Finite Group Databasebeta

← C2×#24919888 #36282902

Subgroups — C2×#24919888 #36282902

Order 21248.

1854 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128422C211yesmaximal, characteristic
2C2×#19128419C211yesmaximal, characteristic
3#24919888C2116yesmaximal, direct product factor
4C2×#19128105C211yesmaximal, characteristic, complemented
5C2×#19128044C211yesmaximal, characteristic, complemented
6C2×#19128043C211yesmaximal, characteristic, complemented
7C2×#19128041C211yesmaximal, characteristic, complemented
8C2×#19127985C211yesmaximal, characteristic, complemented
9C2×#19127984C211yesmaximal, characteristic, complemented
10C2×#19127941C211yesmaximal, characteristic, complemented
11C2×#19127940C211yesmaximal, characteristic, complemented
12C2×#19127793C211yesmaximal, characteristic, complemented
13C2×(C22⋊D83)⋊C8C211yesmaximal, characteristic
14C2×#19127737C211yesmaximal, characteristic, complemented
15C2×#19127736C211yesmaximal, characteristic, complemented
16C2×#485×C83C211yesmaximal, characteristic, complemented
17C22×#13050580C2211yescharacteristic
18C23×C83⋊C8C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20#19128422—24no—
21#19128422C2218yes—
22#19128419—24no—
23#19128419C2218yes—
24C2×#14581791C2211yescharacteristic
25C2×#14581791C2211yescharacteristic
26C2×#14581787—21no—
27C2×#14581786—21no—
28C2×#14581785—21no—
29C2×#14581785—21no—
30C2×#14581778—21no—
31C2×#14581778—21no—
32C2×#14581772C2211yescharacteristic
33C2×#14581771C2211yescharacteristic
34C2×#14581768C2211yescharacteristic
35C2×Q8×Dic83C2211yescharacteristic
36C2×C4×Dic166—21no—
37C2×#14581757—21no—
38C2×#14581757C2211yescharacteristic
39C2×C4×C22⋊D83C2211yescharacteristic
40C2×#14581751C2211yescharacteristic
41C2×#14581750C2211yescharacteristic
42C2×#14581750C2211yescharacteristic
43#19128105C2218yescomplemented
44#19128044C2218yescomplemented
45#19128043C2218yescomplemented
46#19128041C2218yescomplemented
47#19127985C2218yescomplemented
48#19127984C2218yescomplemented
49#19127941C2218yescomplemented
50#19127940C2218yescomplemented
51#19127793C2218yescomplemented
52(C22⋊D83)⋊C8C2218yes—
53#19127737C2218yescomplemented
54#19127736C2218yescomplemented
55C2×#14581726C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581725C2211yescharacteristic
58C2×#14581725C2211yescharacteristic
59C2×#14581724C2211yescharacteristic
60C2×#14581723C2211yescharacteristic
61C2×#14581723C2211yescharacteristic
62C2×Dic83⋊C8C2211yescharacteristic
63C2×#14581717C2211yescharacteristic
64C2×#14581717C2211yescharacteristic
65C2×#14581716C2211yescharacteristic
66C2×#14581715C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C2×C22⋊Q8×C83C2211yescharacteristic
70C2×#117×C83C2211yescharacteristic
71#485×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic
73C2×#106×C83C2211yescharacteristic
74C2×#103×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×C22⋊C8×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×Dic166C2311yescharacteristic
80C22×C22⋊D83D411yescharacteristic
81C22×C4×D83C2311yescharacteristic
82C2×#13050580—24no—
83C2×#13050580C2314yes—
84C22×C83⋊C8—24no—
85C22×C83⋊C8C2311yescharacteristic
86C22×C83⋊C8C2314yes—
87C22×C83⋊C8C2311yescharacteristic
