Finite Group Databasebeta

← C2×#24921997 #36311771

Subgroups — C2×#24921997 #36311771

Order 21248.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921997C2132yesmaximal, direct product factor
2C2×#19128455C212yesmaximal, complemented
3C2×#19128449C212yesmaximal, complemented
4C2×#19128407C212yesmaximal, complemented
5C2×#19128404C212yesmaximal, complemented
6C2×#19128399C212yesmaximal, complemented
7C2×#19128352C212yesmaximal, complemented
8C2×#19128352C214yesmaximal, complemented
9C2×#19128331C212yesmaximal, complemented
10C2×#19128307C212yesmaximal, complemented
11C2×#19128299C214yesmaximal, complemented
12C2×#19128298C212yesmaximal, complemented
13C2×#19128282C212yesmaximal, complemented
14C2×#19128251C211yesmaximal, characteristic, complemented
15C2×#19128235C211yesmaximal, characteristic, complemented
16C22×#125×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2212yes—
18C22×#13050590C2214yes—
19#19128455C22132yescomplemented
20#19128449C22132yescomplemented
21#19128407C22132yescomplemented
22#19128404C22132yescomplemented
23#19128399C22132yescomplemented
24#19128352C22132yescomplemented
25#19128352C22164yescomplemented
26#19128331C22132yescomplemented
27#19128307C22132yescomplemented
28#19128299C22164yescomplemented
29#19128298C22132yescomplemented
30#19128282C22132yescomplemented
31#19128251C22116yescomplemented
32C2×#14581792C2211yescharacteristic
33C2×#14581791C2212yes—
34C2×#14581791C2214yes—
35C2×#14581789C2211yescharacteristic
36#19128235C22116yescomplemented
37C2×#14581787C2214yes—
38C2×#14581787C2214yes—
39C2×#14581786C2212yes—
40C2×#14581784C2211yescharacteristic
41C2×#14581783C2212yes—
42C2×#14581782C2214yes—
43C2×#14581780C2211yescharacteristic
44C2×#14581780C2212yes—
45C2×#14581777C2214yes—
46C2×#14581777C2214yes—
47C2×#14581777C2214yes—
48C2×#14581777C2214yes—
49C2×#14581777C2214yes—
50C2×#14581775C2212yes—
51C2×#14581775C2214yes—
52C2×#14581772C2214yes—
53C2×#14581772C2214yes—
54C2×#14581771C2211yescharacteristic
55C2×#14581770C2214yes—
56C2×#14581770C2214yes—
57C2×#14581770C2214yes—
58C2×#14581770C2214yes—
59C2×#14581767C2212yes—
60C2×#14581767C2214yes—
61C2×#14581767C2212yes—
62C2×#14581767C2214yes—
63C2×#14581767C2214yes—
64C2×#14581766C2212yes—
65C2×#14581766C2214yes—
66C2×#14581766C2211yescharacteristic
67C2×#14581766C2212yes—
68C2×C4×Dic166C2211yescharacteristic
69C2×C4×D332C2211yescharacteristic
70C2×C4×D332C2212yes—
71C2×C4×D332C2212yes—
72C2×#14581754C2214yes—
73C2×#14581754C2212yes—
74C2×#14581754C2212yes—
75C2×C4×C22⋊D83C2212yes—
76C2×C4×C22⋊D83C2214yes—
77C2×#14581750C2212yes—
78C2×#14581749C2212yes—
79C2×C4⋊C4×D83C2212yes—
80C2×C4⋊C4×D83C2214yes—
81C2×#125×C83C2212yes—
82C2×#125×C83C2212yes—
83C2×#125×C83C2212yes—
