—21no—
34C2×#14581748—21no—
35C2×C4⋊C4×D83—21no—
36C2×C4⋊C4×D83—21no—
37C2×C4⋊C4×D83C2211yescharacteristic
38C2×C4⋊C4×D83C2211yescharacteristic
39C2×C42×D83C2211yescharacteristic
40#19128103C2218yescomplemented
41#19128100C2218yescomplemented
42#19128055C2218yescomplemented
43#19128035C2218yescomplemented
44#19128030C2218yescomplemented
45#19128018C2218yes—
46#19128013C2218yes—
47#19128010C2218yescomplemented
48#19128006C2218yescomplemented
49#19128003C2218yescomplemented
50#19127999C2218yescomplemented
51#19127752C2218yescomplemented
52C2×#14581726C2211yescharacteristic
53C2×#14581726C2211yescharacteristic
54C2×#14581725C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581724C2211yescharacteristic
57C2×#14581724C2211yescharacteristic
58C2×#14581723C2211yescharacteristic
59C2×#14581723C2211yescharacteristic
60C2×Dic83⋊C8C2211yescharacteristic
61C2×Dic83⋊C8C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581716C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65C2×#14581713C2211yescharacteristic
66C2×(C2×D83)⋊C8C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C4×C83⋊C8C2211yescharacteristic
69C2×#125×C83C2211yescharacteristic
70C2×#124×C83C2211yescharacteristic
71#488×C83C2218yescomplemented
72C2×#103×C83C2211yescharacteristic
73C2×#103×C83C2211yescharacteristic
74C2×#102×C83C2211yescharacteristic
75C2×#102×C83C2211yescharacteristic
76C2×C4×C8×C83C2211yescharacteristic
77C22×C22⋊D83—21no—
78C23×Dic83—21no—
79C22×C4×D83—21no—
80C22×C4×D83—21no—
81C22×C4×D83D411yescharacteristic
82C22×C4×D83D411yescharacteristic
83C22×C4×D83C2311yescharacteristic
84C22×C83⋊C8C2311yescharacteristic
85C22×C83⋊C8C2311yescharacteristic
86#14581785—28no—
87#14581784—22no—
88#14581784—22no—
89#14581784C2314yes—
90#14581784C2314yes—
91#14581783—22no—
92#14581783—22no—
93#14581783C2314yes—
94#14581783C2314yes—
95#14581782—28no—
96#14581782—28no—
97#14581774—28no—
98#14581768—22no—
99#14581768C2314yes—
100#14581763—22no—
101#14581763C2314yes—
102Q8×Dic83—22no—
103Q8×Dic83C2314yes—
104D4×Dic83—22no—
105D4×Dic83C2314yes—
106(C22⋊D83)⋊C4—28no—
107#14581748—28no—
108C2×C4⋊Dic83—21no—
109C2×C4⋊Dic83—21no—
110C2×C4⋊Dic83—21no—
111C2×C4⋊Dic83C2311yescharacteristic
112C2×C4⋊Dic83C2311yescharacteristic
113C2×C4⋊Dic83C2311yescharacteristic
114C2×C4⋊Dic83C2311yescharacteristic
115C2×Dic83⋊C4—21no—
116C2×Dic83⋊C4—21no—
117C2×Dic83⋊C4—21no—
118C2×Dic83⋊C4—21no—
119C2×Dic83⋊C4—21no—
120C2×Dic83⋊C4—21no—
121C2×Dic83⋊C4—21no—
122C2×Dic83⋊C4—21no—
123C2×Dic83⋊C4—21no—
124C4⋊C4×D83—28no—
125C4⋊C4×D83—28no—
126C4⋊C4×D83—22no—
127C4⋊C4×D83—22no—
128C4⋊C4×D83C2314yes—
129C4⋊C4×D83C2314yes—
130C2×C22⋊Dic83—21no—
131C2×C22⋊Dic83—21no—
132C2×(C2×D83)⋊C4—21no—
133C2×C4×Dic83—21no—
134C2×C4×Dic83D411yescharacteristic
135C2×C4×Dic83D411yescharacteristic
136C2×C4×Dic83C2311yescharacteristic
137C42×D83D414yes—
138C42×D83C2314yes—
139#14581726C2314yes—
140#14581726C2314yes—
141#14581725C2314yes—
142#14581725C2314yes—
