Finite Group Databasebeta

← C2×#24921254 #36312872

Subgroups — C2×#24921254 #36312872

Order 21248.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581840C211yesmaximal, characteristic, complemented
2C22×#14581838C211yesmaximal, characteristic, complemented
3#24921254C2132yesmaximal, direct product factor
4C2×#19128363C211yesmaximal, characteristic, complemented
5C2×#19128362C211yesmaximal, characteristic, complemented
6C2×#19128358C211yesmaximal, characteristic, complemented
7C2×#19128348C213yesmaximal, complemented
8C2×#19128347C213yesmaximal, complemented
9C2×#19128344C213yesmaximal, complemented
10C2×#19128342C213yesmaximal, complemented
11C2×#19128274C213yesmaximal, complemented
12C2×#19128267C213yesmaximal, complemented
13C2×#19128248C213yesmaximal, complemented
14C2×#124×D83C213yesmaximal, complemented
15C2×C4×#13050591C211yesmaximal, characteristic, complemented
16C2×#548×C83C211yesmaximal, characteristic, complemented
17C2×#14581840—216no—
18C2×#14581840C22116yescomplemented
19C2×#14581838—216no—
20C2×#14581838C22116yescomplemented
21C22×#13050591C2211yescharacteristic
22C22×#13050591C2211yescharacteristic
23C22×#13050591C2213yescomplemented
24C22×#13050590C2213yes—
25C22×#13050590C2213yescomplemented
26C22×#13050590C2213yescomplemented
27C22×Q8×D83C2211yescharacteristic, complemented
28C22×Q8×D83C2213yescomplemented
29C23×D332C2213yes—
30C22×D4×D83C2213yes—
31C22×D4×D83C2213yes—
32#19128363C22116yescomplemented
33#19128362C22116yescomplemented
34#19128358C22116yescomplemented
35#19128348C22148yescomplemented
36#19128347C22148yescomplemented
37#19128344C22148yescomplemented
38#19128342C22148yescomplemented
39#19128274C22148yescomplemented
40#19128267C22148yescomplemented
41#19128248C22148yescomplemented
42C2×#14581791C2213yescomplemented
43C2×#14581788C2213yescomplemented
44C2×#14581781C2213yescomplemented
45C2×#14581780C2213yescomplemented
46C2×#14581779C2213yescomplemented
47C2×#14581778C2213yescomplemented
48C2×#14581778C2216yescomplemented
49C2×#14581778C2211yescharacteristic, complemented
50#124×D83C22148yescomplemented
51C2×#14581777C2216yescomplemented
52C2×#14581774C2216yescomplemented
53C2×#14581772C2213yescomplemented
54C2×#14581771C2213yescomplemented
55C2×#14581768C2213yescomplemented
56C2×#14581767C2213yescomplemented
57C2×#14581767C2213yescomplemented
58C2×#14581766C2213yescomplemented
59C2×#14581765C2213yescomplemented
60C2×#14581765C2213yescomplemented
61C2×#14581763C2213yescomplemented
62C2×#14581763C2213yescomplemented
63C2×#14581762C2216yescomplemented
64C2×#14581760C2216yescomplemented
65C4×#13050591C22116yescomplemented
66C2×Q8×Dic83C2211yescharacteristic, complemented
67C2×C4×D332C2213yescomplemented
68C2×C4×D332C2213yescomplemented
69C2×#14581754C2213yescomplemented
70C2×C4×C22⋊D83C2213yescomplemented
71C2×C4×C22⋊D83C2213yescomplemented
72C2×#14581750C2213yescomplemented
73C2×C22⋊C4×D83C2216yescomplemented
