Finite Group Databasebeta

← C2×#24921113 #36312568

Subgroups — C2×#24921113 #36312568

Order 21248.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581840C211yesmaximal, characteristic, complemented
2C23×Q8×D83C211yesmaximal, characteristic, complemented
3#24921113C2132yesmaximal, direct product factor
4C2×#19128366C213yesmaximal, complemented
5C2×Q8×C22⋊D83C211yesmaximal, characteristic, complemented
6C2×#19128364C213yesmaximal, complemented
7C2×#19128363C211yesmaximal, characteristic, complemented
8C2×#19128362C211yesmaximal, characteristic, complemented
9C2×#19128361C213yesmaximal, complemented
10C2×#19128360C213yesmaximal, complemented
11C2×#19128276C213yesmaximal, complemented
12C2×#19128274C213yesmaximal, complemented
13C2×#19128214C213yesmaximal, complemented
14C2×#19128210C213yesmaximal, complemented
15C2×#19128177C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C83C211yesmaximal, characteristic, complemented
17C2×#14581840—216no—
18C2×#14581840C22116yescomplemented
19C22×#13050591C2213yes—
20C22×#13050591C2211yescharacteristic, complemented
21C22×#13050590C2213yes—
22C22×#13050590C2213yescomplemented
23C23×Dic166C2213yes—
24C22×Q8×D83—216no—
25C22×Q8×D83C2213yes—
26C22×Q8×D83C2211yescharacteristic
27C22×Q8×D83C2213yes—
28C22×Q8×D83C2211yescharacteristic
29C22×Q8×D83C22116yescomplemented
30C22×Q8×D83C2213yescomplemented
31C23×C4×D83C2213yes—
32#19128366C22148yescomplemented
33Q8×C22⋊D83C22116yescomplemented
34#19128364C22148yescomplemented
35#19128363C22116yescomplemented
36#19128362C22116yescomplemented
37#19128361C22148yescomplemented
38#19128360C22148yescomplemented
39#19128276C22148yescomplemented
40#19128274C22148yescomplemented
41C2×#14581791C2216yescomplemented
42C2×#14581790C2213yescomplemented
43C2×#14581781C2213yescomplemented
44C2×#14581780C2213yescomplemented
45C2×#14581778C2216yescomplemented
46#19128214C22148yescomplemented
47#19128210C22148yescomplemented
48C2×#14581777C2213yes—
49C2×#14581777C2216yes—
50C2×#14581774C2213yes—
51C2×#14581772C2213yescomplemented
52C2×#14581771C2213yescomplemented
53C2×#14581770C2213yes—
54C2×#14581770C2216yescomplemented
55C2×#14581770C2216yescomplemented
56C2×#14581769C2213yes—
57C2×#14581768C2213yes—
58C2×#14581768C2213yescomplemented
59C2×#14581767C2213yes—
60C2×#14581766C2213yes—
61C2×#14581765C2213yes—
62C2×#14581764C2213yes—
63C2×#14581762C2213yes—
64C2×#14581760C2211yescharacteristic
65#19128177C22116yescomplemented
66C2×Q8×Dic83C2211yescharacteristic, complemented
67C2×C4×Dic166C2213yescomplemented
68C2×#14581757C2213yescomplemented
69C2×C4×D332C2213yes—
70C2×#14581754C2216yes—
71C2×C4×C22⋊D83C2213yes—
72C2×C4×C22⋊D83C2213yes—
73C2×(C22⋊D83)⋊C4C2216yes—
