Finite Group Databasebeta

← C2×#24921547 #36312610

Subgroups — C2×#24921547 #36312610

Order 21248.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921547C2132yesmaximal, direct product factor
2C2×#19128436C211yesmaximal, characteristic, complemented
3C2×#19128434C212yesmaximal, complemented
4C2×#19128431C211yesmaximal, characteristic, complemented
5C2×#19128407C212yesmaximal, complemented
6C2×#19128372C211yesmaximal, characteristic, complemented
7C2×#19128361C212yesmaximal, complemented
8C2×#19128353C214yesmaximal, complemented
9C2×#19128352C212yesmaximal, complemented
10C2×#19128324C212yesmaximal, complemented
11C2×#19128321C214yesmaximal, complemented
12C2×#19128252C211yesmaximal, characteristic, complemented
13C2×#19128248C212yesmaximal, complemented
14C2×#19128236C212yesmaximal, complemented
15C2×#19128233C211yesmaximal, characteristic, complemented
16C2×#19128182C212yesmaximal, complemented
17C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
18C2×#554×C83C211yesmaximal, characteristic, complemented
19C22×#13050591C2212yes—
20C22×#13050590C2212yes—
21C22×#13050590C2214yes—
22C22×Q8×D83C2211yescharacteristic
23#19128436C22116yescomplemented
24#19128434C22132yescomplemented
25#19128431C22116yescomplemented
26#19128407C22132yescomplemented
27#19128372C22116yescomplemented
28#19128361C22132yescomplemented
29#19128353C22164yescomplemented
30#19128352C22132yescomplemented
31#19128324C22132yescomplemented
32#19128321C22164yescomplemented
33#19128252C22116yescomplemented
34#19128248C22132yescomplemented
35C2×#14581791C2212yes—
36C2×#14581791C2212yes—
37C2×#14581790C2214yes—
38C2×#14581789C2211yescharacteristic
39C2×#14581788C2212yes—
40#19128236C22132yescomplemented
41#19128233C22116yescomplemented
42C2×#14581787C2214yes—
43C2×#14581785C2212yes—
44C2×#14581783C2211yescharacteristic
45C2×#14581781C2212yes—
46C2×#14581781C2212yes—
47C2×#14581780C2212yes—
48C2×#14581779C2211yescharacteristic
49C2×#14581778C2214yes—
50C2×#14581778C2214yes—
51C2×#14581777C2214yes—
52C2×#14581777C2214yes—
53C2×#14581775C2214yes—
54C2×#14581774C2214yes—
55C2×#14581774C2212yes—
56C2×#14581772C2214yes—
57C2×#14581772C2211yescharacteristic
58C2×#14581770C2214yes—
59C2×#14581770C2214yes—
60C2×#14581767C2212yes—
61C2×#14581767C2212yes—
62C2×#14581766C2212yes—
63C2×#14581765C2214yes—
64C2×#14581765C2214yes—
65C2×#14581763C2211yescharacteristic
66#19128182C22132yescomplemented
67C2×Q8×Dic83C2211yescharacteristic
68C2×C4×Dic166C2211yescharacteristic
69C2×C4×Dic166C2212yes—
70C2×C4×Dic166C2211yescharacteristic
71C2×#14581757C2212yes—
72C2×#14581757C2211yescharacteristic
73C2×#14581757C2212yes—
