Finite Group Databasebeta

← C2×#24919927 #36282961

Subgroups — C2×#24919927 #36282961

Order 21248.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128355C211yesmaximal, characteristic, complemented
2#24919927C2116yesmaximal, direct product factor
3C2×#19128111C211yesmaximal, characteristic, complemented
4C2×#19128019C211yesmaximal, characteristic, complemented
5C2×#19128017C211yesmaximal, characteristic, complemented
6C2×#19128025C211yesmaximal, characteristic, complemented
7C2×#19128012C211yesmaximal, characteristic, complemented
8C2×#19127998C211yesmaximal, characteristic, complemented
9C2×#19127991C211yesmaximal, characteristic, complemented
10C2×#19127952C211yesmaximal, characteristic, complemented
11C2×#19127935C211yesmaximal, characteristic, complemented
12C2×#19127811C211yesmaximal, characteristic, complemented
13C2×#19127773C211yesmaximal, characteristic, complemented
14C2×#19127744C211yesmaximal, characteristic, complemented
15C22×#14581723C211yesmaximal, characteristic, complemented
16C2×#553×C83C211yesmaximal, characteristic, complemented
17C22×#13050589—21no—
18C22×#13050575C2211yescharacteristic
19C22×#13050574C2211yescharacteristic
20C23×C83⋊C8C2211yescharacteristic
21#19128355—24no—
22#19128355C2218yescomplemented
23C2×#14581792C2211yescharacteristic
24C2×#14581776—21no—
25C2×#14581776—21no—
26C2×#14581772—21no—
27C2×#14581766C2211yescharacteristic
28C2×#14581766C2211yescharacteristic
29C2×C4×D332C2211yescharacteristic
30C22×C4⋊Dic83C2211yescharacteristic
31C22×C4⋊Dic83C2211yescharacteristic
32#19128111C2218yescomplemented
33#19128025C2218yescomplemented
34#19128019C2218yescomplemented
35#19128017C2218yescomplemented
36#19128012C2218yescomplemented
37#19127998C2218yescomplemented
38#19127991C2218yescomplemented
39#19127952C2218yescomplemented
40#19127935C2218yescomplemented
41#19127811C2218yescomplemented
42#19127773C2218yescomplemented
43#19127744C2218yescomplemented
44C2×#14581725C2211yescharacteristic
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×#14581723C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51C2×#14581723C2211yescharacteristic
52C2×#14581723C2211yescharacteristic
53C2×#14581723C2218yescomplemented
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×#14581713C2211yescharacteristic
56C2×#14581713C2211yescharacteristic
57C2×#14581713C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×#14581703C2211yescharacteristic
64#553×C83—24no—
65#553×C83C2218yescomplemented
66C2×#126×C83—21no—
67C2×#125×C83C2211yescharacteristic
68C2×#123×C83—21no—
69C2×#121×C83—21no—
70C2×#121×C83C2211yescharacteristic
71C2×#121×C83C2211yescharacteristic
72C2×C4×D4×C83—21no—
73C2×C4×D4×C83C2211yescharacteristic
74C2×C4×D4×C83C2211yescharacteristic
75C2×#117×C83C2211yescharacteristic
76C22×C4⋊C4×C83C2211yescharacteristic
77C2×#13050589—28no—
78C2×#13050589—48no—
79C22×Dic166—21no—
