Finite Group Databasebeta

← C2×#24921934 #36312033

Subgroups — C2×#24921934 #36312033

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#24921934C2132yesmaximal, direct product factor
2C2×#19128447C214yesmaximal, complemented
3C2×#19128436C211yesmaximal, characteristic, complemented
4C2×#19128436C212yesmaximal, complemented
5C2×#19128429C211yesmaximal, characteristic, complemented
6C2×#19128411C212yesmaximal, complemented
7C2×#19128373C211yesmaximal, characteristic, complemented
8C2×Q8×D332C211yesmaximal, characteristic, complemented
9C2×#19128361C212yesmaximal, complemented
10C2×#19128353C212yesmaximal, complemented
11C2×#19128325C212yesmaximal, complemented
12C2×#19128322C212yesmaximal, complemented
13C2×#19128306C212yesmaximal, complemented
14C2×#19128299C214yesmaximal, complemented
15C2×#19128276C212yesmaximal, complemented
16C2×#19128251C211yesmaximal, characteristic, complemented
17C2×#19128235C211yesmaximal, characteristic, complemented
18C2×#533×C83C211yesmaximal, characteristic, complemented
19C22×#13050591C2212yes—
20C22×#13050590C2212yes—
21C22×Q8×D83C2212yes—
22#19128447C22164yescomplemented
23#19128436C22132yescomplemented
24#19128436C22116yescomplemented
25#19128429C22116yescomplemented
26#19128411C22132yescomplemented
27#19128373C22116yescomplemented
28Q8×D332C22116yescomplemented
29#19128361C22132yescomplemented
30#19128353C22132yescomplemented
31#19128325C22132yescomplemented
32#19128322C22132yescomplemented
33#19128306C22132yescomplemented
34#19128299C22164yescomplemented
35#19128276C22132yescomplemented
36#19128251C22116yescomplemented
37C2×#14581792C2212yes—
38C2×#14581792C2211yescharacteristic
39C2×#14581790C2212yes—
40C2×#14581789C2211yescharacteristic
41C2×#14581789C2212yes—
42#19128235C22116yescomplemented
43C2×#14581787C2214yes—
44C2×#14581786C2212yes—
45C2×#14581784C2211yescharacteristic
46C2×#14581784C2212yes—
47C2×#14581782C2214yes—
48C2×#14581781C2214yes—
49C2×#14581781C2212yes—
50C2×#14581780C2212yes—
51C2×#14581780C2212yes—
52C2×#14581780C2211yescharacteristic
53C2×#14581778C2214yes—
54C2×#14581777C2214yes—
55C2×#14581777C2214yes—
56C2×#14581777C2214yes—
57C2×#14581777C2214yes—
58C2×#14581777C2214yes—
59C2×#14581775C2212yes—
60C2×#14581774C2214yes—
61C2×#14581772C2212yes—
62C2×#14581772C2214yes—
63C2×#14581771C2211yescharacteristic
64C2×#14581770C2214yes—
65C2×#14581770C2214yes—
66C2×#14581770C2214yes—
67C2×#14581768C2214yes—
68C2×#14581767C2212yes—
69C2×#14581767C2214yes—
70C2×#14581766C2212yes—
71C2×#14581766C2211yescharacteristic
72C2×#14581766C2212yes—
