Finite Group Databasebeta

← C2×#19144741 #25964718

Subgroups — C2×#19144741 #25964718

Order 11008.

2430 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
1C2×#14583444C211yesmaximal, characteristic, complemented
2C2×#14583367C211yesmaximal, characteristic, complemented
3#19144741C2116yesmaximal, direct product factor
4C2×#14583223C211yesmaximal, characteristic, complemented
5C2×#14583183C211yesmaximal, characteristic, complemented
6C2×#14583178C211yesmaximal, characteristic, complemented
7C2×#14583098C211yesmaximal, characteristic, complemented
8C2×#14583093C211yesmaximal, characteristic, complemented
9C2×#14583046C211yesmaximal, characteristic, complemented
10C2×#14583042C211yesmaximal, characteristic, complemented
11C2×#14583010C211yesmaximal, characteristic, complemented
12C2×#14583008C211yesmaximal, characteristic, complemented
13C2×#14582998C211yesmaximal, characteristic, complemented
14C2×#14582996C211yesmaximal, characteristic, complemented
15C2×#14582953C211yesmaximal, characteristic, complemented
16C2×C43×#482C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900—21no—
19C22×#10621873C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×D344C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23#14583444—24no—
24#14583444C2218yescomplemented
25C2×#13063324C2211yescharacteristic
26C2×#13063321C2211yescharacteristic
27C2×#13063311—21no—
28C2×#13063299C2211yescharacteristic
29C2×#13063297—21no—
30#14583367—24no—
31#14583367C2218yescomplemented
32C2×#13063290C2211yescharacteristic
33C2×#13063290C2211yescharacteristic
34C2×D4×Dic43C2211yescharacteristic
35C2×#13063287C2211yescharacteristic
36C2×#13063287C2211yescharacteristic
37C2×#13063287C2211yescharacteristic
38C2×(C22⋊D43)⋊C4—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063282—21no—
42C22×C4×Dic43C2211yescharacteristic
43C2×C42×D43—21no—
44#14583223C2218yescomplemented
45#14583183C2218yescomplemented
46#14583178C2218yescomplemented
47#14583098C2218yescomplemented
48#14583093C2218yescomplemented
49#14583046C2218yescomplemented
50#14583042C2218yescomplemented
51#14583010C2218yescomplemented
52#14583008C2218yescomplemented
53#14582998C2218yescomplemented
54#14582996C2218yescomplemented
55#14582953C2218yescomplemented
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#482C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—24no—
80C2×#10621898C2314yes—
81C2×#10621900—28no—
82C2×#10621900—48no—
83C22×Dic86—21no—
84C22×Dic86C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C23×Dic43D411yescharacteristic
93C23×Dic43D411yescharacteristic
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C2×#10621873—24no—
99C2×#10621873C2314yes—
100C2×#10621883—24no—
101C2×#10621883C2314yes—
102C2×D344—24no—
103C2×D344C2314yes—
104C2×#10621882—24no—
105C2×#10621882C2314yes—
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108#13063324—22no—
109#13063324C2314yes—
110#13063321—22no—
111#13063321C2314yes—
112#13063311—28no—
113#13063299—22no—
114#13063299C2314yes—
115#13063297—28no—
116#13063290—22no—
117#13063290—22no—
118#13063290C2314yes—
119#13063290C2314yes—
120D4×Dic43—22no—
121D4×Dic43C2314yes—
122#13063287—22no—
123#13063287—22no—
124#13063287—22no—
125#13063287C2314yes—
126#13063287C2314yes—
127#13063287C2314yes—
128(C22⋊D43)⋊C4—28no—
129(C22⋊D43)⋊C4—28no—
130(C22⋊D43)⋊C4—28no—