80C22×D332C2311yescharacteristic
81C22×C22⋊D83—21no—
82C22×C22⋊D83—21no—
83C23×Dic83—21no—
84C23×Dic83—21no—
85C22×C4×D83—21no—
86C2×#13050575—24no—
87C2×#13050575C2314yes—
88C2×#13050574—24no—
89C2×#13050574C2314yes—
90C22×C83⋊C8—24no—
91C22×C83⋊C8C2311yescharacteristic
92C22×C83⋊C8C2311yescharacteristic
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2314yes—
95C22×C83⋊C8C2311yescharacteristic
96#14581792—22no—
97#14581792C2314yes—
98#14581776—28no—
99#14581776—28no—
100#14581772—28no—
101#14581766—22no—
102#14581766—22no—
103#14581766C2314yes—
104#14581766C2314yes—
105C4×D332—22no—
106C4×D332C2314yes—
107C2×C4⋊Dic83—22no—
108C2×C4⋊Dic83—22no—
109C2×C4⋊Dic83—21no—
110C2×C4⋊Dic83—21no—
111C2×C4⋊Dic83—21no—
112C2×C4⋊Dic83C2314yes—
113C2×C4⋊Dic83C2314yes—
114C2×C4⋊Dic83C2311yescharacteristic
115C2×C4⋊Dic83C2311yescharacteristic
116C2×C4⋊Dic83C2311yescharacteristic
117C2×(C2×D83)⋊C4—21no—
118C2×(C2×D83)⋊C4—21no—
119C2×(C2×D83)⋊C4—21no—
120#14581725C2314yes—
121#14581725C2314yes—
122#14581725C2314yes—
123#14581723C2314yes—
124#14581723C2314yes—
125#14581723C2314yes—
126#14581723C2314yes—
127#14581723C2314yes—
128#14581723C2314yes—
129C4⋊(C83⋊C8)C2314yes—
130#14581713C2314yes—
131#14581713C2314yes—
132#14581713C2314yes—
133#14581712C2314yes—
134#14581712C2314yes—
135#14581712C2314yes—
136C22⋊(C83⋊C8)C2314yes—
137C22⋊(C83⋊C8)C2314yes—
138#14581703C2314yes—
139C22×D4×C83—21no—
140C22×D4×C83—21no—
141C22×D4×C83D411yescharacteristic
142C22×D4×C83C2311yescharacteristic
143C23×C4×C83—21no—
144C23×C4×C83—21no—
145C23×C4×C83C2311yescharacteristic
146C23×C4×C83C2311yescharacteristic
147#126×C83—28no—
148#125×C83—22no—
149#125×C83C2314yes—
150#123×C83—28no—
151#121×C83—28no—
152#121×C83—22no—
153#121×C83—22no—
154#121×C83C2314yes—
155#121×C83C2314yes—
156C4×D4×C83—28no—
157C4×D4×C83—22no—
158C4×D4×C83D414yes—
159C4×D4×C83C2314yes—
160C4×D4×C83C2314yes—
161#117×C83—22no—
162#117×C83C2314yes—
163C2×C4⋊C4×C83—21no—
164C2×C4⋊C4×C83—22no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83D411yescharacteristic
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2314yes—
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83—21no—
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83D411yescharacteristic
177C2×C22⋊C4×C83D411yescharacteristic
178C2×C42×C83—21no—
179C2×C42×C83C2311yescharacteristic
180C23×D83—21no—
181#13050589—432no—
182C2×Dic166—24no—
183C2×Dic166—44no—
184C2×D332—22no—
185C2×D332—22no—
186C2×D332—21no—
187C2×D332C2412yes—
188C2×C22⋊D83—24no—
189C2×C22⋊D83—24no—
190C2×C22⋊D83—44no—
191C2×C22⋊D83—44no—
192C22×Dic83—24no—
193C22×Dic83—24no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—44no—
198C22×Dic83—44no—
199C2×C4×D83—24no—
200C2×C4×D83—44no—
201#13050575—28no—
202#13050574—28no—
203C2×C83⋊C8—22no—
204C2×C83⋊C8—22no—
205C2×C83⋊C8—22no—
206C2×C83⋊C8—28no—
207C2×C83⋊C8#4114yescomplemented
