Finite Group Databasebeta

← C2×#24920042 #36283103

Subgroups — C2×#24920042 #36283103

Order 21248.

2082 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128422C211yesmaximal, characteristic, complemented
2C2×#19128351C211yesmaximal, characteristic
3#24920042C2116yesmaximal, direct product factor
4C2×#19128105C211yesmaximal, characteristic, complemented
5C2×#19128035C211yesmaximal, characteristic, complemented
6C2×#19128034C211yesmaximal, characteristic, complemented
7C2×#19128024C211yesmaximal, characteristic, complemented
8C2×#19128022C211yesmaximal, characteristic, complemented
9C2×#19127984C211yesmaximal, characteristic, complemented
10C2×#19127979C211yesmaximal, characteristic, complemented
11C2×#19127944C211yesmaximal, characteristic, complemented
12C2×SD16×Dic83C211yesmaximal, characteristic, complemented
13C2×#19127777C211yesmaximal, characteristic, complemented
14C2×#19127743C211yesmaximal, characteristic, complemented
15C2×#19127742C211yesmaximal, characteristic, complemented
16C2×#468×C83C211yesmaximal, characteristic, complemented
17C22×#13050589—21no—
18C22×#13050573C2211yescharacteristic
19#19128422—24no—
20#19128422C2218yescomplemented
21#19128351—24no—
22#19128351C2218yes—
23C2×#14581791C2211yescharacteristic
24C2×#14581791C2211yescharacteristic
25C2×#14581787—21no—
26C2×#14581785—21no—
27C2×#14581778—21no—
28C2×#14581774—21no—
29C2×#14581773—21no—
30C2×#14581769—21no—
31C2×#14581768C2211yescharacteristic
32C2×#14581763C2211yescharacteristic
33C2×Q8×Dic83C2211yescharacteristic
34C2×#14581757—21no—
35C2×D4×Dic83C2211yescharacteristic
36C2×C4×C22⋊D83C2211yescharacteristic
37C2×#14581751C2211yescharacteristic
38C2×#14581750C2211yescharacteristic
39C22×C4⋊Dic83C2211yescharacteristic
40C2×C4⋊C4×D83C2211yescharacteristic
41#19128105C2218yescomplemented
42#19128035C2218yescomplemented
43#19128034C2218yescomplemented
44#19128024C2218yescomplemented
45#19128022C2218yescomplemented
46#19127984C2218yescomplemented
47#19127979C2218yescomplemented
48#19127944C2218yescomplemented
49SD16×Dic83C2218yescomplemented
50#19127777C2218yescomplemented
51#19127743C2218yescomplemented
52#19127742C2218yescomplemented
53C2×#14581726C2211yescharacteristic
54C2×#14581726C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581725C2211yescharacteristic
58C2×#14581724C2211yescharacteristic
59C2×#14581724C2211yescharacteristic
60C2×#14581723C2211yescharacteristic
61C2×Dic83⋊C8C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581716C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65C2×#14581713C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C22×SD16×C83C2211yescharacteristic
70C22×M16×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×#121×C83C2211yescharacteristic
73#468×C83C2218yescomplemented
74C2×#107×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#102×C83C2211yescharacteristic
77C2×#13050589—28no—