131#13063282—28no—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×C22⋊Dic43—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D414yes—
146C2×C4×Dic43C2311yescharacteristic
147C2×C4×Dic43C2311yescharacteristic
148C2×C4×Dic43C2314yes—
149C42×D43—28no—
150#13063258C2314yes—
151#13063256C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063250C2314yes—
155#13063248C2314yes—
156#13063247C2314yes—
157#13063245C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160C22⋊(C43⋊C8)C2314yes—
161#13063235C2314yes—
162#13063235C2314yes—
163C22×D4×C43—21no—
164C22×D4×C43C2311yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168#121×C43—22no—
169#121×C43C2314yes—
170#117×C43—22no—
171#117×C43C2314yes—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C42×C43—21no—
178#107×C43C2314yes—
179#106×C43C2314yes—
180#102×C43C2314yes—
181#102×C43C2314yes—
182C22⋊C8×C43C2314yes—
183C24×C43—21no—
184C24×C43C2×D411yescharacteristic
185C23×D43—21no—
186C23×D43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—24no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—44no—
192C2×D4×C43C2412yes—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—28no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—44no—
208C2×C22⋊D43—44no—
209C2×C22⋊D43—44no—
210C22×Dic43—24no—
211C22×Dic43—24no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—42no—
215C22×Dic43—44no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D414yes—
220C22×Dic43C2×D414yes—
221C22×Dic43C2×D411yescharacteristic
222#10621900—432no—
223#10621898—216no—
224#10621898—28no—
225#10621898—28no—
226C2×D172—21no—
227C2×D172—22no—
228C2×D172—21no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172#4114yescomplemented
232C2×D172C2412yes—
233C2×D172C2412yes—
234C2×C4×D43—28no—
235C2×C4×D43—24no—
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—44no—
240C2×C4×D43—44no—
241C2×C4×D43—44no—
242C2×Dic86—21no—
243C2×Dic86—22no—
244C2×Dic86—24no—
245C2×Dic86—44no—
246C2×Dic86#4114yescomplemented
247C2×Dic86C2412yes—
248C2×C8×C43—22no—
249C2×C8×C43—22no—
250C2×C8×C43C2412yes—
251C2×C8×C43C2412yes—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C2412yes—
256C4⋊C4×C43C2412yes—
257C4⋊C4×C43C2412yes—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—24no—
260C42×C43—24no—
261C22⋊Dic43—24no—
262#10621883—28no—
263#10621882—28no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268C4⋊Dic43—21no—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43C2×D414yes—
276C4×Dic43C2×D414yes—
277C4×Dic43C2×D412yes—
278C4×Dic43C2×D412yes—
279C4×Dic43C2412yes—
280C4×Dic43C2412yes—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8C2412yes—
284C2×C43⋊C8C2412yes—
285D344—28no—
286#10621873—28no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43C22×D412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—24no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43—42no—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—48no—
307D4×C43—42no—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4112yes—
321C2×C4×C43C2×#4112yes—
322C2×C4×C43C2511yescharacteristic
323C22⋊D43—216no—
324C22⋊D43—48no—
325C22⋊D43—48no—
326C22⋊D43—48no—
327C2×Dic43—24no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—28no—
333C2×Dic43—22no—
334C2×Dic43—44no—
335C2×Dic43—48no—
336C2×Dic43—42no—
337C2×Dic43AGL(1,ℤ/8)14yes—
338C2×Dic43C22×D412yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C2×Dic43C22×D412yes—
342D172—24no—
343D172—22no—
344D172—22no—
