Finite Group Databasebeta

← C2×#24918718 #36276595

Subgroups — C2×#24918718 #36276595

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×#19128329C211yesmaximal, characteristic, complemented
2C2×#19128306C211yesmaximal, characteristic
3#24918718C2116yesmaximal, direct product factor
4C2×#19128110C211yesmaximal, characteristic, complemented
5C2×#19128103C211yesmaximal, characteristic, complemented
6C2×#19128066C211yesmaximal, characteristic, complemented
7C2×#19128048C211yesmaximal, characteristic, complemented
8C2×#19128020C211yesmaximal, characteristic, complemented
9C2×#19128026C211yesmaximal, characteristic, complemented
10C2×#19128026C211yesmaximal, characteristic, complemented
11C2×#19128015C211yesmaximal, characteristic, complemented
12C2×#19128002C211yesmaximal, characteristic, complemented
13C2×#19128002C211yesmaximal, characteristic, complemented
14C2×#19127992C211yesmaximal, characteristic, complemented
15C2×#19127982C211yesmaximal, characteristic, complemented
16C2×#433×C83C211yesmaximal, characteristic, complemented
17#19128329—24no—
18#19128329C2218yescomplemented
19#19128306—24no—
20#19128306C2218yes—
21C2×#14581792C2211yescharacteristic
22C2×#14581792C2211yescharacteristic
23C2×#14581791—21no—
24C2×#14581789C2211yescharacteristic
25C2×#14581784C2211yescharacteristic
26C2×#14581784C2211yescharacteristic
27C2×#14581784C2211yescharacteristic
28C2×#14581783—21no—
29C2×#14581777—21no—
30C2×#14581777—21no—
31C2×#14581769—21no—
32C2×#14581769—21no—
33C2×#14581766C2211yescharacteristic
34C2×#14581766C2211yescharacteristic
35C2×#14581765—21no—
36C2×#14581765—21no—
37C2×C4×D332C2211yescharacteristic
38C2×C4×D332C2211yescharacteristic
39C2×#14581751C2211yescharacteristic
40C22×C4⋊Dic83C2211yescharacteristic
41#19128110C2218yescomplemented
42#19128103C2218yescomplemented
43#19128066C2218yescomplemented
44#19128048C2218yescomplemented
45#19128026C2218yescomplemented
46#19128026C2218yescomplemented
47#19128020C2218yescomplemented
48#19128015C2218yescomplemented
49#19128002C2218yescomplemented
50#19128002C2218yescomplemented
51#19127992C2218yescomplemented
52#19127982C2218yescomplemented
53C2×#14581726C2211yescharacteristic
54C2×#14581726C2211yescharacteristic
55C2×#14581726C2211yescharacteristic
56C2×#14581726C2211yescharacteristic
57C2×#14581724C2211yescharacteristic
58C2×#14581724C2211yescharacteristic
59C2×#14581724C2211yescharacteristic
60C2×#14581724C2211yescharacteristic
61C2×#14581714C2211yescharacteristic
62C2×#14581714C2211yescharacteristic
63C2×#14581714C2211yescharacteristic
64C2×#14581714C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581714C2211yescharacteristic
68C2×#14581714C2211yescharacteristic
69C2×#117×C83C2211yescharacteristic
70#433×C83C2218yescomplemented
71C2×C4⋊C8×C83C2211yescharacteristic
72C2×C4⋊C8×C83C2211yescharacteristic
73C2×C22⋊C8×C83C2211yescharacteristic
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×#97×C83C2211yescharacteristic
76C2×C4×C8×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×D332—21no—
80C22×D332—21no—
81C22×D332C2311yescharacteristic
82C22×D332C2311yescharacteristic
83C22×C22⋊D83—21no—
84C22×C22⋊D83—21no—
85C23×Dic83—21no—
86C22×C4×D83—21no—
87C22×C4×D83—21no—
88#14581792—22no—
89#14581792—22no—
90#14581792C2314yes—
91#14581792C2314yes—
92#14581791—28no—
