Finite Group Databasebeta

← C2×#24920084 #36283149

Subgroups — C2×#24920084 #36283149

Order 21248.

1930 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128415C211yesmaximal, characteristic
2C2×#19128409C211yesmaximal, characteristic, complemented
3#24920084C2116yesmaximal, direct product factor
4C2×#19128105C211yesmaximal, characteristic, complemented
5C2×#19128040C211yesmaximal, characteristic, complemented
6C2×#19128039C211yesmaximal, characteristic, complemented
7C2×#19128013C211yesmaximal, characteristic, complemented
8C2×#19128012C211yesmaximal, characteristic, complemented
9C2×#19127994C211yesmaximal, characteristic, complemented
10C2×#19127989C211yesmaximal, characteristic, complemented
11C2×#19127944C211yesmaximal, characteristic, complemented
12C2×SD16×Dic83C211yesmaximal, characteristic, complemented
13C2×#19127777C211yesmaximal, characteristic, complemented
14C2×#19127743C211yesmaximal, characteristic, complemented
15C2×#19127742C211yesmaximal, characteristic, complemented
16C2×#468×C83C211yesmaximal, characteristic, complemented
17C22×#13050573C2211yescharacteristic
18#19128415—24no—
19#19128415C2218yes—
20#19128409—24no—
21#19128409C2218yescomplemented
22C2×#14581791C2211yescharacteristic
23C2×#14581791C2211yescharacteristic
24C2×#14581782—21no—
25C2×#14581779—21no—
26C2×#14581778—21no—
27C2×#14581772—21no—
28C2×#14581769—21no—
29C2×#14581768C2211yescharacteristic
30C2×#14581764—21no—
31C2×#14581763C2211yescharacteristic
32C2×Q8×Dic83C2211yescharacteristic
33C2×D4×Dic83C2211yescharacteristic
34C2×C4×C22⋊D83C2211yescharacteristic
35C2×(C22⋊D83)⋊C4—21no—
36C2×#14581751C2211yescharacteristic
37C2×#14581750C2211yescharacteristic
38C2×#14581748—21no—
39C22×C4⋊Dic83C2211yescharacteristic
40C2×C4⋊C4×D83C2211yescharacteristic
41#19128105C2218yescomplemented
42#19128040C2218yescomplemented
43#19128039C2218yescomplemented
44#19128013C2218yescomplemented
45#19128012C2218yescomplemented
46#19127994C2218yescomplemented
47#19127989C2218yescomplemented
48#19127944C2218yescomplemented
49SD16×Dic83C2218yescomplemented
50#19127777C2218yescomplemented
51#19127743C2218yescomplemented
52#19127742C2218yescomplemented
53C2×#14581726C2211yescharacteristic
54C2×#14581726C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581725C2211yescharacteristic
58C2×#14581724C2211yescharacteristic
59C2×#14581724C2211yescharacteristic
60C2×#14581723C2211yescharacteristic
61C2×Dic83⋊C8C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581716C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65C2×#14581713C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C22×SD16×C83C2211yescharacteristic
70C22×M16×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×#121×C83C2211yescharacteristic
73#468×C83C2218yescomplemented