345D172—22no—
346D172—42no—
347D172C2×#4114yescomplemented
348C4×D43—216no—
349C4×D43—48no—
350C4×D43—48no—
351C4×D43—48no—
352Dic86—24no—
353Dic86—22no—
354Dic86—48no—
355Dic86C2×#4114yescomplemented
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C2×#3115—431nomaximal, Sylow
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—44no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—84no—
369C22×C43#52512yes—
370C22×C43C2×AGL(1,ℤ/8)12yes—
371C22×C43#57512yes—
372C22×C43C23×D411yescharacteristic
373C2×D43—24no—
374C2×D43—48no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—84no—
381C4×C43—22no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—42no—
385C4×C43#52512yes—
386C4×C43C22×#4111yescharacteristic
387C4×C43C22×#4111yescharacteristic
388Dic43—24no—
389Dic43—22no—
390Dic43—22no—
391Dic43—22no—
392Dic43—42no—
393Dic43C2×AGL(1,ℤ/8)14yes—
394C2×#532—431no—
395C2×C4×#41—431no—
396#3115—4316no—
397C2×#482—431no—
398C2×#482D4311yescharacteristic, complemented
399C2×#475—431no—
400C2×#474—431no—
401C2×#460—431no—
402C2×#459—431no—
403C2×#449—431no—
404C2×#449—431no—
405C2×#442—431no—
406C2×#442—431no—
407C2×#440—431no—
408C2×#440—431no—
409C2×#432—431no—
410C2×C43—42no—
411C2×C43—82no—
412C2×C43#311514yescomplemented
413C2×C43C2×#52511yescharacteristic
414C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
415C2×C43C2×#57511yescharacteristic
416D43—44no—
417D43—82no—
418C22×#41—431no—
419C22×#41—861no—
420C22×SD16—431no—
421C22×SD16—431no—
422C22×D8—431no—
423C22×D8—431no—
424#532—438no—
425#532—864no—
426C2×C4⋊Q8—431no—
427C2×#127—431no—
428C2×#124—861no—
429C2×#121—431no—
430C2×#121—861no—
431C2×#121C2×D4311yescharacteristic
432C4×#41—438no—
433C4×#41—864no—
434C2×C4×Q8—431no—
435C2×C4×Q8—431no—
436C2×C4×D4—431no—
437C2×C4×D4—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—861no—
441C2×C4×D4—861no—
442C2×C4×D4—861no—
443C2×#117—861no—
444C2×#117C2×D4311yescharacteristic
445C22×C42—431no—
446C22×C42—861no—
447#482—438no—
448#482C2×D4318yescomplemented
449#475—438no—
450#474—438no—
451#460—438no—
452#459—438no—
453#449—438no—
454#449—438no—
455#442—438no—
456#442—438no—
457#440—438no—
458#440—438no—
459#432—438no—
460C2×#107—431no—
461C2×#107C2×D4311yescharacteristic
462C2×#106—431no—
463C2×#106C2×D4311yescharacteristic
464C2×C4⋊C8—431no—
465C2×C4⋊C8—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102—431no—
472C2×#102C2×D4311yescharacteristic
473C2×#102C2×D4311yescharacteristic
474C2×C22⋊C8—431no—
475C2×C22⋊C8C2×D4311yescharacteristic
476C2×#97—431no—
477C2×#97—431no—
478C43C2×#311511yescharacteristic, complemented, Sylow
479C2×#41—434no—
480C2×#41—864no—
481C2×#41—864no—
482C2×#41—868no—
483C2×#41—862no—
484C2×#41—1728no—
485C22×Q8—431no—
486C22×Q8—861no—
487C22×D4—21no—
488C22×D4—431no—
489C22×D4—431no—
490C22×D4—861no—
491C22×D4—861no—
492C22×D4—861no—
493C22×D4—861no—
494C22×D4C22×D4311yescharacteristic
495C23×C4—431no—
496C23×C4—431no—
497C23×C4—861no—
498C23×C4—861no—
499C23×C4—861no—
500C23×C4—861no—
501C23×C4—861no—
502C23×C4C22×D4311yescharacteristic
503C2×SD16—434no—
504C2×SD16—434no—
505C2×SD16—864no—
506C2×SD16—864no—
507C2×D8—434no—
508C2×D8—434no—
509C2×D8—864no—
510C2×D8—864no—
511C22×C8—431no—
512C22×C8—431no—
513C22×C8C22×D4311yescharacteristic
514C22×C8C22×D4311yescharacteristic
515C4⋊Q8—434no—
516C4⋊Q8—862no—
517#127—434no—
518#127—862no—
519#124—868no—
520#121—22no—