78C2×#13050589—48no—
79C22×Dic166—21no—
80C22×Dic166—21no—
81C22×C22⋊D83—21no—
82C22×C22⋊D83D411yescharacteristic
83C23×Dic83—21no—
84C23×Dic83—21no—
85C22×C4×D83—21no—
86C22×C4×D83C2311yescharacteristic
87C2×#13050573—24no—
88C2×#13050573C2314yes—
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2311yescharacteristic
91#14581791—22no—
92#14581791—22no—
93#14581791C2314yes—
94#14581791C2314yes—
95#14581787—28no—
96#14581785—28no—
97#14581778—28no—
98#14581774—28no—
99#14581773—28no—
100#14581769—28no—
101#14581768—22no—
102#14581768C2314yes—
103#14581763—22no—
104#14581763C2314yes—
105Q8×Dic83—22no—
106Q8×Dic83C2314yes—
107#14581757—28no—
108D4×Dic83—22no—
109D4×Dic83C2314yes—
110C4×C22⋊D83D414yes—
111C4×C22⋊D83C2314yes—
112#14581751—22no—
113#14581751C2314yes—
114#14581750—22no—
115#14581750C2314yes—
116C2×C4⋊Dic83—21no—
117C2×C4⋊Dic83—22no—
118C2×C4⋊Dic83—21no—
119C2×C4⋊Dic83C2314yes—
120C2×C4⋊Dic83C2311yescharacteristic
121C2×C4⋊Dic83C2311yescharacteristic
122C2×C4⋊Dic83C2311yescharacteristic
123C2×C4⋊Dic83C2311yescharacteristic
124C2×Dic83⋊C4—21no—
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4D411yescharacteristic
129C4⋊C4×D83—22no—
130C4⋊C4×D83C2314yes—
131C2×C22⋊Dic83—21no—
132C2×C22⋊Dic83—21no—
133C2×C22⋊Dic83—21no—
134C2×C22⋊Dic83D411yescharacteristic
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4D411yescharacteristic
138C2×C4×Dic83—21no—
139C2×C4×Dic83—21no—
140C2×C4×Dic83—21no—
141C2×C4×Dic83C2311yescharacteristic
142#14581726C2314yes—
143#14581726C2314yes—
144#14581725C2314yes—
145#14581725C2314yes—
146#14581725C2314yes—
147#14581724C2314yes—
148#14581724C2314yes—
149#14581723C2314yes—
150Dic83⋊C8C2314yes—
151#14581716C2314yes—
152#14581716C2314yes—
153#14581713C2314yes—
154#14581713C2314yes—
155C22⋊(C83⋊C8)C2314yes—
156(C2×D83)⋊C8C2314yes—
157C8×Dic83C2314yes—
158C22×Q8×C83C2311yescharacteristic
159C22×D4×C83—21no—
160C22×D4×C83C2311yescharacteristic
161C23×C4×C83C2311yescharacteristic
162C2×SD16×C83—24no—
163C2×SD16×C83C2314yes—
164C2×M16×C83—24no—
165C2×M16×C83C2314yes—
166C22×C8×C83C2311yescharacteristic
167C22×C8×C83C2311yescharacteristic
168C22⋊Q8×C83—22no—
169C22⋊Q8×C83C2314yes—
170#121×C83—22no—
171#121×C83C2314yes—
172C2×C4⋊C4×C83—21no—
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83—21no—
177#107×C83C2314yes—
178#103×C83C2314yes—
179#102×C83C2314yes—
180C23×D83C2×D411yescharacteristic
181#13050589—432no—
182C2×Dic166—24no—
183C2×Dic166—24no—
184C2×Dic166—44no—
185C2×Dic166—44no—
186C2×C22⋊D83—24no—
187C2×C22⋊D83—24no—
188C2×C22⋊D83—44no—
189C2×C22⋊D83C2×D414yes—
190C22×Dic83—24no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—24no—
196C22×Dic83—44no—
197C22×Dic83—44no—
198C22×Dic83C2×D411yescharacteristic
199C22×Dic83C2×D411yescharacteristic
200C22×Dic83C2×D411yescharacteristic
201C2×C4×D83—22no—
202C2×C4×D83—22no—
203C2×C4×D83—24no—
204C2×C4×D83—44no—