74C2×C22⋊C4×D83C2216yescomplemented
75C2×C42×D83C2213yescomplemented
76C22×#41×C83C2211yescharacteristic
77C23×Q8×C83C2211yescharacteristic, complemented
78#548×C83C22116yescomplemented
79C2×#124×C83C2213yescomplemented
80C2×C22⋊Q8×C83C2213yescomplemented
81C2×#121×C83C2213yescomplemented
82C2×C4×Q8×C83C2211yescharacteristic, complemented
83C2×C4×D4×C83C2213yescomplemented
84C24×D83C2316yes—
85#14581840—2128no—
86#14581838—2128no—
87C2×#13050591—224no—
88C2×#13050591—28no—
89C2×#13050591D4116yescomplemented
90C2×#13050591C2318yes—
91C2×#13050591C2318yes—
92C2×#13050591C23124yescomplemented
93C2×#13050590—224no—
94C2×#13050590—224no—
95C2×#13050590—224no—
96C2×#13050590C23124yes—
97C2×#13050590C23124yescomplemented
98C2×#13050590C23124yescomplemented
99C22×Dic166C2313yes—
100C22×Dic166C2313yes—
101C22×Dic166C2311yescharacteristic
102C2×Q8×D83—224no—
103C2×Q8×D83—28no—
104C2×Q8×D83C2318yescomplemented
105C2×Q8×D83C23124yescomplemented
106C22×D332—224no—
107C22×D332C23124yes—
108C22×D332C2313yes—
109C22×D332C2313yes—
110C22×D332C2313yes—
111C22×D332C2313yes—
112C22×D332C2313yes—
113C22×C22⋊D83C2313yes—
114C22×C22⋊D83C2313yes—
115C22×C22⋊D83C2313yes—
116C22×C22⋊D83C2311yescharacteristic
117C22×C22⋊D83C2313yes—
118C22×C22⋊D83C2313yes—
119C2×D4×D83—224no—
120C2×D4×D83—224no—
121C2×D4×D83C23124yes—
122C2×D4×D83C23124yes—
123C22×C4×D83C2316yes—
124C22×C4×D83C2313yes—
125C22×C4×D83C2313yes—
126C22×C4×D83C2313yes—
127C22×C4×D83C2313yes—
128C22×C4×D83C2313yes—
129#14581791C23124yescomplemented
130#14581788C23124yescomplemented
131#14581781C23124yescomplemented
132#14581780C23124yescomplemented
133#14581779C23124yescomplemented
134#14581778C23124yescomplemented
135#14581778C23148yescomplemented
136#14581778C2318yescomplemented
137#14581777C23148yescomplemented
138#14581774C23148yescomplemented
139#14581772C23124yescomplemented
140#14581771C23124yescomplemented
141#14581768C23124yescomplemented
142#14581767C23124yescomplemented
143#14581767C23124yescomplemented
144#14581766C23124yescomplemented
145#14581765C23124yescomplemented
146#14581765C23124yescomplemented
147#14581763C23124yescomplemented
148#14581763C23124yescomplemented
149#14581762C23148yescomplemented
150#14581760C23148yescomplemented
151Q8×Dic83C2318yescomplemented
152C4×D332C23124yescomplemented
153C4×D332C23124yescomplemented
154#14581754C23124yescomplemented
155C4×C22⋊D83C23124yescomplemented
156C4×C22⋊D83C23124yescomplemented
157#14581750C23124yescomplemented
158C2×C4⋊Dic83C2313yes—
159C2×C4⋊Dic83C2313yes—
160C2×Dic83⋊C4C2313yes—
161C2×Dic83⋊C4C2313yes—
162C2×C22⋊Dic83C2313yes—
163C2×C22⋊Dic83C2316yes—
164C2×C22⋊Dic83C2311yescharacteristic
165C2×(C2×D83)⋊C4C2313yes—
166C2×(C2×D83)⋊C4C2313yes—
167C2×(C2×D83)⋊C4C2316yes—
168C2×(C2×D83)⋊C4C2316yes—
169C2×(C2×D83)⋊C4C2316yes—
170C2×(C2×D83)⋊C4C2311yescharacteristic
171C2×(C2×D83)⋊C4C2311yescharacteristic
172C22⋊C4×D83C23148yescomplemented
