Finite Group Databasebeta

← C2×#24921937 #36312034

Subgroups — C2×#24921937 #36312034

Order 21248.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921937C2132yesmaximal, direct product factor
2C2×#19128449C214yesmaximal, complemented
3C2×#19128436C212yesmaximal, complemented
4C2×#19128436C211yesmaximal, characteristic, complemented
5C2×#19128407C212yesmaximal, complemented
6C2×#19128373C211yesmaximal, characteristic, complemented
7C2×#19128366C211yesmaximal, characteristic, complemented
8C2×#19128363C212yesmaximal, complemented
9C2×#19128354C212yesmaximal, complemented
10C2×#19128323C212yesmaximal, complemented
11C2×#19128323C212yesmaximal, complemented
12C2×#19128307C212yesmaximal, complemented
13C2×#19128299C214yesmaximal, complemented
14C2×#19128276C212yesmaximal, complemented
15C2×#19128255C211yesmaximal, characteristic, complemented
16C2×#19128252C211yesmaximal, characteristic, complemented
17C2×#19128238C211yesmaximal, characteristic, complemented
18C2×#557×C83C211yesmaximal, characteristic, complemented
19C22×#13050591C2212yes—
20C22×#13050591C2212yes—
21C22×Q8×D83C2212yes—
22#19128449C22164yescomplemented
23#19128436C22132yescomplemented
24#19128436C22116yescomplemented
25#19128407C22132yescomplemented
26#19128373C22116yescomplemented
27#19128366C22116yescomplemented
28#19128363C22132yescomplemented
29#19128354C22132yescomplemented
30#19128323C22132yescomplemented
31#19128323C22132yescomplemented
32#19128307C22132yescomplemented
33#19128299C22164yescomplemented
34#19128276C22132yescomplemented
35#19128255C22116yescomplemented
36#19128252C22116yescomplemented
37C2×#14581791C2211yescharacteristic
38C2×#14581791C2212yes—
39C2×#14581790C2211yescharacteristic
40C2×#14581789C2211yescharacteristic
41C2×#14581789C2212yes—
42#19128238C22116yescomplemented
43C2×#14581787C2212yes—
44C2×#14581786C2214yes—
45C2×#14581783C2211yescharacteristic
46C2×#14581782C2212yes—
47C2×#14581781C2212yes—
48C2×#14581781C2212yes—
49C2×#14581781C2211yescharacteristic
50C2×#14581780C2214yes—
51C2×#14581780C2214yes—
52C2×#14581780C2212yes—
53C2×#14581777C2214yes—
54C2×#14581777C2214yes—
55C2×#14581777C2214yes—
56C2×#14581777C2212yes—
57C2×#14581777C2214yes—
58C2×#14581777C2214yes—
59C2×#14581777C2214yes—
60C2×#14581772C2211yescharacteristic
61C2×#14581772C2214yes—
62C2×#14581770C2214yes—
63C2×#14581770C2214yes—
64C2×#14581770C2214yes—
65C2×#14581770C2214yes—
66C2×#14581770C2212yes—
67C2×#14581768C2211yescharacteristic
68C2×#14581768C2212yes—
69C2×#14581768C2211yescharacteristic
70C2×#14581767C2212yes—
71C2×#14581767C2212yes—