208C2×C83⋊C8C2412yes—
209C2×C83⋊C8C2412yes—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C4⋊Dic83—21no—
213C4⋊Dic83—21no—
214C4⋊Dic83—24no—
215C4⋊Dic83—24no—
216C4⋊Dic83—24no—
217C4⋊Dic83—21no—
218C4⋊Dic83C2412yes—
219C4⋊Dic83C2412yes—
220C4⋊Dic83C2412yes—
221(C2×D83)⋊C4—24no—
222(C2×D83)⋊C4—24no—
223(C2×D83)⋊C4—24no—
224C24×C83—21no—
225C24×C83C2×D411yescharacteristic
226C24×C83C2×D411yescharacteristic
227C2×D4×C83—24no—
228C2×D4×C83—24no—
229C2×D4×C83—24no—
230C2×D4×C83—21no—
231C2×D4×C83—22no—
232C2×D4×C83—22no—
233C2×D4×C83—44no—
234C2×D4×C83—82no—
235C2×D4×C83C2×D414yes—
236C2×D4×C83C2412yes—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—24no—
245C22×C4×C83—24no—
246C22×C4×C83—82no—
247C22×C4×C83—82no—
248C22×C4×C83C2×D412yes—
249C22×C4×C83C2×D412yes—
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2412yes—
255C22×C4×C83C2412yes—
256C22×C4×C83C2411yescharacteristic
257C4⋊C4×C83—21no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83—24no—
260C4⋊C4×C83—24no—
261C4⋊C4×C83—24no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83C2×D414yes—
264C4⋊C4×C83C2412yes—
265C4⋊C4×C83C2412yes—
266C4⋊C4×C83C2412yes—
267C22⋊C4×C83—24no—
268C22⋊C4×C83—24no—
269C22⋊C4×C83—24no—
270C22⋊C4×C83—24no—
271C22⋊C4×C83C2×D414yes—
272C22⋊C4×C83C2×D414yes—
273C42×C83—24no—
274C42×C83C2×D412yes—
275C42×C83C2412yes—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83—22no—
279C23×C83—22no—
280C23×C83—22no—
281C23×C83—22no—
282C23×C83—42no—
283C23×C83—42no—
284C23×C83—42no—
285C23×C83AGL(1,ℤ/8)14yes—
286C23×C83C22×D412yes—
287C23×C83C22×D412yes—
288C23×C83C22×D411yescharacteristic
289C22×D83—22no—
290C22×D83—42no—
291C22×D83—42no—
292C22×D83—42no—
293D4×C83—28no—
294D4×C83—22no—
295D4×C83—22no—
296D4×C83—48no—
297D4×C83—42no—
298D4×C83—84no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—24no—
304C2×C4×C83—24no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—22no—
312C2×C4×C83—42no—
313C2×C4×C83—42no—
314C2×C4×C83—42no—
315C2×C4×C83—84no—
316C2×C4×C83—84no—
317C2×C4×C83C22×D412yes—
318C2×C4×C83C22×D412yes—
319C2×C4×C83C22×D412yes—
320C2×C4×C83C22×D412yes—
321C2×C4×C83C22×D411yescharacteristic
322C2×C4×C83C2×#4112yes—
323C2×C4×C832−1+412yes—
324C2×C4×C83C2511yescharacteristic
325C22⋊D83—48no—
326C22⋊D83—48no—
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—48no—
331C2×Dic83—42no—
332C2×Dic83—42no—
333C2×Dic83—42no—
334C2×Dic83—48no—
335D332—22no—
336D332—22no—
337D332—42no—
338C4×D83—48no—
339Dic166—48no—
340C83⋊C8—22no—
341C83⋊C8—22no—
342C83⋊C8—22no—
343C83⋊C8C2×#4114yescomplemented
344C22×C83—28no—
345C22×C83—22no—
346C22×C83—22no—
347C22×C83—22no—
348C22×C83—22no—
349C22×C83—22no—
350C22×C83—44no—
351C22×C83—42no—
352C22×C83—42no—
353C22×C83—42no—
354C22×C83—84no—
355C22×C83#54712yes—
356C22×C83C2×AGL(1,ℤ/8)14yes—
357C22×C83C2×AGL(1,ℤ/8)12yes—
358C22×C83#57712yes—