74C2×#14581750C2213yes—
75C2×#14581749C2213yes—
76C23×Q8×C83C2211yescharacteristic
77C23×Q8×C83C2211yescharacteristic, complemented
78D4×Q8×C83C22116yescomplemented
79C2×C4⋊Q8×C83C2213yescomplemented
80C2×C22⋊Q8×C83C2213yes—
81C2×C22⋊Q8×C83C2213yescomplemented
82C2×C4×Q8×C83C2211yescharacteristic, complemented
83C2×C4×D4×C83C2213yes—
84C24×D83C2311yescharacteristic
85#14581840—2128no—
86C2×#13050591—224no—
87C2×#13050591—28no—
88C2×#13050591C23124yes—
89C2×#13050591C2318yescomplemented
90C2×#13050590—224no—
91C2×#13050590—224no—
92C2×#13050590C23124yes—
93C2×#13050590C23124yescomplemented
94C22×Dic166—224no—
95C22×Dic166C23124yes—
96C22×Dic166C2313yes—
97C22×Dic166C2316yes—
98C22×Dic166C2313yes—
99C22×Dic166C2313yes—
100C2×Q8×D83—224no—
101C2×Q8×D83—224no—
102C2×Q8×D83—2128no—
103C2×Q8×D83—224no—
104C2×Q8×D83—28no—
105C2×Q8×D83D4116yescomplemented
106C2×Q8×D83C23124yes—
107C2×Q8×D83C2318yes—
108C2×Q8×D83C23124yes—
109C2×Q8×D83C2318yes—
110C2×Q8×D83C23124yescomplemented
111C22×D332C2313yes—
112C22×D332C2313yes—
113C22×D332C2313yes—
114C22×C22⋊D83C2313yes—
115C22×C22⋊D83C2311yescharacteristic
116C22×C22⋊D83C2311yescharacteristic
117C22×C22⋊D83C2313yes—
118C23×Dic83C2313yes—
119C22×C4×D83—224no—
120C22×C4×D83C2316yes—
121C22×C4×D83C2313yes—
122C22×C4×D83C2313yes—
123C22×C4×D83C2313yes—
124C22×C4×D83C2313yes—
125C22×C4×D83C23124yes—
126C22×C4×D83C2313yes—
127#14581791C23148yescomplemented
128#14581790C23124yescomplemented
129#14581781C23124yescomplemented
130#14581780C23124yescomplemented
131#14581778C23148yescomplemented
132#14581777C23124yes—
133#14581777C23148yes—
134#14581774C23124yes—
135#14581772C23124yescomplemented
136#14581771C23124yescomplemented
137#14581770C23124yes—
138#14581770C23148yescomplemented
139#14581770C23148yescomplemented
140#14581769C23124yes—
141#14581768C23124yes—
142#14581768C23124yescomplemented
143#14581767C23124yes—
144#14581766C23124yes—
145#14581765C23124yes—
146#14581764C23124yes—
147#14581762C23124yes—
148#14581760C2318yes—
149Q8×Dic83C2318yescomplemented
150C4×Dic166C23124yescomplemented
151#14581757C23124yescomplemented
152C4×D332C23124yes—
153#14581754C23148yes—
154C4×C22⋊D83C23124yes—
155C4×C22⋊D83C23124yes—
156(C22⋊D83)⋊C4C23148yes—
157#14581750C23124yes—
158#14581749C23124yes—
159C2×C4⋊Dic83C2313yes—
160C2×C4⋊Dic83C2313yes—
161C2×Dic83⋊C4C2313yes—
162C2×Dic83⋊C4C2313yes—
163C2×Dic83⋊C4C2316yes—
164C2×Dic83⋊C4C2313yes—
165C2×Dic83⋊C4C2313yes—
166C2×C22⋊Dic83C2311yescharacteristic
167C2×C22⋊Dic83C2313yes—
168C2×(C2×D83)⋊C4C2311yescharacteristic
169C2×(C2×D83)⋊C4C2313yes—
170C2×(C2×D83)⋊C4C2316yes—
171C2×(C2×D83)⋊C4C2313yes—
172C2×(C2×D83)⋊C4C2313yes—
173C2×(C2×D83)⋊C4C2316yes—
174C2×(C2×D83)⋊C4C2311yescharacteristic