73C2×#14581765C2214yes—
74C2×#14581765C2214yes—
75C2×C4×Dic166C2212yes—
76C2×C4×Dic166C2211yescharacteristic
77C2×#14581757C2212yes—
78C2×C4×D332C2212yes—
79C2×C4×D332C2211yescharacteristic
80C2×C4×D332C2212yes—
81C2×C4×D332C2212yes—
82C2×C4×D332C2212yes—
83C2×C4×D332C2212yes—
84C2×#14581754C2212yes—
85C2×#14581754C2214yes—
86C2×C4×C22⋊D83C2212yes—
87C2×#14581749C2212yes—
88C2×C4⋊C4×D83C2214yes—
89#533×C83C22116yescomplemented
90C2×C4⋊Q8×C83C2211yescharacteristic
91C2×C4⋊Q8×C83C2211yescharacteristic
92C2×#125×C83C2212yes—
93C2×C22⋊Q8×C83C2211yescharacteristic
94C2×C22⋊Q8×C83C2211yescharacteristic
95C2×C22⋊Q8×C83C2212yes—
96C2×C4×Q8×C83C2211yescharacteristic
97C2×C4×Q8×C83C2211yescharacteristic
98C2×C4×Q8×C83C2212yes—
99C2×#117×C83C2212yes—
100C22×C42×C83C2211yescharacteristic
101C2×#13050591—48no—
102C2×#13050591C23116yes—
103C2×#13050590—48no—
104C2×#13050590C23116yes—
105C22×Dic166C2312yes—
106C22×Dic166C2311yescharacteristic
107C22×Dic166C2314yes—
108C2×Q8×D83—48no—
109C2×Q8×D83C23116yes—
110C22×D332C2312yes—
111C22×D332C2312yes—
112C22×D332C2311yescharacteristic
113C22×D332C2314yes—
114C22×D332C2312yes—
115C22×D332C2314yes—
116C22×C22⋊D83C2312yes—
117C22×C22⋊D83C2314yes—
118C22×C4×D83C2312yes—
119C22×C4×D83C2314yes—
120C22×C4×D83C2314yes—
121C22×C4×D83C2314yes—
122C22×C4×D83C2314yes—
123#14581792C23116yes—
124#14581792C2318yes—
125#14581790C23116yes—
126#14581789C2318yes—
127#14581789C23116yes—
128#14581787C23132yes—
129#14581786C23116yes—
130#14581784C2318yes—
131#14581784C23116yes—
132#14581782C23132yes—
133#14581781C23132yes—
134#14581781C23116yes—
135#14581780C23116yes—
136#14581780C23116yes—
137#14581780C2318yes—
138#14581778C23132yes—
139#14581777C23132yes—
140#14581777C23132yes—
141#14581777C23132yes—
142#14581777C23132yes—
143#14581777C23132yes—
144#14581775C23116yes—
145#14581774C23132yes—
146#14581772C23116yes—
147#14581772C23132yes—
148#14581771C2318yes—
149#14581770C23132yes—
150#14581770C23132yes—
151#14581770C23132yes—
152#14581768C23132yes—
153#14581767C23116yes—
154#14581767C23132yes—
155#14581766C23116yes—
156#14581766C23116yes—
157#14581766C2318yes—
158#14581765C23132yes—
159#14581765C23132yes—
160C4×Dic166C23116yes—
161C4×Dic166C2318yes—
162#14581757C23116yes—
163C4×D332C23116yes—
164C4×D332C2318yes—
165C4×D332C23116yes—
166C4×D332C23116yes—
167C4×D332C23116yes—
168C4×D332C23116yes—
169#14581754C23116yes—
170#14581754C23132yes—
171C4×C22⋊D83C23116yes—
172#14581749C23116yes—
173C2×C4⋊Dic83C2314yes—
174C2×C4⋊Dic83C2311yescharacteristic
175C2×C4⋊Dic83C2311yescharacteristic
