Finite Group Databasebeta

← C2×#24919583 #36281116

Subgroups — C2×#24919583 #36281116

Order 21248.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128372C211yesmaximal, characteristic
2#24919583C2116yesmaximal, direct product factor
3C2×#19128067C211yesmaximal, characteristic, complemented
4C2×#19128019C211yesmaximal, characteristic, complemented
5C2×#19128025C211yesmaximal, characteristic, complemented
6C2×#19128005C211yesmaximal, characteristic, complemented
7C2×#19127949C211yesmaximal, characteristic, complemented
8C2×#19127932C211yesmaximal, characteristic, complemented
9C2×#19127901C211yesmaximal, characteristic, complemented
10C2×#19127861C211yesmaximal, characteristic, complemented
11C2×#19127861C211yesmaximal, characteristic, complemented
12C2×#19127806C211yesmaximal, characteristic, complemented
13C2×#19127773C211yesmaximal, characteristic, complemented
14C2×#19127700C211yesmaximal, characteristic, complemented
15C2×#19127695C211yesmaximal, characteristic, complemented
16C2×#552×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C22×#13050590C2211yescharacteristic
19C22×#13050580C2211yescharacteristic
20C22×#13050577C2211yescharacteristic
21C22×#13050577C2211yescharacteristic
22C22×#13050574C2211yescharacteristic
23C23×C83⋊C8C2211yescharacteristic
24#19128372—24no—
25#19128372C2218yes—
26C2×#14581789C2211yescharacteristic
27C2×#14581788—21no—
28C2×#14581766C2211yescharacteristic
29C2×#14581766C2211yescharacteristic
30C2×#14581765—21no—
31C2×#14581765—21no—
32C2×C4×Dic166C2211yescharacteristic
33C2×#14581754—21no—
34#19128067C2218yescomplemented
35#19128025C2218yescomplemented
36#19128019C2218yescomplemented
37#19128005C2218yescomplemented
38#19127949C2218yescomplemented
39#19127932C2218yescomplemented
40#19127901C2218yescomplemented
41#19127861C2218yescomplemented
42#19127861C2218yescomplemented
43#19127806C2218yescomplemented
44#19127773C2218yescomplemented
45C2×#14581725C2211yescharacteristic
46C2×#14581723C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×C4⋊(C83⋊C8)C2211yescharacteristic
49#19127700C2218yescomplemented
50#19127695C2218yescomplemented
51C2×#14581716C2211yescharacteristic
52C2×#14581715C2211yescharacteristic
53C2×#14581715C2211yescharacteristic
54C2×#14581715C2211yescharacteristic
55C2×#14581712C2211yescharacteristic
56C2×#14581712C2211yescharacteristic
57C2×#14581712C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×#14581703C2211yescharacteristic
64#552×C83—24no—
65#552×C83C2218yescomplemented
66C2×#126×C83—21no—
67C2×#125×C83—21no—
68C2×#125×C83C2211yescharacteristic
69C2×#123×C83—21no—
70C2×C22⋊Q8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×C4×Q8×C83C2211yescharacteristic
73C2×C4×D4×C83C2211yescharacteristic
74C2×#117×C83—21no—
75C2×#117×C83C2211yescharacteristic
76C22×C4⋊C4×C83C2211yescharacteristic
77C2×#13050590—24no—
78C2×#13050590—24no—
79C2×#13050590—22no—
80C2×#13050590—22no—
81C2×#13050590—42no—
82C2×#13050590—42no—
83C2×#13050590C2314yes—