359C22×C83C23×D411yescharacteristic
360C2×D83—42no—
361C2×D83—42no—
362C2×D83—42no—
363C2×D83—84no—
364C4×C83—22no—
365C4×C83—22no—
366C4×C83—22no—
367C4×C83—22no—
368C4×C83—42no—
369C4×C83—42no—
370C4×C83—42no—
371C4×C83#54712yes—
372C4×C83C22×#4111yescharacteristic
373C4×C83C2×2−1+411yescharacteristic
374Dic83—42no—
375Dic83—42no—
376Dic83—42no—
377C2×#3345—831nomaximal, Sylow
378C2×C83—24no—
379C2×C83—42no—
380C2×C83—82no—
381C2×C83#334514yescomplemented
382C2×C83C2×#54711yescharacteristic
383C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
384C2×C83C2×#57711yescharacteristic
385D83—82no—
386C2×#553D8311yescharacteristic, complemented
387C2×#547—831no—
388#3345—8316no—
389C2×#501—831no—
390C2×#481—831no—
391C2×#481—831no—
392C2×#482—831no—
393C2×#480—831no—
394C2×#478—831no—
395C2×#476—831no—
396C2×#469—831no—
397C2×#466—831no—
398C2×#442—831no—
399C2×#435—831no—
400C2×#428—831no—
401C22×#106—831no—
402C83C2×#334511yescharacteristic, complemented, Sylow
403C22×#41—1661no—
404C22×D8—831no—
405C22×M16—831no—
406C23×C8—831no—
407#553—24no—
408#553C2×D8318yescomplemented
409#547—838no—
410#547—1664no—
411C2×C4⋊Q8—831no—
412C2×#126—21no—
413C2×#125C2×D8311yescharacteristic
414C2×#123—21no—
415C2×#123—1661no—
416C2×#123—1661no—
417C2×C22⋊Q8—1661no—
418C2×#121—21no—
419C2×#121—831no—
420C2×#121—831no—
421C2×#121C2×D8311yescharacteristic
422C2×#121C2×D8311yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4—831no—
425C2×C4×D4C2×D8311yescharacteristic
426C2×C4×D4C2×D8311yescharacteristic
427C2×#117C2×D8311yescharacteristic
428C22×C4⋊C4—831no—
429C22×C4⋊C4—831no—
430C22×C4⋊C4C2×D8311yescharacteristic
431#501—838no—
432#482—838no—
433#481—838no—
434#481—838no—
435#480—838no—
436#478—838no—
437#476—838no—
438#469—838no—
439#466—838no—
440#442—838no—
441#435—838no—
442#428—838no—
443C2×#107—831no—
444C2×#107—831no—
445C2×#107—831no—
446C2×#106—831no—
447C2×#106—831no—
448C2×#106—831no—
449C2×#106—831no—
450C2×#106—838no—
451C2×#106—831no—
452C2×#106—831no—
453C2×C4⋊C8—831no—
454C2×#102—831no—
455C2×#102—831no—
456C2×#102—831no—
457C2×#102—831no—
458C2×#102—831no—
459C2×#102—831no—
460C2×C22⋊C8—831no—
461C2×C22⋊C8—831no—
462C2×#97—831no—
463C2×#41—3328no—
464C2×#41—1668no—
465C22×Q8—1661no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—831no—
469C22×D4—1661no—
470C22×D4—1661no—
471C22×D4C22⋊D8311yescharacteristic
472C22×D4C22×D8311yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—1661no—
476C23×C4—1661no—
477C23×C4—1661no—
478C23×C4C22×D8311yescharacteristic
479C23×C4C22×D8311yescharacteristic
480C2×D8—834no—
481C2×D8—1664no—
482C2×M16—834no—
483C2×M16—1664no—
484C22×C8—831no—
485C22×C8—831no—
486C22×C8—834no—
487C22×C8—831no—
488C22×C8—831no—
489C22×C8—1664no—
490C4⋊Q8—834no—
491C4⋊Q8—1662no—
492#126—28no—
493#125—22no—
494#125C22×D8314yes—
495#123—28no—
496#123—1668no—
497#123—1668no—
498C22⋊Q8—1668no—
499#121—28no—