84C2×#125×C83C2212yes—
85C2×#125×C83C22116yescomplemented
86C22×C4⋊C4×C83C2211yescharacteristic
87C22×C4⋊C4×C83C2212yes—
88C22×C4⋊C4×C83C2211yescharacteristic
89C22×C4⋊C4×C83C2212yes—
90C22×C42×C83C2211yescharacteristic
91C2×#13050590—48no—
92C2×#13050590—416no—
93C2×#13050590C23116yes—
94C2×#13050590C23132yes—
95C22×Dic166C2311yescharacteristic
96C22×Dic166C2314yes—
97C22×Dic166C2312yes—
98C22×D332C2312yes—
99C22×D332C2314yes—
100C22×D332C2311yescharacteristic
101C22×D332C2312yes—
102C22×D332C2314yes—
103C22×D332C2312yes—
104C22×C22⋊D83C2312yes—
105C22×C22⋊D83C2314yes—
106C22×C4×D83C2312yes—
107C22×C4×D83C2314yes—
108C22×C4×D83C2314yes—
109C22×C4×D83C2314yes—
110C22×C4×D83C2314yes—
111#14581792C2318yes—
112#14581791C23116yes—
113#14581791C23132yes—
114#14581789C2318yes—
115#14581787C23132yes—
116#14581787C23132yes—
117#14581786C23116yes—
118#14581784C2318yes—
119#14581783C23116yes—
120#14581782C23132yes—
121#14581780C2318yes—
122#14581780C23116yes—
123#14581777C23132yes—
124#14581777C23132yes—
125#14581777C23132yes—
126#14581777C23132yes—
127#14581777C23132yes—
128#14581775C23116yes—
129#14581775C23132yes—
130#14581772C23132yes—
131#14581772C23132yes—
132#14581771C2318yes—
133#14581770C23132yes—
134#14581770C23132yes—
135#14581770C23132yes—
136#14581770C23132yes—
137#14581767C23116yes—
138#14581767C23132yes—
139#14581767C23116yes—
140#14581767C23132yes—
141#14581767C23132yes—
142#14581766C23116yes—
143#14581766C23132yes—
144#14581766C2318yes—
145#14581766C23116yes—
146C4×Dic166C2318yes—
147C4×D332C2318yes—
148C4×D332C23116yes—
149C4×D332C23116yes—
150#14581754C23132yes—
151#14581754C23116yes—
152#14581754C23116yes—
153C4×C22⋊D83C23116yes—
154C4×C22⋊D83C23132yes—
155#14581750C23116yes—
156#14581749C23116yes—
157C2×C4⋊Dic83C2312yes—
158C2×C4⋊Dic83C2314yes—
159C2×C4⋊Dic83C2312yes—
160C2×C4⋊Dic83C2311yescharacteristic
161C2×C4⋊Dic83C2311yescharacteristic
162C2×Dic83⋊C4C2312yes—
163C2×Dic83⋊C4C2314yes—
164C2×Dic83⋊C4C2314yes—
165C2×Dic83⋊C4C2312yes—
166C2×Dic83⋊C4C2312yes—
167C2×Dic83⋊C4C2314yes—
168C2×Dic83⋊C4C2312yes—
169C4⋊C4×D83C23116yes—
170C4⋊C4×D83C23132yes—
171C2×C22⋊Dic83C2312yes—
172C2×(C2×D83)⋊C4C2312yes—
173C2×(C2×D83)⋊C4C2312yes—
174C2×(C2×D83)⋊C4C2314yes—
175C2×(C2×D83)⋊C4C2314yes—
176C2×(C2×D83)⋊C4C2312yes—
177C2×(C2×D83)⋊C4C2312yes—
178C2×(C2×D83)⋊C4C2314yes—
179C2×(C2×D83)⋊C4C2314yes—
180C2×(C2×D83)⋊C4C2314yes—
181C2×(C2×D83)⋊C4C2314yes—
182C2×(C2×D83)⋊C4C2314yes—
183C2×C4×Dic83C2312yes—
184C2×C4×Dic83C2314yes—
185C23×C4×C83C2311yescharacteristic
186C23×C4×C83C2311yescharacteristic
187C23×C4×C83C2312yes—
188C23×C4×C83C2311yescharacteristic
189C23×C4×C83C2312yes—
190#125×C83C23116yes—
191#125×C83C23116yes—
192#125×C83C23116yes—
193#125×C83C23116yes—