72C2×#14581767C2214yes—
73C2×#14581767C2214yes—
74C2×#14581767C2214yes—
75C2×#14581767C2211yescharacteristic
76C2×#14581767C2212yes—
77C2×C4×Dic166C2211yescharacteristic
78C2×C4×Dic166C2212yes—
79C2×C4×D332C2212yes—
80C2×C4×D332C2212yes—
81C2×C4×D332C2212yes—
82C2×C4×D332C2214yes—
83C2×C4×D332C2211yescharacteristic
84C2×#14581754C2212yes—
85C2×#14581754C2212yes—
86C2×#14581754C2212yes—
87C2×#14581754C2212yes—
88C2×#14581749C2212yes—
89C2×#14581749C2212yes—
90C2×C4⋊C4×D83C2214yes—
91C2×C42×D83C2211yescharacteristic
92#557×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2212yes—
94C2×C4⋊Q8×C83C2211yescharacteristic
95C2×#125×C83C2212yes—
96C2×#125×C83C2214yes—
97C2×C4×Q8×C83C2212yes—
98C2×C4×Q8×C83C2212yes—
99C2×C4×Q8×C83C2211yescharacteristic
100C2×C4×Q8×C83C2211yescharacteristic
101C2×#13050591—48no—
102C2×#13050591—48no—
103C2×#13050591C23116yes—
104C2×#13050591C23116yes—
105C22×Dic166C2311yescharacteristic
106C22×Dic166C2312yes—
107C22×Dic166C2314yes—
108C2×Q8×D83—48no—
109C2×Q8×D83C23116yes—
110C22×D332C2311yescharacteristic
111C22×D332C2312yes—
112C22×D332C2312yes—
113C22×D332C2312yes—
114C22×D332C2312yes—
115C22×D332C2314yes—
116C22×D332C2314yes—
117C22×D332C2314yes—
118C22×C4×D83C2311yescharacteristic
119C22×C4×D83C2311yescharacteristic
120C22×C4×D83C2312yes—
121C22×C4×D83C2311yescharacteristic
122C22×C4×D83C2314yes—
123C22×C4×D83C2314yes—
124C22×C4×D83C2314yes—
125C22×C4×D83C2314yes—
126#14581791C2318yes—
127#14581791C23116yes—
128#14581790C2318yes—
129#14581789C2318yes—
130#14581789C23116yes—
131#14581787C23116yes—
132#14581786C23132yes—
133#14581783C2318yes—
134#14581782C23116yes—
135#14581781C23116yes—
136#14581781C23116yes—
137#14581781C2318yes—
138#14581780C23132yes—
139#14581780C23132yes—
140#14581780C23116yes—
141#14581777C23132yes—
142#14581777C23132yes—
143#14581777C23132yes—
144#14581777C23132yes—
145#14581777C23132yes—
146#14581777C23116yes—
147#14581777C23132yes—
148#14581772C2318yes—
149#14581772C23132yes—
150#14581770C23132yes—
151#14581770C23132yes—
152#14581770C23132yes—
153#14581770C23132yes—
154#14581770C23116yes—
155#14581768C2318yes—
156#14581768C23116yes—
157#14581768C2318yes—
158#14581767C23116yes—
159#14581767C23116yes—
160#14581767C23132yes—
161#14581767C23132yes—
162#14581767C23132yes—
163#14581767C23116yes—
164#14581767C2318yes—
165C4×Dic166C2318yes—
166C4×Dic166C23116yes—
167C4×D332C23116yes—
168C4×D332C23116yes—
169C4×D332C23116yes—
170C4×D332C23132yes—
171C4×D332C2318yes—
172#14581754C23116yes—
173#14581754C23116yes—
174#14581754C23116yes—
175#14581754C23116yes—
176#14581749C23116yes—