74C2×#14581757C2212yes—
75C4×Q8×D83C22116yescomplemented
76C2×C4×D332C2212yes—
77C2×#14581754C2212yes—
78C2×#14581754C2212yes—
79C2×#14581754C2214yes—
80C2×#14581754C2212yes—
81C2×#14581754C2212yes—
82C2×C4×C22⋊D83C2214yes—
83C2×C4×C22⋊D83C2214yes—
84C2×C4×C22⋊D83C2212yes—
85C2×#14581751C2212yes—
86C2×#14581750C2214yes—
87C2×C4⋊C4×D83C2211yescharacteristic
88C2×C4⋊C4×D83C2212yes—
89C2×C4⋊C4×D83C2214yes—
90C2×C42×D83C2211yescharacteristic
91C2×C42×D83C2212yes—
92#554×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×#125×C83C2212yes—
95C2×C22⋊Q8×C83C2214yes—
96C2×C22⋊Q8×C83C2212yes—
97C2×C4×Q8×C83C2211yescharacteristic
98C2×C4×D4×C83C2211yescharacteristic
99C2×C4×D4×C83C2212yes—
100C22×C4⋊C4×C83C2212yes—
101C2×#13050591—48no—
102C2×#13050591C23116yes—
103C2×#13050590—216no—
104C2×#13050590—416no—
105C2×#13050590C23116yes—
106C2×#13050590C23132yes—
107C22×Dic166C2311yescharacteristic
108C22×Dic166C2312yes—
109C22×Dic166C2314yes—
110C22×Dic166C2311yescharacteristic
111C2×Q8×D83—28no—
112C2×Q8×D83C2318yes—
113C22×D332C2312yes—
114C22×D332C2312yes—
115C22×D332C2314yes—
116C22×D332C2312yes—
117C22×C22⋊D83C2314yes—
118C22×C22⋊D83C2312yes—
119C22×C22⋊D83C2314yes—
120C22×C4×D83C2311yescharacteristic
121C22×C4×D83C2311yescharacteristic
122C22×C4×D83C2312yes—
123C22×C4×D83C2311yescharacteristic
124C22×C4×D83C2312yes—
125C22×C4×D83C2314yes—
126C22×C4×D83C2314yes—
127C22×C4×D83C2314yes—
128#14581791C23116yes—
129#14581791C23116yes—
130#14581790C23132yes—
131#14581789C2318yes—
132#14581788C23116yes—
133#14581787C23132yes—
134#14581785C23116yes—
135#14581783C2318yes—
136#14581781C23116yes—
137#14581781C23116yes—
138#14581780C23116yes—
139#14581779C2318yes—
140#14581778C23132yes—
141#14581778C23132yes—
142#14581777C23132yes—
143#14581777C23132yes—
144#14581775C23132yes—
145#14581774C23132yes—
146#14581774C23116yes—
147#14581772C23132yes—
148#14581772C2318yes—
149#14581770C23132yes—
150#14581770C23132yes—
151#14581767C23116yes—
152#14581767C23116yes—
153#14581766C23116yes—
154#14581765C23132yes—
155#14581765C23132yes—
156#14581763C2318yes—
157Q8×Dic83C2318yes—
158C4×Dic166C2318yes—
159C4×Dic166C23116yes—
160C4×Dic166C2318yes—
161#14581757C23116yes—
162#14581757C23116yes—
163#14581757C2318yes—
164#14581757C23116yes—
165C4×D332C23116yes—
166#14581754C23116yes—
167#14581754C23116yes—
168#14581754C23132yes—
169#14581754C23116yes—
170#14581754C23116yes—
171C4×C22⋊D83C23132yes—
172C4×C22⋊D83C23116yes—
173C4×C22⋊D83C23132yes—
174#14581751C23116yes—
175#14581750C23132yes—
176C2×C4⋊Dic83C2312yes—
177C2×C4⋊Dic83C2311yescharacteristic
178C2×C4⋊Dic83C2312yes—
179C2×C4⋊Dic83C2312yes—
180C2×C4⋊Dic83C2311yescharacteristic