93#14581789—22no—
94#14581789C2314yes—
95#14581784—22no—
96#14581784—22no—
97#14581784—22no—
98#14581784C2314yes—
99#14581784C2314yes—
100#14581784C2314yes—
101#14581783—28no—
102#14581777—28no—
103#14581777—28no—
104#14581769—28no—
105#14581769—28no—
106#14581766—22no—
107#14581766—22no—
108#14581766C2314yes—
109#14581766C2314yes—
110#14581765—28no—
111#14581765—28no—
112C4×D332—22no—
113C4×D332—22no—
114C4×D332C2314yes—
115C4×D332C2314yes—
116#14581751—22no—
117#14581751C2314yes—
118C2×C4⋊Dic83—22no—
119C2×C4⋊Dic83—21no—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83C2314yes—
123C2×C4⋊Dic83C2311yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×C4⋊Dic83C2311yescharacteristic
126C2×C4⋊Dic83C2311yescharacteristic
127C2×C4⋊Dic83C2311yescharacteristic
128C2×C4⋊Dic83C2311yescharacteristic
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4—21no—
135C2×C22⋊Dic83—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×C4×Dic83—21no—
141#14581726C2314yes—
142#14581726C2314yes—
143#14581726C2314yes—
144#14581726C2314yes—
145#14581724C2314yes—
146#14581724C2314yes—
147#14581724C2314yes—
148#14581724C2314yes—
149#14581714C2314yes—
150#14581714C2314yes—
151#14581714C2314yes—
152#14581714C2314yes—
153#14581714C2314yes—
154#14581714C2314yes—
155#14581714C2314yes—
156#14581714C2314yes—
157C23×C4×C83C2311yescharacteristic
158C22×C8×C83C2311yescharacteristic
159C22×C8×C83C2311yescharacteristic
160C22×C8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162#117×C83D414yes—
163#117×C83C2314yes—
164C2×C4⋊C4×C83D411yescharacteristic
165C2×C4⋊C4×C83D411yescharacteristic
166C2×C22⋊C4×C83D411yescharacteristic
167C2×C22⋊C4×C83D411yescharacteristic
168C2×C42×C83C2311yescharacteristic
169C2×C42×C83C2311yescharacteristic
170C4⋊C8×C83C2314yes—
171C4⋊C8×C83C2314yes—
172C22⋊C8×C83C2314yes—
173C22⋊C8×C83C2314yes—
174#97×C83C2314yes—
175C4×C8×C83C2314yes—
176C23×D83—21no—
177C23×D83—21no—
178C2×Dic166—24no—
179C2×Dic166—24no—
180C2×Dic166—82no—
181C2×Dic166—82no—
182C2×D332—22no—
183C2×D332—22no—
184C2×D332—22no—
185C2×D332—22no—
186C2×D332—21no—
187C2×D332—21no—
188C2×D332—24no—
189C2×D332—24no—
190C2×D332—82no—
191C2×D332—82no—
192C2×D332C2412yes—
193C2×D332C2412yes—
194C2×C22⋊D83—24no—
195C2×C22⋊D83—24no—
196C2×C22⋊D83—82no—
197C2×C22⋊D83—82no—
198C22×Dic83—21no—
199C22×Dic83—21no—
200C22×Dic83—21no—
201C22×Dic83—21no—
202C22×Dic83—21no—
203C22×Dic83—21no—
204C22×Dic83—24no—
205C22×Dic83—82no—
206C2×C4×D83—24no—
207C2×C4×D83—24no—
208C2×C4×D83—82no—
209C2×C4×D83—82no—
210C4⋊Dic83—21no—
211C4⋊Dic83—21no—
212C4⋊Dic83—24no—
213C4⋊Dic83—24no—
214C4⋊Dic83—24no—
215C4⋊Dic83—21no—
216C4⋊Dic83—21no—
217C4⋊Dic83—21no—
218C4⋊Dic83—21no—
219C4⋊Dic83C2412yes—
220C4⋊Dic83C2412yes—
221C4⋊Dic83C2412yes—
222C4⋊Dic83C2412yes—
223C4⋊Dic83C2412yes—
224C4⋊Dic83C2412yes—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4—24no—
228Dic83⋊C4—24no—
229Dic83⋊C4—24no—
230Dic83⋊C4—24no—
231C22⋊Dic83—24no—
232(C2×D83)⋊C4—24no—
233(C2×D83)⋊C4—24no—
234(C2×D83)⋊C4—24no—
235(C2×D83)⋊C4—24no—
236C4×Dic83—24no—
237C24×C83C2×D411yescharacteristic
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83C2×D412yes—
241C22×C4×C83C2×D411yescharacteristic
242C22×C4×C83C2×D411yescharacteristic
243C22×C4×C83C2×D411yescharacteristic
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2×D411yescharacteristic