177#14581749C23116yes—
178C2×C4⋊Dic83C2312yes—
179C2×C4⋊Dic83C2311yescharacteristic
180C2×C4⋊Dic83C2311yescharacteristic
181C2×C4⋊Dic83C2312yes—
182C2×Dic83⋊C4C2312yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2312yes—
187C2×Dic83⋊C4C2312yes—
188C2×Dic83⋊C4C2312yes—
189C2×Dic83⋊C4C2312yes—
190C4⋊C4×D83C23132yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2314yes—
198C2×(C2×D83)⋊C4C2314yes—
199C2×(C2×D83)⋊C4C2312yes—
200C2×(C2×D83)⋊C4C2312yes—
201C2×(C2×D83)⋊C4C2314yes—
202C2×(C2×D83)⋊C4C2312yes—
203C2×(C2×D83)⋊C4C2314yes—
204C2×(C2×D83)⋊C4C2314yes—
205C2×C4×Dic83C2311yescharacteristic
206C2×C4×Dic83C2311yescharacteristic
207C2×C4×Dic83C2311yescharacteristic
208C2×C4×Dic83C2312yes—
209C42×D83C2318yes—
210C22×Q8×C83C2311yescharacteristic
211C22×Q8×C83C2312yes—
212C22×Q8×C83C2311yescharacteristic
213C4⋊Q8×C83C23116yes—
214C4⋊Q8×C83C2318yes—
215#125×C83C23116yes—
216#125×C83C23132yes—
217C4×Q8×C83C23116yes—
218C4×Q8×C83C23116yes—
219C4×Q8×C83C2318yes—
220C4×Q8×C83C2318yes—
221C2×C4⋊C4×C83C2311yescharacteristic
222C2×C4⋊C4×C83C2311yescharacteristic
223C2×C4⋊C4×C83C2312yes—
224C2×C4⋊C4×C83C2314yes—
225C2×C4⋊C4×C83C2312yes—
226C2×C4⋊C4×C83C2312yes—
227C2×C4⋊C4×C83C2314yes—
228C2×C4⋊C4×C83C2314yes—
229C2×C4⋊C4×C83C2312yes—
230C2×C42×C83C2312yes—
231C2×C42×C83C2314yes—
232C2×C42×C83C2311yescharacteristic
233C2×C42×C83C2312yes—
234C23×D83C2412yes—
235C23×D83C2411yescharacteristic
236C23×D83C2414yes—
237#13050591—432no—
238#13050591—432no—
239C2×Dic166—24no—
240C2×Dic166—48no—
241C2×Dic166—44no—
242C2×Dic166C2414yes—
243C2×Dic166C24116yes—
244C2×Dic166C2418yes—
245Q8×D83—432no—
246C2×D332—28no—
247C2×D332—24no—
248C2×D332—28no—
249C2×D332—44no—
250C2×D332—44no—
251C2×D332—48no—
252C2×D332—48no—
253C2×D332—48no—
254C2×D332C2418yes—
255C2×D332C2418yes—
256C2×D332C2414yes—
257C2×D332C2418yes—
258C2×D332C24116yes—
259C2×D332C2418yes—
260C2×D332C24116yes—
261C2×D332C24116yes—
262C22×Dic83C2411yescharacteristic
263C22×Dic83C2412yes—
264C22×Dic83C2412yes—
265C22×Dic83C2412yes—
266C22×Dic83C2411yescharacteristic
267C22×Dic83C2411yescharacteristic
268C2×C4×D83—28no—
269C2×C4×D83—24no—
270C2×C4×D83—24no—
271C2×C4×D83—48no—
272C2×C4×D83—42no—
273C2×C4×D83—48no—
274C2×C4×D83—48no—
275C2×C4×D83—48no—
276C2×C4×D83C2414yes—
277C2×C4×D83C2418yes—
278C2×C4×D83C2414yes—
279C2×C4×D83C2414yes—
280C2×C4×D83C24116yes—
281C2×C4×D83C24116yes—
282C2×C4×D83C24116yes—
283C2×C4×D83C24116yes—
284C4⋊Dic83C2414yes—
285C4⋊Dic83C2414yes—
286C4⋊Dic83C2418yes—
287C4⋊Dic83C2418yes—
288Dic83⋊C4C24116yes—
289Dic83⋊C4C2418yes—
290Dic83⋊C4C2418yes—