173C22⋊C4×D83C23148yescomplemented
174C2×C4×Dic83C2311yescharacteristic
175C2×C4×Dic83C2313yes—
176C2×C4×Dic83C2313yes—
177C42×D83C23124yescomplemented
178C2×#41×C83—28no—
179C2×#41×C83C2318yes—
180C22×Q8×C83—28no—
181C22×Q8×C83C2313yes—
182C22×Q8×C83C2311yescharacteristic
183C22×Q8×C83C2318yescomplemented
184C22×D4×C83C2313yes—
185C22×D4×C83C2313yes—
186C23×C4×C83C2313yes—
187C23×C4×C83C2313yes—
188#124×C83C23124yescomplemented
189C22⋊Q8×C83C23124yescomplemented
190#121×C83C23124yescomplemented
191C4×Q8×C83C2318yescomplemented
192C4×D4×C83C23124yescomplemented
193C2×C4⋊C4×C83C2313yes—
194C2×C4⋊C4×C83C2313yes—
195C2×C22⋊C4×C83C2311yescharacteristic
196C2×C22⋊C4×C83C2313yes—
197C2×C22⋊C4×C83C2316yes—
198C2×C42×C83C2313yes—
199C23×D83—224no—
200C23×D83—412no—
201C23×D83—412no—
202C23×D83C2411yescharacteristic
203C23×D83C2413yes—
204C23×D83C2413yes—
205C23×D83C24124yes—
206#13050591—232no—
207#13050591—296no—
208#13050591C2×D4164yescomplemented
209#13050590—296no—
210#13050590—296no—
211#13050590—296no—
212C2×Dic166—212no—
213C2×Dic166—212no—
214C2×Dic166—24no—
215C2×Dic166C24112yes—
216C2×Dic166C24112yes—
217C2×Dic166C2414yes—
218Q8×D83—232no—
219Q8×D83—296no—
220C2×D332—212no—
221C2×D332—212no—
222C2×D332—212no—
223C2×D332—296no—
224C2×D332—46no—
225C2×D332C2×D4124yes—
226C2×D332C24112yes—
227C2×D332C24112yes—
228C2×D332C24112yes—
229C2×D332C24112yes—
230C2×D332C24112yes—
231C2×C22⋊D83—212no—
232C2×C22⋊D83—212no—
233C2×C22⋊D83—212no—
234C2×C22⋊D83—24no—
235C2×C22⋊D83—46no—
236C2×C22⋊D83—46no—
237C2×C22⋊D83C24112yes—
238C2×C22⋊D83C24112yes—
239C2×C22⋊D83C24112yes—
240C2×C22⋊D83C2414yes—
241C2×C22⋊D83C24112yes—
242C2×C22⋊D83C24112yes—
243D4×D83—296no—
244D4×D83—296no—
245C22×Dic83C2411yescharacteristic
246C22×Dic83C2413yes—
247C22×Dic83C2411yescharacteristic
248C22×Dic83C2413yes—
249C22×Dic83C2411yescharacteristic
250C2×C4×D83—224no—
251C2×C4×D83—212no—
252C2×C4×D83—212no—
253C2×C4×D83—46no—
254C2×C4×D83—46no—
255C2×C4×D83C2×D4124yes—
256C2×C4×D83C24112yes—
257C2×C4×D83C24112yes—
258C2×C4×D83C24124yes—
259C2×C4×D83C24112yes—
260C2×C4×D83C24112yes—
261C2×C4×D83C24112yes—
262C4⋊Dic83C24112yes—
263C4⋊Dic83C24112yes—
264Dic83⋊C4C24112yes—
265Dic83⋊C4C24112yes—
266C22⋊Dic83C24124yes—
267C22⋊Dic83C2414yes—
268C22⋊Dic83C24112yes—
269(C2×D83)⋊C4C24124yes—
270(C2×D83)⋊C4C24124yes—
271(C2×D83)⋊C4C24124yes—
272(C2×D83)⋊C4C2414yes—
273(C2×D83)⋊C4C24112yes—
274(C2×D83)⋊C4C2414yes—
275(C2×D83)⋊C4C24112yes—
276C4×Dic83C2414yes—
277C4×Dic83C24112yes—
278C4×Dic83C24112yes—
279C24×C83C2411yescharacteristic
280C24×C83C2413yes—
281#41×C83—232no—
282C2×Q8×C83—232no—
283C2×Q8×C83—212no—
284C2×Q8×C83C2×D418yes—
285C2×Q8×C83C24112yes—
286C2×Q8×C83C2414yes—
287C2×D4×C83—212no—
288C2×D4×C83—46no—
289C2×D4×C83C24112yes—
290C2×D4×C83C24112yes—
291C22×C4×C83—212no—
292C22×C4×C83—212no—
293C22×C4×C83C24112yes—
294C22×C4×C83C24112yes—
295C22×C4×C83C2411yescharacteristic
296C22×C4×C83C2413yes—