175C2×(C2×D83)⋊C4C2313yes—
176C2×C4×Dic83C2313yes—
177C2×C4×Dic83C2316yes—
178C22×Q8×C83—28no—
179C22×Q8×C83—28no—
180C22×Q8×C83C2318yes—
181C22×Q8×C83C2313yes—
182C22×Q8×C83C2313yes—
183C22×Q8×C83C2311yescharacteristic
184C22×Q8×C83C2318yescomplemented
185C22×D4×C83C2311yescharacteristic
186C23×C4×C83C2313yes—
187C23×C4×C83C2313yes—
188C4⋊Q8×C83C23124yescomplemented
189C22⋊Q8×C83C23124yes—
190C22⋊Q8×C83C23124yescomplemented
191C4×Q8×C83C2318yescomplemented
192C4×D4×C83C23124yes—
193C2×C4⋊C4×C83C2313yes—
194C2×C4⋊C4×C83C2313yes—
195C2×C4⋊C4×C83C2316yes—
196C2×C22⋊C4×C83C2313yes—
197C2×C22⋊C4×C83C2313yes—
198C2×C42×C83C2313yes—
199C23×D83—24no—
200C23×D83—24no—
201C23×D83—24no—
202C23×D83C2414yes—
203C23×D83C2413yes—
204C23×D83C2411yescharacteristic
205C23×D83C2411yescharacteristic
206#13050591—232no—
207#13050591—296no—
208#13050590—296no—
209#13050590—296no—
210C2×Dic166—212no—
211C2×Dic166—224no—
212C2×Dic166—212no—
213C2×Dic166—296no—
214C2×Dic166C2×D4124yes—
215C2×Dic166C24112yes—
216C2×Dic166C24124yes—
217C2×Dic166C24112yes—
218C2×Dic166C24112yes—
219Q8×D83—232no—
220Q8×D83—296no—
221Q8×D83—296no—
222Q8×D83—296no—
223Q8×D83C2×D4164yescomplemented
224C2×D332—212no—
225C2×D332—212no—
226C2×D332—212no—
227C2×D332C24112yes—
228C2×D332C24112yes—
229C2×D332C24112yes—
230C2×C22⋊D83—212no—
231C2×C22⋊D83—24no—
232C2×C22⋊D83—24no—
233C2×C22⋊D83—212no—
234C2×C22⋊D83C2414yes—
235C2×C22⋊D83C2414yes—
236C2×C22⋊D83C24112yes—
237C2×C22⋊D83C24112yes—
238C22×Dic83—212no—
239C22×Dic83C24112yes—
240C22×Dic83C2411yescharacteristic
241C22×Dic83C2413yes—
242C22×Dic83C2411yescharacteristic
243C22×Dic83C2413yes—
244C22×Dic83C2413yes—
245C2×C4×D83—212no—
246C2×C4×D83—212no—
247C2×C4×D83—212no—
248C2×C4×D83—212no—
249C2×C4×D83—224no—
250C2×C4×D83—296no—
251C2×C4×D83C2×D4124yes—
252C2×C4×D83C24112yes—
253C2×C4×D83C24112yes—
254C2×C4×D83C24112yes—
255C2×C4×D83C24124yes—
256C2×C4×D83C24112yes—
257C2×C4×D83C24112yes—
258C4⋊Dic83C24112yes—
259C4⋊Dic83C24112yes—
260Dic83⋊C4C24112yes—
261Dic83⋊C4C24112yes—
262Dic83⋊C4C24124yes—
263Dic83⋊C4C24112yes—
264Dic83⋊C4C24112yes—
265C22⋊Dic83C2414yes—
266C22⋊Dic83C24112yes—
267(C2×D83)⋊C4C2414yes—
268(C2×D83)⋊C4C2414yes—
269(C2×D83)⋊C4C24112yes—
270(C2×D83)⋊C4C24112yes—
271(C2×D83)⋊C4C24112yes—
272(C2×D83)⋊C4C24112yes—
273(C2×D83)⋊C4C24124yes—
274(C2×D83)⋊C4C24124yes—
275C4×Dic83C24124yes—
276C4×Dic83C24112yes—
277C24×C83C2411yescharacteristic
278C24×C83C2411yescharacteristic
279C2×Q8×C83—232no—
280C2×Q8×C83—232no—
281C2×Q8×C83—212no—
282C2×Q8×C83—212no—
283C2×Q8×C83C2×D418yes—
284C2×Q8×C83C24112yes—
285C2×Q8×C83C24112yes—
286C2×Q8×C83C2414yes—
287C2×D4×C83—24no—
288C2×D4×C83C2414yes—
289C22×C4×C83—212no—