291Dic83⋊C4C2418yes—
292Dic83⋊C4C2418yes—
293Dic83⋊C4C2418yes—
294Dic83⋊C4C2418yes—
295Dic83⋊C4C2418yes—
296(C2×D83)⋊C4C2418yes—
297(C2×D83)⋊C4C2418yes—
298(C2×D83)⋊C4C2418yes—
299(C2×D83)⋊C4C24116yes—
300(C2×D83)⋊C4C24116yes—
301(C2×D83)⋊C4C24116yes—
302(C2×D83)⋊C4C24116yes—
303(C2×D83)⋊C4C24116yes—
304(C2×D83)⋊C4C2418yes—
305(C2×D83)⋊C4C2418yes—
306(C2×D83)⋊C4C24116yes—
307(C2×D83)⋊C4C2418yes—
308(C2×D83)⋊C4C24116yes—
309(C2×D83)⋊C4C2418yes—
310C4×Dic83C2414yes—
311C4×Dic83C2414yes—
312C4×Dic83C2418yes—
313C4×Dic83C2414yes—
314C2×Q8×C83—28no—
315C2×Q8×C83—24no—
316C2×Q8×C83—24no—
317C2×Q8×C83C2414yes—
318C2×Q8×C83C2418yes—
319C2×Q8×C83C2414yes—
320C22×C4×C83C2412yes—
321C22×C4×C83C2414yes—
322C22×C4×C83C2412yes—
323C22×C4×C83C2411yescharacteristic
324C22×C4×C83C2412yes—
325C22×C4×C83C2412yes—
326C22×C4×C83C2411yescharacteristic
327C22×C4×C83C2411yescharacteristic
328C4⋊C4×C83C2418yes—
329C4⋊C4×C83C2414yes—
330C4⋊C4×C83C2418yes—
331C4⋊C4×C83C24116yes—
332C4⋊C4×C83C24116yes—
333C4⋊C4×C83C2414yes—
334C4⋊C4×C83C2418yes—
335C4⋊C4×C83C24116yes—
336C4⋊C4×C83C2418yes—
337C42×C83C24116yes—
338C42×C83C2418yes—
339C42×C83C2418yes—
340C42×C83C2414yes—
341C23×C83C2511yescharacteristic
342C22×D83—24no—
343C22×D83—22no—
344C22×D83—28no—
345C22×D83—22no—
346C22×D83—24no—
347C22×D83—28no—
348C22×D83—22no—
349C22×D83—28no—
350C22×D83—24no—
351C22×D83C2514yes—
352C22×D83C2512yes—
353C22×D83C2518yes—
354Q8×C83—216no—
355Q8×C83—28no—
356Q8×C83—28no—
357C2×C4×C83—24no—
358C2×C4×C83—28no—
359C2×C4×C83—24no—
360C2×C4×C83—24no—
361C2×C4×C83—22no—
362C2×C4×C83—24no—
363C2×C4×C83H(5,𝔽2)14yes—
364C2×C4×C832−1+414yes—
365C2×C4×C83C2514yes—
366C2×C4×C83C2514yes—
367C2×C4×C83C2512yes—
368C2×C4×C83C2514yes—
369C2×C4×C83C2518yes—
370C2×C4×C83C2514yes—
371C2×C4×C83C2512yes—
372C2×C4×C83C2512yes—
373C2×Dic83—22no—
374C2×Dic83—24no—
375C2×Dic83—24no—
376C2×Dic83—22no—
377C2×Dic83—24no—
378C2×Dic83—22no—
379C2×Dic83C2512yes—
380C2×Dic83C2512yes—
381C2×Dic83C2512yes—
382C2×Dic83C2514yes—
383C2×Dic83C2514yes—
384C2×Dic83C2514yes—
385D332—216no—
386D332—216no—
387D332—28no—
388D332—416no—
389D332—48no—
390D332—48no—
391D332—416no—
392D332—416no—
393C4×D83—216no—
394C4×D83—28no—
395C4×D83—28no—
396C4×D83—44no—
397C4×D83—416no—
398C4×D83—416no—
399C4×D83—416no—
400C4×D83—416no—
401Dic166—28no—
402Dic166—416no—
403Dic166—48no—
404C22×C83C2×H(5,𝔽2)12yes—
405C22×C83C2×2−1+412yes—
406C22×C83#58512yes—
407C22×C83C2611yescharacteristic
408C2×D83—24no—
409C2×D83—22no—
410C2×D83—28no—
411C2×D83—22no—
412C2×D83—24no—
413C2×D83—28no—
414C2×D83—22no—
415C2×D83—28no—
416C2×D83—24no—