74C2×#107×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#102×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×C22⋊D83—21no—
80C22×C22⋊D83D411yescharacteristic
81C23×Dic83—21no—
82C23×Dic83—21no—
83C22×C4×D83—21no—
84C22×C4×D83C2311yescharacteristic
85C2×#13050573—24no—
86C2×#13050573C2314yes—
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2311yescharacteristic
89#14581791—22no—
90#14581791—22no—
91#14581791C2314yes—
92#14581791C2314yes—
93#14581782—28no—
94#14581779—28no—
95#14581778—28no—
96#14581772—28no—
97#14581769—28no—
98#14581768—22no—
99#14581768C2314yes—
100#14581764—28no—
101#14581763—22no—
102#14581763C2314yes—
103Q8×Dic83—22no—
104Q8×Dic83C2314yes—
105D4×Dic83—22no—
106D4×Dic83C2314yes—
107C4×C22⋊D83D414yes—
108C4×C22⋊D83C2314yes—
109(C22⋊D83)⋊C4—28no—
110#14581751—22no—
111#14581751C2314yes—
112#14581750—22no—
113#14581750C2314yes—
114#14581748—28no—
115C2×C4⋊Dic83—21no—
116C2×C4⋊Dic83—22no—
117C2×C4⋊Dic83—21no—
118C2×C4⋊Dic83C2311yescharacteristic
119C2×C4⋊Dic83C2314yes—
120C2×C4⋊Dic83C2311yescharacteristic
121C2×C4⋊Dic83C2311yescharacteristic
122C2×C4⋊Dic83C2311yescharacteristic
123C2×Dic83⋊C4—21no—
124C2×Dic83⋊C4—21no—
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4D411yescharacteristic
128C4⋊C4×D83—22no—
129C4⋊C4×D83C2314yes—
130C2×C22⋊Dic83—21no—
131C2×C22⋊Dic83—21no—
132C2×C22⋊Dic83—21no—
133C2×C22⋊Dic83D411yescharacteristic
134C2×(C2×D83)⋊C4—21no—
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4D411yescharacteristic
137C2×C4×Dic83—21no—
138C2×C4×Dic83—21no—
139C2×C4×Dic83—21no—
140C2×C4×Dic83C2311yescharacteristic
141#14581726C2314yes—
142#14581726C2314yes—
143#14581725C2314yes—
144#14581725C2314yes—
145#14581725C2314yes—
146#14581724C2314yes—
147#14581724C2314yes—
148#14581723C2314yes—
149Dic83⋊C8C2314yes—
150#14581716C2314yes—
151#14581716C2314yes—
152#14581713C2314yes—
153#14581713C2314yes—
154C22⋊(C83⋊C8)C2314yes—
155(C2×D83)⋊C8C2314yes—
156C8×Dic83C2314yes—
157C22×Q8×C83C2311yescharacteristic
158C22×D4×C83—21no—
159C22×D4×C83C2311yescharacteristic
160C23×C4×C83C2311yescharacteristic
161C2×SD16×C83—24no—
162C2×SD16×C83C2314yes—
163C2×M16×C83—24no—
164C2×M16×C83C2314yes—
165C22×C8×C83C2311yescharacteristic
166C22×C8×C83C2311yescharacteristic
167C22⋊Q8×C83—22no—
168C22⋊Q8×C83C2314yes—
169#121×C83—22no—
170#121×C83C2314yes—
171C2×C4⋊C4×C83—21no—
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176#107×C83C2314yes—
177#103×C83C2314yes—
178#102×C83C2314yes—
179C23×D83C2×D411yescharacteristic
180C2×Dic166—24no—
181C2×Dic166—24no—
182C2×Dic166—82no—
183C2×Dic166—82no—
184C2×C22⋊D83—24no—
185C2×C22⋊D83—24no—
186C2×C22⋊D83—82no—
187C2×C22⋊D83C2×D414yes—
188C22×Dic83—21no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—24no—
193C22×Dic83—24no—
194C22×Dic83—44no—
195C22×Dic83—82no—
196C22×Dic83C2×D411yescharacteristic
197C22×Dic83C2×D411yescharacteristic