84C2×#13050590C2314yes—
85C22×Dic166C2311yescharacteristic
86C22×D332—21no—
87C22×D332—21no—
88C22×D332C2311yescharacteristic
89C22×D332C2311yescharacteristic
90C22×C22⋊D83—21no—
91C22×C22⋊D83—21no—
92C22×C22⋊D83—21no—
93C22×C22⋊D83—21no—
94C22×C4×D83—21no—
95C22×C4×D83—21no—
96C2×#13050580—24no—
97C2×#13050580C2314yes—
98C2×#13050577—42no—
99C2×#13050577—42no—
100C2×#13050577C2314yes—
101C2×#13050577C2314yes—
102C2×#13050574—42no—
103C2×#13050574C2314yes—
104C22×C83⋊C8—42no—
105C22×C83⋊C8C2311yescharacteristic
106C22×C83⋊C8C2311yescharacteristic
107C22×C83⋊C8C2311yescharacteristic
108C22×C83⋊C8C2311yescharacteristic
109C22×C83⋊C8C2314yes—
110#14581789—22no—
111#14581789C2314yes—
112#14581788—28no—
113#14581766—22no—
114#14581766—22no—
115#14581766C2314yes—
116#14581766C2314yes—
117#14581765—28no—
118#14581765—28no—
119C4×Dic166—22no—
120C4×Dic166C2314yes—
121#14581754—28no—
122C2×C4⋊Dic83C2311yescharacteristic
123C2×Dic83⋊C4—21no—
124C2×(C2×D83)⋊C4—21no—
125C2×(C2×D83)⋊C4—21no—
126C2×C4×Dic83—21no—
127#14581725C2314yes—
128#14581723C2314yes—
129#14581723C2314yes—
130C4⋊(C83⋊C8)C2314yes—
131#14581716C2314yes—
132#14581715C2314yes—
133#14581715C2314yes—
134#14581715C2314yes—
135#14581712C2314yes—
136#14581712C2314yes—
137#14581712C2314yes—
138#14581712C2314yes—
139#14581712C2314yes—
140#14581712C2314yes—
141C22⋊(C83⋊C8)C2314yes—
142C22⋊(C83⋊C8)C2314yes—
143#14581703C2314yes—
144C22×Q8×C83C2311yescharacteristic
145C22×D4×C83D411yescharacteristic
146C23×C4×C83—21no—
147C23×C4×C83C2311yescharacteristic
148C23×C4×C83C2311yescharacteristic
149#126×C83—28no—
150#125×C83—28no—
151#125×C83—22no—
152#125×C83C2314yes—
153#123×C83—28no—
154C22⋊Q8×C83—22no—
155C22⋊Q8×C83—22no—
156C22⋊Q8×C83C2314yes—
157C22⋊Q8×C83C2314yes—
158C4×Q8×C83—22no—
159C4×Q8×C83C2314yes—
160C4×D4×C83D414yes—
161C4×D4×C83C2314yes—
162#117×C83—22no—
163#117×C83—28no—
164#117×C83C2314yes—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—22no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83—21no—
171C2×C4⋊C4×C83—21no—
172C2×C4⋊C4×C83D411yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C4⋊C4×C83C2314yes—
176C2×C4⋊C4×C83C2311yescharacteristic
177C2×C22⋊C4×C83—21no—
178C2×C22⋊C4×C83—21no—
179C2×C22⋊C4×C83—21no—
180C2×C22⋊C4×C83D411yescharacteristic
181C2×C22⋊C4×C83D411yescharacteristic
182C2×C42×C83—21no—
183C2×C42×C83—21no—
184C2×C42×C83C2311yescharacteristic
185C23×D83—21no—
186C23×D83—21no—
187#13050590—28no—
188#13050590—28no—
189#13050590—44no—
190#13050590—44no—
191#13050590—48no—
192#13050590—48no—
193C2×Dic166—21no—
194C2×Dic166—22no—
195C2×Dic166#4114yes—
196C2×Dic166C2412yes—
197C2×D332—22no—
198C2×D332—22no—
199C2×D332—22no—
200C2×D332—22no—
201C2×D332—21no—
202C2×D332—21no—
203C2×D332—24no—
204C2×D332—24no—
205C2×D332—44no—
206C2×D332—82no—
207C2×D332C2412yes—
208C2×D332C2412yes—
209C2×C22⋊D83—24no—
210C2×C22⋊D83—24no—
211C2×C22⋊D83—24no—
212C2×C22⋊D83—24no—
213C2×C22⋊D83—44no—
214C2×C22⋊D83—44no—
215C2×C22⋊D83—82no—
216C2×C22⋊D83—82no—