290C22×C4×C83—212no—
291C22×C4×C83C24112yes—
292C22×C4×C83C24112yes—
293C22×C4×C83C2413yes—
294C22×C4×C83C2413yes—
295C22×C4×C83C2413yes—
296C22×C4×C83C2411yescharacteristic
297C22×C4×C83C2413yes—
298C4⋊C4×C83C24112yes—
299C4⋊C4×C83C24112yes—
300C4⋊C4×C83C24124yes—
301C22⋊C4×C83C24112yes—
302C22⋊C4×C83C24112yes—
303C42×C83C24112yes—
304C23×C83—22no—
305C23×C83—22no—
306C23×C83—22no—
307C23×C83—22no—
308C23×C83—22no—
309C23×C832−1+414yescomplemented
310C23×C83C2512yes—
311C23×C83C2512yes—
312C23×C83C2511yescharacteristic
313C22×D83—232no—
314C22×D83—22no—
315C22×D83—22no—
316C22×D83—22no—
317C22×D83—22no—
318C22×D83—28no—
319C22×D83—28no—
320C22×D83—28no—
321C22×D83—26no—
322C22×D83—26no—
323C22×D83—26no—
324C22×D83C22×D414yes—
325C22×D832−1+414yescomplemented
326C22×D83C2516yes—
327C22×D83C2512yes—
328C22×D83C2512yes—
329Q8×C83—224no—
330Q8×C83—224no—
331Q8×C83C22×D4116yes—
332D4×C83—28no—
333C2×C4×C83—26no—
334C2×C4×C83—26no—
335C2×C4×C83—22no—
336C2×C4×C83—26no—
337C2×C4×C83—224no—
338C2×C4×C83—224no—
339C2×C4×C83C22×D4112yes—
340C2×C4×C83C2512yes—
341C2×C4×C83C2516yes—
342C2×C4×C83C2516yes—
343C2×C4×C83C2516yes—
344C2×C4×C83C2516yes—
345C22⋊D83—224no—
346C22⋊D83—28no—
347C22⋊D83—28no—
348C22⋊D83—224no—
349C2×Dic83—22no—
350C2×Dic83—26no—
351C2×Dic83—22no—
352C2×Dic83—26no—
353C2×Dic83—224no—
354C2×Dic83C22×D4112yes—
355C2×Dic83C2512yes—
356C2×Dic83C2516yes—
357C2×Dic83C2516yes—
358C2×Dic83C2512yes—
359C2×Dic83C2516yes—
360D332—224no—
361D332—224no—
362D332—224no—
363C4×D83—224no—
364C4×D83—224no—
365C4×D83—224no—
366C4×D83—224no—
367C4×D83—248no—
368C4×D83C22×D4148yes—
369Dic166—224no—
370Dic166—248no—
371Dic166—224no—
372Dic166C22×D4148yes—
373C22×C83—22no—
374C22×C83—22no—
375C22×C83—28no—
376C22×C83—22no—
377C22×C83—22no—
378C22×C83—22no—
379C22×C83—44no—
380C22×C83C23×D412yes—
381C22×C83C2×2−1+412yes—
382C22×C83C2×2−1+412yes—
383C22×C83C2×2−1+414yescomplemented
384C22×C83C2611yescharacteristic
385C2×D83—232no—
386C2×D83—22no—
387C2×D83—22no—
388C2×D83—22no—
389C2×D83—22no—
390C2×D83—28no—
391C2×D83—28no—
392C2×D83—26no—
393C2×D83—26no—
394C2×D83—26no—
395C2×D83—412no—
396C2×D83C23×D414yes—
397C2×D83C2×2−1+414yescomplemented
398C4×C83—26no—
399C4×C83—26no—
400C4×C83—26no—
401C4×C83—22no—
402C4×C83C23×D4112yes—
403Dic83—26no—
404Dic83—22no—
405Dic83—22no—
406Dic83—26no—
407Dic83C23×D4112yes—
408C2×#3486—831nomaximal, Sylow
409C2×C83—24no—
410C2×C83—42no—
411C2×C83#348614yescomplemented
412C2×C83C24×D411yescharacteristic
413C2×C83C22×2−1+411yescharacteristic
414C2×C83C22×2−1+411yescharacteristic
415D83—24no—
416D83—24no—
417D83—46no—
418C22×2−1+4—831no—
419C24×Q8—831no—
420#3486—8332no—
421C2×D4×Q8—831no—
422C2×D4×Q8—833no—