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2314yes—
187C2×Dic83⋊C4C2312yes—
188C4⋊C4×D83C2318yes—
189C4⋊C4×D83C23116yes—
190C4⋊C4×D83C23132yes—
191C2×C22⋊Dic83C2312yes—
192C2×C22⋊Dic83C2312yes—
193C2×C22⋊Dic83C2312yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2312yes—
197C2×(C2×D83)⋊C4C2314yes—
198C2×(C2×D83)⋊C4C2314yes—
199C2×(C2×D83)⋊C4C2314yes—
200C2×(C2×D83)⋊C4C2314yes—
201C2×C4×Dic83C2312yes—
202C2×C4×Dic83C2311yescharacteristic
203C2×C4×Dic83C2311yescharacteristic
204C2×C4×Dic83C2312yes—
205C2×C4×Dic83C2311yescharacteristic
206C2×C4×Dic83C2312yes—
207C2×C4×Dic83C2314yes—
208C2×C4×Dic83C2312yes—
209C42×D83C2318yes—
210C42×D83C23116yes—
211C22×Q8×C83C2311yescharacteristic
212C22×Q8×C83C2312yes—
213C22×D4×C83C2311yescharacteristic
214C23×C4×C83C2312yes—
215C23×C4×C83C2314yes—
216C4⋊Q8×C83C2318yes—
217#125×C83C23116yes—
218C22⋊Q8×C83C23132yes—
219C22⋊Q8×C83C23116yes—
220C4×Q8×C83C2318yes—
221C4×D4×C83C2318yes—
222C4×D4×C83C23116yes—
223C2×C4⋊C4×C83C23116yes—
224C2×C4⋊C4×C83C2311yescharacteristic
225C2×C4⋊C4×C83C2314yes—
226C2×C4⋊C4×C83C2312yes—
227C2×C4⋊C4×C83C2311yescharacteristic
228C2×C4⋊C4×C83C2312yes—
229C2×C4⋊C4×C83C2312yes—
230C2×C4⋊C4×C83C2314yes—
231C2×C22⋊C4×C83C2312yes—
232C2×C22⋊C4×C83C2314yes—
233C2×C42×C83C2312yes—
234C2×C42×C83C2311yescharacteristic
235C23×D83C2414yes—
236C23×D83C2411yescharacteristic
237#13050591—432no—
238#13050590—264no—
239#13050590—464no—
240C2×Dic166—24no—
241C2×Dic166—28no—
242C2×Dic166—48no—
243C2×Dic166#4118yescomplemented
244C2×Dic166C2418yes—
245C2×Dic166C2414yes—
246C2×Dic166C24116yes—
247C2×Dic166C2414yes—
248Q8×D83—232no—
249C2×D332—216no—
250C2×D332—28no—
251C2×D332—28no—
252C2×D332—44no—
253C2×D332C24116yes—
254C2×D332C2418yes—
255C2×D332C2418yes—
256C2×D332C2418yes—
257C2×C22⋊D83—28no—
258C2×C22⋊D83—216no—
259C2×C22⋊D83—48no—
260C2×C22⋊D83C2418yes—
261C2×C22⋊D83C24116yes—
262C2×C22⋊D83C24116yes—
263C22×Dic83C2411yescharacteristic
264C22×Dic83C2412yes—
265C22×Dic83C2412yes—
266C22×Dic83C2411yescharacteristic
267C22×Dic83C2411yescharacteristic
268C22×Dic83C2412yes—
269C22×Dic83C2412yes—
270C2×C4×D83—28no—
271C2×C4×D83—24no—
272C2×C4×D83—24no—
273C2×C4×D83—24no—
274C2×C4×D83—28no—
275C2×C4×D83—216no—
276C2×C4×D83—48no—
277C2×C4×D83—48no—
278C2×C4×D83C2414yes—
279C2×C4×D83C2418yes—
280C2×C4×D83C24116yes—
281C2×C4×D83C2414yes—
282C2×C4×D83C2414yes—
283C2×C4×D83C2418yes—
284C2×C4×D83C24116yes—
285C2×C4×D83C24116yes—
286C4⋊Dic83C2414yes—
287C4⋊Dic83C2414yes—
288C4⋊Dic83C2418yes—
289C4⋊Dic83C2418yes—
290C4⋊Dic83C2418yes—
291Dic83⋊C4C2418yes—
292Dic83⋊C4C24116yes—
293Dic83⋊C4C2418yes—
294Dic83⋊C4C2418yes—
295Dic83⋊C4C24116yes—
