Finite Group Databasebeta

← C2×#24917818 #36273641

Subgroups — C2×#24917818 #36273641

Order 21248.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128331C211yesmaximal, characteristic, complemented
2C2×#19128264C211yesmaximal, characteristic
3#24917818C2116yesmaximal, direct product factor
4C2×#19128064C211yesmaximal, characteristic, complemented
5C2×#19128061C211yesmaximal, characteristic, complemented
6C2×#19128059C211yesmaximal, characteristic, complemented
7C2×#19128058C211yesmaximal, characteristic, complemented
8C2×#19128054C211yesmaximal, characteristic, complemented
9C2×#19128047C211yesmaximal, characteristic, complemented
10C2×#19128046C211yesmaximal, characteristic, complemented
11C2×#19127699C211yesmaximal, characteristic, complemented
12C2×#19127704C211yesmaximal, characteristic, complemented
13C2×#19127694C211yesmaximal, characteristic, complemented
14C2×#102×D83C211yesmaximal, characteristic, complemented
15C2×#19127658C211yesmaximal, characteristic, complemented
16C2×#490×C83C211yesmaximal, characteristic, complemented
17C22×#13050589C2211yescharacteristic
18C22×D4×D83C2211yescharacteristic
19C22×#13050573C2211yescharacteristic
20C22×C8×D83C2211yescharacteristic
21#19128331—24no—
22#19128331C2218yescomplemented
23#19128264—24no—
24#19128264C2218yes—
25C2×#14581792C2211yescharacteristic, complemented
26C2×#14581791—21no—
27C2×#14581791C2211yescharacteristic, complemented
28C2×#14581788C2211yescharacteristic
29C2×#14581783C2211yescharacteristic, complemented
30C2×#14581782—21no—
31C2×#14581780C2211yescharacteristic
32C2×#14581779C2211yescharacteristic
33C2×#14581772—21no—
34C2×#14581770—21no—
35C2×#14581764—21no—
36C2×#14581764—21no—
37C2×#14581760—21no—
38C2×#14581760—21no—
39C2×#14581750C2211yescharacteristic
40C2×#14581749C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic
42#19128064C2218yescomplemented
43#19128061C2218yescomplemented
44#19128059C2218yescomplemented
45#19128058C2218yescomplemented
46#19128054C2218yescomplemented
47#19128047C2218yescomplemented
48#19128046C2218yescomplemented
49#19127704C2218yescomplemented
50#19127699C2218yescomplemented
51#19127694C2218yescomplemented
52C2×#14581717C2211yescharacteristic, complemented
53C2×#14581717C2211yescharacteristic, complemented
54C2×#14581715C2211yescharacteristic, complemented
55C2×#14581715C2211yescharacteristic, complemented
56C2×#14581714C2211yescharacteristic
57C2×#14581714C2211yescharacteristic
58C2×#14581713C2211yescharacteristic
59C2×#14581713C2211yescharacteristic
60C2×#14581713C2211yescharacteristic, complemented
61C2×#14581713C2211yescharacteristic, complemented
62C2×#14581712C2211yescharacteristic
63C2×#14581712C2211yescharacteristic
64#102×D83C2218yescomplemented
65#19127658C2218yescomplemented
66C2×#14581702C2211yescharacteristic, complemented