217C22×Dic83—21no—
218C22×Dic83—21no—
219C2×C4×D83—24no—
220C2×C4×D83—24no—
221C2×C4×D83—44no—
222C2×C4×D83—44no—
223#13050580—28no—
224#13050577—44no—
225#13050577—44no—
226#13050574—44no—
227C2×C83⋊C8—22no—
228C2×C83⋊C8—22no—
229C2×C83⋊C8—22no—
230C2×C83⋊C8—22no—
231C2×C83⋊C8—44no—
232C2×C83⋊C8C2412yes—
233C2×C83⋊C8C2412yes—
234C2×C83⋊C8C2412yes—
235C2×C83⋊C8C2412yes—
236C4⋊Dic83—21no—
237C4⋊Dic83C2412yes—
238Dic83⋊C4—24no—
239(C2×D83)⋊C4—24no—
240(C2×D83)⋊C4—24no—
241C4×Dic83—24no—
242C24×C83C2×D411yescharacteristic
243C24×C83C2×D411yescharacteristic
244C2×Q8×C83—21no—
245C2×Q8×C83—22no—
246C2×Q8×C83—22no—
247C2×Q8×C83C2412yes—
248C2×D4×C83—42no—
249C2×D4×C83C2×D414yes—
250C22×C4×C83—22no—
251C22×C4×C83—22no—
252C22×C4×C83—22no—
253C22×C4×C83—22no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—24no—
259C22×C4×C83—44no—
260C22×C4×C83C2×D412yes—
261C22×C4×C83C2×D412yes—
262C22×C4×C83C2×D411yescharacteristic
263C22×C4×C83C2×D411yescharacteristic
264C22×C4×C83C2×D411yescharacteristic
265C22×C4×C83C2×D411yescharacteristic
266C22×C4×C83C2412yes—
267C22×C4×C83C2412yes—
268C22×C4×C83C2411yescharacteristic
269C4⋊C4×C83—21no—
270C4⋊C4×C83—21no—
271C4⋊C4×C83—24no—
272C4⋊C4×C83—24no—
273C4⋊C4×C83—24no—
274C4⋊C4×C83—24no—
275C4⋊C4×C83—24no—
276C4⋊C4×C83—24no—
277C4⋊C4×C83—21no—
278C4⋊C4×C83C2×D414yes—
279C4⋊C4×C83C2412yes—
280C4⋊C4×C83C2412yes—
281C4⋊C4×C83C2412yes—
282C22⋊C4×C83—24no—
283C22⋊C4×C83—24no—
284C22⋊C4×C83—24no—
285C22⋊C4×C83C2×D414yes—
286C22⋊C4×C83C2×D414yes—
287C42×C83—24no—
288C42×C83—24no—
289C42×C83C2×D412yes—
290C42×C83C2412yes—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83C22×D412yes—
298C23×C83C22×D412yes—
299C23×C83C22×D411yescharacteristic
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—42no—
303C22×D83—42no—
304C22×D83—42no—
305C22×D83—42no—
306C22×D83—42no—
307C22×D83—42no—
308Q8×C83—22no—
309Q8×C83—22no—
310Q8×C83—42no—
311D4×C83—44no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—24no—
317C2×C4×C83—24no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—48no—
327C2×C4×C83—42no—
328C2×C4×C83—42no—
329C2×C4×C83—42no—
330C2×C4×C83—42no—
331C2×C4×C83C22×D412yes—
332C2×C4×C83C22×D412yes—
333C2×C4×C83C22×D412yes—
334C2×C4×C83C22×D412yes—
335C2×C4×C83C22×D411yescharacteristic
336C2×C4×C83C2×#4112yes—
337C2×C4×C83H(5,𝔽2)12yes—
338C2×C4×C83C2511yescharacteristic
339C22⋊D83—48no—
340C22⋊D83—48no—
341C22⋊D83—84no—
342C22⋊D83—84no—
343C2×Dic83—24no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—42no—
347D332—22no—
348D332—22no—
349D332—22no—
350D332—22no—
351D332—48no—
352D332—42no—
353D332—42no—
354D332—84no—
355C4×D83—48no—
356C4×D83—48no—
357Dic166—24no—
358Dic166—22no—
359Dic166C2×#4114yes—
360C83⋊C8—22no—
361C83⋊C8—22no—
362C83⋊C8—22no—
363C83⋊C8—22no—
364C22×C83—22no—
365C22×C83—22no—
366C22×C83—22no—
367C22×C83—22no—
368C22×C83—22no—
369C22×C83—22no—
370C22×C83—44no—
371C22×C83—44no—
372C22×C83#54612yes—
373C22×C83#57512yes—
374C22×C83#57712yes—