194C2×C4⋊C4×C83C23116yes—
195C2×C4⋊C4×C83C2318yes—
196C2×C4⋊C4×C83C2312yes—
197C2×C4⋊C4×C83C2314yes—
198C2×C4⋊C4×C83C2312yes—
199C2×C4⋊C4×C83C2314yes—
200C2×C4⋊C4×C83C2314yes—
201C2×C4⋊C4×C83C2314yes—
202C2×C4⋊C4×C83C2312yes—
203C2×C4⋊C4×C83C2312yes—
204C2×C4⋊C4×C83C2318yes—
205C2×C4⋊C4×C83C23116yes—
206C2×C42×C83C2311yescharacteristic
207C2×C42×C83C2311yescharacteristic
208C2×C42×C83C2311yescharacteristic
209C2×C42×C83C2311yescharacteristic
210C2×C42×C83C2318yes—
211C23×D83C2412yes—
212C23×D83C2414yes—
213#13050590—432no—
214#13050590—464no—
215C2×Dic166—42no—
216C2×Dic166—48no—
217C2×Dic166—44no—
218C2×Dic166C2414yes—
219C2×Dic166C24116yes—
220C2×Dic166C2418yes—
221C2×D332—28no—
222C2×D332—48no—
223C2×D332—44no—
224C2×D332—42no—
225C2×D332—48no—
226C2×D332—44no—
227C2×D332C2418yes—
228C2×D332C24116yes—
229C2×D332C2414yes—
230C2×D332C2418yes—
231C2×D332C24116yes—
232C2×D332C2418yes—
233C2×C22⋊D83—28no—
234C2×C22⋊D83—216no—
235C2×C22⋊D83C24116yes—
236C2×C22⋊D83C2418yes—
237C22×Dic83C2414yes—
238C22×Dic83C2412yes—
239C22×Dic83C2412yes—
240C22×Dic83C2412yes—
241C2×C4×D83—28no—
242C2×C4×D83—48no—
243C2×C4×D83—48no—
244C2×C4×D83—48no—
245C2×C4×D83—48no—
246C2×C4×D83C2418yes—
247C2×C4×D83C24116yes—
248C2×C4×D83C24116yes—
249C2×C4×D83C24116yes—
250C2×C4×D83C24116yes—
251C4⋊Dic83C2414yes—
252C4⋊Dic83C2418yes—
253C4⋊Dic83C24116yes—
254C4⋊Dic83C2418yes—
255C4⋊Dic83C2414yes—
256Dic83⋊C4C24116yes—
257Dic83⋊C4C24116yes—
258Dic83⋊C4C2418yes—
259Dic83⋊C4C2418yes—
260Dic83⋊C4C24116yes—
261Dic83⋊C4C2418yes—
262Dic83⋊C4C2418yes—
263C22⋊Dic83C2418yes—
264(C2×D83)⋊C4C2418yes—
265(C2×D83)⋊C4C24116yes—
266(C2×D83)⋊C4C24116yes—
267(C2×D83)⋊C4C24116yes—
268(C2×D83)⋊C4C24116yes—
269(C2×D83)⋊C4C2418yes—
270(C2×D83)⋊C4C24116yes—
271(C2×D83)⋊C4C24116yes—
272(C2×D83)⋊C4C24116yes—
273(C2×D83)⋊C4C2418yes—
274(C2×D83)⋊C4C2418yes—
275C4×Dic83C24116yes—
276C4×Dic83C2418yes—
277C24×C83C2411yescharacteristic
278C22×C4×C83—24no—
279C22×C4×C83—28no—
280C22×C4×C83—24no—
281C22×C4×C83—44no—
282C22×C4×C83—42no—
283C22×C4×C83C2414yes—
284C22×C4×C83C2414yes—
285C22×C4×C83C2418yes—
286C22×C4×C83C2411yescharacteristic
287C22×C4×C83C2414yes—
288C22×C4×C83C2414yes—
289C22×C4×C83C2411yescharacteristic
290C22×C4×C83C2411yescharacteristic
291C22×C4×C83C2411yescharacteristic
292C22×C4×C83C2411yescharacteristic
293C22×C4×C83C2414yes—
294C22×C4×C83C2418yes—
295C22×C4×C83C2411yescharacteristic
296C4⋊C4×C83C24116yes—
297C4⋊C4×C83C24116yes—
298C4⋊C4×C83C24116yes—
299C4⋊C4×C83C2418yes—
300C4⋊C4×C83C2418yes—
301C4⋊C4×C83C2418yes—
302C4⋊C4×C83C24116yes—
303C4⋊C4×C83C2418yes—
304C42×C83C2414yes—
305C42×C83C2414yes—
306C42×C83C2414yes—
307C42×C83C2414yes—
308C23×C83—22no—
309C23×C83—22no—
310C23×C83H(5,𝔽2)14yes—