417C2×D83—48no—
418C2×D83—44no—
419C2×D83—416no—
420C4×C83—28no—
421C4×C83—24no—
422C4×C83—24no—
423C4×C83—24no—
424C4×C83—24no—
425C4×C83—22no—
426C4×C83C2×H(5,𝔽2)14yes—
427C4×C83C2×2−1+414yes—
428Dic83—24no—
429Dic83—24no—
430Dic83—22no—
431Dic83—22no—
432Dic83—22no—
433Dic83—24no—
434C2×#3554—831nomaximal, Sylow
435C2×C83#355414yescomplemented
436C2×C83C22×H(5,𝔽2)11yescharacteristic
437C2×C83C22×2−1+411yescharacteristic
438C2×C83C2×#58511yescharacteristic
439D83—44no—
440D83—42no—
441D83—48no—
442#3554—8332no—
443C2×#562—834no—
444C2×#559—832no—
445C2×#559—831no—
446C2×#557D8311yescharacteristic, complemented
447C2×#554—832no—
448C2×#550—831no—
449C2×D4×Q8—831no—
450C2×#548—832no—
451C2×#547—832no—
452C2×#542—832no—
453C2×#542—832no—
454C2×#540—832no—
455C2×#539—834no—
456C2×#536—832no—
457C2×#533—831no—
458C2×#532—831no—
459C2×#529—831no—
460C83C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—832no—
462C22×#41—832no—
463C23×Q8—832no—
464#562—8364no—
465#559—8332no—
466#559—8316no—
467#557C2×D83116yescomplemented
468#554—8332no—
469#550—8316no—
470D4×Q8—8316no—
471#548—8332no—
472#547—8332no—
473#542—8332no—
474#542—8332no—
475#540—8332no—
476#539—8364no—
477#536—8332no—
478#533—8316no—
479#532—8316no—
480C2×C4⋊Q8—831no—
481C2×C4⋊Q8—831no—
482C2×C4⋊Q8—832no—
483C2×C4⋊Q8C2×D8311yescharacteristic
484C2×C4⋊Q8C2×D8312yes—
485C2×#127—831no—
486C2×#127—832no—
487#529—8316no—
488C2×#126—832no—
489C2×#126—834no—
490C2×#125—831no—
491C2×#125—832no—
492C2×#125C2×D8314yes—
493C2×#125C2×D8312yes—
494C2×#124—831no—
495C2×#124—832no—
496C2×#124—832no—
497C2×#124—832no—
498C2×#124—834no—
499C2×#124—834no—
500C2×#123—832no—
501C2×#123—834no—
502C2×#123—834no—
503C2×#123—834no—
504C2×#123—834no—
505C2×#123—834no—
506C2×#123—834no—
507C2×C22⋊Q8—831no—
508C2×C22⋊Q8—831no—
509C2×C22⋊Q8—832no—
510C2×C22⋊Q8—832no—
511C2×C22⋊Q8—831no—
512C2×C22⋊Q8—834no—
513C2×C22⋊Q8—834no—
514C2×C22⋊Q8—834no—
515C2×C22⋊Q8—834no—
516C2×C22⋊Q8—834no—
517C2×#121—831no—
518C2×#121—832no—
519C2×#121—832no—
520C2×#121—834no—
521C2×#121—834no—
522C2×#121—834no—
523C2×#121—832no—
524C2×C4×Q8—831no—
525C2×C4×Q8—832no—
526C2×C4×Q8C2×D8311yescharacteristic
527C2×C4×Q8C2×D8311yescharacteristic
528C2×C4×Q8C2×D8312yes—
529C2×C4×Q8C2×D8312yes—
530C2×C4×D4—832no—
531C2×C4×D4—832no—
532C2×C4×D4—832no—
533C2×C4×D4—832no—
534C2×C4×D4—832no—
535C2×C4×D4—831no—
536C2×C4×D4—834no—
537C2×C4×D4—832no—
538C2×C4×D4—832no—
539C2×#117—832no—
540C2×#117—832no—
541C22×C4⋊C4—834no—
542C22×C42—831no—
543C2×#41—3328no—
544C2×#41—3328no—
545C2×#41—8316no—
546C2×#41—8316no—