246C22×C4×C83C2412yes—
247C22×C4×C83C2411yescharacteristic
248C2×C8×C83—22no—
249C2×C8×C83—22no—
250C2×C8×C83—22no—
251C2×C8×C83—22no—
252C2×C8×C83C2412yes—
253C2×C8×C83C2412yes—
254C2×C8×C83C2412yes—
255C2×C8×C83C2412yes—
256C4⋊C4×C83C2×D414yes—
257C4⋊C4×C83C2×D414yes—
258C22⋊C4×C83C2×D414yes—
259C22⋊C4×C83C2×D414yes—
260C42×C83C2×D412yes—
261C42×C83C2×D412yes—
262C42×C83C2412yes—
263C42×C83C2412yes—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83C22×D412yes—
268C23×C83C22×D411yescharacteristic
269C22×D83—22no—
270C22×D83—22no—
271C22×D83—42no—
272C22×D83—42no—
273C22×D83—42no—
274C22×D83—42no—
275C22×D83—42no—
276C22×D83—42no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—24no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83C22×D412yes—
286C2×C4×C83C22×D412yes—
287C2×C4×C83C22×D412yes—
288C2×C4×C83C22×D412yes—
289C2×C4×C83C22×D412yes—
290C2×C4×C83C22×D411yescharacteristic
291C2×C4×C832−1+412yes—
292C2×C4×C832−1+412yes—
293C2×C4×C83C2511yescharacteristic
294C22⋊D83—84no—
295C22⋊D83—84no—
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—42no—
307C2×Dic83—42no—
308C2×Dic83—84no—
309D332—22no—
310D332—22no—
311D332—22no—
312D332—22no—
313D332—42no—
314D332—42no—
315D332—84no—
316D332—84no—
317C4×D83—84no—
318C4×D83—84no—
319Dic166—84no—
320Dic166—84no—
321C8×C83—22no—
322C8×C83—22no—
323C8×C83—22no—
324C8×C83—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—44no—
329C22×C83#53612yes—
330C22×C83#57612yes—
331C22×C83#57712yes—
332C22×C83C23×D411yescharacteristic
333C2×D83—42no—
334C2×D83—42no—
335C2×D83—42no—
336C2×D83—42no—
337C2×D83—42no—
338C2×D83—42no—
339C2×D83—84no—
340C2×D83—84no—
341C4×C83—22no—
342C4×C83—22no—
343C4×C83—22no—
344C4×C83—22no—
345C4×C83—22no—
346C4×C83#53612yes—
347C4×C83C2×2−1+411yescharacteristic
348C4×C83C2×2−1+411yescharacteristic
349Dic83—42no—
350Dic83—42no—
351Dic83—42no—
352Dic83—42no—
353Dic83—42no—
354Dic83—42no—
355C2×#3241—831nomaximal, Sylow
356C2×C83—42no—
357C2×C83#324114yescomplemented
358C2×C83C2×#53611yescharacteristic
359C2×C83C2×#57611yescharacteristic
360C2×C83C2×#57711yescharacteristic
361D83—82no—
362D83—82no—
363C2×#544—831no—
364C2×#540—831no—
365#3241—8316no—
366C2×#501—831no—
367C2×#499—831no—
368C2×#490—831no—
369C2×#486—831no—
370C2×#481—831no—
371C2×#482—831no—
372C2×#482—831no—
373C2×#480—831no—
374C2×#478—831no—
375C2×#478—831no—
376C2×#476—831no—
377C2×#474—831no—
378C2×#433D8311yescharacteristic, complemented
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—831no—
398C2×#121—1661no—
399C2×#121—1661no—
400C2×C4×D4—831no—
401C2×C4×D4—831no—
402C2×#117—831no—
403C2×#117C2×D8311yescharacteristic
404C22×C4⋊C4—831no—
405#501—838no—
406#499—838no—
407#490—838no—
408#486—838no—
409#482—838no—
410#482—838no—
411#481—838no—
412#480—838no—
413#478—838no—
414#478—838no—
415#476—838no—
416#474—838no—
417#433C2×D8318yescomplemented
418C2×#107—831no—
419C2×#107—831no—
420C2×#107—831no—
421C2×#107—831no—
422C2×#106—831no—
423C2×#106—831no—
424C2×#106—831no—
425C2×#106—831no—
426C2×C4⋊C8C2×D8311yescharacteristic
427C2×C4⋊C8C2×D8311yescharacteristic
428C2×#102—831no—
429C2×#102—831no—
430C2×#102—831no—
431C2×#102—831no—
432C2×#102—831no—
433C2×#102—831no—
434C2×#102—831no—
435C2×#102—831no—
436C2×C22⋊C8C2×D8311yescharacteristic