176C2×C4⋊Dic83C2312yes—
177C2×C4⋊Dic83C2312yes—
178C2×Dic83⋊C4C2312yes—
179C2×Dic83⋊C4C2314yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C2312yes—
185C4⋊C4×D83C23132yes—
186C2×C22⋊Dic83C2312yes—
187C2×(C2×D83)⋊C4C2312yes—
188C2×(C2×D83)⋊C4C2312yes—
189C2×(C2×D83)⋊C4C2312yes—
190C2×(C2×D83)⋊C4C2314yes—
191C2×(C2×D83)⋊C4C2314yes—
192C2×(C2×D83)⋊C4C2314yes—
193C2×(C2×D83)⋊C4C2314yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×C4×Dic83C2312yes—
199C2×C4×Dic83C2314yes—
200C22×Q8×C83C2311yescharacteristic
201C22×Q8×C83C2311yescharacteristic
202C22×Q8×C83C2312yes—
203C23×C4×C83C2311yescharacteristic
204C23×C4×C83C2311yescharacteristic
205C23×C4×C83C2311yescharacteristic
206C4⋊Q8×C83C2318yes—
207C4⋊Q8×C83C2318yes—
208#125×C83C23116yes—
209C22⋊Q8×C83C2318yes—
210C22⋊Q8×C83C2318yes—
211C22⋊Q8×C83C23116yes—
212C4×Q8×C83C2318yes—
213C4×Q8×C83C2318yes—
214C4×Q8×C83C23116yes—
215#117×C83C23116yes—
216C2×C4⋊C4×C83C2312yes—
217C2×C4⋊C4×C83C2312yes—
218C2×C4⋊C4×C83C2312yes—
219C2×C4⋊C4×C83C2312yes—
220C2×C4⋊C4×C83C2312yes—
221C2×C4⋊C4×C83C2312yes—
222C2×C4⋊C4×C83C2311yescharacteristic
223C2×C4⋊C4×C83C2311yescharacteristic
224C2×C4⋊C4×C83C2312yes—
225C2×C22⋊C4×C83C2312yes—
226C2×C22⋊C4×C83C2312yes—
227C2×C42×C83C2311yescharacteristic
228C2×C42×C83C2311yescharacteristic
229C2×C42×C83C2311yescharacteristic
230C2×C42×C83C2311yescharacteristic
231C2×C42×C83C2318yes—
232C2×C42×C83C2312yes—
233C2×C42×C83C2312yes—
234C23×D83C2412yes—
235C23×D83C2414yes—
236#13050591—432no—
237#13050590—432no—
238C2×Dic166—28no—
239C2×Dic166—24no—
240C2×Dic166—48no—
241C2×Dic166C2414yes—
242C2×Dic166C2418yes—
243C2×Dic166C24116yes—
244Q8×D83—432no—
245C2×D332—28no—
246C2×D332—28no—
247C2×D332—24no—
248C2×D332—44no—
249C2×D332—48no—
250C2×D332—48no—
251C2×D332C2418yes—
252C2×D332C2414yes—
253C2×D332C2418yes—
254C2×D332C24116yes—
255C2×D332C24116yes—
256C2×D332C2418yes—
257C2×C22⋊D83—44no—
258C2×C22⋊D83—48no—
259C2×C22⋊D83C2418yes—
260C2×C22⋊D83C24116yes—
261C22×Dic83C2412yes—
262C22×Dic83C2414yes—
263C22×Dic83C2412yes—
264C22×Dic83C2412yes—
265C2×C4×D83—28no—
266C2×C4×D83—48no—
267C2×C4×D83—48no—
268C2×C4×D83—48no—
269C2×C4×D83—48no—
270C2×C4×D83C2418yes—
271C2×C4×D83C24116yes—
272C2×C4×D83C24116yes—
273C2×C4×D83C24116yes—
274C2×C4×D83C24116yes—
275C4⋊Dic83C2418yes—
276C4⋊Dic83C2414yes—
277C4⋊Dic83C2418yes—
278C4⋊Dic83C24116yes—
279C4⋊Dic83C2414yes—
280Dic83⋊C4C24116yes—
281Dic83⋊C4C24116yes—
282Dic83⋊C4C2418yes—
283Dic83⋊C4C2418yes—
284Dic83⋊C4C2418yes—
285Dic83⋊C4C24116yes—
286Dic83⋊C4C2418yes—
287C22⋊Dic83C2418yes—