547C22×Q8—3328no—
548C22×Q8—8316no—
549C22×Q8—832no—
550C22×Q8—834no—
551C22×Q8—831no—
552C22×Q8C22×D8311yescharacteristic
553C22×Q8C22×D8312yes—
554C22×Q8C22×D8311yescharacteristic
555C22×D4—832no—
556C22×D4—832no—
557C22×D4—834no—
558C22×D4—834no—
559C22×D4—834no—
560C22×D4—832no—
561C22×D4—831no—
562C22×D4—832no—
563C23×C4—834no—
564C23×C4—834no—
565C23×C4—834no—
566C23×C4—834no—
567C23×C4—831no—
568C23×C4—831no—
569C23×C4—832no—
570C23×C4—831no—
571C4⋊Q8—838no—
572C4⋊Q8—838no—
573C4⋊Q8—8316no—
574C4⋊Q8C22×D8318yes—
575C4⋊Q8C22×D83116yes—
576#127—838no—
577#127—8316no—
578#126—8316no—
579#126—8332no—
580#125—838no—
581#125—8316no—
582#125C22×D83132yes—
583#125C22×D83116yes—
584#124—838no—
585#124—8316no—
586#124—8316no—
587#124—8316no—
588#124—8332no—
589#124—8332no—
590#123—8316no—
591#123—8332no—
592#123—8332no—
593#123—8332no—
594#123—8332no—
595#123—8332no—
596#123—8332no—
597C22⋊Q8—838no—
598C22⋊Q8—838no—
599C22⋊Q8—8316no—
600C22⋊Q8—8316no—
601C22⋊Q8—8332no—
602C22⋊Q8—8332no—
603C22⋊Q8—8332no—
604C22⋊Q8—8332no—
605C22⋊Q8—838no—
606C22⋊Q8—8332no—
607#121—838no—
608#121—8316no—
609#121—8316no—
610#121—8332no—
611#121—8332no—
612#121—8332no—
613#121—8316no—
614C4×Q8—838no—
615C4×Q8—8316no—
616C4×Q8C22×D8318yes—
617C4×Q8C22×D8318yes—
618C4×Q8C22×D83116yes—
619C4×Q8C22×D83116yes—
620C4×D4—8316no—
621C4×D4—8316no—
622C4×D4—8316no—
623C4×D4—8316no—
624C4×D4—8316no—
625C4×D4—838no—
626C4×D4—8332no—
627C4×D4—8316no—
628C4×D4—8316no—
629#117—8316no—
630#117—8316no—
631C2×C4⋊C4—832no—
632C2×C4⋊C4—832no—
633C2×C4⋊C4—834no—
634C2×C4⋊C4—832no—
635C2×C4⋊C4—832no—
636C2×C4⋊C4—832no—
637C2×C4⋊C4—832no—
638C2×C4⋊C4—831no—
639C2×C4⋊C4—832no—
640C2×C4⋊C4—831no—
641C2×C4⋊C4—832no—
642C2×C4⋊C4—832no—
643C2×C4⋊C4—8332no—
644C2×C4⋊C4C22×D8314yes—
645C2×C4⋊C4C22×D8311yescharacteristic
646C2×C4⋊C4C22×D8312yes—
647C2×C4⋊C4C22×D8312yes—
648C2×C4⋊C4C22×D8311yescharacteristic
649C2×C4⋊C4C22×D8312yes—
650C2×C4⋊C4C22×D8314yes—
651C2×C4⋊C4C22×D8314yes—
652C2×C4⋊C4C22×D8312yes—
653C2×C22⋊C4—832no—
654C2×C22⋊C4—832no—
655C2×C22⋊C4—832no—
656C2×C22⋊C4—832no—
657C2×C22⋊C4—832no—
658C2×C22⋊C4—832no—
659C2×C22⋊C4—834no—
660C2×C22⋊C4—834no—
661C2×C22⋊C4—834no—
662C2×C22⋊C4—834no—
663C2×C22⋊C4—834no—
664C2×C22⋊C4—832no—
665C2×C22⋊C4—834no—
666C2×C22⋊C4—834no—
667C2×C42—831no—
668C2×C42—832no—
669C2×C42—831no—
670C2×C42—831no—
671C2×C42—838no—
672C2×C42C22×D8312yes—
673C2×C42C22×D8312yes—
674C2×C42C22×D8311yescharacteristic
675C2×C42C22×D8314yes—
676C24—832no—
677C24—834no—
678C24—831no—
679#41—33232no—
680#41—33232no—