205C2×C4×D83C2×D412yes—
206C2×C4×D83C2412yes—
207#13050573—28no—
208C2×C83⋊C8—22no—
209C2×C83⋊C8—22no—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C4⋊Dic83—21no—
213C4⋊Dic83—21no—
214C4⋊Dic83—24no—
215C4⋊Dic83—21no—
216C4⋊Dic83—21no—
217C4⋊Dic83—24no—
218C4⋊Dic83C2412yes—
219C4⋊Dic83C2412yes—
220C4⋊Dic83C2412yes—
221C4⋊Dic83C2412yes—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4C2×D414yes—
227C22⋊Dic83—24no—
228C22⋊Dic83—24no—
229C22⋊Dic83—24no—
230C22⋊Dic83C2×D414yes—
231(C2×D83)⋊C4—24no—
232(C2×D83)⋊C4—24no—
233(C2×D83)⋊C4C2×D414yes—
234C4×Dic83—24no—
235C4×Dic83—24no—
236C4×Dic83—24no—
237C4×Dic83C2×D412yes—
238C4×Dic83C2412yes—
239C24×C83—21no—
240C24×C83C2×D411yescharacteristic
241C2×Q8×C83—21no—
242C2×Q8×C83—22no—
243C2×Q8×C83—22no—
244C2×Q8×C83C2412yes—
245C2×D4×C83—24no—
246C2×D4×C83—21no—
247C2×D4×C83—22no—
248C2×D4×C83—22no—
249C2×D4×C83—44no—
250C2×D4×C83C2412yes—
251C22×C4×C83—22no—
252C22×C4×C83—22no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2×D412yes—
258C22×C4×C83C2412yes—
259C22×C4×C83C2411yescharacteristic
260SD16×C83—28no—
261M16×C83—28no—
262C2×C8×C83—22no—
263C2×C8×C83#4114yescomplemented
264C2×C8×C83C2412yes—
265C2×C8×C83C2412yes—
266C4⋊C4×C83—24no—
267C4⋊C4×C83—21no—
268C4⋊C4×C83—21no—
269C4⋊C4×C83C2412yes—
270C4⋊C4×C83C2412yes—
271C22⋊C4×C83—24no—
272C22⋊C4×C83—24no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—42no—
278C23×C83—42no—
279C23×C83—42no—
280C23×C83C22×D412yes—
281C23×C83C22×D411yescharacteristic
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—22no—
285C22×D83C22×D412yes—
286Q8×C83—22no—
287Q8×C83—22no—
288Q8×C83—42no—
289D4×C83—22no—
290D4×C83—22no—
291D4×C83—48no—
292D4×C83—42no—
293C2×C4×C83—22no—
294C2×C4×C83—24no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—42no—
301C2×C4×C83—42no—
302C2×C4×C83—42no—
303C2×C4×C83C22×D412yes—
304C2×C4×C83C22×D411yescharacteristic
305C2×C4×C83C2×#4112yes—
306C2×C4×C832−1+412yes—
307C2×C4×C83C2511yescharacteristic
308C22⋊D83—28no—
309C22⋊D83—48no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—48no—
317C2×Dic83—42no—
318C2×Dic83—42no—
319C2×Dic83—42no—
320C2×Dic83—42no—
321C2×Dic83—48no—
322C2×Dic83AGL(1,ℤ/8)14yes—
323C2×Dic83C22×D412yes—
324C2×Dic83C22×D412yes—
325C2×Dic83C22×D412yes—
326C4×D83—24no—
327C4×D83—22no—
328C4×D83—22no—
329C4×D83—48no—
330Dic166—48no—
331Dic166—48no—
332C8×C83—22no—
333C8×C83C2×#4114yescomplemented
334C83⋊C8—22no—
335C83⋊C8—22no—
336C22×C83—22no—
337C22×C83—22no—
338C22×C83—22no—
339C22×C83—44no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83—42no—
343C22×C83—84no—
344C22×C83#54712yes—
345C22×C83C2×AGL(1,ℤ/8)12yes—
346C22×C83#57812yes—
347C22×C83C23×D411yescharacteristic
348C2×D83—22no—
349C2×D83—22no—
350C2×D83—22no—
351C2×D83—44no—
352C4×C83—22no—
353C4×C83—42no—
354C4×C83—42no—
355C4×C83—42no—
356C4×C83#54712yes—
357C4×C83C22×#4111yescharacteristic