297C22×C4×C83C2413yes—
298C22×C4×C83C2411yescharacteristic
299C22×C4×C83C2413yes—
300C4⋊C4×C83C24112yes—
301C4⋊C4×C83C24112yes—
302C22⋊C4×C83C24124yes—
303C22⋊C4×C83C2414yes—
304C22⋊C4×C83C24112yes—
305C42×C83C24112yes—
306C23×C83—22no—
307C23×C83—26no—
308C23×C83—22no—
309C23×C83—26no—
310C23×C83—22no—
311C23×C83—26no—
312C23×C83C2516yes—
313C23×C83C2512yes—
314C23×C83C2511yescharacteristic
315C22×D83—26no—
316C22×D83—26no—
317C22×D83—22no—
318C22×D83—26no—
319C22×D83—22no—
320C22×D83—26no—
321C22×D83—22no—
322C22×D83—26no—
323C22×D83—248no—
324C22×D83—424no—
325C22×D83—424no—
326C22×D83—848no—
327C22×D83C22×D4112yes—
328C22×D83C2516yes—
329C22×D83C2512yes—
330C22×D83C2516yes—
331Q8×C83—224no—
332Q8×C83C22×D4116yes—
333D4×C83—224no—
334D4×C83—412no—
335C2×C4×C83—22no—
336C2×C4×C83—26no—
337C2×C4×C83—26no—
338C2×C4×C83—22no—
339C2×C4×C83—224no—
340C2×C4×C83—224no—
341C2×C4×C83C22×D4112yes—
342C2×C4×C83C2512yes—
343C2×C4×C83C2516yes—
344C2×C4×C83C2516yes—
345C2×C4×C83C2512yes—
346C2×C4×C83C2516yes—
347C22⋊D83—224no—
348C22⋊D83—224no—
349C22⋊D83—224no—
350C22⋊D83—28no—
351C22⋊D83—412no—
352C22⋊D83—412no—
353C2×Dic83—22no—
354C2×Dic83—26no—
355C2×Dic83—22no—
356C2×Dic83—26no—
357C2×Dic83C22×D414yes—
358C2×Dic83C2512yes—
359C2×Dic83C2516yes—
360C2×Dic83C2516yes—
361C2×Dic83C2512yes—
362C2×Dic83C2512yes—
363D332—224no—
364D332—224no—
365D332—224no—
366D332—412no—
367D332C22×D4148yes—
368C4×D83—248no—
369C4×D83—224no—
370C4×D83—224no—
371C4×D83—412no—
372C4×D83—412no—
373C4×D83C22×D4148yes—
374Dic166—224no—
375Dic166—224no—
376Dic166—28no—
377C22×C83—22no—
378C22×C83—26no—
379C22×C83—22no—
380C22×C83—26no—
381C22×C83—22no—
382C22×C83—26no—
383C22×C83—412no—
384C22×C83—44no—
385C22×C83C23×D412yes—
386C22×C83#58512yes—
387C22×C83#58512yes—
388C22×C83C2611yescharacteristic
389C2×D83—26no—
390C2×D83—26no—
391C2×D83—224no—
392C2×D83—22no—
393C2×D83—26no—
394C2×D83—22no—
395C2×D83—26no—
396C2×D83—22no—
397C2×D83—26no—
398C2×D83—44no—
399C2×D83—412no—
400C2×D83—848no—
401C2×D83C23×D4112yes—
402C4×C83—26no—
403C4×C83—22no—
404C4×C83—22no—
405C4×C83—26no—
406C4×C83C23×D4112yes—
407Dic83—26no—
408Dic83—22no—
409Dic83—22no—
410Dic83—26no—
411Dic83C23×D414yes—
412C2×#3500—831nomaximal, Sylow
413C2×C83—46no—
414C2×C83—42no—
415C2×C83#350014yescomplemented
416C2×C83C24×D411yescharacteristic
417C2×C83C2×#58511yescharacteristic
418C2×C83C2×#58511yescharacteristic
419D83—212no—
420D83—42no—
421D83—46no—
422C22×2−1+4—831no—
423C22×H(5,𝔽2)—831no—
424#3500—8332no—
425C2×#548—831no—
426C2×#548—831no—
427C2×#548—831no—
428C2×#548D8311yescharacteristic, complemented
429C2×#546—833no—
430C2×#546—833no—
431C2×#546—833no—
432C2×#546—833no—
433C2×#536—833no—
434C2×#535—833no—
435C2×#532—833no—
436C22×#124—833no—
437C2×C4×#41—831no—
438C83C2×#350011yescharacteristic, complemented, Sylow
439C2×2−1+4—8316no—
440C2×2−1+4—16616no—
441C2×H(5,𝔽2)—8316no—
442C2×H(5,𝔽2)—16616no—