423C2×D4×Q8—833no—
424C2×D4×Q8D8311yescharacteristic, complemented
425C2×#548—831no—
426C2×#548—833no—
427C2×#548—831no—
428C2×#548—833no—
429C2×#536—833no—
430C2×#536—833no—
431C2×#525—833no—
432C2×#525—833no—
433C2×#519—831no—
434C83C2×#348611yescharacteristic, complemented, Sylow
435C2×2−1+4—8316no—
436C2×2−1+4—16616no—
437C22×#41—833no—
438C22×#41—831no—
439C22×#41—833no—
440C22×#41—833no—
441C23×Q8—831no—
442C23×Q8—833no—
443C23×Q8—833no—
444C23×Q8—831no—
445C23×Q8—8316no—
446C23×Q8—833no—
447C23×Q8—833no—
448C23×Q8—16616no—
449C23×Q8C2×D8311yescharacteristic
450C23×Q8C2×D8311yescharacteristic, complemented
451C24×C4—833no—
452D4×Q8—8316no—
453D4×Q8—8348no—
454D4×Q8—8348no—
455D4×Q8C2×D83116yescomplemented
456#548—8316no—
457#548—8348no—
458#548—8316no—
459#548—8348no—
460#536—8348no—
461#536—8348no—
462C2×C4⋊Q8—833no—
463C2×C4⋊Q8—836no—
464C2×C4⋊Q8C2×D8313yescomplemented
465C2×#124—833no—
466C2×#124—836no—
467C2×#124—833no—
468#525—8348no—
469#525—8348no—
470C2×#123—836no—
471C2×#123—833no—
472C2×#123—833no—
473C2×C22⋊Q8—833no—
474C2×C22⋊Q8—833no—
475C2×C22⋊Q8—833no—
476C2×C22⋊Q8—833no—
477C2×C22⋊Q8—836no—
478C2×C22⋊Q8—836no—
479C2×C22⋊Q8—833no—
480C2×C22⋊Q8—833no—
481C2×C22⋊Q8C2×D8313yes—
482C2×C22⋊Q8C2×D8313yescomplemented
483C2×#121—833no—
484C2×#121—833no—
485C2×#121—833no—
486C2×#121—833no—
487C2×#120—831no—
488C2×#120—833no—
489#519—8316no—
490C2×C4×Q8—831no—
491C2×C4×Q8—833no—
492C2×C4×Q8—833no—
493C2×C4×Q8C2×D8311yescharacteristic, complemented
494C2×C4×D4—833no—
495C2×C4×D4—833no—
496C2×C4×D4—836no—
497C2×C4×D4—836no—
498C2×C4×D4—833no—
499C2×C4×D4C2×D8313yes—
500C2×#117—833no—
501C2×#117—833no—
502C25—831no—
5032−1+4—166128no—
504C2×#41—8324no—
505C2×#41—838no—
506C2×#41—8324no—
507C2×#41—8324no—
508C2×#41—16624no—
509C2×#41—16624no—
510C2×#41—16624no—
511C2×#41—1668no—
512C22×Q8—28no—
513C22×Q8—28no—
514C22×Q8—8316no—
515C22×Q8—838no—
516C22×Q8—8324no—
517C22×Q8—8324no—
518C22×Q8—838no—
519C22×Q8—8324no—
520C22×Q8—833no—
521C22×Q8—836no—
522C22×Q8—833no—
523C22×Q8—833no—
524C22×Q8—8324no—
525C22×Q8—16624no—
526C22×Q8—16624no—
527C22×Q8—166128no—
528C22×Q8—16624no—
529C22×Q8—16624no—
530C22×Q8—1668no—
531C22×Q8C22×D8313yes—
532C22×Q8C22×D8313yes—
533C22×Q8C22×D8318yes—
534C22×Q8C22×D8311yescharacteristic
535C22×Q8C22×D8318yescomplemented
536C22×D4—831no—
537C22×D4—833no—
538C22×D4—831no—
539C22×D4—833no—
540C22×D4—833no—
541C22×D4—833no—
542C22×D4—833no—
543C22×D4C22×D8311yescharacteristic
544C23×C4—833no—
545C23×C4—833no—
546C23×C4—833no—
547C23×C4—833no—
548C23×C4—836no—
549C23×C4—833no—
550C23×C4—833no—
551C23×C4—8324no—
552C23×C4—16624no—
553C23×C4C22×D8313yes—
554C23×C4C22×D8313yes—
555C4⋊Q8—8324no—