67C2×C4×C83⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic83C2211yescharacteristic, complemented
69C2×#127×C83C2211yescharacteristic
70C2×#125×C83C2211yescharacteristic, complemented
71#490×C83C2218yescomplemented
72C2×#102×C83C2211yescharacteristic
73C2×#102×C83C2211yescharacteristic
74C2×#102×C83C2211yescharacteristic, complemented
75C2×#102×C83C2211yescharacteristic, complemented
76C2×#97×C83C2211yescharacteristic, complemented
77C24×D83—21no—
78C2×#13050589—22no—
79C2×#13050589—24no—
80C2×#13050589—24no—
81C2×#13050589C2314yes—
82C22×Dic166—21no—
83C22×Dic166—21no—
84C22×Dic166C2311yescharacteristic
85C22×D332C2311yescharacteristic
86C22×C22⋊D83—21no—
87C22×C22⋊D83—21no—
88C22×C22⋊D83—21no—
89C22×C22⋊D83—21no—
90C2×D4×D83—22no—
91C2×D4×D83—24no—
92C2×D4×D83—24no—
93C2×D4×D83C2314yes—
94C23×Dic83—21no—
95C22×C4×D83—21no—
96C22×C4×D83C2311yescharacteristic
97C2×#13050573—24no—
98C2×#13050573C2314yes—
99C22×C83⋊C8C2311yescharacteristic
100C22×C83⋊C8C2311yescharacteristic
101C2×C8×D83—24no—
102C2×C8×D83C2314yes—
103#14581792—22no—
104#14581792C2314yescomplemented
105#14581791—28no—
106#14581791—22no—
107#14581791C2314yescomplemented
108#14581788—22no—
109#14581788C2314yes—
110#14581783—22no—
111#14581783C2314yescomplemented
112#14581782—28no—
113#14581780—22no—
114#14581780C2314yes—
115#14581779—22no—
116#14581779C2314yes—
117#14581772—28no—
118#14581770—28no—
119#14581764—28no—
120#14581764—28no—
121#14581760—28no—
122#14581760—28no—
123#14581750—22no—
124#14581750C2314yes—
125#14581749D414yes—
126#14581749C2314yes—
127C2×C4⋊Dic83—21no—
128C2×C4⋊Dic83—21no—
129C2×C4⋊Dic83C2311yescharacteristic
130C2×C4⋊Dic83C2311yescharacteristic
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4D411yescharacteristic
135C2×Dic83⋊C4D411yescharacteristic
136C4⋊C4×D83—22no—
137C4⋊C4×D83C2314yes—
138C2×C22⋊Dic83—21no—
139C2×C22⋊Dic83—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4D411yescharacteristic
144C2×(C2×D83)⋊C4D411yescharacteristic
145C2×C4×Dic83—21no—
146C2×C4×Dic83C2311yescharacteristic
147#14581717C2314yescomplemented
148#14581717C2314yescomplemented
149#14581715C2314yescomplemented
150#14581715C2314yescomplemented
151#14581714C2314yes—
152#14581714C2314yes—
153#14581713C2314yes—
154#14581713C2314yes—
155#14581713C2314yescomplemented
156#14581713C2314yescomplemented
157#14581712C2314yes—
158#14581712C2314yes—
159#14581702C2314yescomplemented
160C4×C83⋊C8C2314yescomplemented
161C8×Dic83C2314yescomplemented
162C22×D4×C83—21no—
163C22×D4×C83—21no—
164C22×D4×C83C2311yescharacteristic
165C22×D4×C83C2311yescharacteristic
166C22×C8×C83C2311yescharacteristic
167C22×C8×C83C2311yescharacteristic
168#127×C83—22no—
169#127×C83C2314yes—
170#125×C83—22no—
171#125×C83C2314yescomplemented
172C2×C4⋊C4×C83—21no—
173C2×C4⋊C4×C83—21no—
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C4⋊C4×C83C2311yescharacteristic