288(C2×D83)⋊C4C24116yes—
289(C2×D83)⋊C4C24116yes—
290(C2×D83)⋊C4C24116yes—
291(C2×D83)⋊C4C24116yes—
292(C2×D83)⋊C4C2418yes—
293(C2×D83)⋊C4C24116yes—
294(C2×D83)⋊C4C2418yes—
295(C2×D83)⋊C4C24116yes—
296(C2×D83)⋊C4C24116yes—
297(C2×D83)⋊C4C2418yes—
298(C2×D83)⋊C4C2418yes—
299C4×Dic83C24116yes—
300C4×Dic83C2418yes—
301C24×C83C2411yescharacteristic
302C2×Q8×C83—24no—
303C2×Q8×C83—24no—
304C2×Q8×C83—44no—
305C2×Q8×C83C2414yes—
306C2×Q8×C83C2414yes—
307C2×Q8×C83C2418yes—
308C22×C4×C83—24no—
309C22×C4×C83—24no—
310C22×C4×C83—42no—
311C22×C4×C83C2414yes—
312C22×C4×C83C2411yescharacteristic
313C22×C4×C83C2412yes—
314C22×C4×C83C2412yes—
315C22×C4×C83C2412yes—
316C22×C4×C83C2411yescharacteristic
317C22×C4×C83C2412yes—
318C22×C4×C83C2414yes—
319C22×C4×C83C2411yescharacteristic
320C22×C4×C83C2411yescharacteristic
321C22×C4×C83C2414yes—
322C22×C4×C83C2411yescharacteristic
323C22×C4×C83C2411yescharacteristic
324C4⋊C4×C83C2418yes—
325C4⋊C4×C83C2414yes—
326C4⋊C4×C83C2418yes—
327C4⋊C4×C83C2418yes—
328C4⋊C4×C83C2418yes—
329C4⋊C4×C83C2418yes—
330C4⋊C4×C83C2414yes—
331C4⋊C4×C83C2418yes—
332C4⋊C4×C83C2418yes—
333C22⋊C4×C83C2418yes—
334C22⋊C4×C83C2418yes—
335C42×C83C2414yes—
336C42×C83C2414yes—
337C42×C83C2418yes—
338C42×C83C2418yes—
339C42×C83C2414yes—
340C42×C83C2414yes—
341C23×C83—22no—
342C23×C83—22no—
343C23×C83—22no—
344C23×C83C2512yes—
345C23×C83C2511yescharacteristic
346C22×D83—24no—
347C22×D83—28no—
348C22×D83—24no—
349C22×D83—28no—
350C22×D83—28no—
351C22×D83—24no—
352C22×D83C2514yes—
353C22×D83C2518yes—
354Q8×C83—28no—
355Q8×C83—28no—
356Q8×C83—48no—
357C2×C4×C83—22no—
358C2×C4×C83—24no—
359C2×C4×C83—24no—
360C2×C4×C83—22no—
361C2×C4×C83—22no—
362C2×C4×C83—22no—
363C2×C4×C83—24no—
364C2×C4×C83—24no—
365C2×C4×C83—28no—
366C2×C4×C83—28no—
367C2×C4×C83—44no—
368C2×C4×C83H(5,𝔽2)14yes—
369C2×C4×C832−1+414yes—
370C2×C4×C83C2512yes—
371C2×C4×C83C2512yes—
372C2×C4×C83C2512yes—
373C2×C4×C83C2512yes—
374C2×C4×C83C2514yes—
375C2×C4×C83C2514yes—
376C2×C4×C83C2514yes—
377C2×C4×C83C2514yes—
378C2×C4×C83C2512yes—
379C2×C4×C83C2512yes—
380C22⋊D83—48no—
381C22⋊D83—416no—
382C2×Dic83—24no—
383C2×Dic83—28no—
384C2×Dic83—24no—
385C2×Dic83—24no—
386C2×Dic83C2514yes—
387C2×Dic83C2514yes—
388C2×Dic83C2518yes—
389C2×Dic83C2514yes—
390D332—216no—
391D332—216no—
392D332—28no—
393D332—48no—
394D332—416no—
395D332—416no—
396C4×D83—216no—
397C4×D83—416no—
398C4×D83—416no—
399C4×D83—416no—
400C4×D83—416no—
401Dic166—216no—
402Dic166—28no—
403Dic166—416no—
404C22×C83—22no—
405C22×C83—22no—
406C22×C83—22no—
407C22×C83—44no—