296Dic83⋊C4C2418yes—
297Dic83⋊C4C2418yes—
298C22⋊Dic83C2418yes—
299C22⋊Dic83C2418yes—
300C22⋊Dic83C2418yes—
301(C2×D83)⋊C4C24116yes—
302(C2×D83)⋊C4C24116yes—
303(C2×D83)⋊C4C24116yes—
304(C2×D83)⋊C4C24116yes—
305(C2×D83)⋊C4C2418yes—
306(C2×D83)⋊C4C24116yes—
307(C2×D83)⋊C4C24116yes—
308C4×Dic83C2418yes—
309C4×Dic83C24116yes—
310C4×Dic83C2414yes—
311C4×Dic83C2414yes—
312C4×Dic83C2418yes—
313C4×Dic83C2418yes—
314C4×Dic83C2418yes—
315C4×Dic83C2414yes—
316C24×C83C2412yes—
317C2×Q8×C83—24no—
318C2×Q8×C83—44no—
319C2×Q8×C83C2414yes—
320C2×Q8×C83C2418yes—
321C2×D4×C83—24no—
322C2×D4×C83C2414yes—
323C22×C4×C83—28no—
324C22×C4×C83—48no—
325C22×C4×C83C2418yes—
326C22×C4×C83C2412yes—
327C22×C4×C83C2412yes—
328C22×C4×C83C2411yescharacteristic
329C22×C4×C83C2414yes—
330C22×C4×C83C2412yes—
331C22×C4×C83C24116yes—
332C22×C4×C83C2411yescharacteristic
333C22×C4×C83C2411yescharacteristic
334C4⋊C4×C83C2418yes—
335C4⋊C4×C83C2418yes—
336C4⋊C4×C83C24116yes—
337C4⋊C4×C83C24116yes—
338C4⋊C4×C83C2414yes—
339C4⋊C4×C83C2418yes—
340C4⋊C4×C83C2414yes—
341C22⋊C4×C83C2418yes—
342C22⋊C4×C83C24116yes—
343C42×C83C2418yes—
344C42×C83C2414yes—
345C23×C83—24no—
346C23×C83—24no—
347C23×C83—24no—
348C23×C83C2514yes—
349C23×C83C2511yescharacteristic
350C22×D83—22no—
351C22×D83—22no—
352C22×D83—28no—
353C22×D83—28no—
354C22×D83—28no—
355C22×D83H(5,𝔽2)14yes—
356C22×D83C2518yes—
357C22×D83C2512yes—
358Q8×C83—28no—
359Q8×C83—48no—
360D4×C83—28no—
361C2×C4×C83—24no—
362C2×C4×C83—24no—
363C2×C4×C83—24no—
364C2×C4×C83—28no—
365C2×C4×C83—22no—
366C2×C4×C83—216no—
367C2×C4×C83—416no—
368C2×C4×C83C2×#4114yes—
369C2×C4×C832−1+414yes—
370C2×C4×C83C2514yes—
371C2×C4×C83C2512yes—
372C2×C4×C83C2514yes—
373C2×C4×C83C2514yes—
374C2×C4×C83C2518yes—
375C2×C4×C83C2512yes—
376C2×C4×C83C2512yes—
377C22⋊D83—216no—
378C22⋊D83—232no—
379C22⋊D83—416no—
380C2×Dic83—22no—
381C2×Dic83—22no—
382C2×Dic83—24no—
383C2×Dic83—24no—
384C2×Dic83—22no—
385C2×Dic83—24no—
386C2×Dic83C2×#4118yes—
387C2×Dic83C2512yes—
388C2×Dic83C2514yes—
389C2×Dic83C2512yes—
390C2×Dic83C2514yes—
391C2×Dic83C2512yes—
392C2×Dic83C2514yes—
393C2×Dic83C2514yes—
394D332—232no—
395D332—216no—
396D332—216no—
397D332—48no—
398C4×D83—216no—
399C4×D83—28no—
400C4×D83—28no—
401C4×D83—28no—
402C4×D83—216no—
403C4×D83—232no—
404C4×D83—416no—
405C4×D83—416no—
406Dic166—28no—
407Dic166—216no—
408Dic166—416no—
409Dic166C2×#41116yescomplemented
410C22×C83—24no—
411C22×C83—24no—
412C22×C83—24no—
413C22×C83—48no—
414C22×C83C22×#4112yes—
415C22×C83C2×H(5,𝔽2)12yes—
416C22×C83C2×2−1+412yes—
417C22×C83C2611yescharacteristic
418C2×D83—22no—
419C2×D83—22no—
420C2×D83—28no—
421C2×D83—28no—