88C2×C8×D83—24no—
89C2×C8×D83C2314yes—
90#14581791—22no—
91#14581791—22no—
92#14581791C2314yes—
93#14581791C2314yes—
94#14581787—28no—
95#14581786—28no—
96#14581785—28no—
97#14581785—28no—
98#14581778—28no—
99#14581778—28no—
100#14581772—22no—
101#14581772C2314yes—
102#14581771—22no—
103#14581771C2314yes—
104#14581768—22no—
105#14581768C2314yes—
106Q8×Dic83—22no—
107Q8×Dic83C2314yes—
108C4×Dic166—28no—
109#14581757—28no—
110#14581757—22no—
111#14581757C2314yes—
112C4×C22⋊D83D414yes—
113C4×C22⋊D83C2314yes—
114#14581751—22no—
115#14581751C2314yes—
116#14581750—22no—
117#14581750—22no—
118#14581750C2314yes—
119#14581750C2314yes—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83—21no—
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×Dic83⋊C4D411yescharacteristic
131C2×C22⋊Dic83—21no—
132C2×C22⋊Dic83—21no—
133C2×C22⋊Dic83D411yescharacteristic
134C2×(C2×D83)⋊C4—21no—
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4D411yescharacteristic
139C2×C4×Dic83—21no—
140C2×C4×Dic83—21no—
141C2×C4×Dic83—21no—
142C2×C4×Dic83—21no—
143C2×C4×Dic83—21no—
144C2×C4×Dic83C2311yescharacteristic
145#14581726C2314yes—
146#14581725C2314yes—
147#14581725C2314yes—
148#14581725C2314yes—
149#14581724C2314yes—
150#14581723C2314yes—
151#14581723C2314yes—
152Dic83⋊C8C2314yes—
153#14581717C2314yes—
154#14581717C2314yes—
155#14581716C2314yes—
156#14581715C2314yes—
157(C2×D83)⋊C8C2314yes—
158C8×Dic83C2314yes—
159C22×Q8×C83C2311yescharacteristic
160C23×C4×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163C22⋊Q8×C83—22no—
164C22⋊Q8×C83C2314yes—
165#117×C83—22no—
166#117×C83C2314yes—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C22⋊C4×C83—21no—
172C2×C22⋊C4×C83—21no—
173C2×C42×C83—21no—
174#107×C83C2314yes—
175#106×C83C2314yes—
176#103×C83C2314yes—
177#103×C83C2314yes—
178C22⋊C8×C83C2314yes—
179C23×D83C2×D411yescharacteristic
180C2×Dic166—22no—
181C2×Dic166—22no—
182C2×Dic166—21no—
183C2×Dic166—24no—
184C2×Dic166—24no—
185C2×Dic166—44no—
186C2×Dic166—44no—
187C2×Dic166C2412yes—
188C2×C22⋊D83—24no—
189C2×C22⋊D83C2×D414yes—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83C2×D411yescharacteristic
195C22×Dic83C2×D411yescharacteristic
196C22×Dic83C2×D411yescharacteristic
197C2×C4×D83—22no—
198C2×C4×D83—22no—
199C2×C4×D83C2×D412yes—
200C2×C4×D83C2412yes—
201#13050580—28no—
202C2×C83⋊C8—22no—
203C2×C83⋊C8—28no—
204C2×C83⋊C8#4114yes—
205C2×C83⋊C8C2412yes—
206C2×C83⋊C8C2412yes—
207C8×D83—28no—
208C4⋊Dic83—21no—
209C4⋊Dic83—21no—
210C4⋊Dic83—21no—
211C4⋊Dic83—24no—
212C4⋊Dic83—24no—
213C4⋊Dic83C2412yes—
214C4⋊Dic83C2412yes—
215C4⋊Dic83C2412yes—
216Dic83⋊C4—24no—
217Dic83⋊C4—24no—
218Dic83⋊C4—24no—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221Dic83⋊C4C2×D414yes—
222C22⋊Dic83—24no—
223C22⋊Dic83—24no—
224C22⋊Dic83C2×D414yes—
225(C2×D83)⋊C4—24no—
226(C2×D83)⋊C4—24no—
227(C2×D83)⋊C4—24no—
228(C2×D83)⋊C4—24no—
229(C2×D83)⋊C4C2×D414yes—
230C4×Dic83—24no—
231C4×Dic83—24no—
232C4×Dic83—24no—
233C4×Dic83—24no—
234C4×Dic83—24no—
235C4×Dic83C2×D412yes—
236C4×Dic83C2412yes—
237C24×C83C2×D411yescharacteristic
238C2×Q8×C83—21no—
239C2×Q8×C83—22no—
240C2×Q8×C83—22no—
241C2×Q8×C83C2412yes—
242C22×C4×C83—22no—