143#14581724C2314yes—
144#14581724C2314yes—
145#14581723C2314yes—
146#14581723C2314yes—
147Dic83⋊C8C2314yes—
148Dic83⋊C8C2314yes—
149#14581716C2314yes—
150#14581716C2314yes—
151#14581713C2314yes—
152#14581713C2314yes—
153(C2×D83)⋊C8C2314yes—
154(C2×D83)⋊C8C2314yes—
155C4×C83⋊C8C2314yes—
156C22×Q8×C83C2311yescharacteristic
157C22×D4×C83C2311yescharacteristic
158C22×C8×C83C2311yescharacteristic
159C22×C8×C83C2311yescharacteristic
160#125×C83—22no—
161#125×C83C2314yes—
162#124×C83—22no—
163#124×C83C2314yes—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83C2311yescharacteristic
167C2×C4⋊C4×C83C2311yescharacteristic
168C2×C22⋊C4×C83—21no—
169C2×C22⋊C4×C83—21no—
170C2×C42×C83C2311yescharacteristic
171#103×C83C2314yes—
172#103×C83C2314yes—
173#102×C83C2314yes—
174#102×C83C2314yes—
175C4×C8×C83C2314yes—
176C23×D83C2×D411yescharacteristic
177C2×C22⋊D83—24no—
178C2×C22⋊D83—44no—
179C22×Dic83—21no—
180C22×Dic83—21no—
181C22×Dic83—21no—
182C22×Dic83—21no—
183C22×Dic83—24no—
184C22×Dic83—44no—
185C22×Dic83C2×D411yescharacteristic
186C22×Dic83C2×D411yescharacteristic
187C22×Dic83C2×D411yescharacteristic
188C2×C4×D83—24no—
189C2×C4×D83—22no—
190C2×C4×D83—22no—
191C2×C4×D83—24no—
192C2×C4×D83—24no—
193C2×C4×D83—42no—
194C2×C4×D83—44no—
195C2×C4×D83—44no—
196C2×C4×D83C2×D412yes—
197C2×C4×D83C2×D414yes—
198C2×C4×D83C2×D414yes—
199C2×C4×D83C2412yes—
200C2×C83⋊C8—22no—
201C2×C83⋊C8—22no—
202C2×C83⋊C8C2412yes—
203C2×C83⋊C8C2412yes—
204C4⋊Dic83—21no—
205C4⋊Dic83—21no—
206C4⋊Dic83—21no—
207C4⋊Dic83—21no—
208C4⋊Dic83—24no—
209C4⋊Dic83—24no—
210C4⋊Dic83—24no—
211C4⋊Dic83C2412yes—
212C4⋊Dic83C2412yes—
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⋊C4—24no—
223Dic83⋊C4—24no—
224C22⋊Dic83—24no—
225C22⋊Dic83—24no—
226(C2×D83)⋊C4—24no—
227C4×Dic83—24no—
228C4×Dic83C2×D414yes—
229C4×Dic83C2×D414yes—
230C4×Dic83C2×D412yes—
231C4×Dic83C2412yes—
232C24×C83—21no—
233C2×Q8×C83—21no—
234C2×Q8×C83—22no—
235C2×Q8×C83—22no—
236C2×Q8×C83C2412yes—
237C2×D4×C83—21no—
238C2×D4×C83—22no—
239C2×D4×C83—22no—
240C2×D4×C83C2412yes—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2×D411yescharacteristic
246C22×C4×C83C2411yescharacteristic
247C2×C8×C83—22no—
248C2×C8×C83—22no—
249C2×C8×C83C2412yes—
250C2×C8×C83C2412yes—
251C4⋊C4×C83—24no—
252C4⋊C4×C83—24no—
253C4⋊C4×C83—21no—
254C4⋊C4×C83—21no—
255C4⋊C4×C83C2412yes—
256C4⋊C4×C83C2412yes—
257C22⋊C4×C83—24no—
258C22⋊C4×C83—24no—
259C42×C83C2×D412yes—
260C42×C83C2412yes—
261C23×C83—22no—
262C23×C83—42no—
263C23×C83—42no—
264C23×C83—42no—
265C23×C83C22×D411yescharacteristic
266C22×D83—22no—
267C22×D83—22no—
268C22×D83#13514yes—
269C22×D83C22×D412yes—
270Q8×C83—22no—
271Q8×C83—22no—
272Q8×C83—42no—
273D4×C83—22no—
274D4×C83—22no—
275D4×C83—42no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—42no—
282C2×C4×C83—42no—
283C2×C4×C83—42no—
284C2×C4×C83C22×D412yes—
285C2×C4×C83C22×D412yes—
286C2×C4×C83C22×D411yescharacteristic
287C2×C4×C832−1+412yes—
288C2×C4×C832−1+412yes—