422C2×D83—28no—
423C2×D83—28no—
424C2×D83—416no—
425C2×D83C2×H(5,𝔽2)14yes—
426C4×C83—24no—
427C4×C83—24no—
428C4×C83—28no—
429C4×C83—24no—
430C4×C83—22no—
431C4×C83C22×#4114yes—
432C4×C83C2×2−1+414yes—
433Dic83—22no—
434Dic83—24no—
435Dic83—24no—
436Dic83—22no—
437Dic83—24no—
438Dic83—22no—
439Dic83C22×#4118yes—
440C2×#3522—831nomaximal, Sylow
441C2×C83—44no—
442C2×C83#352214yescomplemented
443C2×C83C23×#4111yescharacteristic
444C2×C83C22×H(5,𝔽2)11yescharacteristic
445C2×C83C22×2−1+411yescharacteristic
446D83—24no—
447D83—48no—
448#3522—8332no—
449C2×#559—831no—
450C2×#559—832no—
451C2×Q82—831no—
452C2×#554—832no—
453C2×#554D8311yescharacteristic, complemented
454C2×#550—831no—
455C2×#548—832no—
456C2×#547—834no—
457C2×#547—832no—
458C2×#542—834no—
459C2×#542—832no—
460C2×#532—831no—
461C2×#532—832no—
462C2×#529—832no—
463C2×#529—831no—
464C2×#520—832no—
465C22×C4×Q8—831no—
466C83C2×#352211yescharacteristic, complemented, Sylow
467C22×#41—832no—
468C22×#41—834no—
469C22×#41—832no—
470C23×Q8—831no—
471#559—8316no—
472#559—8332no—
473Q82—8316no—
474#554—8332no—
475#554C2×D83116yescomplemented
476#550—8316no—
477#548—8332no—
478#547—8364no—
479#547—8332no—
480#542—8364no—
481#542—8332no—
482#532—8316no—
483#532—8332no—
484C2×C4⋊Q8—834no—
485C2×C4⋊Q8—832no—
486C2×C4⋊Q8—832no—
487C2×C4⋊Q8C2×D8311yescharacteristic
488C2×#127—832no—
489C2×#127—831no—
490#529—8332no—
491#529—8316no—
492C2×#126—834no—
493C2×#126—832no—
494C2×#125—831no—
495C2×#125C2×D8312yes—
496C2×#124—832no—
497C2×#124—832no—
498C2×#124—831no—
499C2×#124—834no—
500C2×#124—834no—
501C2×#124—832no—
502C2×#123—834no—
503C2×#123—834no—
504C2×#123—834no—
505C2×#123—832no—
506C2×#123—834no—
507C2×C22⋊Q8—831no—
508C2×C22⋊Q8—834no—
509C2×C22⋊Q8—834no—
510C2×C22⋊Q8—834no—
511C2×C22⋊Q8C2×D8314yes—
512C2×C22⋊Q8C2×D8312yes—
513C2×#121—831no—
514C2×#121—832no—
515C2×#121—832no—
516C2×#121—832no—
517C2×#121—834no—
518C2×#121—834no—
519#520—8332no—
520C2×C4×Q8—831no—
521C2×C4×Q8—8316no—
522C2×C4×Q8—831no—
523C2×C4×Q8—832no—
524C2×C4×Q8—832no—
525C2×C4×Q8—832no—
526C2×C4×Q8—831no—
527C2×C4×Q8—832no—
528C2×C4×Q8—831no—
529C2×C4×Q8C2×D8311yescharacteristic
530C2×C4×D4—834no—
531C2×C4×D4—834no—
532C2×C4×D4—832no—
533C2×C4×D4—832no—
534C2×C4×D4—832no—
535C2×C4×D4—834no—
536C2×C4×D4—832no—
537C2×C4×D4—832no—
538C2×C4×D4—832no—
539C2×C4×D4C2×D8311yescharacteristic
540C2×C4×D4C2×D8312yes—
541C2×#117—832no—
542C2×#117—834no—
543C22×C4⋊C4—832no—
544C22×C4⋊C4—831no—
545C22×C4⋊C4—834no—
546C22×C4⋊C4C2×D8312yes—
547C22×C42—831no—
548C22×C42—832no—
549C2×#41—33216no—
550C2×#41—3328no—
551C2×#41—8316no—
552C2×#41—8332no—
553C2×#41—8316no—
554C2×#41—16616no—