176C2×C42×C83C2311yescharacteristic
177#102×C83C2314yes—
178#102×C83C2314yes—
179#102×C83C2314yescomplemented
180#102×C83C2314yescomplemented
181#97×C83C2314yescomplemented
182C23×D83—21no—
183C23×D83—24no—
184C23×D83—44no—
185C23×D83—82no—
186C23×D83—82no—
187C23×D83C2×D411yescharacteristic
188#13050589—28no—
189#13050589—28no—
190#13050589—48no—
191C2×Dic166—22no—
192C2×Dic166—22no—
193C2×Dic166—21no—
194C2×Dic166—24no—
195C2×Dic166—24no—
196C2×Dic166—82no—
197C2×Dic166—82no—
198C2×Dic166C2412yes—
199C2×D332—22no—
200C2×D332—22no—
201C2×D332—21no—
202C2×D332C2412yes—
203C2×C22⋊D83—24no—
204C2×C22⋊D83—24no—
205C2×C22⋊D83—24no—
206C2×C22⋊D83—24no—
207C2×C22⋊D83—44no—
208C2×C22⋊D83—44no—
209C2×C22⋊D83—82no—
210C2×C22⋊D83—82no—
211D4×D83—28no—
212D4×D83—28no—
213D4×D83—48no—
214C22×Dic83—21no—
215C22×Dic83—21no—
216C22×Dic83—21no—
217C22×Dic83—24no—
218C22×Dic83—44no—
219C22×Dic83C2×D411yescharacteristic
220C22×Dic83C2×D411yescharacteristic
221C22×Dic83C2×D411yescharacteristic
222C2×C4×D83—24no—
223C2×C4×D83—82no—
224C2×C4×D83C2×D412yes—
225C2×C4×D83#4114yes—
226C2×C4×D83#4114yes—
227C2×C4×D83C2412yes—
228#13050573—28no—
229C2×C83⋊C8—22no—
230C2×C83⋊C8—22no—
231C2×C83⋊C8C2412yes—
232C2×C83⋊C8C2412yes—
233C8×D83—28no—
234C4⋊Dic83—24no—
235C4⋊Dic83—21no—
236C4⋊Dic83—21no—
237C4⋊Dic83—24no—
238C4⋊Dic83C2412yes—
239C4⋊Dic83C2412yes—
240Dic83⋊C4—24no—
241Dic83⋊C4—24no—
242Dic83⋊C4—24no—
243Dic83⋊C4C2×D414yes—
244Dic83⋊C4C2×D414yes—
245C22⋊Dic83—24no—
246C22⋊Dic83—24no—
247(C2×D83)⋊C4—24no—
248(C2×D83)⋊C4—24no—
249(C2×D83)⋊C4—24no—
250(C2×D83)⋊C4C2×D414yes—
251(C2×D83)⋊C4C2×D414yes—
252C4×Dic83—24no—
253C4×Dic83C2×D412yes—
254C4×Dic83C2412yes—
255C24×C83—21no—
256C24×C83—21no—
257C2×D4×C83—21no—
258C2×D4×C83—21no—
259C2×D4×C83—24no—
260C2×D4×C83—24no—
261C2×D4×C83—22no—
262C2×D4×C83—22no—
263C2×D4×C83—22no—
264C2×D4×C83—22no—
265C2×D4×C83—82no—
266C2×D4×C83—82no—
267C2×D4×C83C2412yes—
268C2×D4×C83C2412yes—
269C22×C4×C83—21no—
270C22×C4×C83—21no—
271C22×C4×C83C2×D411yescharacteristic
272C22×C4×C83C2×D411yescharacteristic
273C22×C4×C83C2411yescharacteristic
274C2×C8×C83—22no—
275C2×C8×C83—22no—
276C2×C8×C83C2412yes—
277C2×C8×C83C2412yes—
278C4⋊C4×C83—24no—
279C4⋊C4×C83—24no—
280C4⋊C4×C83—21no—
281C4⋊C4×C83—21no—
282C4⋊C4×C83C2412yes—
283C4⋊C4×C83C2412yes—
284C42×C83C2×D412yes—
285C42×C83C2412yes—
286C23×C83—22no—
287C23×C83—22no—
288C23×C83—42no—
289C23×C83—42no—
290C23×C83—42no—
291C23×C83—42no—
292C23×C83—42no—
293C23×C83—42no—
294C23×C83C22×D411yescharacteristic
295C22×D83—22no—
296C22×D83—22no—
297C22×D83—22no—
298C22×D83—42no—
299C22×D83—42no—
300C22×D83—42no—
301C22×D83—48no—
302C22×D83—84no—
303C22×D83—84no—
304C22×D83—816no—
305C22×D83#12414yes—
306C22×D83C22×D412yes—
307D4×C83—22no—
308D4×C83—22no—
309D4×C83—22no—
310D4×C83—22no—
311D4×C83—42no—
312D4×C83—42no—