311C23×C83C2512yes—
312C23×C83C2511yescharacteristic
313C22×D83—24no—
314C22×D83—28no—
315C22×D83—24no—
316C22×D83—28no—
317C22×D83—28no—
318C22×D83—24no—
319C22×D83C2514yes—
320C22×D83C2518yes—
321C2×C4×C83—22no—
322C2×C4×C83—28no—
323C2×C4×C83—22no—
324C2×C4×C83—28no—
325C2×C4×C83—216no—
326C2×C4×C83—22no—
327C2×C4×C83—28no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—28no—
331C2×C4×C83—44no—
332C2×C4×C83—48no—
333C2×C4×C832−1+414yes—
334C2×C4×C83C2512yes—
335C2×C4×C83C2512yes—
336C2×C4×C83C2512yes—
337C2×C4×C83C2512yes—
338C2×C4×C83C2512yes—
339C2×C4×C83C2518yes—
340C2×C4×C83C2518yes—
341C2×C4×C83C2512yes—
342C22⋊D83—232no—
343C22⋊D83—216no—
344C2×Dic83—28no—
345C2×Dic83—24no—
346C2×Dic83—24no—
347C2×Dic83—24no—
348C2×Dic83C2514yes—
349C2×Dic83C2514yes—
350C2×Dic83C2518yes—
351C2×Dic83C2514yes—
352D332—216no—
353D332—44no—
354D332—416no—
355D332—48no—
356D332—48no—
357D332—416no—
358C4×D83—216no—
359C4×D83—416no—
360C4×D83—416no—
361C4×D83—416no—
362C4×D83—416no—
363Dic166—44no—
364Dic166—48no—
365Dic166—416no—
366C22×C83—22no—
367C22×C83—22no—
368C22×C83—28no—
369C22×C83C2×H(5,𝔽2)14yes—
370C22×C83C2×H(5,𝔽2)12yes—
371C22×C83C2×2−1+412yes—
372C22×C83#58512yes—
373C22×C83C2611yescharacteristic
374C2×D83—24no—
375C2×D83—28no—
376C2×D83—24no—
377C2×D83—28no—
378C2×D83—28no—
379C2×D83—24no—
380C2×D83—48no—
381C2×D83—416no—
382C4×C83—22no—
383C4×C83—28no—
384C4×C83—22no—
385C4×C83—22no—
386C4×C83—22no—
387C4×C83—28no—
388C4×C83—22no—
389C4×C83C2×2−1+414yes—
390Dic83—28no—
391Dic83—24no—
392Dic83—24no—
393Dic83—24no—
394C2×#3559—831nomaximal, Sylow
395C2×C83—24no—
396C2×C83#355914yescomplemented
397C2×C83C22×H(5,𝔽2)11yescharacteristic
398C2×C83C22×2−1+411yescharacteristic
399C2×C83C2×#58511yescharacteristic
400D83—44no—
401D83—48no—
402#3559—8332no—
403C2×#563—832no—
404C2×#562—832no—
405C2×#554—832no—
406C2×#553—832no—
407C2×#553—832no—
408C2×#547—834no—
409C2×#547—832no—
410C2×#544—832no—
411C2×#540—832no—
412C2×#539—834no—
413C2×#539—832no—
414C2×#537—832no—
415C2×#532—831no—
416C2×#529—831no—
417C22×#125D8311yescharacteristic, complemented
418C83C2×#355911yescharacteristic, complemented, Sylow
419C22×#41—832no—
420C22×#41—834no—
421#563—8332no—
422#562—8332no—
423#554—8332no—
424#553—8332no—
425#553—8332no—
426#547—8364no—
427#547—8332no—
428#544—8332no—
429#540—8332no—
430#539—8364no—
431#539—8332no—
432#537—8332no—
433#532—8316no—
434C2×C4⋊Q8—832no—
435C2×C4⋊Q8—834no—
436C2×C4⋊Q8—831no—
437C2×#127—831no—
438#529—8316no—
439C2×#126—834no—
440C2×#126—834no—
441C2×#126—832no—
442C2×#125—834no—
443C2×#125—832no—
444C2×#125—831no—
445C2×#125C2×D8312yes—
446C2×#125C2×D8312yes—
447C2×#125C2×D8312yes—
448C2×#125C2×D8312yes—
449C2×#125C2×D83116yescomplemented