555C22×Q8—838no—
556C22×Q8—834no—
557C22×Q8—831no—
558C22×Q8—831no—
559C22×Q8—832no—
560C22×Q8—1668no—
561C22×Q8C22×D8311yescharacteristic
562C22×Q8C22×D8312yes—
563C22×D4—834no—
564C22×D4—834no—
565C22×D4—832no—
566C22×D4—832no—
567C22×D4—832no—
568C22×D4—832no—
569C22×D4—834no—
570C22×D4C22×D8311yescharacteristic
571C23×C4—834no—
572C23×C4—834no—
573C23×C4—831no—
574C23×C4—832no—
575C23×C4—834no—
576C23×C4—832no—
577C23×C4—831no—
578C23×C4—831no—
579C23×C4C22×D8312yes—
580C23×C4C22×D8314yes—
581C4⋊Q8—8332no—
582C4⋊Q8—8316no—
583C4⋊Q8—8316no—
584C4⋊Q8C22×D8318yes—
585#127—8316no—
586#127—838no—
587#126—8332no—
588#126—8316no—
589#125—838no—
590#125C22×D83116yes—
591#124—8316no—
592#124—8316no—
593#124—838no—
594#124—8332no—
595#124—8332no—
596#124—8316no—
597#123—8332no—
598#123—8332no—
599#123—8332no—
600#123—8316no—
601#123—8332no—
602C22⋊Q8—8332no—
603C22⋊Q8—8332no—
604C22⋊Q8—838no—
605C22⋊Q8—8332no—
606C22⋊Q8C22×D83132yes—
607C22⋊Q8C22×D83116yes—
608#121—838no—
609#121—8316no—
610#121—8316no—
611#121—8316no—
612#121—8332no—
613#121—8332no—
614C4×Q8—838no—
615C4×Q8—838no—
616C4×Q8—8316no—
617C4×Q8—8316no—
618C4×Q8—8316no—
619C4×Q8—838no—
620C4×Q8—8316no—
621C4×Q8—838no—
622C4×Q8C22×D8318yes—
623C4×D4—8332no—
624C4×D4—8332no—
625C4×D4—8316no—
626C4×D4—8316no—
627C4×D4—8316no—
628C4×D4—8332no—
629C4×D4—8316no—
630C4×D4—8316no—
631C4×D4—8316no—
632C4×D4C22×D8318yes—
633C4×D4C22×D83116yes—
634#117—8316no—
635#117—8332no—
636C2×C4⋊C4—832no—
637C2×C4⋊C4—832no—
638C2×C4⋊C4—834no—
639C2×C4⋊C4—832no—
640C2×C4⋊C4—831no—
641C2×C4⋊C4—832no—
642C2×C4⋊C4—832no—
643C2×C4⋊C4—832no—
644C2×C4⋊C4—831no—
645C2×C4⋊C4—832no—
646C2×C4⋊C4—834no—
647C2×C4⋊C4—832no—
648C2×C4⋊C4—8316no—
649C2×C4⋊C4—838no—
650C2×C4⋊C4—8332no—
651C2×C4⋊C4C22×D8311yescharacteristic
652C2×C4⋊C4C22×D8314yes—
653C2×C4⋊C4C22×D8312yes—
654C2×C4⋊C4C22×D8312yes—
655C2×C4⋊C4C22×D83116yes—
656C2×C4⋊C4C22×D8311yescharacteristic
657C2×C4⋊C4C22×D8312yes—
658C2×C4⋊C4C22×D8314yes—
659C2×C22⋊C4—832no—
660C2×C22⋊C4—832no—
661C2×C22⋊C4—832no—
662C2×C22⋊C4—834no—
663C2×C22⋊C4—834no—
664C2×C22⋊C4—832no—
665C2×C22⋊C4—834no—
666C2×C22⋊C4—834no—
667C2×C22⋊C4—834no—
668C2×C22⋊C4—834no—
669C2×C22⋊C4C22×D8312yes—
670C2×C22⋊C4C22×D8314yes—
671C2×C42—832no—
672C2×C42—831no—
673C2×C42—834no—
674C2×C42—832no—
675C2×C42—831no—
676C2×C42—832no—
677C2×C42—831no—
678C2×C42—832no—
679C2×C42—838no—
680C2×C42—8316no—
681C2×C42C22×D8312yes—
682C2×C42C22×D8311yescharacteristic
683C24—831no—
684C24—834no—
685C24C23×D8312yes—
686#41—33264no—
687#41—33232no—
688#41—16664no—
689C2×Q8—24no—
690C2×Q8—44no—
691C2×Q8—3328no—
692C2×Q8—838no—
693C2×Q8—8316no—