313D4×C83—84no—
314D4×C83—84no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—42no—
320C2×C4×C83—42no—
321C2×C4×C83C22×D412yes—
322C2×C4×C83C22×D412yes—
323C2×C4×C83C22×D411yescharacteristic
324C2×C4×C83C2×#4112yes—
325C2×C4×C83C2×#4112yes—
326C2×C4×C83C2511yescharacteristic
327C22⋊D83—48no—
328C22⋊D83—48no—
329C22⋊D83—84no—
330C22⋊D83—84no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—42no—
337C2×Dic83—42no—
338C2×Dic83—42no—
339C2×Dic83—48no—
340C2×Dic83#12414yes—
341C2×Dic83C22×D412yes—
342C2×Dic83C22×D412yes—
343C2×Dic83C22×D412yes—
344D332—22no—
345D332—22no—
346D332—42no—
347C4×D83—84no—
348C4×D83#12418yes—
349C4×D83C2×#4114yes—
350C4×D83C2×#4114yes—
351Dic166—22no—
352Dic166—22no—
353Dic166—42no—
354Dic166—84no—
355Dic166—84no—
356C8×C83—22no—
357C8×C83—22no—
358C83⋊C8—22no—
359C83⋊C8—22no—
360C22×C83—42no—
361C22×C83—42no—
362C22×C83—42no—
363C22×C83—42no—
364C22×C83—42no—
365C22×C83—42no—
366C22×C83—84no—
367C22×C83—84no—
368C22×C83C2×#12412yes—
369C22×C83#57612yes—
370C22×C83#57712yes—
371C22×C83C23×D411yescharacteristic
372C2×D83—28no—
373C2×D83—22no—
374C2×D83—22no—
375C2×D83—42no—
376C2×D83—42no—
377C2×D83—42no—
378C2×D83—816no—
379C2×D83—84no—
380C2×D83C2×#12414yes—
381C4×C83—22no—
382C4×C83—22no—
383C4×C83—42no—
384C4×C83—42no—
385C4×C83C2×#12412yes—
386C4×C83C22×#4111yescharacteristic
387C4×C83C22×#4111yescharacteristic
388Dic83—22no—
389Dic83—22no—
390Dic83—42no—
391Dic83—42no—
392Dic83—42no—
393Dic83C2×#12414yes—
394C2×#3136—831nomaximal, Sylow
395C2×C83—82no—
396C2×C83—82no—
397C2×C83#313614yescomplemented
398C2×C83C22×#12411yescharacteristic
399C2×C83C2×#57611yescharacteristic
400C2×C83C2×#57711yescharacteristic
401D83—24no—
402D83—82no—
403C2×#544—831no—
404C2×#535—831no—
405#3136—8316no—
406C2×#490—831no—
407C2×#490D8311yescharacteristic, complemented
408C2×#489—831no—
409C2×#489—831no—
410C2×#488—831no—
411C2×#488—831no—
412C2×#486—831no—
413C2×#486—831no—
414C2×#417—831no—
415C2×#418—831no—
416C2×#416—831no—
417C22×#102—831no—
418C2×#405—831no—
419C83C2×#313611yescharacteristic, complemented, Sylow
420C22×#41—831no—
421C23×D4—831no—
422C22×M16—831no—
423C23×C8—831no—
424#544—838no—
425#544—1664no—
426#535—838no—
427#535—1664no—
428C2×C4⋊Q8—831no—
429C2×C4⋊Q8—831no—
430C2×C4⋊Q8—1661no—
431C2×#127—831no—
432C2×#127C2×D8311yescharacteristic
433C2×#125—831no—
434C2×#125—1661no—
435C2×#125C2×D8311yescharacteristic, complemented
436C2×#124—831no—
437C2×#124—831no—
438C2×C22⋊Q8—1661no—
439C2×C22⋊Q8—1661no—
440C2×#121—1661no—
441C2×#121—1661no—
442C2×#120—1661no—
443C2×#120—1661no—
444C2×#117—831no—
445C2×#117—831no—
446C22×C4⋊C4—831no—
447#490—838no—
448#490C2×D8318yescomplemented
449#489—838no—
450#489—838no—
451#488—838no—
452#488—838no—
453#486—838no—
454#486—838no—
455#418—838no—
456#417—838no—
457#416—838no—
458C2×#103—831no—
459C2×#103—831no—