556C4⋊Q8—8348no—
557C4⋊Q8C22×D83124yescomplemented
558#124—8324no—
559#124—8348no—
560#124—8324no—
561#123—8348no—
562#123—8324no—
563#123—8324no—
564C22⋊Q8—8324no—
565C22⋊Q8—8324no—
566C22⋊Q8—8324no—
567C22⋊Q8—8324no—
568C22⋊Q8—8348no—
569C22⋊Q8—8348no—
570C22⋊Q8—8324no—
571C22⋊Q8—8324no—
572C22⋊Q8C22×D83124yes—
573C22⋊Q8C22×D83124yescomplemented
574#121—8324no—
575#121—8324no—
576#121—8324no—
577#121—8324no—
578#120—838no—
579#120—8324no—
580C4×Q8—838no—
581C4×Q8—8324no—
582C4×Q8—8324no—
583C4×Q8C22×D8318yescomplemented
584C4×D4—8324no—
585C4×D4—8324no—
586C4×D4—8348no—
587C4×D4—8348no—
588C4×D4—8324no—
589C4×D4C22×D83124yes—
590#117—8324no—
591#117—8324no—
592C2×C4⋊C4—833no—
593C2×C4⋊C4—833no—
594C2×C4⋊C4—833no—
595C2×C4⋊C4—833no—
596C2×C4⋊C4—836no—
597C2×C4⋊C4—833no—
598C2×C4⋊C4—833no—
599C2×C4⋊C4C22×D8313yes—
600C2×C4⋊C4C22×D8316yes—
601C2×C4⋊C4C22×D8313yes—
602C2×C22⋊C4—831no—
603C2×C22⋊C4—833no—
604C2×C22⋊C4—833no—
605C2×C22⋊C4—831no—
606C2×C22⋊C4—833no—
607C2×C22⋊C4—831no—
608C2×C22⋊C4—833no—
609C2×C22⋊C4—836no—
610C2×C22⋊C4—836no—
611C2×C22⋊C4—833no—
612C2×C22⋊C4C22×D8313yes—
613C2×C22⋊C4C22×D8313yes—
614C2×C42—836no—
615C2×C42—833no—
616C2×C42C22×D8313yes—
617C24—831no—
618C24—831no—
619C24—834no—
620C24—833no—
621C24—1664no—
622C24—1664no—
623C24—1664no—
624C24C23×D8311yescharacteristic
625C24C23×D8311yescharacteristic
626#41—16696no—
627#41—16696no—
628#41—16696no—
629#41—16632no—
630C2×Q8—232no—
631C2×Q8—232no—
632C2×Q8—212no—
633C2×Q8—212no—
634C2×Q8—8364no—
635C2×Q8—8324no—
636C2×Q8—8312no—
637C2×Q8—8324no—
638C2×Q8—8312no—
639C2×Q8—8312no—
640C2×Q8—16624no—
641C2×Q8—16612no—
642C2×Q8—16696no—
643C2×Q8—16696no—
644C2×Q8—16696no—
645C2×Q8—16696no—
646C2×Q8—16632no—
647C2×Q8—16612no—
648C2×Q8D4×D8318yes—
649C2×Q8C23×D83112yes—
650C2×Q8C23×D83112yes—
651C2×Q8C23×D8314yes—
652C2×D4—24no—
653C2×D4—834no—
654C2×D4—8312no—
655C2×D4—834no—
656C2×D4—8312no—
657C2×D4—8312no—
658C2×D4—8312no—
659C2×D4—8312no—
660C2×D4—16612no—
661C2×D4—16612no—
662C2×D4—16612no—
663C2×D4—1664no—
664C2×D4—1664no—
665C2×D4—16612no—
666C2×D4—16612no—
667C2×D4C23×D8314yes—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—833no—
671C22×C4—8324no—
672C22×C4—8312no—
673C22×C4—8312no—
674C22×C4—831no—
675C22×C4—833no—
676C22×C4—833no—
677C22×C4—831no—
678C22×C4—8312no—
679C22×C4—8312no—
680C22×C4—8324no—
681C22×C4—8312no—
682C22×C4—8312no—
683C22×C4—16612no—
684C22×C4—16696no—
685C22×C4—16624no—
686C22×C4—16612no—
687C22×C4—16612no—
688C22×C4—16612no—
689C22×C4—16612no—
690C22×C4C23×D83112yes—
691C22×C4C23×D83112yes—
692C22×C4C23×D8313yes—
693C22×C4C23×D8311yescharacteristic
694C22×C4C23×D8313yes—
695C22×C4C23×D8313yes—
696C22×C4C23×D8313yes—