243C22×C4×C83—22no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
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—21no—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83C2412yes—
261C4⋊C4×C83C2412yes—
262C4⋊C4×C83C2412yes—
263C22⋊C4×C83—24no—
264C22⋊C4×C83—24no—
265C42×C83—24no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83C22×D412yes—
270C23×C83C22×D411yescharacteristic
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83C22×D412yes—
275Q8×C83—22no—
276Q8×C83—22no—
277Q8×C83—42no—
278C2×C4×C83—22no—
279C2×C4×C83—24no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—42no—
287C2×C4×C83—42no—
288C2×C4×C83—42no—
289C2×C4×C83—42no—
290C2×C4×C83C22×D412yes—
291C2×C4×C83C22×D411yescharacteristic
292C2×C4×C83C2×#4112yes—
293C2×C4×C832−1+412yes—
294C2×C4×C83C2511yescharacteristic
295C22⋊D83—28no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—42no—
303C2×Dic83—42no—
304C2×Dic83—42no—
305C2×Dic83—42no—
306C2×Dic83#13514yes—
307C2×Dic83C22×D412yes—
308C2×Dic83C22×D412yes—
309C2×Dic83C22×D412yes—
310C4×D83—24no—
311C4×D83—22no—
312C4×D83—22no—
313Dic166—22no—
314Dic166—22no—
315Dic166—42no—
316Dic166—48no—
317Dic166—48no—
318C8×C83—22no—
319C8×C83—22no—
320C83⋊C8—22no—
321C83⋊C8C2×#4114yes—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—22no—
325C22×C83—44no—
326C22×C83#54712yes—
327C22×C83C2×#13512yes—
328C22×C83#57812yes—
329C22×C83C23×D411yescharacteristic
330C2×D83—22no—
331C2×D83—22no—
332C2×D83—22no—
333C2×D83—44no—
334C4×C83—22no—
335C4×C83—42no—
336C4×C83—42no—
337C4×C83—42no—
338C4×C83—42no—
339C4×C83#54712yes—
340C4×C83C22×#4111yescharacteristic
341C4×C83C2×2−1+411yescharacteristic
342Dic83—22no—
343Dic83—22no—
344Dic83—42no—
345Dic83—42no—
346Dic83—42no—
347Dic83—42no—
348Dic83C2×#13514yes—
349C2×#3342—831nomaximal, Sylow
350C2×C83—42no—
351C2×C83#334214yescomplemented
352C2×C83C2×#54711yescharacteristic
353C2×C83C22×#13511yescharacteristic
354C2×C83C2×#57811yescharacteristic
355D83—42no—
356C2×#556—831no—
357C2×#556—831no—
358#3342—8316no—
359C2×#500—831no—
360C2×#485—831no—
361C2×#485—831no—
362C2×#485—831no—
363C2×#485D8311yescharacteristic, complemented
364C2×#475—831no—
365C2×#475—831no—
366C2×#467—831no—
367C2×#467—831no—
368C2×C4×Q16—831no—
369C2×C8×D4—831no—
370C2×#427—831no—
371C2×#427—831no—
372C83C2×#334211yescharacteristic, complemented, Sylow
373C22×Q16—831no—
374C23×C8—831no—
375C23×C8—831no—
376#556—838no—
377#556—838no—
378#556—1664no—
379#556—1664no—
380C2×C4⋊Q8—831no—
381C2×C4⋊Q8—831no—
382C2×#126—1661no—
383C2×#126—1661no—
384C2×#126—1661no—
385C2×#126—1661no—
386C2×#124—1661no—
387C2×#124—1661no—
388C2×C22⋊Q8—831no—
389C2×C22⋊Q8—831no—
390C2×C22⋊Q8—831no—
391C2×C22⋊Q8C2×D8311yescharacteristic
392C2×C4×Q8—831no—
393C2×C4×Q8—831no—
394C2×C4×Q8—1661no—
395C2×C4×Q8—1661no—
396C2×C4×D4—831no—
397C2×#117—831no—
398C2×#117—831no—
399C2×#117—831no—
400C2×#117C2×D8311yescharacteristic
401#500—838no—
402#485—838no—
403#485—838no—
404#485—838no—
405#485C2×D8318yescomplemented
406#475—838no—
407#475—838no—
408#467—838no—
409#467—838no—
410C4×Q16—838no—
411C8×D4—838no—
412#427—838no—
413#427—838no—
414C2×#107—831no—
415C2×#107—831no—
416C2×#107—831no—
417C2×#107—831no—