358C4×C83C2×2−1+411yescharacteristic
359Dic83—22no—
360Dic83—22no—
361Dic83—42no—
362Dic83—42no—
363Dic83—42no—
364Dic83—42no—
365Dic83C2×AGL(1,ℤ/8)14yes—
366C2×#3353—831nomaximal, Sylow
367C2×C83—42no—
368C2×C83—82no—
369C2×C83#335314yescomplemented
370C2×C83C2×#54711yescharacteristic
371C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
372C2×C83C2×#57811yescharacteristic
373D83—42no—
374C2×#556—831no—
375C2×#547—831no—
376#3353—8316no—
377C2×#500—831no—
378C2×#484—831no—
379C2×#484—831no—
380C2×#482—831no—
381C2×#482—831no—
382C2×#475—831no—
383C2×#474—831no—
384C2×#468—831no—
385C2×#468D8311yescharacteristic, complemented
386C2×C4×SD16—831no—
387C2×#436—831no—
388C2×#428—831no—
389C2×#428—831no—
390C83C2×#335311yescharacteristic, complemented, Sylow
391C22×#41—1661no—
392C22×SD16C2×D8311yescharacteristic
393C22×M16—831no—
394C22×M16C2×D8311yescharacteristic
395#556—838no—
396#556—1664no—
397#547—838no—
398#547—1664no—
399C2×C4⋊Q8—831no—
400C2×C4⋊Q8—831no—
401C2×#126—1661no—
402C2×#126—1661no—
403C2×#124—1661no—
404C2×#123—1661no—
405C2×#123—1661no—
406C2×C22⋊Q8—831no—
407C2×C22⋊Q8—1661no—
408C2×C22⋊Q8C2×D8311yescharacteristic
409C2×#121—831no—
410C2×#121C2×D8311yescharacteristic
411C2×C4×Q8—831no—
412C2×C4×Q8—1661no—
413C2×C4×D4—831no—
414C2×C4×D4—831no—
415C2×#117—831no—
416C2×#117—831no—
417C22×C4⋊C4—831no—
418C22×C4⋊C4—831no—
419#500—838no—
420#484—838no—
421#484—838no—
422#482—838no—
423#482—838no—
424#475—838no—
425#474—838no—
426#468—838no—
427#468C2×D8318yescomplemented
428C4×SD16—838no—
429#436—838no—
430#428—838no—
431#428—838no—
432C2×#107—831no—
433C2×#107—831no—
434C2×#107—831no—
435C2×#107—831no—
436C2×#107—831no—
437C2×#107C2×D8311yescharacteristic
438C2×#106—831no—
439C2×#106—831no—
440C2×#106—831no—
441C2×C4⋊C8—831no—
442C2×#103—831no—
443C2×#103—831no—
444C2×#103C2×D8311yescharacteristic
445C2×#102—831no—
446C2×#102—831no—
447C2×#102C2×D8311yescharacteristic
448C2×C22⋊C8—831no—
449C2×C22⋊C8—831no—
450C2×C4×C8—831no—
451C2×#41—3328no—
452C2×#41—1668no—
453C22×Q8—1661no—
454C22×Q8—1661no—
455C22×Q8C22×D8311yescharacteristic
456C22×D4—21no—
457C22×D4—831no—
458C22×D4—1661no—
459C22×D4C22×D8311yescharacteristic
460C23×C4—831no—
461C23×C4—1661no—
462C23×C4—1661no—
463C23×C4—1661no—
464C23×C4C22×D8311yescharacteristic
465C2×SD16—24no—
466C2×SD16C22×D8314yes—
467C2×M16—24no—
468C2×M16—834no—
469C2×M16—1664no—
470C2×M16C22×D8314yes—
471C22×C8—831no—
472C22×C8—831no—
473C22×C8C22×D8311yescharacteristic
474C22×C8C22×D8311yescharacteristic
475C4⋊Q8—834no—
476C4⋊Q8—834no—
477C4⋊Q8—1662no—
478C4⋊Q8—1662no—
479#126—1668no—
480#126—1668no—
481#124—1668no—
482#123—1668no—
483#123—1668no—
484C22⋊Q8—22no—
485C22⋊Q8—834no—
486C22⋊Q8—1668no—
487C22⋊Q8—1662no—
488C22⋊Q8C22×D8314yes—
489#121—22no—
490#121—834no—
491#121—1662no—
492#121C22×D8314yes—
493C4×Q8—834no—
494C4×Q8—1662no—
495C4×Q8—1668no—
496C4×D4—834no—