198C22×Dic83C2×D411yescharacteristic
199C2×C4×D83—22no—
200C2×C4×D83—22no—
201C2×C4×D83—24no—
202C2×C4×D83—82no—
203C2×C4×D83C2×D412yes—
204C2×C4×D83C2412yes—
205#13050573—28no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—22no—
208C2×C83⋊C8C2412yes—
209C2×C83⋊C8C2412yes—
210C4⋊Dic83—21no—
211C4⋊Dic83—21no—
212C4⋊Dic83—24no—
213C4⋊Dic83—21no—
214C4⋊Dic83—21no—
215C4⋊Dic83—24no—
216C4⋊Dic83C2412yes—
217C4⋊Dic83C2412yes—
218C4⋊Dic83C2412yes—
219C4⋊Dic83C2412yes—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4C2×D414yes—
225C22⋊Dic83—24no—
226C22⋊Dic83—24no—
227C22⋊Dic83—24no—
228C22⋊Dic83C2×D414yes—
229(C2×D83)⋊C4—24no—
230(C2×D83)⋊C4—24no—
231(C2×D83)⋊C4C2×D414yes—
232C4×Dic83—24no—
233C4×Dic83—24no—
234C4×Dic83—24no—
235C4×Dic83C2×D412yes—
236C4×Dic83C2412yes—
237C24×C83—21no—
238C24×C83C2×D411yescharacteristic
239C2×Q8×C83—21no—
240C2×Q8×C83—22no—
241C2×Q8×C83—22no—
242C2×Q8×C83C2412yes—
243C2×D4×C83—24no—
244C2×D4×C83—21no—
245C2×D4×C83—22no—
246C2×D4×C83—22no—
247C2×D4×C83—82no—
248C2×D4×C83C2412yes—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2×D412yes—
256C22×C4×C83C2412yes—
257C22×C4×C83C2411yescharacteristic
258SD16×C83—28no—
259M16×C83—28no—
260C2×C8×C83—22no—
261C2×C8×C83#4114yes—
262C2×C8×C83C2412yes—
263C2×C8×C83C2412yes—
264C4⋊C4×C83—24no—
265C4⋊C4×C83—21no—
266C4⋊C4×C83—21no—
267C4⋊C4×C83C2412yes—
268C4⋊C4×C83C2412yes—
269C22⋊C4×C83—24no—
270C22⋊C4×C83—24no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—42no—
276C23×C83—42no—
277C23×C83—42no—
278C23×C83C22×D412yes—
279C23×C83C22×D411yescharacteristic
280C22×D83—22no—
281C22×D83—22no—
282C22×D83—22no—
283C22×D83C22×D412yes—
284Q8×C83—22no—
285Q8×C83—22no—
286Q8×C83—42no—
287D4×C83—22no—
288D4×C83—22no—
289D4×C83—42no—
290D4×C83—84no—
291C2×C4×C83—22no—
292C2×C4×C83—24no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—42no—
299C2×C4×C83—42no—
300C2×C4×C83—42no—
301C2×C4×C83C22×D412yes—
302C2×C4×C83C22×D411yescharacteristic
303C2×C4×C83C2×#4112yes—
304C2×C4×C832−1+412yes—
305C2×C4×C83C2511yescharacteristic
306C22⋊D83—28no—
307C22⋊D83—84no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—42no—
315C2×Dic83—42no—
316C2×Dic83—42no—
317C2×Dic83—42no—
318C2×Dic83—48no—
319C2×Dic83—84no—
320C2×Dic83#13714yes—
321C2×Dic83C22×D412yes—
322C2×Dic83C22×D412yes—
323C2×Dic83C22×D412yes—
324C4×D83—24no—
325C4×D83—22no—
326C4×D83—22no—
327C4×D83—84no—
328Dic166—84no—
329Dic166—84no—
330C8×C83—22no—
331C8×C83C2×#4114yes—
332C83⋊C8—22no—
333C83⋊C8—22no—
334C22×C83—22no—
335C22×C83—22no—
336C22×C83—22no—
337C22×C83—44no—
338C22×C83—42no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—84no—
342C22×C83#54712yes—
343C22×C83C2×#13712yes—
344C22×C83#57612yes—
345C22×C83C23×D411yescharacteristic
346C2×D83—22no—
347C2×D83—22no—
348C2×D83—22no—
349C2×D83—44no—
350C4×C83—22no—