289C2×C4×C83C2511yescharacteristic
290C22⋊D83—48no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—48no—
299C2×Dic83—42no—
300C2×Dic83—42no—
301C2×Dic83—42no—
302C2×Dic83—42no—
303C2×Dic83C22×D412yes—
304C2×Dic83C22×D412yes—
305C2×Dic83C22×D412yes—
306C4×D83—28no—
307C4×D83—24no—
308C4×D83—22no—
309C4×D83—22no—
310C4×D83—44no—
311C4×D83—48no—
312C4×D83—48no—
313C8×C83—22no—
314C8×C83—22no—
315C83⋊C8—22no—
316C83⋊C8—22no—
317C22×C83—42no—
318C22×C83—42no—
319C22×C83—42no—
320C22×C83—84no—
321C22×C83#53612yes—
322C22×C83C2×#13512yes—
323C22×C83#57512yes—
324C22×C83C23×D411yescharacteristic
325C2×D83—22no—
326C2×D83—28no—
327C2×D83—22no—
328C2×D83C2×#13514yes—
329C4×C83—22no—
330C4×C83—22no—
331C4×C83—42no—
332C4×C83—42no—
333C4×C83—42no—
334C4×C83#53612yes—
335C4×C83C2×2−1+411yescharacteristic
336C4×C83C2×2−1+411yescharacteristic
337Dic83—22no—
338Dic83—22no—
339Dic83—22no—
340Dic83—42no—
341Dic83—42no—
342Dic83—42no—
343Dic83—42no—
344C2×#3232—831nomaximal, Sylow
345C2×C83—82no—
346C2×C83#323214yescomplemented
347C2×C83C2×#53611yescharacteristic
348C2×C83C22×#13511yescharacteristic
349C2×C83C2×#57511yescharacteristic
350D83—24no—
351C2×#529—831no—
352C22×#125—831no—
353#3232—8316no—
354C2×#499—831no—
355C2×#499—831no—
356C2×#488—831no—
357C2×#488D8311yescharacteristic, complemented
358C2×#484—831no—
359C2×#481—831no—
360C2×#483—831no—
361C2×#480—831no—
362C2×#479—831no—
363C2×#479—831no—
364C2×#478—831no—
365C2×#478—831no—
366C2×#431—831no—
367C83C2×#323211yescharacteristic, complemented, Sylow
368#529—838no—
369#529—1664no—
370C2×#126—1661no—
371C2×#125—838no—
372C2×#125—831no—
373C2×#125—831no—
374C2×#125—831no—
375C2×#125—831no—
376C2×#125—1661no—
377C2×#125—1661no—
378C2×#125—1664no—
379C2×#125C2×D8311yescharacteristic
380C2×#124C2×D8311yescharacteristic
381C2×#123—1661no—
382C2×C22⋊Q8—831no—
383C2×#121—831no—
384C2×C4×Q8—831no—
385C2×C4×D4—831no—
386C2×C4×D4—1661no—
387C2×#117—1661no—
388C22×C4⋊C4—831no—
389C22×C4⋊C4—831no—
390C22×C4⋊C4—1661no—
391C22×C4⋊C4—1661no—
392C22×C42—831no—
393#499—838no—
394#499—838no—
395#488—838no—
396#488C2×D8318yescomplemented
397#484—838no—
398#483—838no—
399#481—838no—
400#480—838no—
401#479—838no—
402#479—838no—
403#478—838no—
404#478—838no—
405#431—838no—
406C2×#107—831no—
407C2×#107—831no—
408C2×#107—831no—
409C2×#107—831no—
410C2×#106—831no—
411C2×#106—831no—
412C2×#106—831no—
413C2×#106—831no—
414C2×C4⋊C8—831no—
415C2×C4⋊C8—831no—
416C2×#103—831no—
417C2×#103—831no—
418C2×#103C2×D8311yescharacteristic
419C2×#103C2×D8311yescharacteristic
420C2×#102—831no—
421C2×#102—831no—
422C2×#102C2×D8311yescharacteristic
423C2×#102C2×D8311yescharacteristic
424C2×C22⋊C8—831no—
425C2×C22⋊C8—831no—
426C2×C4×C8—831no—
427C2×C4×C8C2×D8311yescharacteristic
428C22×Q8C22×D8311yescharacteristic
429C22×D4—1661no—
430C22×D4C22×D8311yescharacteristic
431C23×C4—831no—
432C23×C4—831no—
433C23×C4—831no—
434C23×C4—1661no—
435C23×C4—1661no—
436C23×C4—1661no—