450C2×#124—831no—
451C2×#124—832no—
452C2×#123—832no—
453C2×#123—834no—
454C2×#123—834no—
455C2×#123—834no—
456C2×#123—834no—
457C2×#123—834no—
458C2×#123—834no—
459C2×C22⋊Q8—831no—
460C2×C22⋊Q8—834no—
461C2×C22⋊Q8—834no—
462C2×C22⋊Q8—834no—
463C2×C22⋊Q8—834no—
464C2×C22⋊Q8—834no—
465C2×C22⋊Q8—834no—
466C2×#121—831no—
467C2×#121—832no—
468C2×#121—832no—
469C2×#121—834no—
470C2×#121—834no—
471C2×#121—834no—
472C2×#121—832no—
473C2×#121—834no—
474C2×#121—832no—
475C2×C4×Q8—831no—
476C2×C4×D4—832no—
477C2×C4×D4—834no—
478C2×C4×D4—834no—
479C2×C4×D4—832no—
480C2×C4×D4—832no—
481C2×C4×D4—831no—
482C2×C4×D4—832no—
483C2×C4×D4—832no—
484C2×#117—832no—
485C2×#117—832no—
486C22×C4⋊C4—834no—
487C22×C4⋊C4—832no—
488C22×C4⋊C4C2×D8312yes—
489C22×C4⋊C4C2×D8311yescharacteristic
490C22×C4⋊C4C2×D8312yes—
491C22×C4⋊C4C2×D8311yescharacteristic
492C22×C42C2×D8311yescharacteristic
493C2×#41—3328no—
494C2×#41—33216no—
495C2×#41—8316no—
496C2×#41—8332no—
497C22×Q8—831no—
498C22×Q8—834no—
499C22×Q8—832no—
500C22×D4—832no—
501C22×D4—834no—
502C22×D4—834no—
503C22×D4—831no—
504C22×D4—832no—
505C22×D4—834no—
506C22×D4—832no—
507C22×D4—832no—
508C23×C4—834no—
509C23×C4—834no—
510C23×C4—834no—
511C23×C4—834no—
512C23×C4—832no—
513C23×C4C22×D8312yes—
514C23×C4C22×D8311yescharacteristic
515C23×C4C22×D8311yescharacteristic
516C23×C4C22×D8312yes—
517C23×C4C22×D8311yescharacteristic
518C4⋊Q8—8316no—
519C4⋊Q8—8332no—
520C4⋊Q8—838no—
521#127—838no—
522#126—8332no—
523#126—8332no—
524#126—8316no—
525#125—8332no—
526#125—8316no—
527#125—838no—
528#125C22×D83116yes—
529#125C22×D83116yes—
530#125C22×D83116yes—
531#125C22×D83116yes—
532#124—838no—
533#124—8316no—
534#123—8316no—
535#123—8332no—
536#123—8332no—
537#123—8332no—
538#123—8332no—
539#123—8332no—
540#123—8332no—
541C22⋊Q8—838no—
542C22⋊Q8—8332no—
543C22⋊Q8—8332no—
544C22⋊Q8—8332no—
545C22⋊Q8—8332no—
546C22⋊Q8—8332no—
547C22⋊Q8—8332no—
548#121—838no—
549#121—8316no—
550#121—8316no—
551#121—8332no—
552#121—8332no—
553#121—8332no—
554#121—8316no—
555#121—8332no—
556#121—8316no—
557C4×Q8—838no—
558C4×D4—8316no—
559C4×D4—8332no—
560C4×D4—8332no—
561C4×D4—8316no—
562C4×D4—8316no—
563C4×D4—838no—
564C4×D4—8316no—
565C4×D4—8316no—
566#117—8316no—
567#117—8316no—
568C2×C4⋊C4—832no—
569C2×C4⋊C4—832no—
570C2×C4⋊C4—834no—
571C2×C4⋊C4—834no—
572C2×C4⋊C4—834no—
573C2×C4⋊C4—832no—
574C2×C4⋊C4—832no—
575C2×C4⋊C4—832no—
576C2×C4⋊C4—834no—
577C2×C4⋊C4—832no—
578C2×C4⋊C4—831no—
579C2×C4⋊C4—831no—
580C2×C4⋊C4—8332no—
581C2×C4⋊C4—8316no—
582C2×C4⋊C4C22×D8312yes—
583C2×C4⋊C4C22×D8314yes—
584C2×C4⋊C4C22×D8312yes—
585C2×C4⋊C4C22×D8314yes—
586C2×C4⋊C4C22×D8314yes—
587C2×C4⋊C4C22×D8314yes—
588C2×C4⋊C4C22×D8312yes—
589C2×C4⋊C4C22×D8312yes—
590C2×C4⋊C4C22×D83116yes—