460C2×#103—831no—
461C2×#103—831no—
462C2×#102—831no—
463C2×#102—831no—
464C2×#102—831no—
465C2×#102—831no—
466C2×#102—831no—
467C2×#102—831no—
468C2×#102—831no—
469C2×#102—831no—
470C2×#102—838no—
471C2×#102C2×D8311yescharacteristic
472C2×#102C2×D8311yescharacteristic
473C2×#102C2×D8311yescharacteristic, complemented
474C2×#102C2×D8311yescharacteristic, complemented
475#405—838no—
476C2×#97—831no—
477C2×#97C2×D8311yescharacteristic, complemented
478C2×C4×C8—831no—
479C2×C4×C8—831no—
480C25—1661no—
481C2×#41—834no—
482C2×#41—1664no—
483C2×#41—1664no—
484C2×#41—1662no—
485C22×Q8—831no—
486C22×Q8—1661no—
487C22×Q8—1661no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—834no—
491C22×D4—831no—
492C22×D4—1662no—
493C22×D4—1664no—
494C22×D4—1664no—
495C22×D4—1661no—
496C22×D4—1661no—
497C22×D4—1661no—
498C22×D4—1661no—
499C22×D4C22×D8311yescharacteristic
500C22×D4C22×D8311yescharacteristic
501C23×C4—831no—
502C23×C4—1661no—
503C23×C4—1661no—
504C2×M16—834no—
505C2×M16—1664no—
506C22×C8—831no—
507C22×C8—831no—
508C22×C8—834no—
509C22×C8—1664no—
510C22×C8C22×D8311yescharacteristic
511C22×C8C22×D8311yescharacteristic
512C4⋊Q8—834no—
513C4⋊Q8—834no—
514C4⋊Q8—1662no—
515C4⋊Q8—1668no—
516C4⋊Q8—1662no—
517#127—22no—
518#127—834no—
519#127—1662no—
520#127C22×D8314yes—
521#125—22no—
522#125—834no—
523#125—1662no—
524#125—1668no—
525#125C22×D8314yescomplemented
526#124—834no—
527#124—834no—
528#124—1662no—
529#124—1662no—
530C22⋊Q8—1668no—
531C22⋊Q8—1668no—
532#121—1668no—
533#121—1668no—
534#120—1668no—
535#120—1668no—
536#117—834no—
537#117—834no—
538#117—834no—
539#117—1662no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—831no—
543C2×C4⋊C4—831no—
544C2×C4⋊C4—831no—
545C2×C4⋊C4—831no—
546C2×C4⋊C4—834no—
547C2×C4⋊C4—1662no—
548C2×C4⋊C4—1661no—
549C2×C4⋊C4—1661no—
550C2×C4⋊C4—1661no—
551C2×C4⋊C4—1661no—
552C2×C4⋊C4—1661no—
553C2×C4⋊C4C22×D8311yescharacteristic
554C2×C4⋊C4C22×D8311yescharacteristic
555C2×C22⋊C4—831no—
556C2×C22⋊C4—831no—
557C2×C22⋊C4—1661no—
558C2×C22⋊C4—1661no—
559C2×C22⋊C4—1661no—
560C2×C22⋊C4—1661no—
561C2×C22⋊C4—1661no—
562C2×C42—831no—
563C2×C42—1661no—
564C2×C42C22×D8311yescharacteristic
565#103—834no—
566#103—834no—
567#103—834no—
568#103—834no—
569#102—834no—
570#102—834no—
571#102—834no—
572#102—834no—
573#102—834no—
574#102—834no—
575#102—834no—
576#102—834no—
577#102C22×D8314yes—
578#102C22×D8314yes—
579#102C22×D8314yescomplemented
580#102C22×D8314yescomplemented
581#97—834no—
582#97C22×D8314yescomplemented
583C4×C8—834no—
584C4×C8—834no—
585C24—21no—
586C24—21no—
587C24—3324no—
588C24—831no—
589C24—6642no—
590C24—6642no—
591C24—1664no—
592C24—1661no—
593#41—3328no—
594#41—1668no—
595#41—1668no—
596C2×Q8—832no—
597C2×Q8—6642no—
598C2×Q8—6642no—
599C2×Q8—1664no—
600C2×Q8—1662no—
601C2×Q8—1662no—
602C2×Q8—1661no—