437C2×C22⋊C8C2×D8311yescharacteristic
438C2×#97C2×D8311yescharacteristic
439C2×C4×C8C2×D8311yescharacteristic
440C22×Q8—1661no—
441C22×Q8—1661no—
442C22×D4—831no—
443C22×D4—831no—
444C22×D4—1661no—
445C22×D4—1661no—
446C22×D4—1661no—
447C22×D4—1661no—
448C23×C4—1661no—
449C23×C4—1661no—
450C23×C4—1661no—
451C23×C4C22×D8311yescharacteristic
452C22×C8C22×D8311yescharacteristic
453C22×C8C22×D8311yescharacteristic
454C22×C8C22×D8311yescharacteristic
455C22×C8C22×D8311yescharacteristic
456C4⋊Q8—834no—
457C4⋊Q8—834no—
458C4⋊Q8—1668no—
459C4⋊Q8—1662no—
460C4⋊Q8—1662no—
461#127—834no—
462#127—1662no—
463#125—834no—
464#125—834no—
465#125—834no—
466#125—1668no—
467#125—1662no—
468#125—1662no—
469#125—1662no—
470#123—1668no—
471#123—1668no—
472C22⋊Q8—1668no—
473C22⋊Q8—1668no—
474#121—834no—
475#121—834no—
476#121—1662no—
477#121—1662no—
478#121—1668no—
479#121—1668no—
480C4×D4—834no—
481C4×D4—834no—
482C4×D4—1662no—
483C4×D4—1662no—
484#117—834no—
485#117—1662no—
486#117D33214yes—
487#117C22×D8314yes—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—831no—
490C2×C4⋊C4—834no—
491C2×C4⋊C4—831no—
492C2×C4⋊C4—831no—
493C2×C4⋊C4—831no—
494C2×C4⋊C4—831no—
495C2×C4⋊C4—1661no—
496C2×C4⋊C4—1662no—
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⋊C4—1661no—
504C2×C4⋊C4—1661no—
505C2×C4⋊C4D33211yescharacteristic
506C2×C4⋊C4D33211yescharacteristic
507C2×C22⋊C4—1661no—
508C2×C22⋊C4—1661no—
509C2×C22⋊C4—1661no—
510C2×C22⋊C4—1661no—
511C2×C22⋊C4—1661no—
512C2×C22⋊C4D33211yescharacteristic
513C2×C22⋊C4D33211yescharacteristic
514C2×C42—1661no—
515C2×C42C22×D8311yescharacteristic
516C2×C42C22×D8311yescharacteristic
517#107—834no—
518#107—834no—
519#107—834no—
520#107—834no—
521#106—834no—
522#106—834no—
523#106—834no—
524#106—834no—
525C4⋊C8C22×D8314yes—
526C4⋊C8C22×D8314yes—
527#102—834no—
528#102—834no—
529#102—834no—
530#102—834no—
531#102—834no—
532#102—834no—
533#102—834no—
534#102—834no—
535C22⋊C8C22×D8314yes—
536C22⋊C8C22×D8314yes—
537#97C22×D8314yes—
538C4×C8C22×D8314yes—
539C24—1661no—
540C24—1661no—
541C24C2×D33211yescharacteristic
542C2×Q8—6642no—
543C2×Q8—6642no—
544C2×Q8—1664no—
545C2×Q8—1664no—
546C2×D4—832no—
547C2×D4—832no—
548C2×D4—6642no—
549C2×D4—6642no—
550C2×D4—6642no—
551C2×D4—6642no—
552C2×D4—1664no—
553C2×D4—1664no—
554C2×D4—1661no—
555C2×D4—1661no—
556C2×D4—1664no—
557C2×D4—1664no—
558C2×D4—1662no—
559C2×D4—1662no—
560C2×D4—1662no—
561C2×D4—1662no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—6642no—
565C22×C4—6642no—
566C22×C4—6642no—
567C22×C4—1661no—
568C22×C4—1661no—
569C22×C4—1661no—
570C22×C4—1661no—
571C22×C4—1661no—
572C22×C4—1661no—
573C22×C4—1664no—
574C22×C4—1664no—
575C22×C4—1664no—
576C22×C4C2×D33212yes—
577C22×C4C2×D33211yescharacteristic
578C22×C4C2×D33211yescharacteristic
579C22×C4C2×D33211yescharacteristic
580C22×C4C2×D33211yescharacteristic
581C22×C4C2×D33211yescharacteristic
582C22×C4C23×D8312yes—
583C22×C4C23×D8311yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8C23×D8312yes—
589C2×C8C23×D8312yes—
590C2×C8C23×D8312yes—
591C2×C8C23×D8312yes—
592C4⋊C4—832no—
593C4⋊C4—832no—
594C4⋊C4—832no—
595C4⋊C4—832no—
596C4⋊C4—832no—
597C4⋊C4—832no—
598C4⋊C4—1664no—
599C4⋊C4—1661no—
600C4⋊C4—1661no—
601C4⋊C4—1661no—
602C4⋊C4—1661no—
603C4⋊C4—1661no—
604C4⋊C4—1661no—
605C4⋊C4—1664no—
606C4⋊C4—1664no—
607C4⋊C4—1664no—