591C2×C4⋊C4C22×D8318yes—
592C2×C4⋊C4C22×D83116yes—
593C2×C4⋊C4C22×D8318yes—
594C2×C22⋊C4—832no—
595C2×C22⋊C4—832no—
596C2×C22⋊C4—834no—
597C2×C22⋊C4—832no—
598C2×C22⋊C4—832no—
599C2×C22⋊C4—834no—
600C2×C22⋊C4—834no—
601C2×C22⋊C4—834no—
602C2×C22⋊C4—834no—
603C2×C22⋊C4—834no—
604C2×C22⋊C4—834no—
605C2×C22⋊C4—832no—
606C2×C42—832no—
607C2×C42—834no—
608C2×C42C22×D8311yescharacteristic
609C2×C42C22×D8311yescharacteristic
610C2×C42C22×D8311yescharacteristic
611C2×C42C22×D8311yescharacteristic
612C2×C42C22×D8318yes—
613C24—832no—
614C24—834no—
615C24C23×D8311yescharacteristic
616#41—33232no—
617#41—33264no—
618C2×Q8—3328no—
619C2×Q8—3324no—
620C2×Q8—3322no—
621C2×Q8—834no—
622C2×Q8—8316no—
623C2×Q8—838no—
624C2×D4—3328no—
625C2×D4—3324no—
626C2×D4—3328no—
627C2×D4—3324no—
628C2×D4—3322no—
629C2×D4—838no—
630C2×D4—8316no—
631C2×D4—8316no—
632C2×D4—834no—
633C2×D4—838no—
634C2×D4—8316no—
635C2×D4—838no—
636C2×D4—838no—
637C2×D4—1668no—
638C2×D4—16616no—
639C2×D4—1668no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—42no—
645C22×C4—3328no—
646C22×C4—3328no—
647C22×C4—3328no—
648C22×C4—3328no—
649C22×C4—8316no—
650C22×C4—8316no—
651C22×C4—8316no—
652C22×C4—8316no—
653C22×C4—832no—
654C22×C4—832no—
655C22×C4—832no—
656C22×C4—834no—
657C22×C4—838no—
658C22×C4—1668no—
659C22×C4C23×D8314yes—
660C22×C4C23×D8314yes—
661C22×C4C23×D8318yes—
662C22×C4C23×D8314yes—
663C22×C4C23×D8311yescharacteristic
664C22×C4C23×D8311yescharacteristic
665C22×C4C23×D8311yescharacteristic
666C22×C4C23×D8311yescharacteristic
667C22×C4C23×D8311yescharacteristic
668C22×C4C23×D8314yes—
669C22×C4C23×D8314yes—
670C22×C4C23×D8318yes—
671C22×C4C23×D8311yescharacteristic
672C4⋊C4—838no—
673C4⋊C4—838no—
674C4⋊C4—8316no—
675C4⋊C4—8316no—
676C4⋊C4—8316no—
677C4⋊C4—838no—
678C4⋊C4—838no—
679C4⋊C4—838no—
680C4⋊C4—8316no—
681C4⋊C4—838no—
682C4⋊C4—834no—
683C4⋊C4—834no—
684C4⋊C4C23×D8318yes—
685C4⋊C4C23×D83116yes—
686C4⋊C4C23×D8318yes—
687C4⋊C4C23×D83116yes—
688C4⋊C4C23×D83116yes—
689C4⋊C4C23×D83116yes—
690C4⋊C4C23×D8318yes—
691C4⋊C4C23×D8318yes—
692C22⋊C4—838no—
693C22⋊C4—838no—
694C22⋊C4—8316no—
695C22⋊C4—838no—
696C22⋊C4—838no—
697C22⋊C4—8316no—
698C22⋊C4—8316no—
699C22⋊C4—8316no—
700C22⋊C4—8316no—
701C22⋊C4—8316no—
702C22⋊C4—8316no—
703C22⋊C4—838no—
704C42—838no—
705C42—8316no—
706C42C23×D8314yes—
707C42C23×D8314yes—
708C42C23×D8314yes—
709C42C23×D8314yes—
710C23—22no—
711C23—22no—
712C23—834no—
713C23—838no—
714C23—1664no—
715C23—1668no—
716C23—1664no—
717C23—1668no—
718C23—1668no—
719C23—1664no—
720C23#1458183814yes—
721C23C24×D8312yes—
722C23C24×D8311yescharacteristic
723Q8—33216no—
724Q8—3328no—
725Q8—3324no—
726D4—33216no—
727D4—3328no—
728D4—33216no—
729D4—3328no—
730D4—3324no—