694C2×Q8—834no—
695C2×Q8—834no—
696C2×Q8—838no—
697C2×Q8—1668no—
698C2×Q8—16632no—
699C2×Q8—1664no—
700C2×Q8C23×D8314yes—
701C2×Q8C23×D8318yes—
702C2×D4—24no—
703C2×D4—3324no—
704C2×D4—3328no—
705C2×D4—8316no—
706C2×D4—8316no—
707C2×D4—838no—
708C2×D4—838no—
709C2×D4—838no—
710C2×D4—838no—
711C2×D4—8316no—
712C2×D4—16616no—
713C2×D4—16616no—
714C2×D4—1668no—
715C2×D4—1668no—
716C2×D4—1668no—
717C2×D4C23×D8314yes—
718C22×C4—28no—
719C22×C4—48no—
720C22×C4—3328no—
721C22×C4—3328no—
722C22×C4—8316no—
723C22×C4—8316no—
724C22×C4—832no—
725C22×C4—831no—
726C22×C4—832no—
727C22×C4—831no—
728C22×C4—831no—
729C22×C4—832no—
730C22×C4—832no—
731C22×C4—834no—
732C22×C4—834no—
733C22×C4—838no—
734C22×C4—838no—
735C22×C4—834no—
736C22×C4—8316no—
737C22×C4—1668no—
738C22×C4—16616no—
739C22×C4—1668no—
740C22×C4—1664no—
741C22×C4—1664no—
742C22×C4—1664no—
743C22×C4C23×D8318yes—
744C22×C4C23×D8312yes—
745C22×C4C23×D8312yes—
746C22×C4C23×D8311yescharacteristic
747C22×C4C23×D8314yes—
748C22×C4C23×D8312yes—
749C22×C4C23×D83116yes—
750C22×C4C23×D8311yescharacteristic
751C22×C4C23×D8311yescharacteristic
752C4⋊C4—838no—
753C4⋊C4—838no—
754C4⋊C4—8316no—
755C4⋊C4—838no—
756C4⋊C4—834no—
757C4⋊C4—838no—
758C4⋊C4—838no—
759C4⋊C4—838no—
760C4⋊C4—834no—
761C4⋊C4—838no—
762C4⋊C4—8316no—
763C4⋊C4—838no—
764C4⋊C4C23×D8314yes—
765C4⋊C4C23×D83116yes—
766C4⋊C4C23×D8318yes—
767C4⋊C4C23×D8318yes—
768C4⋊C4C23×D8314yes—
769C4⋊C4C23×D8318yes—
770C4⋊C4C23×D83116yes—
771C22⋊C4—838no—
772C22⋊C4—838no—
773C22⋊C4—838no—
774C22⋊C4—8316no—
775C22⋊C4—8316no—
776C22⋊C4—838no—
777C22⋊C4—8316no—
778C22⋊C4—8316no—
779C22⋊C4—8316no—
780C22⋊C4—8316no—
781C22⋊C4C23×D8318yes—
782C22⋊C4C23×D83116yes—
783C42—838no—
784C42—834no—
785C42—834no—
786C42—838no—
787C42—834no—
788C42—838no—
789C42—8316no—
790C42—838no—
791C42C23×D8318yes—
792C42C23×D8314yes—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—834no—
797C23—832no—
798C23—838no—
799C23—1668no—
800C23—1668no—
801C23—1668no—
802C23—1662no—
803C23—1662no—
804C23C24×D8314yes—
805C23C24×D8311yescharacteristic
806Q8—28no—
807Q8—48no—
808Q8—33216no—
809Q8—8316no—
810Q8—16616no—
811Q8—1668no—
812D4—28no—
813D4—3328no—
814D4—33216no—
815D4—16632no—
816D4—16632no—
817D4—16616no—
818D4—16616no—
819D4—16616no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—28no—
824C2×C4—22no—
825C2×C4—216no—
826C2×C4—416no—
827C2×C4—33216no—
828C2×C4—33216no—
829C2×C4—838no—
830C2×C4—834no—
831C2×C4—832no—
832C2×C4—834no—
833C2×C4—832no—
834C2×C4—832no—
835C2×C4—834no—
836C2×C4—834no—
837C2×C4—16616no—
838C2×C4—16632no—
839C2×C4—16616no—
840C2×C4—1668no—
841C2×C4—1662no—
842C2×C4—1662no—
843C2×C4—1664no—