603C2×Q8—1664no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—82no—
613C2×D4—82no—
614C2×D4—3324no—
615C2×D4—3328no—
616C2×D4—3324no—
617C2×D4—832no—
618C2×D4—6642no—
619C2×D4—6642no—
620C2×D4—1668no—
621C2×D4—1668no—
622C2×D4—1664no—
623C2×D4—1664no—
624C2×D4—1664no—
625C2×D4—1664no—
626C2×D4—1661no—
627C2×D4—1662no—
628C2×D4—1662no—
629C2×D4C23×D8312yes—
630C2×D4C23×D8312yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—3324no—
634C22×C4—831no—
635C22×C4—832no—
636C22×C4—834no—
637C22×C4—834no—
638C22×C4—832no—
639C22×C4—831no—
640C22×C4—831no—
641C22×C4—6642no—
642C22×C4—1664no—
643C22×C4—1664no—
644C22×C4—1661no—
645C22×C4—1661no—
646C22×C4—1661no—
647C22×C4D4×D8311yescharacteristic
648C22×C4D4×D8311yescharacteristic
649C22×C4C23×D8311yescharacteristic
650M16—1668no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—832no—
654C2×C8—832no—
655C2×C8—1668no—
656C2×C8—1662no—
657C2×C8—1662no—
658C2×C8C23×D8312yes—
659C2×C8C23×D8312yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—834no—
665C4⋊C4—834no—
666C4⋊C4—832no—
667C4⋊C4—832no—
668C4⋊C4—1664no—
669C4⋊C4—1664no—
670C4⋊C4—1664no—
671C4⋊C4—1664no—
672C4⋊C4—1661no—
673C4⋊C4—1661no—
674C4⋊C4—1664no—
675C4⋊C4C23×D8312yes—
676C4⋊C4C23×D8312yes—
677C22⋊C4—834no—
678C22⋊C4—834no—
679C22⋊C4—1664no—
680C22⋊C4—1664no—
681C22⋊C4—1664no—
682C22⋊C4—1664no—
683C22⋊C4—1664no—
684C42—832no—
685C42—832no—
686C42—1664no—
687C42D4×D8312yes—
688C42C23×D8312yes—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—3328no—
698C23—3322no—
699C23—3322no—
700C23—3322no—
701C23—834no—
702C23—832no—
703C23—6644no—
704C23—6644no—
705C23—66416no—
706C23—1662no—
707C23—1662no—
708C23—1662no—
709C23C2×D4×D8311yescharacteristic
710Q8—3322no—
711Q8—6644no—
712Q8—6644no—
713Q8—1662no—
714Q8—1662no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—84no—
723D4—3328no—
724D4—3328no—
725D4—3322no—
726D4—6644no—
727D4—6644no—
728D4—1662no—
729D4—1662no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—3322no—
737C2×C4—3322no—
738C2×C4—3322no—
739C2×C4—3328no—
740C2×C4—834no—
741C2×C4—832no—
742C2×C4—838no—
743C2×C4—834no—
744C2×C4—834no—
745C2×C4—832no—
746C2×C4—832no—
747C2×C4—6644no—
748C2×C4—1662no—
749C2×C4—1662no—
750C2×C4—1662no—
751C2×C4—1662no—
752C2×C4—1662no—
753C2×C4C2×D4×D8312yes—
754C2×C4C2×D4×D8312yes—
755C2×C4C2×D4×D8311yescharacteristic
756C2×C4#41×D8312yes—
757C2×C4#41×D8312yes—
758C2×C4C24×D8311yescharacteristic
759C8—22no—
760C8—22no—
761C8—1662no—
762C8—1662no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—3322no—
772C22—3322no—
773C22—3322no—
774C22—834no—
775C22—66416no—
776C22—6644no—
777C22—1668no—
778C22—1662no—
779C22—1662no—
780C22#124×D8312yes—
781C22#1912850512yes—
782C22#1912851112yes—
783C22C22×D4×D8311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—3322no—
789C4—3322no—
790C4—3322no—
791C4—834no—
792C4—1662no—
793C4—1662no—