731D4—16616no—
732D4—16632no—
733D4—16616no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—216no—
739C2×C4—22no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—33216no—
747C2×C4—33216no—
748C2×C4—33216no—
749C2×C4—33216no—
750C2×C4—834no—
751C2×C4—834no—
752C2×C4—834no—
753C2×C4—838no—
754C2×C4—1668no—
755C2×C4—1664no—
756C2×C4—1664no—
757C2×C4—1664no—
758C2×C4—16616no—
759C2×C4#1458184014yes—
760C2×C4C24×D8318yes—
761C2×C4C24×D8312yes—
762C2×C4C24×D8312yes—
763C2×C4C24×D8312yes—
764C2×C4C24×D8312yes—
765C2×C4C24×D8312yes—
766C2×C4C24×D8318yes—
767C2×C4C24×D8312yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—3328no—
772C22—33216no—
773C22—1664no—
774C22—1668no—
775C22—1664no—
776C22—1668no—
777C22—1668no—
778C22—1664no—
779C22C2×#1458183814yes—
780C22C2×#1458183812yes—
781C22C2×#1458184012yes—
782C22#1912853712yes—
783C22C25×D8311yescharacteristic
784C4—22no—
785C4—28no—
786C4—22no—
787C4—22no—
788C4—28no—
789C4—22no—
790C4—22no—
791C4—1668no—
792C4—1664no—
793C4—1664no—
794C4—1664no—
795C4C2×#1458184014yes—
796C2—24no—
797C2—3324no—
798C2—3328no—
799C2#2492199714yesdirect product factor
800C2C22×#1458183811yescharacteristic
801C2C22×#1458184011yescharacteristic
802C2C2×#1912853711yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC22×#125×C83C2
socleC23×C83C25
hypercenterC22×#125D83
hypocenterC83C2×#3559
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #24921997C2direct (N × H)
2. C2×#19128455C2semidirect
3. C2×#19128449C2semidirect
4. C2×#19128407C2semidirect
5. C2×#19128404C2semidirect
6. C2×#19128399C2semidirect
7. C2×#19128352C2semidirect
8. C2×#19128352C2semidirect
9. C2×#19128331C2semidirect
10. C2×#19128307C2semidirect
11. C2×#19128299C2semidirect
12. C2×#19128298C2semidirect
13. C2×#19128282C2semidirect
14. C2×#19128251C2semidirect
15. C2×#19128235C2semidirect
16. C22×#125×C83C2semidirect
19. #19128455C22semidirect
20. #19128449C22semidirect
21. #19128407C22semidirect
22. #19128404C22semidirect
23. #19128399C22semidirect
24. #19128352C22semidirect
25. #19128352C22semidirect
26. #19128331C22semidirect
27. #19128307C22semidirect
28. #19128299C22semidirect
29. #19128298C22semidirect
30. #19128282C22semidirect
31. #19128251C22semidirect
36. #19128235C22semidirect
85. C2×#125×C83C22semidirect
396. C2×C83#3559semidirect
417. C22×#125D83semidirect
418. C83C2×#3559semidirect
449. C2×#125C2×D83semidirect
799. C2#24921997direct (N × H)

Maximal subgroups

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

subgroupindex
#249219972
C2×#191284552
C2×#191284492
C2×#191284072
C2×#191284042
C2×#191283992
C2×#191283522
C2×#191283312
C2×#191283072
C2×#191282992
C2×#191282982
C2×#191282822
C2×#191282512
C2×#191282352
C22×#125×C832
C2×#355983