443C22×#41—831no—
444C22×#41—831no—
445C22×#41—833no—
446C22×#41—833no—
447C22×#41—833no—
448C22×#41—833no—
449C22×#41C2×D8311yescharacteristic
450C23×Q8—833no—
451C23×Q8—831no—
452C23×Q8C2×D8311yescharacteristic, complemented
453C23×D4—833no—
454C23×D4—833no—
455C23×D4—833no—
456#548—8316no—
457#548—8316no—
458#548—8316no—
459#548C2×D83116yescomplemented
460#546—8348no—
461#546—8348no—
462#546—8348no—
463#546—8348no—
464#536—8348no—
465#535—8348no—
466#532—8348no—
467C2×C4⋊Q8—833no—
468C2×#127—833no—
469C2×#124—833no—
470C2×#124—833no—
471C2×#124—8348no—
472C2×#124—833no—
473C2×#124—836no—
474C2×#124—831no—
475C2×#124—833no—
476C2×#124C2×D8313yescomplemented
477C2×#123—836no—
478C2×#123—836no—
479C2×C22⋊Q8—833no—
480C2×C22⋊Q8—833no—
481C2×C22⋊Q8—833no—
482C2×C22⋊Q8C2×D8313yescomplemented
483C2×#121—833no—
484C2×#121—833no—
485C2×#121—833no—
486C2×#121—833no—
487C2×#121—833no—
488C2×#121—833no—
489C2×#121—833no—
490C2×#121C2×D8313yescomplemented
491C2×#120—836no—
492C2×#120—836no—
493C4×#41—8316no—
494C2×C4×Q8—831no—
495C2×C4×Q8C2×D8311yescharacteristic, complemented
496C2×C4×D4—833no—
497C2×C4×D4—833no—
498C2×C4×D4—833no—
499C2×C4×D4—833no—
500C2×C4×D4—833no—
501C2×C4×D4C2×D8313yescomplemented
502C2×#117—833no—
503C22×C22⋊C4—836no—
504C22×C22⋊C4—836no—
505C22×C42—833no—
506C25—836no—
5072−1+4—166128no—
508H(5,𝔽2)—166128no—
509C2×#41—28no—
510C2×#41—8316no—
511C2×#41—838no—
512C2×#41—8324no—
513C2×#41—838no—
514C2×#41—8324no—
515C2×#41—8324no—
516C2×#41—8324no—
517C2×#41—16624no—
518C2×#41—16624no—
519C2×#41—16624no—
520C2×#41—16624no—
521C2×#41—1668no—
522C2×#41C22×D8318yes—
523C22×Q8—28no—
524C22×Q8—8324no—
525C22×Q8—838no—
526C22×Q8—833no—
527C22×Q8—833no—
528C22×Q8—831no—
529C22×Q8—16624no—
530C22×Q8—1668no—
531C22×Q8C22×D8313yes—
532C22×Q8C22×D8311yescharacteristic
533C22×Q8C22×D8318yescomplemented
534C22×D4—833no—
535C22×D4—833no—
536C22×D4—833no—
537C22×D4—833no—
538C22×D4—833no—
539C22×D4—831no—
540C22×D4—8324no—
541C22×D4—8324no—
542C22×D4—833no—
543C22×D4—833no—
544C22×D4—833no—
545C22×D4—833no—
546C22×D4—833no—
547C22×D4—8324no—
548C22×D4—16624no—
549C22×D4—16624no—
550C22×D4—16624no—
551C22×D4C22×D8313yes—
552C22×D4C22×D8313yes—
553C23×C4—833no—
554C23×C4—833no—
555C23×C4—833no—
556C23×C4—836no—
557C23×C4—833no—
558C23×C4—833no—
559C23×C4C22×D8313yes—
560C23×C4C22×D8313yes—
561C4⋊Q8—8324no—
562#127—8324no—
563#124—8324no—
564#124—8324no—
565#124—8324no—
566#124—8348no—
567#124—838no—
568#124—8324no—
569#124C22×D83124yescomplemented
570#123—8348no—
571#123—8348no—
572C22⋊Q8—8324no—
573C22⋊Q8—8324no—
574C22⋊Q8—8324no—
575C22⋊Q8C22×D83124yescomplemented
576#121—8324no—
577#121—8324no—
578#121—8324no—
579#121—8324no—
580#121—8324no—
581#121—8324no—
582#121—8324no—
583#121C22×D83124yescomplemented
584#120—8348no—
585#120—8348no—
586C4×Q8—838no—
587C4×Q8C22×D8318yescomplemented
588C4×D4—8324no—
589C4×D4—8324no—
590C4×D4—8324no—