497C4×D4—834no—
498C4×D4—834no—
499C4×D4—1662no—
500#117—834no—
501#117—834no—
502#117—1662no—
503#117—1662no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—831no—
506C2×C4⋊C4—831no—
507C2×C4⋊C4—831no—
508C2×C4⋊C4—834no—
509C2×C4⋊C4—831no—
510C2×C4⋊C4—831no—
511C2×C4⋊C4—834no—
512C2×C4⋊C4—1662no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4—1661no—
516C2×C4⋊C4—1661no—
517C2×C4⋊C4—1661no—
518C2×C4⋊C4—1661no—
519C2×C4⋊C4—1662no—
520C2×C4⋊C4C22×D8311yescharacteristic
521C2×C4⋊C4C22×D8311yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—831no—
525C2×C22⋊C4—831no—
526C2×C22⋊C4—1661no—
527C2×C22⋊C4—1661no—
528C2×C22⋊C4—1661no—
529C2×C22⋊C4—1661no—
530C2×C22⋊C4—1661no—
531C2×C42—831no—
532C2×C42—1661no—
533C2×C42—1661no—
534C2×C42—1661no—
535#107—834no—
536#107—834no—
537#107—834no—
538#107—834no—
539#107—834no—
540#107C22×D8314yes—
541#106—834no—
542#106—834no—
543#106—834no—
544C4⋊C8—834no—
545#103—834no—
546#103—834no—
547#103C22×D8314yes—
548#102—834no—
549#102—834no—
550#102C22×D8314yes—
551C22⋊C8—834no—
552C22⋊C8—834no—
553C4×C8—834no—
554C24—21no—
555C24—831no—
556C24D4×D8311yescharacteristic
557#41—33232no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—3324no—
562C2×Q8—3324no—
563C2×Q8—1664no—
564C2×Q8—1664no—
565C2×Q8C23×D8312yes—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—44no—
571C2×D4—3324no—
572C2×D4—834no—
573C2×D4—1664no—
574C2×D4—1664no—
575C2×D4C23×D8312yes—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—3324no—
582C22×C4—3324no—
583C22×C4—3324no—
584C22×C4—831no—
585C22×C4—831no—
586C22×C4—831no—
587C22×C4—832no—
588C22×C4—832no—
589C22×C4—1664no—
590C22×C4—1664no—
591C22×C4—1664no—
592C22×C4—1661no—
593C22×C4—1661no—
594C22×C4—1661no—
595C22×C4—1661no—
596C22×C4—1662no—
597C22×C4—1662no—
598C22×C4D4×D8312yes—
599C22×C4D4×D8311yescharacteristic
600C22×C4C23×D8312yes—
601C22×C4C23×D8311yescharacteristic
602SD16—28no—
603M16—28no—
604M16—1668no—
605C2×C8—22no—
606C2×C8—832no—
607C2×C8—832no—
608C2×C8—1662no—
609C2×C8—1662no—
610C2×C8#1305058914yescomplemented
611C2×C8C23×D8312yes—
612C2×C8C23×D8312yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—834no—
617C4⋊C4—832no—
618C4⋊C4—832no—
619C4⋊C4—832no—
620C4⋊C4—832no—
621C4⋊C4—1664no—
622C4⋊C4—1664no—
623C4⋊C4—1664no—
624C4⋊C4—1664no—
625C4⋊C4—1664no—
626C4⋊C4—1661no—
627C4⋊C4—1661no—
628C4⋊C4—1664no—
629C4⋊C4—1661no—
630C4⋊C4—1661no—
631C4⋊C4C23×D8312yes—
632C4⋊C4C23×D8312yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—834no—
636C22⋊C4—834no—
637C22⋊C4—1664no—
638C22⋊C4—1664no—
639C22⋊C4—1664no—
640C22⋊C4—1664no—
641C22⋊C4—1664no—
642C42—832no—
643C42—832no—
644C42—1664no—
645C42—1664no—
646C42—1664no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—832no—
655C23—1662no—
656C23—1662no—
657C23—1662no—
658C23C2×D4×D8312yes—
659C23C2×D4×D8311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—3328no—