351C4×C83—42no—
352C4×C83—42no—
353C4×C83—42no—
354C4×C83#54712yes—
355C4×C83C22×#4111yescharacteristic
356C4×C83C2×2−1+411yescharacteristic
357Dic83—22no—
358Dic83—22no—
359Dic83—42no—
360Dic83—42no—
361Dic83—42no—
362Dic83—42no—
363Dic83C2×#13714yes—
364C2×#3357—831nomaximal, Sylow
365C2×C83—42no—
366C2×C83—82no—
367C2×C83#335714yescomplemented
368C2×C83C2×#54711yescharacteristic
369C2×C83C22×#13711yescharacteristic
370C2×C83C2×#57611yescharacteristic
371D83—42no—
372C2×#555—831no—
373C2×#554—831no—
374#3357—8316no—
375C2×#500—831no—
376C2×#485—831no—
377C2×#485—831no—
378C2×#480—831no—
379C2×#480—831no—
380C2×#477—831no—
381C2×#476—831no—
382C2×#468—831no—
383C2×#468D8311yescharacteristic, complemented
384C2×C4×SD16—831no—
385C2×#436—831no—
386C2×#428—831no—
387C2×#428—831no—
388C83C2×#335711yescharacteristic, complemented, Sylow
389C22×SD16C2×D8311yescharacteristic
390C22×M16—831no—
391C22×M16C2×D8311yescharacteristic
392#555—838no—
393#555—1664no—
394#554—838no—
395#554—1664no—
396C2×C4⋊Q8—831no—
397C2×C4⋊Q8—831no—
398C2×#125—1661no—
399C2×#124—1661no—
400C2×#124—1661no—
401C2×C22⋊Q8—831no—
402C2×C22⋊Q8—1661no—
403C2×C22⋊Q8—1661no—
404C2×C22⋊Q8C2×D8311yescharacteristic
405C2×#121—831no—
406C2×#121—1661no—
407C2×#121C2×D8311yescharacteristic
408C2×C4×Q8—831no—
409C2×C4×D4—831no—
410C2×C4×D4—831no—
411C2×C4×D4—1661no—
412C2×#117—831no—
413C2×#117—831no—
414C2×#117—1661no—
415C22×C4⋊C4—831no—
416C22×C4⋊C4—831no—
417#500—838no—
418#485—838no—
419#485—838no—
420#480—838no—
421#480—838no—
422#477—838no—
423#476—838no—
424#468—838no—
425#468C2×D8318yescomplemented
426C4×SD16—838no—
427#436—838no—
428#428—838no—
429#428—838no—
430C2×#107—831no—
431C2×#107—831no—
432C2×#107—831no—
433C2×#107—831no—
434C2×#107—831no—
435C2×#107C2×D8311yescharacteristic
436C2×#106—831no—
437C2×#106—831no—
438C2×#106—831no—
439C2×C4⋊C8—831no—
440C2×#103—831no—
441C2×#103—831no—
442C2×#103C2×D8311yescharacteristic
443C2×#102—831no—
444C2×#102—831no—
445C2×#102C2×D8311yescharacteristic
446C2×C22⋊C8—831no—
447C2×C22⋊C8—831no—
448C2×C4×C8—831no—
449C22×Q8—1661no—
450C22×Q8—1661no—
451C22×Q8C22×D8311yescharacteristic
452C22×D4—21no—
453C22×D4—831no—
454C22×D4—1661no—
455C22×D4C22×D8311yescharacteristic
456C23×C4—831no—
457C23×C4—1661no—
458C23×C4—1661no—
459C23×C4—1661no—
460C23×C4C22×D8311yescharacteristic
461C2×SD16—24no—
462C2×SD16C22×D8314yes—
463C2×M16—24no—
464C2×M16—834no—
465C2×M16—1664no—
466C2×M16C22×D8314yes—
467C22×C8—831no—
468C22×C8—831no—
469C22×C8C22×D8311yescharacteristic
470C22×C8C22×D8311yescharacteristic
471C4⋊Q8—834no—
472C4⋊Q8—834no—
473C4⋊Q8—1662no—
474C4⋊Q8—1662no—
475#125—1668no—
476#124—1668no—
477#124—1668no—
478C22⋊Q8—22no—
479C22⋊Q8—834no—
480C22⋊Q8—1668no—
481C22⋊Q8—1668no—
482C22⋊Q8—1662no—
483C22⋊Q8C22×D8314yes—
484#121—22no—
485#121—834no—
486#121—1662no—