844C2×C4—1664no—
845C2×C4—1662no—
846C2×C4—1664no—
847C2×C4—1668no—
848C2×C4—1668no—
849C2×C4#41×D8314yes—
850C2×C4#1458184014yes—
851C2×C4C24×D8314yes—
852C2×C4C24×D8314yes—
853C2×C4C24×D8312yes—
854C2×C4C24×D8318yes—
855C2×C4C24×D8314yes—
856C2×C4C24×D8312yes—
857C2×C4C24×D8312yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—48no—
862C22—33216no—
863C22—834no—
864C22—1668no—
865C22—1668no—
866C22—1668no—
867C22—1662no—
868C22—1662no—
869C22—1668no—
870C22C2×#41×D8312yes—
871C22H(5,𝔽2)×D8312yes—
872C22C2×#1458184012yes—
873C22C25×D8311yescharacteristic
874C4—24no—
875C4—24no—
876C4—24no—
877C4—28no—
878C4—22no—
879C4—838no—
880C4—1662no—
881C4—1662no—
882C4—1664no—
883C4—1664no—
884C4—1662no—
885C4—1664no—
886C4C2×#41×D8314yes—
887C4C2×#1458184014yes—
888C2—44no—
889C2—3328no—
890C2—1664no—
891C2#2492154714yesdirect product factor
892C2C22×#41×D8311yescharacteristic
893C2C2×H(5,𝔽2)×D8311yescharacteristic
894C2C22×#1458184011yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#554×C83C2
socleC23×C83C25
hypercenterC2×#554D83
hypocenterC83C2×#3522
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #24921547C2direct (N × H)
2. C2×#19128436C2semidirect
3. C2×#19128434C2semidirect
4. C2×#19128431C2semidirect
5. C2×#19128407C2semidirect
6. C2×#19128372C2semidirect
7. C2×#19128361C2semidirect
8. C2×#19128353C2semidirect
9. C2×#19128352C2semidirect
10. C2×#19128324C2semidirect
11. C2×#19128321C2semidirect
12. C2×#19128252C2semidirect
13. C2×#19128248C2semidirect
14. C2×#19128236C2semidirect
15. C2×#19128233C2semidirect
16. C2×#19128182C2semidirect
17. C2×C4×Q8×D83C2semidirect
18. C2×#554×C83C2semidirect
23. #19128436C22semidirect
24. #19128434C22semidirect
25. #19128431C22semidirect
26. #19128407C22semidirect
27. #19128372C22semidirect
28. #19128361C22semidirect
29. #19128353C22semidirect
30. #19128352C22semidirect
31. #19128324C22semidirect
32. #19128321C22semidirect
33. #19128252C22semidirect
34. #19128248C22semidirect
40. #19128236C22semidirect
41. #19128233C22semidirect
66. #19128182C22semidirect
75. C4×Q8×D83C22semidirect
92. #554×C83C22semidirect
243. C2×Dic166#41semidirect
409. Dic166C2×#41semidirect
442. C2×C83#3522semidirect
453. C2×#554D83semidirect
466. C83C2×#3522semidirect
475. #554C2×D83semidirect
891. C2#24921547direct (N × H)

Maximal subgroups

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

subgroupindex
#249215472
C2×#191284362
C2×#191284342
C2×#191284312
C2×#191284072
C2×#191283722
C2×#191283612
C2×#191283532
C2×#191283522
C2×#191283242
C2×#191283212
C2×#191282522
C2×#191282482
C2×#191282362
C2×#191282332
C2×#191281822
C2×C4×Q8×D832
C2×#554×C832
C2×#352283