664Q8—3328no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—42no—
669D4—3328no—
670D4—1668no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—3328no—
682C2×C4—3328no—
683C2×C4—3322no—
684C2×C4—3322no—
685C2×C4—3322no—
686C2×C4—3322no—
687C2×C4—3328no—
688C2×C4—834no—
689C2×C4—832no—
690C2×C4—832no—
691C2×C4—832no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1662no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4—1662no—
698C2×C4—1664no—
699C2×C4—1662no—
700C2×C4—1662no—
701C2×C4C2×D4×D8312yes—
702C2×C4C2×D4×D8311yescharacteristic
703C2×C4C2×#1305058912yes—
704C2×C4#1458183912yes—
705C2×C4C24×D8311yescharacteristic
706C8—22no—
707C8—1662no—
708C8—1662no—
709C8C2×#1305058914yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—3324no—
719C22—1662no—
720C22—1662no—
721C22—1662no—
722C22#1912835112yes—
723C22AGL(1,ℤ/8)×D8312yes—
724C22#1912851712yes—
725C22C22×D4×D8311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—3322no—
731C4—3322no—
732C4—3322no—
733C4—3322no—
734C4—834no—
735C4—1662no—
736C4—1662no—
737C4#1912835112yes—
738C4C22×#1305058911yescharacteristic
739C4C2×#1458183911yescharacteristic
740C2—42no—
741C2—82no—
742C2—3322no—
743C2#2492004214yesdirect product factor
744C2C2×#1912835111yescharacteristic
745C2C2×AGL(1,ℤ/8)×D8311yescharacteristic
746C2C2×#1912851711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#468×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128351C2
hypercenterC2×#468D83
hypocenterC83C2×#3353
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#19128422C2semidirect
3. #24920042C2direct (N × H)
4. C2×#19128105C2semidirect
5. C2×#19128035C2semidirect
6. C2×#19128034C2semidirect
7. C2×#19128024C2semidirect
8. C2×#19128022C2semidirect
9. C2×#19127984C2semidirect
10. C2×#19127979C2semidirect
11. C2×#19127944C2semidirect
12. C2×SD16×Dic83C2semidirect
13. C2×#19127777C2semidirect
14. C2×#19127743C2semidirect
15. C2×#19127742C2semidirect
16. C2×#468×C83C2semidirect
20. #19128422C22semidirect
41. #19128105C22semidirect
42. #19128035C22semidirect
43. #19128034C22semidirect
44. #19128024C22semidirect
45. #19128022C22semidirect
46. #19127984C22semidirect
47. #19127979C22semidirect
48. #19127944C22semidirect
49. SD16×Dic83C22semidirect
50. #19127777C22semidirect
51. #19127743C22semidirect
52. #19127742C22semidirect
73. #468×C83C22semidirect
263. C2×C8×C83#41semidirect
333. C8×C83C2×#41semidirect
369. C2×C83#3353semidirect
385. C2×#468D83semidirect
390. C83C2×#3353semidirect
427. #468C2×D83semidirect
610. C2×C8#13050589semidirect
709. C8C2×#13050589semidirect
743. C2#24920042direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284222
C2×#191283512
#249200422
C2×#191281052
C2×#191280352
C2×#191280342
C2×#191280242
C2×#191280222
C2×#191279842
C2×#191279792
C2×#191279442
C2×SD16×Dic832
C2×#191277772
C2×#191277432
C2×#191277422
C2×#468×C832
C2×#335383