681C2×Q8—28no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—3328no—
685C2×Q8—3324no—
686C2×Q8—33232no—
687C2×Q8—838no—
688C2×Q8—8316no—
689C2×Q8—834no—
690C2×Q8—1664no—
691C2×Q8C23×D8314yes—
692C2×Q8C23×D8318yes—
693C2×Q8C23×D8314yes—
694C2×D4—3328no—
695C2×D4—3328no—
696C2×D4—3324no—
697C2×D4—3324no—
698C2×D4—3328no—
699C2×D4—838no—
700C2×D4—838no—
701C2×D4—8316no—
702C2×D4—8316no—
703C2×D4—8316no—
704C2×D4—838no—
705C2×D4—834no—
706C2×D4—838no—
707C2×D4—1668no—
708C2×D4—1668no—
709C2×D4—1664no—
710C22×C4—3328no—
711C22×C4—3328no—
712C22×C4—3328no—
713C22×C4—3328no—
714C22×C4—3322no—
715C22×C4—834no—
716C22×C4—8316no—
717C22×C4—8316no—
718C22×C4—8316no—
719C22×C4—8316no—
720C22×C4—831no—
721C22×C4—831no—
722C22×C4—831no—
723C22×C4—832no—
724C22×C4—832no—
725C22×C4—832no—
726C22×C4—834no—
727C22×C4—834no—
728C22×C4—838no—
729C22×C4—1668no—
730C22×C4—1664no—
731C22×C4—1664no—
732C22×C4C23×D8311yescharacteristic
733C22×C4C23×D8312yes—
734C22×C4C23×D8312yes—
735C22×C4C23×D8312yes—
736C22×C4C23×D8314yes—
737C22×C4C23×D8312yes—
738C22×C4C23×D8311yescharacteristic
739C22×C4C23×D8311yescharacteristic
740C4⋊C4—838no—
741C4⋊C4—838no—
742C4⋊C4—8316no—
743C4⋊C4—838no—
744C4⋊C4—838no—
745C4⋊C4—838no—
746C4⋊C4—838no—
747C4⋊C4—834no—
748C4⋊C4—838no—
749C4⋊C4—834no—
750C4⋊C4—838no—
751C4⋊C4—838no—
752C4⋊C4C23×D83116yes—
753C4⋊C4C23×D8314yes—
754C4⋊C4C23×D8318yes—
755C4⋊C4C23×D8318yes—
756C4⋊C4C23×D8314yes—
757C4⋊C4C23×D8318yes—
758C4⋊C4C23×D83116yes—
759C4⋊C4C23×D83116yes—
760C4⋊C4C23×D8318yes—
761C22⋊C4—838no—
762C22⋊C4—838no—
763C22⋊C4—838no—
764C22⋊C4—838no—
765C22⋊C4—838no—
766C22⋊C4—838no—
767C22⋊C4—8316no—
768C22⋊C4—8316no—
769C22⋊C4—8316no—
770C22⋊C4—8316no—
771C22⋊C4—8316no—
772C22⋊C4—838no—
773C22⋊C4—8316no—
774C22⋊C4—8316no—
775C42—834no—
776C42—834no—
777C42—834no—
778C42—838no—
779C42C23×D8314yes—
780C42C23×D8318yes—
781C42C23×D8318yes—
782C42C23×D83116yes—
783C23—834no—
784C23—838no—
785C23—832no—
786C23—1664no—
787C23—1668no—
788C23—1662no—
789C23—1662no—
790C23—1664no—
791C23—1668no—
792C23—1668no—
793C23—1662no—
794C23—1664no—
795C23C24×D8311yescharacteristic
796Q8—216no—
797Q8—28no—
798Q8—28no—
799Q8—33216no—
800Q8—3328no—
801Q8—1668no—
802D4—33216no—
803D4—33216no—
804D4—3328no—
805D4—3328no—
806D4—33216no—
807D4—16616no—
808D4—16616no—
809D4—1668no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—33216no—
817C2×C4—33216no—
818C2×C4—33216no—
819C2×C4—33216no—
820C2×C4—3324no—
821C2×C4—832no—
822C2×C4—832no—
823C2×C4—832no—
824C2×C4—834no—
825C2×C4—834no—
826C2×C4—834no—
827C2×C4—1662no—
828C2×C4—1664no—
829C2×C4—1664no—
830C2×C4—1662no—