437C22×C8—831no—
438C22×C8—831no—
439C22×C8C22×D8311yescharacteristic
440C22×C8C22×D8311yescharacteristic
441#126—1668no—
442#125—22no—
443#125—834no—
444#125—834no—
445#125—834no—
446#125—834no—
447#125—1668no—
448#125—1668no—
449#125—1662no—
450#125—1662no—
451#125—1662no—
452#125—1662no—
453#125C22×D8314yes—
454#124—22no—
455#124C22×D8314yes—
456#123—1668no—
457C22⋊Q8—834no—
458C22⋊Q8—1662no—
459#121—834no—
460#121—1662no—
461C4×Q8—834no—
462C4×Q8—1662no—
463C4×D4—834no—
464C4×D4—1662no—
465C4×D4—1668no—
466#117—1668no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—831no—
470C2×C4⋊C4—831no—
471C2×C4⋊C4—831no—
472C2×C4⋊C4—831no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—1662no—
476C2×C4⋊C4—1662no—
477C2×C4⋊C4—1668no—
478C2×C4⋊C4—1668no—
479C2×C4⋊C4—1661no—
480C2×C4⋊C4—1661no—
481C2×C4⋊C4—1661no—
482C2×C4⋊C4—1661no—
483C2×C4⋊C4—1661no—
484C2×C4⋊C4—1661no—
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⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—1661no—
496C2×C22⋊C4—1661no—
497C2×C22⋊C4—1661no—
498C2×C42—831no—
499C2×C42—831no—
500C2×C42—831no—
501C2×C42—834no—
502C2×C42—834no—
503C2×C42—1661no—
504C2×C42C22×D8311yescharacteristic
505#107—834no—
506#107—834no—
507#107—834no—
508#107—834no—
509#106—834no—
510#106—834no—
511#106—834no—
512#106—834no—
513C4⋊C8—834no—
514C4⋊C8—834no—
515#103—834no—
516#103—834no—
517#103C22×D8314yes—
518#103C22×D8314yes—
519#102—834no—
520#102—834no—
521#102C22×D8314yes—
522#102C22×D8314yes—
523C22⋊C8—834no—
524C22⋊C8—834no—
525C4×C8—834no—
526C4×C8C22×D8314yes—
527C24—21no—
528C24—831no—
529C2×Q8—21no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8C23×D8312yes—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—3324no—
537C2×D4—1664no—
538C2×D4C23×D8312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—3322no—
543C22×C4—3324no—
544C22×C4—3324no—
545C22×C4—3324no—
546C22×C4—834no—
547C22×C4—831no—
548C22×C4—831no—
549C22×C4—831no—
550C22×C4—832no—
551C22×C4—834no—
552C22×C4—832no—
553C22×C4—1664no—
554C22×C4—1664no—
555C22×C4—1664no—
556C22×C4—1664no—
557C22×C4—1661no—
558C22×C4—1661no—
559C22×C4—1661no—
560C22×C4—1661no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4D4×D8311yescharacteristic
564C22×C4D4×D8311yescharacteristic
565C22×C4C23×D8311yescharacteristic
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—832no—
569C2×C8—832no—
570C2×C8—1662no—
571C2×C8—1662no—
572C2×C8C23×D8312yes—
573C2×C8C23×D8312yes—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—832no—
579C4⋊C4—832no—
580C4⋊C4—832no—
581C4⋊C4—832no—
582C4⋊C4—1664no—
583C4⋊C4—1664no—
584C4⋊C4—1664no—
585C4⋊C4—1664no—
586C4⋊C4—1664no—
587C4⋊C4—1664no—
588C4⋊C4—1664no—
589C4⋊C4—1664no—
590C4⋊C4—1661no—
591C4⋊C4—1661no—
592C4⋊C4—1661no—
593C4⋊C4—1661no—
594C4⋊C4—1664no—
595C4⋊C4—1664no—
596C4⋊C4—1664no—
597C4⋊C4—1664no—
598C4⋊C4C23×D8312yes—
599C4⋊C4C23×D8312yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—1664no—
603C22⋊C4—1664no—