408C22×C83C2×H(5,𝔽2)12yes—
409C22×C83C2×2−1+412yes—
410C22×C83#58512yes—
411C22×C83C2611yescharacteristic
412C2×D83—24no—
413C2×D83—28no—
414C2×D83—24no—
415C2×D83—28no—
416C2×D83—28no—
417C2×D83—24no—
418C2×D83—48no—
419C2×D83—416no—
420C4×C83—24no—
421C4×C83—22no—
422C4×C83—24no—
423C4×C83—22no—
424C4×C83—24no—
425C4×C83—22no—
426C4×C83—24no—
427C4×C83—22no—
428C4×C83C2×H(5,𝔽2)14yes—
429C4×C83C2×2−1+414yes—
430Dic83—28no—
431Dic83—24no—
432Dic83—24no—
433Dic83—24no—
434C2×#3554—831nomaximal, Sylow
435C2×C83—42no—
436C2×C83#355414yescomplemented
437C2×C83C22×H(5,𝔽2)11yescharacteristic
438C2×C83C22×2−1+411yescharacteristic
439C2×C83C2×#58511yescharacteristic
440D83—44no—
441D83—48no—
442#3554—8332no—
443C2×#562—834no—
444C2×#559—832no—
445C2×#559—831no—
446C2×#557—831no—
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×#533D8311yescharacteristic, complemented
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#557—8316no—
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#533C2×D83116yescomplemented
479#532—8316no—
480C2×C4⋊Q8—832no—
481C2×C4⋊Q8—831no—
482C2×C4⋊Q8—832no—
483C2×C4⋊Q8C2×D8311yescharacteristic
484C2×C4⋊Q8C2×D8311yescharacteristic
485C2×#127—831no—
486C2×#127—832no—
487#529—8316no—
488C2×#126—834no—
489C2×#126—832no—
490C2×#125—834no—
491C2×#125—831no—
492C2×#125—832no—
493C2×#125C2×D8312yes—
494C2×#124—832no—
495C2×#124—834no—
496C2×#124—834no—
497C2×#124—831no—
498C2×#124—832no—
499C2×#124—832no—
500C2×#123—832no—
501C2×#123—834no—
502C2×#123—834no—
503C2×#123—834no—
504C2×#123—834no—
505C2×#123—834no—
506C2×#123—834no—
507C2×C22⋊Q8—834no—
508C2×C22⋊Q8—831no—
509C2×C22⋊Q8—834no—
510C2×C22⋊Q8—834no—
511C2×C22⋊Q8—834no—
512C2×C22⋊Q8—834no—
513C2×C22⋊Q8—832no—
514C2×C22⋊Q8C2×D8311yescharacteristic
515C2×C22⋊Q8C2×D8311yescharacteristic
516C2×C22⋊Q8C2×D8312yes—
517C2×#121—831no—
518C2×#121—832no—
519C2×#121—832no—
520C2×#121—834no—
521C2×#121—832no—
522C2×#121—834no—
523C2×#121—834no—
524C2×C4×Q8—832no—
525C2×C4×Q8—831no—
526C2×C4×Q8—832no—
527C2×C4×Q8C2×D8311yescharacteristic
528C2×C4×Q8C2×D8311yescharacteristic
529C2×C4×Q8C2×D8312yes—
530C2×C4×D4—832no—
531C2×C4×D4—834no—
532C2×C4×D4—832no—
533C2×C4×D4—831no—
534C2×C4×D4—832no—
535C2×C4×D4—832no—
536C2×C4×D4—832no—
537C2×C4×D4—832no—
538C2×C4×D4—832no—
539C2×#117—832no—
540C2×#117C2×D8312yes—
541C22×C4⋊C4—834no—
542C22×C42C2×D8311yescharacteristic
543C2×#41—3328no—
544C2×#41—3328no—
545C2×#41—8316no—
546C2×#41—8316no—
547C22×Q8—3328no—
548C22×Q8—8316no—
549C22×Q8—834no—
550C22×Q8—831no—
551C22×Q8—832no—
552C22×Q8C22×D8311yescharacteristic