697C4⋊C4—8312no—
698C4⋊C4—8312no—
699C4⋊C4—8312no—
700C4⋊C4—8312no—
701C4⋊C4—8324no—
702C4⋊C4—8312no—
703C4⋊C4—8312no—
704C4⋊C4C23×D83112yes—
705C4⋊C4C23×D83124yes—
706C4⋊C4C23×D83112yes—
707C22⋊C4—834no—
708C22⋊C4—8312no—
709C22⋊C4—8312no—
710C22⋊C4—834no—
711C22⋊C4—8312no—
712C22⋊C4—834no—
713C22⋊C4—8312no—
714C22⋊C4—8324no—
715C22⋊C4—8324no—
716C22⋊C4—8312no—
717C22⋊C4C23×D83112yes—
718C22⋊C4C23×D83112yes—
719C42—8324no—
720C42—8312no—
721C42C23×D83112yes—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—834no—
728C23—834no—
729C23—832no—
730C23—832no—
731C23—836no—
732C23—1668no—
733C23—1668no—
734C23—16632no—
735C23—1666no—
736C23—1666no—
737C23—1666no—
738C23—1662no—
739C23—1662no—
740C23—1662no—
741C23—1662no—
742C23—1668no—
743C23#1458184014yescomplemented
744C23C24×D8312yes—
745C23C24×D8312yes—
746C23C24×D8311yescharacteristic
747Q8—224no—
748Q8—224no—
749Q8—8348no—
750Q8—16648no—
751Q8—16624no—
752Q8—16624no—
753Q8C2×D4×D83116yes—
754D4—28no—
755D4—16624no—
756D4—16624no—
757D4—16624no—
758D4—1668no—
759D4—1668no—
760D4—16624no—
761D4—16624no—
762C2×C4—26no—
763C2×C4—26no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—8312no—
769C2×C4—836no—
770C2×C4—8348no—
771C2×C4—832no—
772C2×C4—836no—
773C2×C4—836no—
774C2×C4—832no—
775C2×C4—16624no—
776C2×C4—16648no—
777C2×C4—16624no—
778C2×C4—16624no—
779C2×C4—1662no—
780C2×C4—1666no—
781C2×C4—1662no—
782C2×C4—1666no—
783C2×C4—16624no—
784C2×C4—16624no—
785C2×C4C2×D4×D83112yes—
786C2×C4C24×D8316yes—
787C2×C4C24×D8312yes—
788C2×C4C24×D8316yes—
789C2×C4C24×D8316yes—
790C2×C4C24×D8316yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—33212no—
799C22—834no—
800C22—834no—
801C22—16632no—
802C22—1666no—
803C22—1666no—
804C22—1666no—
805C22—1668no—
806C22—1668no—
807C22—1662no—
808C22—1662no—
809C22—1662no—
810C22—1662no—
811C22C22×D4×D8312yes—
812C222−1+4×D8312yes—
813C22C2×#1458184012yes—
814C22C2×#1458184014yescomplemented
815C22C25×D8311yescharacteristic
816C4—26no—
817C4—26no—
818C4—26no—
819C4—22no—
820C4—8312no—
821C4—1662no—
822C4—1666no—
823C4—1662no—
824C4—1666no—
825C4C22×D4×D83112yes—
826C2—24no—
827C2—42no—
828C2—3326no—
829C2—1664no—
830C2—1664no—
831C2#2492111314yesdirect product factor
832C2C23×D4×D8311yescharacteristic
833C2C2×2−1+4×D8311yescharacteristic
834C2C22×#1458184011yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×D4×Q8×C83C2
socleC23×C83C25
hypercenterC2×D4×Q8D83
hypocenterC83C2×#3486
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14581840C2semidirect
2. C23×Q8×D83C2semidirect
3. #24921113C2direct (N × H)
4. C2×#19128366C2semidirect
5. C2×Q8×C22⋊D83C2semidirect
6. C2×#19128364C2semidirect
7. C2×#19128363C2semidirect
8. C2×#19128362C2semidirect