487#121—1668no—
488#121C22×D8314yes—
489C4×Q8—834no—
490C4×Q8—1662no—
491C4×D4—834no—
492C4×D4—834no—
493C4×D4—834no—
494C4×D4—1662no—
495C4×D4—1668no—
496#117—834no—
497#117—834no—
498#117—1668no—
499#117—1662no—
500#117—1662no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—831no—
503C2×C4⋊C4—831no—
504C2×C4⋊C4—831no—
505C2×C4⋊C4—834no—
506C2×C4⋊C4—831no—
507C2×C4⋊C4—831no—
508C2×C4⋊C4—834no—
509C2×C4⋊C4—1662no—
510C2×C4⋊C4—1661no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4—1661no—
516C2×C4⋊C4—1662no—
517C2×C4⋊C4C22×D8311yescharacteristic
518C2×C4⋊C4C22×D8311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—831no—
522C2×C22⋊C4—831no—
523C2×C22⋊C4—1661no—
524C2×C22⋊C4—1661no—
525C2×C22⋊C4—1661no—
526C2×C22⋊C4—1661no—
527C2×C22⋊C4—1661no—
528C2×C42—831no—
529C2×C42—1661no—
530C2×C42—1661no—
531C2×C42—1661no—
532#107—834no—
533#107—834no—
534#107—834no—
535#107—834no—
536#107—834no—
537#107C22×D8314yes—
538#106—834no—
539#106—834no—
540#106—834no—
541C4⋊C8—834no—
542#103—834no—
543#103—834no—
544#103C22×D8314yes—
545#102—834no—
546#102—834no—
547#102C22×D8314yes—
548C22⋊C8—834no—
549C22⋊C8—834no—
550C4×C8—834no—
551C24—21no—
552C24—831no—
553C24D4×D8311yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—6642no—
558C2×Q8—6642no—
559C2×Q8—1664no—
560C2×Q8—1664no—
561C2×Q8C23×D8312yes—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—82no—
567C2×D4—834no—
568C2×D4—6642no—
569C2×D4—1664no—
570C2×D4—1664no—
571C2×D4C23×D8312yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—3324no—
578C22×C4—831no—
579C22×C4—831no—
580C22×C4—831no—
581C22×C4—832no—
582C22×C4—832no—
583C22×C4—6642no—
584C22×C4—6642no—
585C22×C4—1664no—
586C22×C4—1664no—
587C22×C4—1661no—
588C22×C4—1661no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1664no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4D4×D8312yes—
595C22×C4D4×D8311yescharacteristic
596C22×C4C23×D8312yes—
597C22×C4C23×D8311yescharacteristic
598SD16—28no—
599M16—28no—
600M16—1668no—
601C2×C8—22no—
602C2×C8—832no—
603C2×C8—832no—
604C2×C8—1662no—
605C2×C8—1662no—
606C2×C8#1305058914yes—
607C2×C8C23×D8312yes—
608C2×C8C23×D8312yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—834no—
613C4⋊C4—832no—
614C4⋊C4—832no—
615C4⋊C4—832no—
616C4⋊C4—832no—
617C4⋊C4—1664no—
618C4⋊C4—1664no—
619C4⋊C4—1664no—
620C4⋊C4—1664no—
621C4⋊C4—1664no—
622C4⋊C4—1661no—
623C4⋊C4—1664no—
624C4⋊C4—1661no—
625C4⋊C4—1661no—
626C4⋊C4—1661no—
627C4⋊C4C23×D8312yes—
628C4⋊C4C23×D8312yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—834no—
632C22⋊C4—834no—
633C22⋊C4—1664no—
634C22⋊C4—1664no—
635C22⋊C4—1664no—
636C22⋊C4—1664no—
637C22⋊C4—1664no—
638C42—832no—
639C42—832no—
640C42—1664no—
641C42—1664no—
642C42—1664no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—832no—
651C23—1662no—
652C23—1662no—