608C4⋊C4—1664no—
609C4⋊C4—1664no—
610C4⋊C4—1664no—
611C4⋊C4—1664no—
612C4⋊C4—1664no—
613C4⋊C4C2×D33214yes—
614C4⋊C4C2×D33214yes—
615C22⋊C4—1664no—
616C22⋊C4—1664no—
617C22⋊C4—1664no—
618C22⋊C4—1664no—
619C22⋊C4—1664no—
620C22⋊C4C2×D33214yes—
621C22⋊C4C2×D33214yes—
622C42—1664no—
623C42C2×D33212yes—
624C42C2×D33212yes—
625C42C23×D8312yes—
626C42C23×D8312yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—3322no—
631C23—3322no—
632C23—3322no—
633C23—3322no—
634C23—3322no—
635C23—3322no—
636C23—1662no—
637C23—1662no—
638C23C22×D33212yes—
639C23C22×D33211yescharacteristic
640Q8—6644no—
641Q8—6644no—
642D4—3322no—
643D4—3322no—
644D4—6644no—
645D4—6644no—
646D4—6644no—
647D4—6644no—
648D4—1662no—
649D4—1662no—
650D4—1662no—
651D4—1662no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—3322no—
661C2×C4—3322no—
662C2×C4—3322no—
663C2×C4—3322no—
664C2×C4—3322no—
665C2×C4—3322no—
666C2×C4—6644no—
667C2×C4—6644no—
668C2×C4—6644no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4C22×D33212yes—
676C2×C4C22×D33212yes—
677C2×C4C22×D33212yes—
678C2×C4C22×D33212yes—
679C2×C4C22×D33212yes—
680C2×C4C22×D33211yescharacteristic
681C2×C4#1458183912yes—
682C2×C4#1458183912yes—
683C2×C4C24×D8311yescharacteristic
684C8—22no—
685C8—22no—
686C8—22no—
687C8—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—3322no—
693C22—3322no—
694C22—3322no—
695C22—3322no—
696C22—3322no—
697C22—3322no—
698C22—6644no—
699C22—6644no—
700C22#1912827712yes—
701C22#1912850612yes—
702C22#1912851312yes—
703C22C23×D33211yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—3322no—
710C4—3322no—
711C4—3322no—
712C4—3322no—
713C4—3322no—
714C4—3322no—
715C4#1912827712yes—
716C4C2×#1458183911yescharacteristic
717C4C2×#1458183911yescharacteristic
718C2—42no—
719C2—6642no—
720C2—6642no—
721C2#2491871814yesdirect product factor
722C2C2×#1912827711yescharacteristic
723C2C2×#1912850611yescharacteristic
724C2C2×#1912851311yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#433×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128306C2
hypercenterC2×#433D83
hypocenterC83C2×#3241
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#19128329C2semidirect
3. #24918718C2direct (N × H)
4. C2×#19128110C2semidirect
5. C2×#19128103C2semidirect
6. C2×#19128066C2semidirect
7. C2×#19128048C2semidirect
8. C2×#19128020C2semidirect
9. C2×#19128026C2semidirect
10. C2×#19128026C2semidirect
11. C2×#19128015C2semidirect
12. C2×#19128002C2semidirect
13. C2×#19128002C2semidirect
14. C2×#19127992C2semidirect
15. C2×#19127982C2semidirect
16. C2×#433×C83C2semidirect
18. #19128329C22semidirect
41. #19128110C22semidirect
42. #19128103C22semidirect
43. #19128066C22semidirect
44. #19128048C22semidirect
45. #19128026C22semidirect
46. #19128026C22semidirect
47. #19128020C22semidirect
48. #19128015C22semidirect
49. #19128002C22semidirect
50. #19128002C22semidirect
51. #19127992C22semidirect
52. #19127982C22semidirect
70. #433×C83C22semidirect
357. C2×C83#3241semidirect
378. C2×#433D83semidirect
379. C83C2×#3241semidirect
417. #433C2×D83semidirect
721. C2#24918718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283292
C2×#191283062
#249187182
C2×#191281102
C2×#191281032
C2×#191280662
C2×#191280482
C2×#191280202
C2×#191280262
C2×#191280152
C2×#191280022
C2×#191279922
C2×#191279822
C2×#433×C832
C2×#324183