9. C2×#19128361C2semidirect
10. C2×#19128360C2semidirect
11. C2×#19128276C2semidirect
12. C2×#19128274C2semidirect
13. C2×#19128214C2semidirect
14. C2×#19128210C2semidirect
15. C2×#19128177C2semidirect
16. C2×D4×Q8×C83C2semidirect
18. C2×#14581840C22semidirect
20. C22×#13050591C22semidirect
22. C22×#13050590C22semidirect
29. C22×Q8×D83C22semidirect
30. C22×Q8×D83C22semidirect
32. #19128366C22semidirect
33. Q8×C22⋊D83C22semidirect
34. #19128364C22semidirect
35. #19128363C22semidirect
36. #19128362C22semidirect
37. #19128361C22semidirect
38. #19128360C22semidirect
39. #19128276C22semidirect
40. #19128274C22semidirect
41. C2×#14581791C22semidirect
42. C2×#14581790C22semidirect
43. C2×#14581781C22semidirect
44. C2×#14581780C22semidirect
45. C2×#14581778C22semidirect
46. #19128214C22semidirect
47. #19128210C22semidirect
51. C2×#14581772C22semidirect
52. C2×#14581771C22semidirect
54. C2×#14581770C22semidirect
55. C2×#14581770C22semidirect
58. C2×#14581768C22semidirect
65. #19128177C22semidirect
66. C2×Q8×Dic83C22semidirect
67. C2×C4×Dic166C22semidirect
68. C2×#14581757C22semidirect
77. C23×Q8×C83C22semidirect
78. D4×Q8×C83C22semidirect
79. C2×C4⋊Q8×C83C22semidirect
81. C2×C22⋊Q8×C83C22semidirect
82. C2×C4×Q8×C83C22semidirect
89. C2×#13050591C23semidirect
93. C2×#13050590C23semidirect
105. C2×Q8×D83D4semidirect
110. C2×Q8×D83C23semidirect
127. #14581791C23semidirect
128. #14581790C23semidirect
129. #14581781C23semidirect
130. #14581780C23semidirect
131. #14581778C23semidirect
135. #14581772C23semidirect
136. #14581771C23semidirect
138. #14581770C23semidirect
139. #14581770C23semidirect
142. #14581768C23semidirect
149. Q8×Dic83C23semidirect
150. C4×Dic166C23semidirect
151. #14581757C23semidirect
184. C22×Q8×C83C23semidirect
188. C4⋊Q8×C83C23semidirect
190. C22⋊Q8×C83C23semidirect
191. C4×Q8×C83C23semidirect
223. Q8×D83C2×D4semidirect
309. C23×C832−1+4semidirect
325. C22×D832−1+4semidirect
383. C22×C83C2×2−1+4semidirect
397. C2×D83C2×2−1+4semidirect
411. C2×C83#3486semidirect
424. C2×D4×Q8D83semidirect
434. C83C2×#3486semidirect
450. C23×Q8C2×D83semidirect
455. D4×Q8C2×D83semidirect
464. C2×C4⋊Q8C2×D83semidirect
482. C2×C22⋊Q8C2×D83semidirect
493. C2×C4×Q8C2×D83semidirect
535. C22×Q8C22×D83semidirect
557. C4⋊Q8C22×D83semidirect
573. C22⋊Q8C22×D83semidirect
583. C4×Q8C22×D83semidirect
743. C23#14581840semidirect
814. C22C2×#14581840semidirect
831. C2#24921113direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145818402
C23×Q8×D832
#249211132
C2×#191283662
C2×Q8×C22⋊D832
C2×#191283642
C2×#191283632
C2×#191283622
C2×#191283612
C2×#191283602
C2×#191282762
C2×#191282742
C2×#191282142
C2×#191282102
C2×#191281772
C2×D4×Q8×C832
C2×#348683