500#121—22no—
501#121—22no—
502#121—834no—
503#121—834no—
504#121—1662no—
505#121—1662no—
506#121C22×D8314yes—
507#121C22×D8314yes—
508C4×D4—28no—
509C4×D4—22no—
510C4×D4—834no—
511C4×D4—1662no—
512C4×D4C22⋊D8314yes—
513C4×D4C22×D8314yes—
514C4×D4C22×D8314yes—
515#117—22no—
516#117C22×D8314yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—831no—
522C2×C4⋊C4—831no—
523C2×C4⋊C4—831no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—834no—
526C2×C4⋊C4—1661no—
527C2×C4⋊C4—1661no—
528C2×C4⋊C4—1662no—
529C2×C4⋊C4—1662no—
530C2×C4⋊C4—1661no—
531C2×C4⋊C4C22⋊D8311yescharacteristic
532C2×C4⋊C4C22×D8311yescharacteristic
533C2×C4⋊C4C22×D8311yescharacteristic
534C2×C4⋊C4C22×D8314yes—
535C2×C4⋊C4C22×D8311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—1661no—
541C2×C22⋊C4—1661no—
542C2×C22⋊C4—1661no—
543C2×C22⋊C4C22⋊D8311yescharacteristic
544C2×C22⋊C4C22⋊D8311yescharacteristic
545C2×C42—21no—
546C2×C42C22×D8311yescharacteristic
547#107—834no—
548#107—834no—
549#107—834no—
550#106—834no—
551#106—834no—
552#106—834no—
553#106—834no—
554#106—834no—
555#106—834no—
556C4⋊C8—834no—
557#102—834no—
558#102—834no—
559#102—834no—
560#102—834no—
561#102—834no—
562#102—834no—
563C22⋊C8—834no—
564C22⋊C8—834no—
565#97—834no—
566C24—21no—
567C24—1661no—
568C24C2×C22⋊D8311yescharacteristic
569C24C2×C22⋊D8311yescharacteristic
570#41—33232no—
571C2×Q8—3324no—
572C2×Q8—1664no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—44no—
580C2×D4—82no—
581C2×D4—3324no—
582C2×D4—3324no—
583C2×D4—832no—
584C2×D4—1664no—
585C2×D4—1664no—
586C2×D4—1661no—
587C2×D4—1662no—
588C2×D4—1662no—
589C2×D4C2×C22⋊D8314yes—
590C2×D4C23×D8312yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—3324no—
603C22×C4—3324no—
604C22×C4—3324no—
605C22×C4—1664no—
606C22×C4—1664no—
607C22×C4—1661no—
608C22×C4—1661no—
609C22×C4—1661no—
610C22×C4—1664no—
611C22×C4C2×C22⋊D8312yes—
612C22×C4C2×C22⋊D8312yes—
613C22×C4C2×C22⋊D8311yescharacteristic
614C22×C4C2×C22⋊D8311yescharacteristic
615C22×C4C2×C22⋊D8311yescharacteristic
616C22×C4C2×C22⋊D8311yescharacteristic
617C22×C4C23×D8312yes—
618C22×C4C23×D8312yes—
619C22×C4C23×D8311yescharacteristic
620D8—1668no—
621M16—1668no—
622C2×C8—834no—
623C2×C8—832no—
624C2×C8—832no—
625C2×C8—832no—
626C2×C8—832no—
627C2×C8—1668no—
628C2×C8—1662no—
629C2×C8—1662no—
630C2×C8—1662no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—832no—
638C4⋊C4—832no—
639C4⋊C4—832no—
640C4⋊C4—1661no—
641C4⋊C4—1661no—
642C4⋊C4—1661no—
643C4⋊C4—1664no—
644C4⋊C4—1664no—
645C4⋊C4—1664no—
646C4⋊C4C2×C22⋊D8314yes—
647C4⋊C4C23×D8312yes—
648C4⋊C4C23×D8312yes—
649C4⋊C4C23×D8312yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—1664no—
655C22⋊C4—1664no—
656C22⋊C4—1664no—
657C22⋊C4C2×C22⋊D8314yes—
658C22⋊C4C2×C22⋊D8314yes—
659C42—24no—
660C42C2×C22⋊D8312yes—
661C42C23×D8312yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—3322no—