591C4×D4—8324no—
592C4×D4—8324no—
593C4×D4C22×D83124yescomplemented
594#117—8324no—
595C2×C4⋊C4—833no—
596C2×C4⋊C4—833no—
597C2×C4⋊C4—833no—
598C2×C4⋊C4—833no—
599C2×C4⋊C4C22×D8313yes—
600C2×C4⋊C4C22×D8313yes—
601C2×C22⋊C4—833no—
602C2×C22⋊C4—836no—
603C2×C22⋊C4—831no—
604C2×C22⋊C4—833no—
605C2×C22⋊C4—833no—
606C2×C22⋊C4—836no—
607C2×C22⋊C4—836no—
608C2×C22⋊C4—836no—
609C2×C22⋊C4—831no—
610C2×C22⋊C4—831no—
611C2×C22⋊C4—8348no—
612C2×C22⋊C4—8348no—
613C2×C22⋊C4C22×D8313yes—
614C2×C22⋊C4C22×D8316yes—
615C2×C22⋊C4C22×D8311yescharacteristic
616C2×C42—833no—
617C2×C42—833no—
618C2×C42—831no—
619C2×C42—8324no—
620C2×C42C22×D8313yes—
621C24—33212no—
622C24—33212no—
623C24—8324no—
624C24—833no—
625C24—833no—
626C24—831no—
627C24—16624no—
628C24C23×D8313yes—
629C24C23×D8311yescharacteristic
630#41—232no—
631#41—8364no—
632#41—16696no—
633#41—16696no—
634#41—16696no—
635#41—16696no—
636#41—16632no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—8312no—
640C2×Q8—8312no—
641C2×Q8—834no—
642C2×Q8—16612no—
643C2×Q8—1664no—
644C2×Q8—16696no—
645C2×Q8—16632no—
646C2×Q8—16612no—
647C2×Q8D4×D8318yes—
648C2×Q8C23×D83112yes—
649C2×Q8C23×D8314yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—3326no—
653C2×D4—3326no—
654C2×D4—3326no—
655C2×D4—8312no—
656C2×D4—8312no—
657C2×D4—8312no—
658C2×D4—8312no—
659C2×D4—8312no—
660C2×D4—834no—
661C2×D4—8324no—
662C2×D4—8312no—
663C2×D4—8312no—
664C2×D4—8312no—
665C2×D4—8312no—
666C2×D4—8312no—
667C2×D4—16696no—
668C2×D4—16612no—
669C2×D4—16612no—
670C2×D4—16696no—
671C2×D4—16612no—
672C2×D4—1664no—
673C2×D4—16696no—
674C2×D4—16612no—
675C2×D4—16612no—
676C2×D4—16612no—
677C2×D4C23×D83112yes—
678C2×D4C23×D83112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—3326no—
682C22×C4—3326no—
683C22×C4—8312no—
684C22×C4—8312no—
685C22×C4—831no—
686C22×C4—8324no—
687C22×C4—8312no—
688C22×C4—831no—
689C22×C4—833no—
690C22×C4—833no—
691C22×C4—831no—
692C22×C4—8324no—
693C22×C4—8312no—
694C22×C4—8312no—
695C22×C4—16624no—
696C22×C4—16612no—
697C22×C4—16612no—
698C22×C4C23×D83112yes—
699C22×C4C23×D83112yes—
700C22×C4C23×D8311yescharacteristic
701C22×C4C23×D8313yes—
702C22×C4C23×D8313yes—
703C22×C4C23×D8311yescharacteristic
704C22×C4C23×D8313yes—
705C4⋊C4—8312no—
706C4⋊C4—8312no—
707C4⋊C4—8312no—
708C4⋊C4—8312no—
709C4⋊C4C23×D83112yes—
710C4⋊C4C23×D83112yes—
711C22⋊C4—8312no—
712C22⋊C4—8324no—
713C22⋊C4—834no—
714C22⋊C4—8312no—
715C22⋊C4—8312no—
716C22⋊C4—8324no—
717C22⋊C4—8324no—
718C22⋊C4—8324no—
719C22⋊C4—834no—
720C22⋊C4—834no—
721C22⋊C4C23×D83112yes—
722C22⋊C4C23×D83124yes—
723C22⋊C4C23×D8314yes—
724C42—834no—
725C42—8312no—
726C42—8312no—
727C42C23×D83112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—33224no—
735C23—33224no—
736C23—8312no—
737C23—836no—
738C23—836no—
739C23—832no—
740C23—66448no—
741C23—16648no—
742C23—1662no—
743C23—1666no—
744C23—1662no—
745C23—1666no—
746C23—1662no—
747C23—1666no—
748C23—1666no—