553C22×Q8C22×D8311yescharacteristic
554C22×Q8C22×D8312yes—
555C22×D4—832no—
556C22×D4—834no—
557C22×D4—832no—
558C22×D4—834no—
559C22×D4—834no—
560C22×D4—831no—
561C22×D4—832no—
562C22×D4—832no—
563C23×C4—834no—
564C23×C4—834no—
565C23×C4—834no—
566C23×C4—834no—
567C23×C4—832no—
568C23×C4C22×D8311yescharacteristic
569C23×C4C22×D8311yescharacteristic
570C23×C4C22×D8311yescharacteristic
571C4⋊Q8—8316no—
572C4⋊Q8—838no—
573C4⋊Q8—8316no—
574C4⋊Q8C22×D8318yes—
575C4⋊Q8C22×D8318yes—
576#127—838no—
577#127—8316no—
578#126—8332no—
579#126—8316no—
580#125—8332no—
581#125—838no—
582#125—8316no—
583#125C22×D83116yes—
584#124—8316no—
585#124—8332no—
586#124—8332no—
587#124—838no—
588#124—8316no—
589#124—8316no—
590#123—8316no—
591#123—8332no—
592#123—8332no—
593#123—8332no—
594#123—8332no—
595#123—8332no—
596#123—8332no—
597C22⋊Q8—8332no—
598C22⋊Q8—838no—
599C22⋊Q8—8332no—
600C22⋊Q8—8332no—
601C22⋊Q8—8332no—
602C22⋊Q8—8332no—
603C22⋊Q8—8316no—
604C22⋊Q8C22×D8318yes—
605C22⋊Q8C22×D8318yes—
606C22⋊Q8C22×D83116yes—
607#121—838no—
608#121—8316no—
609#121—8316no—
610#121—8332no—
611#121—8316no—
612#121—8332no—
613#121—8332no—
614C4×Q8—8316no—
615C4×Q8—838no—
616C4×Q8—8316no—
617C4×Q8C22×D8318yes—
618C4×Q8C22×D8318yes—
619C4×Q8C22×D83116yes—
620C4×D4—8316no—
621C4×D4—8332no—
622C4×D4—8316no—
623C4×D4—838no—
624C4×D4—8316no—
625C4×D4—8316no—
626C4×D4—8316no—
627C4×D4—8316no—
628C4×D4—8316no—
629#117—8316no—
630#117C22×D83116yes—
631C2×C4⋊C4—832no—
632C2×C4⋊C4—834no—
633C2×C4⋊C4—834no—
634C2×C4⋊C4—832no—
635C2×C4⋊C4—832no—
636C2×C4⋊C4—831no—
637C2×C4⋊C4—831no—
638C2×C4⋊C4—832no—
639C2×C4⋊C4—832no—
640C2×C4⋊C4—834no—
641C2×C4⋊C4—834no—
642C2×C4⋊C4—832no—
643C2×C4⋊C4—8332no—
644C2×C4⋊C4C22×D8312yes—
645C2×C4⋊C4C22×D8312yes—
646C2×C4⋊C4C22×D8312yes—
647C2×C4⋊C4C22×D8312yes—
648C2×C4⋊C4C22×D8311yescharacteristic
649C2×C4⋊C4C22×D8311yescharacteristic
650C2×C4⋊C4C22×D8312yes—
651C2×C4⋊C4C22×D8312yes—
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—834no—
659C2×C22⋊C4—834no—
660C2×C22⋊C4—834no—
661C2×C22⋊C4—834no—
662C2×C22⋊C4—834no—
663C2×C22⋊C4—834no—
664C2×C22⋊C4—834no—
665C2×C22⋊C4C22×D8312yes—
666C2×C22⋊C4C22×D8312yes—
667C2×C42—832no—
668C2×C42—834no—
669C2×C42C22×D8311yescharacteristic
670C2×C42C22×D8312yes—
671C2×C42C22×D8312yes—
672C2×C42C22×D8311yescharacteristic
673C2×C42C22×D8311yescharacteristic
674C2×C42C22×D8311yescharacteristic
675C2×C42C22×D8318yes—
676C24—832no—
677C24—834no—
678C24C23×D8311yescharacteristic
679#41—33232no—
680#41—33232no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—44no—