672C23—3322no—
673C23—3322no—
674C23—1662no—
675C23#1458181714yes—
676C23C22×C22⋊D8312yes—
677C23C22×C22⋊D8312yes—
678C23C22×C22⋊D8311yescharacteristic
679Q8—3328no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—42no—
685D4—84no—
686D4—3328no—
687D4—3328no—
688D4—3322no—
689D4—1662no—
690D4—1662no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—3328no—
710C2×C4—3328no—
711C2×C4—3322no—
712C2×C4—3322no—
713C2×C4—3322no—
714C2×C4—3328no—
715C2×C4—1662no—
716C2×C4—1662no—
717C2×C4—1662no—
718C2×C4C22×C22⋊D8312yes—
719C2×C4C22×C22⋊D8312yes—
720C2×C4C22×C22⋊D8312yes—
721C2×C4C22×C22⋊D8312yes—
722C2×C4C22×C22⋊D8311yescharacteristic
723C2×C4#41×D8312yes—
724C2×C4#1458183912yes—
725C2×C4C24×D8311yescharacteristic
726C8—834no—
727C8—1662no—
728C8—1662no—
729C8—1662no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—3322no—
742C22—3322no—
743C22—3322no—
744C22—6644no—
745C22#1912835012yes—
746C22C2×#1458181714yes—
747C22C2×#1458181712yes—
748C22#1912851212yes—
749C22C23×C22⋊D8311yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—3322no—
758C4—3322no—
759C4—3322no—
760C4#1912835012yes—
761C4C2×#41×D8311yescharacteristic
762C4C2×#1458183911yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—6642no—
767C2#2491992714yesdirect product factor
768C2C2×#1912835011yescharacteristic
769C2C22×#1458181711yescharacteristic
770C2C2×#1912851211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#553×C83C2
socleC23×C83C22×D4
hypercenterC2×#553D83
hypocenterC83C2×#3345
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#19128355C2semidirect
2. #24919927C2direct (N × H)
3. C2×#19128111C2semidirect
4. C2×#19128019C2semidirect
5. C2×#19128017C2semidirect
6. C2×#19128025C2semidirect
7. C2×#19128012C2semidirect
8. C2×#19127998C2semidirect
9. C2×#19127991C2semidirect
10. C2×#19127952C2semidirect
11. C2×#19127935C2semidirect
12. C2×#19127811C2semidirect
13. C2×#19127773C2semidirect
14. C2×#19127744C2semidirect
15. C22×#14581723C2semidirect
16. C2×#553×C83C2semidirect
22. #19128355C22semidirect
32. #19128111C22semidirect
33. #19128025C22semidirect
34. #19128019C22semidirect
35. #19128017C22semidirect
36. #19128012C22semidirect
37. #19127998C22semidirect
38. #19127991C22semidirect
39. #19127952C22semidirect
40. #19127935C22semidirect
41. #19127811C22semidirect
42. #19127773C22semidirect
43. #19127744C22semidirect
53. C2×#14581723C22semidirect
65. #553×C83C22semidirect
207. C2×C83⋊C8#41semidirect
343. C83⋊C8C2×#41semidirect
381. C2×C83#3345semidirect
386. C2×#553D83semidirect
402. C83C2×#3345semidirect
408. #553C2×D83semidirect
767. C2#24919927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283552
#249199272
C2×#191281112
C2×#191280192
C2×#191280172
C2×#191280252
C2×#191280122
C2×#191279982
C2×#191279912
C2×#191279522
C2×#191279352
C2×#191278112
C2×#191277732
C2×#191277442
C22×#145817232
C2×#553×C832
C2×#334583