749C23—1666no—
750C23C24×D8316yes—
751C23C24×D8312yes—
752C23C24×D8311yescharacteristic
753Q8—224no—
754Q8—16624no—
755Q8—1668no—
756Q8—16624no—
757Q8C2×D4×D83116yes—
758D4—224no—
759D4—412no—
760D4—33212no—
761D4—33212no—
762D4—33212no—
763D4—8348no—
764D4—16624no—
765D4—16624no—
766D4—16624no—
767D4—1668no—
768D4—16624no—
769D4—16624no—
770D4—16624no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—33212no—
778C2×C4—33212no—
779C2×C4—834no—
780C2×C4—832no—
781C2×C4—8348no—
782C2×C4—832no—
783C2×C4—836no—
784C2×C4—836no—
785C2×C4—832no—
786C2×C4—16648no—
787C2×C4—1662no—
788C2×C4—1666no—
789C2×C4—1662no—
790C2×C4—1666no—
791C2×C4—16624no—
792C2×C4—16624no—
793C2×C4C2×D4×D83112yes—
794C2×C4C24×D8312yes—
795C2×C4C24×D8316yes—
796C2×C4C24×D8316yes—
797C2×C4C24×D8312yes—
798C2×C4C24×D8316yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—33212no—
808C22—3324no—
809C22—8312no—
810C22—66448no—
811C22—1662no—
812C22—1666no—
813C22—1662no—
814C22—1666no—
815C22—1662no—
816C22—1666no—
817C22—1666no—
818C22—1666no—
819C22—16624no—
820C22C22×D4×D8312yes—
821C22#1912853712yes—
822C22#1912853812yes—
823C22C25×D8311yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—834no—
829C4—1662no—
830C4—1666no—
831C4—1662no—
832C4—1666no—
833C4C22×D4×D83112yes—
834C2—46no—
835C2—42no—
836C2—3326no—
837C2—3322no—
838C2—16612no—
839C2#2492125414yesdirect product factor
840C2C23×D4×D8311yescharacteristic
841C2C2×#1912853711yescharacteristic
842C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#548×C83C2
socleC23×C83C25
hypercenterC2×#548D83
hypocenterC83C2×#3500
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14581840C2semidirect
2. C22×#14581838C2semidirect
3. #24921254C2direct (N × H)
4. C2×#19128363C2semidirect
5. C2×#19128362C2semidirect
6. C2×#19128358C2semidirect
7. C2×#19128348C2semidirect
8. C2×#19128347C2semidirect
9. C2×#19128344C2semidirect
10. C2×#19128342C2semidirect
11. C2×#19128274C2semidirect
12. C2×#19128267C2semidirect
13. C2×#19128248C2semidirect
14. C2×#124×D83C2semidirect
15. C2×C4×#13050591C2semidirect
16. C2×#548×C83C2semidirect
18. C2×#14581840C22semidirect
20. C2×#14581838C22semidirect
23. C22×#13050591C22semidirect
25. C22×#13050590C22semidirect
26. C22×#13050590C22semidirect
27. C22×Q8×D83C22semidirect
28. C22×Q8×D83C22semidirect
32. #19128363C22semidirect
33. #19128362C22semidirect
34. #19128358C22semidirect
35. #19128348C22semidirect
36. #19128347C22semidirect
37. #19128344C22semidirect
38. #19128342C22semidirect
39. #19128274C22semidirect
40. #19128267C22semidirect
41. #19128248C22semidirect
42. C2×#14581791C22semidirect
43. C2×#14581788C22semidirect
44. C2×#14581781C22semidirect
45. C2×#14581780C22semidirect
46. C2×#14581779C22semidirect
47. C2×#14581778C22semidirect
48. C2×#14581778C22semidirect
49. C2×#14581778C22semidirect
50. #124×D83C22semidirect
51. C2×#14581777C22semidirect
52. C2×#14581774C22semidirect