794C4#124×D8312yes—
795C4C2×#41×D8311yescharacteristic
796C4C2×#41×D8311yescharacteristic
797C2—82no—
798C2—82no—
799C2—6642no—
800C2—1664no—
801C2#2491781814yesdirect product factor
802C2C2×#124×D8311yescharacteristic
803C2C2×#1912850511yescharacteristic
804C2C2×#1912851111yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#490×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128264C2
hypercenterC2×#490D83
hypocenterC83C2×#3136
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#19128331C2semidirect
3. #24917818C2direct (N × H)
4. C2×#19128064C2semidirect
5. C2×#19128061C2semidirect
6. C2×#19128059C2semidirect
7. C2×#19128058C2semidirect
8. C2×#19128054C2semidirect
9. C2×#19128047C2semidirect
10. C2×#19128046C2semidirect
11. C2×#19127699C2semidirect
12. C2×#19127704C2semidirect
13. C2×#19127694C2semidirect
14. C2×#102×D83C2semidirect
15. C2×#19127658C2semidirect
16. C2×#490×C83C2semidirect
22. #19128331C22semidirect
25. C2×#14581792C22semidirect
27. C2×#14581791C22semidirect
29. C2×#14581783C22semidirect
42. #19128064C22semidirect
43. #19128061C22semidirect
44. #19128059C22semidirect
45. #19128058C22semidirect
46. #19128054C22semidirect
47. #19128047C22semidirect
48. #19128046C22semidirect
49. #19127704C22semidirect
50. #19127699C22semidirect
51. #19127694C22semidirect
52. C2×#14581717C22semidirect
53. C2×#14581717C22semidirect
54. C2×#14581715C22semidirect
55. C2×#14581715C22semidirect
60. C2×#14581713C22semidirect
61. C2×#14581713C22semidirect
64. #102×D83C22semidirect
65. #19127658C22semidirect
66. C2×#14581702C22semidirect
67. C2×C4×C83⋊C8C22semidirect
68. C2×C8×Dic83C22semidirect
70. C2×#125×C83C22semidirect
71. #490×C83C22semidirect
74. C2×#102×C83C22semidirect
75. C2×#102×C83C22semidirect
76. C2×#97×C83C22semidirect
104. #14581792C23semidirect
107. #14581791C23semidirect
111. #14581783C23semidirect
147. #14581717C23semidirect
148. #14581717C23semidirect
149. #14581715C23semidirect
150. #14581715C23semidirect
155. #14581713C23semidirect
156. #14581713C23semidirect
159. #14581702C23semidirect
160. C4×C83⋊C8C23semidirect
161. C8×Dic83C23semidirect
171. #125×C83C23semidirect
179. #102×C83C23semidirect
180. #102×C83C23semidirect
181. #97×C83C23semidirect
397. C2×C83#3136semidirect
407. C2×#490D83semidirect
419. C83C2×#3136semidirect
435. C2×#125C2×D83semidirect
448. #490C2×D83semidirect
473. C2×#102C2×D83semidirect
474. C2×#102C2×D83semidirect
477. C2×#97C2×D83semidirect
525. #125C22×D83semidirect
579. #102C22×D83semidirect
580. #102C22×D83semidirect
582. #97C22×D83semidirect
801. C2#24917818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283312
C2×#191282642
#249178182
C2×#191280642
C2×#191280612
C2×#191280592
C2×#191280582
C2×#191280542
C2×#191280472
C2×#191280462
C2×#191276992
C2×#191277042
C2×#191276942
C2×#102×D832
C2×#191276582
C2×#490×C832
C2×#313683