604C22⋊C4—1664no—
605C42—834no—
606C42—832no—
607C42—834no—
608C42—832no—
609C42—1664no—
610C42D4×D8312yes—
611C42C23×D8312yes—
612C23—22no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—834no—
617C23—832no—
618C23—1662no—
619C23—1662no—
620C23C2×D4×D8311yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624D4—22no—
625D4—22no—
626D4—42no—
627D4—3328no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—3324no—
637C2×C4—3328no—
638C2×C4—3328no—
639C2×C4—3322no—
640C2×C4—3322no—
641C2×C4—3322no—
642C2×C4—3322no—
643C2×C4—3328no—
644C2×C4—832no—
645C2×C4—832no—
646C2×C4—832no—
647C2×C4—1668no—
648C2×C4—1662no—
649C2×C4—1662no—
650C2×C4—1662no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4—1662no—
655C2×C4—1664no—
656C2×C4—1662no—
657C2×C4—1662no—
658C2×C4C2×D4×D8312yes—
659C2×C4C2×D4×D8312yes—
660C2×C4C2×D4×D8311yescharacteristic
661C2×C4#1458183912yes—
662C2×C4#1458183912yes—
663C2×C4C24×D8311yescharacteristic
664C8—22no—
665C8—22no—
666C8—1662no—
667C8—1662no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—84no—
672C22—834no—
673C22—1662no—
674C22—1668no—
675C22—1662no—
676C22#1912827112yes—
677C22#135×D8312yes—
678C22#1912849812yes—
679C22C22×D4×D8311yescharacteristic
680C4—22no—
681C4—22no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—3322no—
686C4—3322no—
687C4—3322no—
688C4—3322no—
689C4—1662no—
690C4—1662no—
691C4—1662no—
692C4#1912827112yes—
693C4C2×#1458183911yescharacteristic
694C4C2×#1458183911yescharacteristic
695C2—82no—
696C2—1664no—
697C2#2491862614yesdirect product factor
698C2C2×#1912827111yescharacteristic
699C2C2×#135×D8311yescharacteristic
700C2C2×#1912849811yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#488×C83C2
socleC23×C83C22×D4
prime radicalC2×#14581763C22
hypercenterC2×#488D83
hypocenterC83C2×#3232
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
2. C2×#125×D83C2semidirect
3. #24918626C2direct (N × H)
4. C2×#19128103C2semidirect
5. C2×#19128100C2semidirect
6. C2×#19128055C2semidirect
7. C2×#19128035C2semidirect
9. C2×#19128030C2semidirect
11. C2×#19128010C2semidirect
12. C2×#19128006C2semidirect
13. C2×#19128003C2semidirect
14. C2×#19127999C2semidirect
15. C2×#19127752C2semidirect
16. C2×#488×C83C2semidirect
27. #125×D83C22semidirect
40. #19128103C22semidirect
41. #19128100C22semidirect
42. #19128055C22semidirect
43. #19128035C22semidirect
44. #19128030C22semidirect
47. #19128010C22semidirect
48. #19128006C22semidirect
49. #19128003C22semidirect
50. #19127999C22semidirect
51. #19127752C22semidirect
71. #488×C83C22semidirect
346. C2×C83#3232semidirect
357. C2×#488D83semidirect
367. C83C2×#3232semidirect
396. #488C2×D83semidirect
697. C2#24918626direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282302
C2×#125×D832
#249186262
C2×#191281032
C2×#191281002
C2×#191280552
C2×#191280352
C2×#191280182
C2×#191280302
C2×#191280132
C2×#191280102
C2×#191280062
C2×#191280032
C2×#191279992
C2×#191277522
C2×#488×C832
C2×#323283