53. C2×#14581772C22semidirect
54. C2×#14581771C22semidirect
55. C2×#14581768C22semidirect
56. C2×#14581767C22semidirect
57. C2×#14581767C22semidirect
58. C2×#14581766C22semidirect
59. C2×#14581765C22semidirect
60. C2×#14581765C22semidirect
61. C2×#14581763C22semidirect
62. C2×#14581763C22semidirect
63. C2×#14581762C22semidirect
64. C2×#14581760C22semidirect
65. C4×#13050591C22semidirect
66. C2×Q8×Dic83C22semidirect
67. C2×C4×D332C22semidirect
68. C2×C4×D332C22semidirect
69. C2×#14581754C22semidirect
70. C2×C4×C22⋊D83C22semidirect
71. C2×C4×C22⋊D83C22semidirect
72. C2×#14581750C22semidirect
73. C2×C22⋊C4×D83C22semidirect
74. C2×C22⋊C4×D83C22semidirect
75. C2×C42×D83C22semidirect
77. C23×Q8×C83C22semidirect
78. #548×C83C22semidirect
79. C2×#124×C83C22semidirect
80. C2×C22⋊Q8×C83C22semidirect
81. C2×#121×C83C22semidirect
82. C2×C4×Q8×C83C22semidirect
83. C2×C4×D4×C83C22semidirect
89. C2×#13050591D4semidirect
92. C2×#13050591C23semidirect
97. C2×#13050590C23semidirect
98. C2×#13050590C23semidirect
104. C2×Q8×D83C23semidirect
105. C2×Q8×D83C23semidirect
129. #14581791C23semidirect
130. #14581788C23semidirect
131. #14581781C23semidirect
132. #14581780C23semidirect
133. #14581779C23semidirect
134. #14581778C23semidirect
135. #14581778C23semidirect
136. #14581778C23semidirect
137. #14581777C23semidirect
138. #14581774C23semidirect
139. #14581772C23semidirect
140. #14581771C23semidirect
141. #14581768C23semidirect
142. #14581767C23semidirect
143. #14581767C23semidirect
144. #14581766C23semidirect
145. #14581765C23semidirect
146. #14581765C23semidirect
147. #14581763C23semidirect
148. #14581763C23semidirect
149. #14581762C23semidirect
150. #14581760C23semidirect
151. Q8×Dic83C23semidirect
152. C4×D332C23semidirect
153. C4×D332C23semidirect
154. #14581754C23semidirect
155. C4×C22⋊D83C23semidirect
156. C4×C22⋊D83C23semidirect
157. #14581750C23semidirect
172. C22⋊C4×D83C23semidirect
173. C22⋊C4×D83C23semidirect
177. C42×D83C23semidirect
183. C22×Q8×C83C23semidirect
188. #124×C83C23semidirect
189. C22⋊Q8×C83C23semidirect
190. #121×C83C23semidirect
191. C4×Q8×C83C23semidirect
192. C4×D4×C83C23semidirect
208. #13050591C2×D4semidirect
415. C2×C83#3500semidirect
428. C2×#548D83semidirect
438. C83C2×#3500semidirect
452. C23×Q8C2×D83semidirect
459. #548C2×D83semidirect
476. C2×#124C2×D83semidirect
482. C2×C22⋊Q8C2×D83semidirect
490. C2×#121C2×D83semidirect
495. C2×C4×Q8C2×D83semidirect
501. C2×C4×D4C2×D83semidirect
533. C22×Q8C22×D83semidirect
569. #124C22×D83semidirect
575. C22⋊Q8C22×D83semidirect
583. #121C22×D83semidirect
587. C4×Q8C22×D83semidirect
593. C4×D4C22×D83semidirect
839. C2#24921254direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145818402
C22×#145818382
#249212542
C2×#191283632
C2×#191283622
C2×#191283582
C2×#191283482
C2×#191283472
C2×#191283442
C2×#191283422
C2×#191282742
C2×#191282672
C2×#191282482
C2×#124×D832
C2×C4×#130505912
C2×#548×C832
C2×#350083