831C2×C4—1664no—
832C2×C4—1662no—
833C2×C4—16616no—
834C2×C4—1668no—
835C2×C4—1668no—
836C2×C4#1458183814yes—
837C2×C4#1458184014yes—
838C2×C4C24×D8312yes—
839C2×C4C24×D8314yes—
840C2×C4C24×D8314yes—
841C2×C4C24×D8314yes—
842C2×C4C24×D8318yes—
843C2×C4C24×D8314yes—
844C2×C4C24×D8312yes—
845C2×C4C24×D8312yes—
846C22—3328no—
847C22—33216no—
848C22—3324no—
849C22—1664no—
850C22—1668no—
851C22—1662no—
852C22—1662no—
853C22—1664no—
854C22—1668no—
855C22—1668no—
856C22—1662no—
857C22—1664no—
858C22C2×#1458183812yes—
859C22C2×#1458184012yes—
860C22#1912853812yes—
861C22C25×D8311yescharacteristic
862C4—24no—
863C4—28no—
864C4—24no—
865C4—24no—
866C4—22no—
867C4—24no—
868C4—1662no—
869C4—1664no—
870C4—1664no—
871C4—1662no—
872C4—1664no—
873C4—1662no—
874C4C2×#1458183814yes—
875C4C2×#1458184014yes—
876C2—3324no—
877C2—3328no—
878C2—3322no—
879C2#2492193714yesdirect product factor
880C2C22×#1458183811yescharacteristic
881C2C22×#1458184011yescharacteristic
882C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#557×C83C2
socleC23×C83C25
hypercenterC2×#557D83
hypocenterC83C2×#3554
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #24921937C2direct (N × H)
2. C2×#19128449C2semidirect
3. C2×#19128436C2semidirect
4. C2×#19128436C2semidirect
5. C2×#19128407C2semidirect
6. C2×#19128373C2semidirect
7. C2×#19128366C2semidirect
8. C2×#19128363C2semidirect
9. C2×#19128354C2semidirect
10. C2×#19128323C2semidirect
11. C2×#19128323C2semidirect
12. C2×#19128307C2semidirect
13. C2×#19128299C2semidirect
14. C2×#19128276C2semidirect
15. C2×#19128255C2semidirect
16. C2×#19128252C2semidirect
17. C2×#19128238C2semidirect
18. C2×#557×C83C2semidirect
22. #19128449C22semidirect
23. #19128436C22semidirect
24. #19128436C22semidirect
25. #19128407C22semidirect
26. #19128373C22semidirect
27. #19128366C22semidirect
28. #19128363C22semidirect
29. #19128354C22semidirect
30. #19128323C22semidirect
31. #19128323C22semidirect
32. #19128307C22semidirect
33. #19128299C22semidirect
34. #19128276C22semidirect
35. #19128255C22semidirect
36. #19128252C22semidirect
42. #19128238C22semidirect
92. #557×C83C22semidirect
435. C2×C83#3554semidirect
446. C2×#557D83semidirect
460. C83C2×#3554semidirect
467. #557C2×D83semidirect
879. C2#24921937direct (N × H)

Maximal subgroups

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

subgroupindex
#249219372
C2×#191284492
C2×#191284362
C2×#191284072
C2×#191283732
C2×#191283662
C2×#191283632
C2×#191283542
C2×#191283232
C2×#191283072
C2×#191282992
C2×#191282762
C2×#191282552
C2×#191282522
C2×#191282382
C2×#557×C832
C2×#355483