375C22×C83C23×D411yescharacteristic
376C2×D83—42no—
377C2×D83—42no—
378C2×D83—42no—
379C2×D83—42no—
380C2×D83—42no—
381C2×D83—42no—
382C2×D83—84no—
383C2×D83—84no—
384C4×C83—22no—
385C4×C83—22no—
386C4×C83—22no—
387C4×C83—22no—
388C4×C83—42no—
389C4×C83—42no—
390C4×C83—42no—
391C4×C83—42no—
392C4×C83#54612yes—
393C4×C83C22×#4111yescharacteristic
394C4×C83C2×H(5,𝔽2)11yescharacteristic
395Dic83—24no—
396Dic83—42no—
397C2×#3317—831nomaximal, Sylow
398C2×C83—42no—
399C2×C83—42no—
400C2×C83#331714yescomplemented
401C2×C83C2×#54611yescharacteristic
402C2×C83C2×#57511yescharacteristic
403C2×C83C2×#57711yescharacteristic
404D83—82no—
405D83—82no—
406C2×#552D8311yescharacteristic, complemented
407C2×#550—831no—
408#3317—8316no—
409C2×#490—831no—
410C2×#481—831no—
411C2×#482—831no—
412C2×#479—831no—
413C2×#468—831no—
414C2×#465—831no—
415C2×#460—831no—
416C2×#452—831no—
417C2×#452—831no—
418C2×#441—831no—
419C2×#435—831no—
420C2×#417—831no—
421C2×#416—831no—
422C83C2×#331711yescharacteristic, complemented, Sylow
423C22×#41—831no—
424C22×#41—831no—
425C22×Q16—831no—
426C22×SD16—831no—
427C22×SD16—831no—
428C22×M16—831no—
429C23×C8—831no—
430#552—24no—
431#552C2×D8318yescomplemented
432#550—838no—
433#550—1664no—
434C2×#127—831no—
435C2×#127—1661no—
436C2×#126—21no—
437C2×#125—21no—
438C2×#125C2×D8311yescharacteristic
439C2×#123—21no—
440C2×C22⋊Q8C2×D8311yescharacteristic
441C2×C22⋊Q8C2×D8311yescharacteristic
442C2×#121—831no—
443C2×#121—831no—
444C2×#121—1661no—
445C2×#121—1661no—
446C2×C4×Q8—831no—
447C2×C4×Q8C2×D8311yescharacteristic
448C2×C4×D4—1661no—
449C2×C4×D4C2×D8311yescharacteristic
450C2×#117—21no—
451C2×#117C2×D8311yescharacteristic
452C22×C4⋊C4C2×D8311yescharacteristic
453#490—838no—
454#482—838no—
455#481—838no—
456#479—838no—
457#468—838no—
458#465—838no—
459#460—838no—
460#452—838no—
461#452—838no—
462#441—838no—
463#435—838no—
464C2×#107—831no—
465C2×#106—831no—
466C2×#106—831no—
467C2×C4⋊C8—831no—
468#417—838no—
469#416—838no—
470C2×#103—831no—
471C2×#103—831no—
472C2×#103—831no—
473C2×#103—831no—
474C2×#102—831no—
475C2×#102—831no—
476C2×#102—831no—
477C2×#102—831no—
478C2×#102—831no—
479C2×#102—831no—
480C2×C22⋊C8—831no—
481C2×C22⋊C8—831no—
482C2×#97—831no—
483C2×#41—3322no—
484C2×#41—3322no—
485C2×#41—834no—
486C2×#41—834no—
487C2×#41—1664no—
488C2×#41—1664no—
489C2×#41—1662no—
490C2×#41—1662no—
491C22×Q8—831no—
492C22×Q8C22×D8311yescharacteristic
493C22×D4—831no—
494C22×D4—831no—
495C22×D4—1661no—
496C22×D4—1661no—
497C22×D4—1661no—
498C22×D4—1661no—
499C22×D4—1661no—
500C22×D4—1661no—
501C22×D4C22⋊D8311yescharacteristic
502C23×C4—21no—
503C23×C4—1661no—
504C23×C4—1661no—
505C23×C4C22×D8311yescharacteristic
506C23×C4C22×D8311yescharacteristic
507C2×Q16—834no—
508C2×Q16—1664no—
509C2×SD16—3322no—
510C2×SD16—3322no—
511C2×SD16—834no—
512C2×SD16—834no—
513C2×M16—3322no—
514C2×M16—834no—
515C22×C8—3322no—
516C22×C8—834no—
517C22×C8—831no—
518C22×C8—831no—
519C22×C8—831no—
520C22×C8—831no—
521#127—834no—