684C2×Q8—3328no—
685C2×Q8—33232no—
686C2×Q8—8316no—
687C2×Q8—834no—
688C2×Q8—838no—
689C2×Q8—1668no—
690C2×Q8—1664no—
691C2×Q8C23×D8314yes—
692C2×Q8C23×D8314yes—
693C2×Q8C23×D8318yes—
694C2×D4—3328no—
695C2×D4—3324no—
696C2×D4—3328no—
697C2×D4—3328no—
698C2×D4—3324no—
699C2×D4—838no—
700C2×D4—8316no—
701C2×D4—838no—
702C2×D4—8316no—
703C2×D4—8316no—
704C2×D4—834no—
705C2×D4—838no—
706C2×D4—838no—
707C2×D4—1668no—
708C2×D4—1664no—
709C2×D4—1668no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—3328no—
714C22×C4—3328no—
715C22×C4—3328no—
716C22×C4—3328no—
717C22×C4—8316no—
718C22×C4—8316no—
719C22×C4—8316no—
720C22×C4—8316no—
721C22×C4—832no—
722C22×C4—832no—
723C22×C4—834no—
724C22×C4—832no—
725C22×C4—838no—
726C22×C4—1668no—
727C22×C4C23×D8314yes—
728C22×C4C23×D8314yes—
729C22×C4C23×D8312yes—
730C22×C4C23×D8311yescharacteristic
731C22×C4C23×D8311yescharacteristic
732C22×C4C23×D8311yescharacteristic
733C22×C4C23×D8311yescharacteristic
734C22×C4C23×D8312yes—
735C22×C4C23×D8312yes—
736C22×C4C23×D8312yes—
737C22×C4C23×D8314yes—
738C22×C4C23×D8311yescharacteristic
739C22×C4C23×D8311yescharacteristic
740C4⋊C4—838no—
741C4⋊C4—8316no—
742C4⋊C4—8316no—
743C4⋊C4—838no—
744C4⋊C4—838no—
745C4⋊C4—834no—
746C4⋊C4—834no—
747C4⋊C4—838no—
748C4⋊C4—838no—
749C4⋊C4—8316no—
750C4⋊C4—8316no—
751C4⋊C4—838no—
752C4⋊C4C23×D8318yes—
753C4⋊C4C23×D8318yes—
754C4⋊C4C23×D8318yes—
755C4⋊C4C23×D8318yes—
756C4⋊C4C23×D8314yes—
757C4⋊C4C23×D8314yes—
758C4⋊C4C23×D8318yes—
759C4⋊C4C23×D8318yes—
760C4⋊C4C23×D8318yes—
761C22⋊C4—838no—
762C22⋊C4—838no—
763C22⋊C4—838no—
764C22⋊C4—838no—
765C22⋊C4—838no—
766C22⋊C4—8316no—
767C22⋊C4—8316no—
768C22⋊C4—8316no—
769C22⋊C4—8316no—
770C22⋊C4—8316no—
771C22⋊C4—8316no—
772C22⋊C4—8316no—
773C22⋊C4C23×D8318yes—
774C22⋊C4C23×D8318yes—
775C42—838no—
776C42—8316no—
777C42C23×D8314yes—
778C42C23×D8314yes—
779C42C23×D8314yes—
780C42C23×D8314yes—
781C42C23×D8318yes—
782C42C23×D8318yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—834no—
787C23—838no—
788C23—1664no—
789C23—1668no—
790C23—1664no—
791C23—1668no—
792C23—1668no—
793C23—1664no—
794C23C24×D8312yes—
795C23C24×D8311yescharacteristic
796Q8—28no—
797Q8—28no—
798Q8—48no—
799Q8—33216no—
800Q8—16616no—
801Q8—1668no—
802D4—33216no—
803D4—3328no—
804D4—33216no—
805D4—33216no—
806D4—3328no—
807D4—16616no—
808D4—1668no—
809D4—16616no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—33216no—
822C2×C4—33216no—
823C2×C4—33216no—
824C2×C4—33216no—
825C2×C4—834no—
826C2×C4—834no—
827C2×C4—838no—
828C2×C4—834no—
829C2×C4—1664no—