418C2×#107C2×D8311yescharacteristic
419C2×#106—831no—
420C2×#106—831no—
421C2×#106—831no—
422C2×#106C2×D8311yescharacteristic
423C2×C4⋊C8—831no—
424C2×#103—831no—
425C2×#103—831no—
426C2×#103—831no—
427C2×#103—831no—
428C2×#103C2×D8311yescharacteristic
429C2×#103C2×D8311yescharacteristic
430C2×C22⋊C8—831no—
431C2×C22⋊C8C2×D8311yescharacteristic
432C2×C4×C8—831no—
433C22×Q8—831no—
434C22×Q8—1661no—
435C22×Q8—1661no—
436C22×Q8C22×D8311yescharacteristic
437C22×D4—831no—
438C23×C4—831no—
439C23×C4C22×D8311yescharacteristic
440C2×Q16—834no—
441C2×Q16—1664no—
442C22×C8—831no—
443C22×C8—831no—
444C22×C8—834no—
445C22×C8—834no—
446C22×C8—1664no—
447C22×C8—1664no—
448C22×C8C22×D8311yescharacteristic
449C22×C8C22×D8311yescharacteristic
450C4⋊Q8—834no—
451C4⋊Q8—834no—
452C4⋊Q8—1662no—
453C4⋊Q8—1662no—
454#126—1668no—
455#126—1668no—
456#126—1668no—
457#126—1668no—
458#124—1668no—
459#124—1668no—
460C22⋊Q8—22no—
461C22⋊Q8—834no—
462C22⋊Q8—834no—
463C22⋊Q8—834no—
464C22⋊Q8—1662no—
465C22⋊Q8—1662no—
466C22⋊Q8—1662no—
467C22⋊Q8C22×D8314yes—
468C4×Q8—834no—
469C4×Q8—834no—
470C4×Q8—1668no—
471C4×Q8—1662no—
472C4×Q8—1662no—
473C4×Q8—1668no—
474C4×D4—834no—
475C4×D4—834no—
476#117—22no—
477#117—834no—
478#117—834no—
479#117—834no—
480#117—1662no—
481#117—1662no—
482#117—1662no—
483#117C22×D8314yes—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—831no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—831no—
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⋊C4—1661no—
496C2×C4⋊C4C22×D8311yescharacteristic
497C2×C4⋊C4C22×D8311yescharacteristic
498C2×C4⋊C4C22×D8311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—831no—
502C2×C22⋊C4—831no—
503C2×C22⋊C4—1661no—
504C2×C22⋊C4—1661no—
505C2×C22⋊C4—1661no—
506C2×C22⋊C4—1661no—
507C2×C22⋊C4—1661no—
508C2×C22⋊C4—1661no—
509C2×C42—21no—
510C2×C42—831no—
511C2×C42—1661no—
512C2×C42—1661no—
513C2×C42—1661no—
514C2×C42—1661no—
515C2×C42—1661no—
516#107—834no—
517#107—834no—
518#107—834no—
519#107—834no—
520#107C22×D8314yes—
521#106—834no—
522#106—834no—
523#106—834no—
524#106C22×D8314yes—
525C4⋊C8—834no—
526#103—834no—
527#103—834no—
528#103—834no—
529#103—834no—
530#103C22×D8314yes—
531#103C22×D8314yes—
532C22⋊C8—834no—
533C22⋊C8C22×D8314yes—
534C4×C8—834no—
535C24—831no—
536C24D4×D8311yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—3324no—
541C2×Q8—3324no—
542C2×Q8—832no—
543C2×Q8—1664no—
544C2×Q8—1664no—
545C2×Q8—1662no—
546C2×Q8—1662no—
547C2×Q8—1661no—
548C2×Q8C23×D8312yes—
549C2×D4—834no—
550C2×D4—1664no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—831no—
558C22×C4—831no—
559C22×C4—831no—
560C22×C4—832no—
561C22×C4—832no—
562C22×C4—1661no—
563C22×C4—1661no—
564C22×C4—1661no—
565C22×C4—1661no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4D4×D8312yes—
569C22×C4D4×D8311yescharacteristic
570C22×C4C23×D8312yes—
571C22×C4C23×D8311yescharacteristic
572Q16—1668no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—834no—
576C2×C8—832no—
577C2×C8—832no—
578C2×C8—1668no—
579C2×C8—1668no—
580C2×C8—1662no—
581C2×C8C23×D8312yes—
582C2×C8C23×D8312yes—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—834no—
588C4⋊C4—832no—
589C4⋊C4—832no—
590C4⋊C4—832no—