522#127—1668no—
523#127—1662no—
524#126—28no—
525#125—28no—
526#125—22no—
527#125C22×D8314yes—
528#123—28no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8C22×D8314yes—
532C22⋊Q8C22×D8314yes—
533#121—834no—
534#121—834no—
535#121—1662no—
536#121—1662no—
537#121—1668no—
538#121—1668no—
539C4×Q8—22no—
540C4×Q8—834no—
541C4×Q8—1662no—
542C4×Q8C22×D8314yes—
543C4×D4—1668no—
544C4×D4C22⋊D8314yes—
545C4×D4C22×D8314yes—
546#117—22no—
547#117—28no—
548#117C22×D8314yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—831no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4C22⋊D8311yescharacteristic
559C2×C4⋊C4C22×D8311yescharacteristic
560C2×C4⋊C4C22×D8311yescharacteristic
561C2×C4⋊C4C22×D8314yes—
562C2×C4⋊C4C22×D8311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—1661no—
567C2×C22⋊C4—1661no—
568C2×C22⋊C4C22⋊D8311yescharacteristic
569C2×C22⋊C4C22⋊D8311yescharacteristic
570C2×C42—21no—
571C2×C42—21no—
572C2×C42—1661no—
573C2×C42C22×D8311yescharacteristic
574#107—834no—
575#106—834no—
576#106—834no—
577C4⋊C8—834no—
578#103—834no—
579#103—834no—
580#103—834no—
581#103—834no—
582#102—834no—
583#102—834no—
584#102—834no—
585#102—834no—
586#102—834no—
587#102—834no—
588C22⋊C8—834no—
589C22⋊C8—834no—
590#97—834no—
591C24—1661no—
592C24—1661no—
593C24C2×C22⋊D8311yescharacteristic
594C24C2×C22⋊D8311yescharacteristic
595#41—3328no—
596#41—3328no—
597#41—3324no—
598#41—3324no—
599#41—1668no—
600#41—1668no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—834no—
605C2×Q8—832no—
606C2×Q8—1661no—
607C2×Q8—1662no—
608C2×Q8C23×D8312yes—
609C2×D4—42no—
610C2×D4—3324no—
611C2×D4—3324no—
612C2×D4—3324no—
613C2×D4—832no—
614C2×D4—832no—
615C2×D4—6642no—
616C2×D4—6642no—
617C2×D4—6642no—
618C2×D4—1664no—
619C2×D4—1664no—
620C2×D4—1664no—
621C2×D4—1664no—
622C2×D4—1664no—
623C2×D4—1661no—
624C2×D4—1661no—
625C2×D4—1664no—
626C2×D4—1662no—
627C2×D4—1662no—
628C2×D4—1662no—
629C2×D4—1662no—
630C2×D4C2×C22⋊D8314yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—44no—
641C22×C4—3324no—
642C22×C4—3324no—
643C22×C4—1661no—
644C22×C4—1664no—
645C22×C4—1664no—
646C22×C4—1661no—
647C22×C4C2×C22⋊D8312yes—
648C22×C4C2×C22⋊D8312yes—
649C22×C4C2×C22⋊D8311yescharacteristic
650C22×C4C2×C22⋊D8311yescharacteristic
651C22×C4C2×C22⋊D8311yescharacteristic
652C22×C4C2×C22⋊D8311yescharacteristic
653C22×C4C23×D8312yes—
654C22×C4C23×D8312yes—
655C22×C4C23×D8311yescharacteristic
656Q16—1668no—
657SD16—3324no—
658SD16—3324no—
659M16—3324no—
660C2×C8—3324no—
661C2×C8—832no—
662C2×C8—832no—
663C2×C8—832no—
664C2×C8—832no—
665C2×C8—1662no—
666C2×C8—1662no—
667C2×C8—1662no—
668C2×C8—1662no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—832no—
679C4⋊C4—1661no—
680C4⋊C4—1664no—
681C4⋊C4C2×C22⋊D8314yes—
682C4⋊C4C23×D8312yes—
683C4⋊C4C23×D8312yes—
684C4⋊C4C23×D8312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—1664no—
689C22⋊C4—1664no—
690C22⋊C4C2×C22⋊D8314yes—
691C22⋊C4C2×C22⋊D8314yes—
692C42—24no—
693C42—24no—
694C42—1664no—
695C42C2×C22⋊D8312yes—