830C2×C4—1668no—
831C2×C4—1664no—
832C2×C4—1664no—
833C2×C4—16616no—
834C2×C4#1458183814yes—
835C2×C4#1458184014yes—
836C2×C4C24×D8314yes—
837C2×C4C24×D8312yes—
838C2×C4C24×D8312yes—
839C2×C4C24×D8312yes—
840C2×C4C24×D8312yes—
841C2×C4C24×D8314yes—
842C2×C4C24×D8314yes—
843C2×C4C24×D8314yes—
844C2×C4C24×D8312yes—
845C2×C4C24×D8312yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—3328no—
851C22—33216no—
852C22—1664no—
853C22—1668no—
854C22—1664no—
855C22—1668no—
856C22—1668no—
857C22—1664no—
858C22C2×#1458183812yes—
859C22C2×#1458184012yes—
860C22#1912853712yes—
861C22C25×D8311yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—24no—
870C4—1664no—
871C4—1668no—
872C4—1664no—
873C4—1664no—
874C4C2×#1458183814yes—
875C4C2×#1458184014yes—
876C2—42no—
877C2—3324no—
878C2—3328no—
879C2#2492193414yesdirect product factor
880C2C22×#1458183811yescharacteristic
881C2C22×#1458184011yescharacteristic
882C2C2×#1912853711yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#533×C83C2
socleC23×C83C25
hypercenterC2×#533D83
hypocenterC83C2×#3554
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #24921934C2direct (N × H)
2. C2×#19128447C2semidirect
3. C2×#19128436C2semidirect
4. C2×#19128436C2semidirect
5. C2×#19128429C2semidirect
6. C2×#19128411C2semidirect
7. C2×#19128373C2semidirect
8. C2×Q8×D332C2semidirect
9. C2×#19128361C2semidirect
10. C2×#19128353C2semidirect
11. C2×#19128325C2semidirect
12. C2×#19128322C2semidirect
13. C2×#19128306C2semidirect
14. C2×#19128299C2semidirect
15. C2×#19128276C2semidirect
16. C2×#19128251C2semidirect
17. C2×#19128235C2semidirect
18. C2×#533×C83C2semidirect
22. #19128447C22semidirect
23. #19128436C22semidirect
24. #19128436C22semidirect
25. #19128429C22semidirect
26. #19128411C22semidirect
27. #19128373C22semidirect
28. Q8×D332C22semidirect
29. #19128361C22semidirect
30. #19128353C22semidirect
31. #19128325C22semidirect
32. #19128322C22semidirect
33. #19128306C22semidirect
34. #19128299C22semidirect
35. #19128276C22semidirect
36. #19128251C22semidirect
42. #19128235C22semidirect
89. #533×C83C22semidirect
436. C2×C83#3554semidirect
457. C2×#533D83semidirect
460. C83C2×#3554semidirect
478. #533C2×D83semidirect
879. C2#24921934direct (N × H)

Maximal subgroups

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

subgroupindex
#249219342
C2×#191284472
C2×#191284362
C2×#191284292
C2×#191284112
C2×#191283732
C2×Q8×D3322
C2×#191283612
C2×#191283532
C2×#191283252
C2×#191283222
C2×#191283062
C2×#191282992
C2×#191282762
C2×#191282512
C2×#191282352
C2×#533×C832
C2×#355483