591C4⋊C4—1664no—
592C4⋊C4—1664no—
593C4⋊C4—1664no—
594C4⋊C4—1664no—
595C4⋊C4—1664no—
596C4⋊C4—1664no—
597C4⋊C4—1661no—
598C4⋊C4—1661no—
599C4⋊C4—1661no—
600C4⋊C4—1664no—
601C4⋊C4C23×D8312yes—
602C4⋊C4C23×D8312yes—
603C4⋊C4C23×D8312yes—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—834no—
607C22⋊C4—834no—
608C22⋊C4—1664no—
609C22⋊C4—1664no—
610C22⋊C4—1664no—
611C22⋊C4—1664no—
612C22⋊C4—1664no—
613C22⋊C4—1664no—
614C42—24no—
615C42—832no—
616C42—832no—
617C42—1664no—
618C42—1664no—
619C42—1664no—
620C42—1664no—
621C42—1664no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—832no—
626C23—1662no—
627C23—1662no—
628C23—1662no—
629C23C2×D4×D8312yes—
630C23C2×D4×D8311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—3328no—
635Q8—3328no—
636Q8—3322no—
637Q8—1662no—
638Q8—1662no—
639D4—1668no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—3322no—
653C2×C4—3322no—
654C2×C4—3322no—
655C2×C4—3322no—
656C2×C4—834no—
657C2×C4—832no—
658C2×C4—832no—
659C2×C4—832no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1664no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4C2×D4×D8312yes—
670C2×C4C2×D4×D8311yescharacteristic
671C2×C4#41×D8312yes—
672C2×C4#1458183912yes—
673C2×C4C24×D8311yescharacteristic
674C8—22no—
675C8—22no—
676C8—834no—
677C8—1662no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—3324no—
683C22—1662no—
684C22—1662no—
685C22—1662no—
686C22#1912834912yes—
687C22#135×D8312yes—
688C22#1912851712yes—
689C22C22×D4×D8311yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—3322no—
696C4—3322no—
697C4—3322no—
698C4—3322no—
699C4—834no—
700C4—1662no—
701C4—1662no—
702C4#1912834912yes—
703C4C2×#41×D8311yescharacteristic
704C4C2×#1458183911yescharacteristic
705C2—42no—
706C2—3322no—
707C2#2491988814yesdirect product factor
708C2C2×#1912834911yescharacteristic
709C2C2×#135×D8311yescharacteristic
710C2C2×#1912851711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#485×C83C2
socleC23×C83C22×D4
prime radicalC22×C22⋊D83D4
hypercenterC2×#485D83
hypocenterC83C2×#3342
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #24919888C2direct (N × H)
4. C2×#19128105C2semidirect
5. C2×#19128044C2semidirect
6. C2×#19128043C2semidirect
7. C2×#19128041C2semidirect
8. C2×#19127985C2semidirect
9. C2×#19127984C2semidirect
10. C2×#19127941C2semidirect
11. C2×#19127940C2semidirect
12. C2×#19127793C2semidirect
14. C2×#19127737C2semidirect
15. C2×#19127736C2semidirect
16. C2×#485×C83C2semidirect
43. #19128105C22semidirect
44. #19128044C22semidirect
45. #19128043C22semidirect
46. #19128041C22semidirect
47. #19127985C22semidirect
48. #19127984C22semidirect
49. #19127941C22semidirect
50. #19127940C22semidirect
51. #19127793C22semidirect
53. #19127737C22semidirect
54. #19127736C22semidirect
71. #485×C83C22semidirect
351. C2×C83#3342semidirect
363. C2×#485D83semidirect
372. C83C2×#3342semidirect
405. #485C2×D83semidirect
707. C2#24919888direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284222
C2×#191284192
#249198882
C2×#191281052
C2×#191280442
C2×#191280432
C2×#191280412
C2×#191279852
C2×#191279842
C2×#191279412
C2×#191279402
C2×#191277932
C2×(C22⋊D83)⋊C82
C2×#191277372
C2×#191277362
C2×#485×C832
C2×#334283