696C42C23×D8312yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—3322no—
704C23—3322no—
705C23—3322no—
706C23—3322no—
707C23—3322no—
708C23—3322no—
709C23—1662no—
710C23—1662no—
711C23C22×C22⋊D8312yes—
712C23C22×C22⋊D8312yes—
713C23C22×C22⋊D8311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—834no—
718Q8—1664no—
719Q8—1662no—
720D4—44no—
721D4—3328no—
722D4—3328no—
723D4—3328no—
724D4—3322no—
725D4—3322no—
726D4—6644no—
727D4—6644no—
728D4—6644no—
729D4—1662no—
730D4—1662no—
731D4—1662no—
732D4—1662no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—3328no—
753C2×C4—3328no—
754C2×C4—3322no—
755C2×C4—1662no—
756C2×C4—1664no—
757C2×C4—1662no—
758C2×C4C22×C22⋊D8312yes—
759C2×C4C22×C22⋊D8312yes—
760C2×C4C22×C22⋊D8312yes—
761C2×C4C22×C22⋊D8312yes—
762C2×C4C22×C22⋊D8311yescharacteristic
763C2×C4#41×D8312yes—
764C2×C4#1458183812yes—
765C2×C4C24×D8311yescharacteristic
766C8—1662no—
767C8—1662no—
768C8—1662no—
769C8—1662no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—3322no—
779C22—3322no—
780C22—3322no—
781C22—3322no—
782C22—3322no—
783C22—3322no—
784C22—6644no—
785C22—6644no—
786C22#1912833912yes—
787C22#1912849912yes—
788C22#1912850912yes—
789C22C23×C22⋊D8311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—3322no—
799C4—1664no—
800C4#1912833912yes—
801C4C2×#41×D8311yescharacteristic
802C4C2×#1458183811yescharacteristic
803C2—42no—
804C2—42no—
805C2—6642no—
806C2—6642no—
807C2#2491958314yesdirect product factor
808C2C2×#1912833911yescharacteristic
809C2C2×#1912849911yescharacteristic
810C2C2×#1912850911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#552×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128372C2
hypercenterC2×#552D83
hypocenterC83C2×#3317
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #24919583C2direct (N × H)
3. C2×#19128067C2semidirect
4. C2×#19128019C2semidirect
5. C2×#19128025C2semidirect
6. C2×#19128005C2semidirect
7. C2×#19127949C2semidirect
8. C2×#19127932C2semidirect
9. C2×#19127901C2semidirect
10. C2×#19127861C2semidirect
11. C2×#19127861C2semidirect
12. C2×#19127806C2semidirect
13. C2×#19127773C2semidirect
14. C2×#19127700C2semidirect
15. C2×#19127695C2semidirect
16. C2×#552×C83C2semidirect
34. #19128067C22semidirect
35. #19128025C22semidirect
36. #19128019C22semidirect
37. #19128005C22semidirect
38. #19127949C22semidirect
39. #19127932C22semidirect
40. #19127901C22semidirect
41. #19127861C22semidirect
42. #19127861C22semidirect
43. #19127806C22semidirect
44. #19127773C22semidirect
49. #19127700C22semidirect
50. #19127695C22semidirect
65. #552×C83C22semidirect
400. C2×C83#3317semidirect
406. C2×#552D83semidirect
422. C83C2×#3317semidirect
431. #552C2×D83semidirect
807. C2#24919583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283722
#249195832
C2×#191280672
C2×#191280192
C2×#191280252
C2×#191280052
C2×#191279492
C2×#191279322
C2×#191279012
C2×#191278612
C2×#191278062
C2×#191277732
C2×#191277002
C2×#191276952
C2×#552×C832
C2×#331783