653C23—1662no—
654C23C2×D4×D8312yes—
655C23C2×D4×D8311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—6644no—
660Q8—6644no—
661D4—22no—
662D4—22no—
663D4—42no—
664D4—84no—
665D4—6644no—
666D4—1668no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—3322no—
678C2×C4—3322no—
679C2×C4—3322no—
680C2×C4—3322no—
681C2×C4—3328no—
682C2×C4—834no—
683C2×C4—832no—
684C2×C4—832no—
685C2×C4—832no—
686C2×C4—6644no—
687C2×C4—6644no—
688C2×C4—1662no—
689C2×C4—1662no—
690C2×C4—1662no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1664no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4C2×D4×D8312yes—
698C2×C4C2×D4×D8311yescharacteristic
699C2×C4C2×#1305058912yes—
700C2×C4#1458183912yes—
701C2×C4C24×D8311yescharacteristic
702C8—22no—
703C8—1662no—
704C8—1662no—
705C8C2×#1305058914yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—3324no—
715C22—1662no—
716C22—1662no—
717C22—1662no—
718C22#1912835112yes—
719C22#137×D8312yes—
720C22#1912850512yes—
721C22C22×D4×D8311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—3322no—
727C4—3322no—
728C4—3322no—
729C4—3322no—
730C4—834no—
731C4—1662no—
732C4—1662no—
733C4#1912835112yes—
734C4C22×#1305058911yescharacteristic
735C4C2×#1458183911yescharacteristic
736C2—42no—
737C2—82no—
738C2—3322no—
739C2#2492008414yesdirect product factor
740C2C2×#1912835111yescharacteristic
741C2C2×#137×D8311yescharacteristic
742C2C2×#1912850511yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#468×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128415C2
hypercenterC2×#468D83
hypocenterC83C2×#3357
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#19128409C2semidirect
3. #24920084C2direct (N × H)
4. C2×#19128105C2semidirect
5. C2×#19128040C2semidirect
6. C2×#19128039C2semidirect
7. C2×#19128013C2semidirect
8. C2×#19128012C2semidirect
9. C2×#19127994C2semidirect
10. C2×#19127989C2semidirect
11. C2×#19127944C2semidirect
12. C2×SD16×Dic83C2semidirect
13. C2×#19127777C2semidirect
14. C2×#19127743C2semidirect
15. C2×#19127742C2semidirect
16. C2×#468×C83C2semidirect
21. #19128409C22semidirect
41. #19128105C22semidirect
42. #19128040C22semidirect
43. #19128039C22semidirect
44. #19128013C22semidirect
45. #19128012C22semidirect
46. #19127994C22semidirect
47. #19127989C22semidirect
48. #19127944C22semidirect
49. SD16×Dic83C22semidirect
50. #19127777C22semidirect
51. #19127743C22semidirect
52. #19127742C22semidirect
73. #468×C83C22semidirect
367. C2×C83#3357semidirect
383. C2×#468D83semidirect
388. C83C2×#3357semidirect
425. #468C2×D83semidirect
739. C2#24920084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284152
C2×#191284092
#249200842
C2×#191281052
C2×#191280402
C2×#191280392
C2×#191280132
C2×#191280122
C2×#191279942
C2×#191279892
C2×#191279442
C2×SD16×Dic832
C2×#191277772
C2×#191277432
C2×#191277422
C2×#468×C832
C2×#335783