521#121—434no—
522#121—868no—
523#121—862no—
524#121C22×D4314yes—
525C4×Q8—434no—
526C4×Q8—434no—
527C4×Q8—862no—
528C4×Q8—862no—
529C4×D4—434no—
530C4×D4—434no—
531C4×D4—434no—
532C4×D4—434no—
533C4×D4—868no—
534C4×D4—862no—
535C4×D4—862no—
536C4×D4—862no—
537C4×D4—862no—
538C4×D4—868no—
539C4×D4—868no—
540#117—22no—
541#117—868no—
542#117C22×D4314yes—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C4⋊C4C22×D4311yescharacteristic
549C2×C4⋊C4C22×D4311yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C42—21no—
558C2×C42—431no—
559C2×C42—434no—
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—431no—
563C2×C42—434no—
564C2×C42—868no—
565C2×C42—861no—
566C2×C42—861no—
567#107—434no—
568#107C22×D4314yes—
569#106—434no—
570#106C22×D4314yes—
571C4⋊C8—434no—
572C4⋊C8—434no—
573#103—434no—
574#103—434no—
575#102—434no—
576#102—434no—
577#102—434no—
578#102—434no—
579#102C22×D4314yes—
580#102C22×D4314yes—
581C22⋊C8—434no—
582C22⋊C8C22×D4314yes—
583#97—434no—
584#97—434no—
585C24—21no—
586C24—861no—
587C24—861no—
588C24D4×D4311yescharacteristic
589#41—868no—
590#41—868no—
591#41—8616no—
592#41—17232no—
593C2×Q8—434no—
594C2×Q8—432no—
595C2×Q8—864no—
596C2×Q8—861no—
597C2×Q8—862no—
598C2×Q8—1724no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—44no—
604C2×D4—434no—
605C2×D4—432no—
606C2×D4—432no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—868no—
610C2×D4—864no—
611C2×D4—864no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—862no—
615C2×D4—862no—
616C2×D4—862no—
617C2×D4—1724no—
618C2×D4—1724no—
619C2×D4—1724no—
620C2×D4C23×D4312yes—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—431no—
627C22×C4—434no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—434no—
632C22×C4—864no—
633C22×C4—864no—
634C22×C4—864no—
635C22×C4—868no—
636C22×C4—864no—
637C22×C4—864no—
638C22×C4—861no—
639C22×C4—864no—
640C22×C4—861no—
641C22×C4—1724no—
642C22×C4—1724no—
643C22×C4—1724no—
644C22×C4—1722no—
645C22×C4—1724no—
646C22×C4D4×D4312yes—
647C22×C4D4×D4311yescharacteristic
648C22×C4C23×D4312yes—
649C22×C4C23×D4311yescharacteristic
650SD16—868no—
651SD16—868no—
652D8—868no—
653D8—868no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—432no—
657C2×C8—432no—
658C2×C8—862no—
659C2×C8—862no—
660C2×C8C23×D4312yes—
661C2×C8C23×D4312yes—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—432no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—864no—
669C4⋊C4—861no—
670C4⋊C4C23×D4312yes—
671C4⋊C4C23×D4312yes—
672C4⋊C4C23×D4312yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C42—24no—
681C42—434no—
682C42—434no—
683C42—432no—
684C42—432no—
685C42—432no—
686C42—432no—
687C42—864no—
688C42—864no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—864no—
697C23—862no—
698C23—862no—
699C23—1722no—
700C23—1722no—
701C23—1722no—
702C23—1722no—
703C23—1722no—
704C23C2×D4×D4312yes—
705C23C2×D4×D4311yescharacteristic
706Q8—434no—
707Q8—864no—
708Q8—862no—
709Q8—1728no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—434no—
715D4—8616no—
716D4—864no—
717D4—862no—
718D4—862no—
719D4—862no—
720D4—1728no—
721D4—1728no—
722D4—1728no—
723D4—1722no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—434no—
735C2×C4—432no—
736C2×C4—432no—
737C2×C4—432no—
738C2×C4—432no—
739C2×C4—8616no—
740C2×C4—868no—
741C2×C4—864no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—1728no—
748C2×C4—1728no—
749C2×C4—1728no—
750C2×C4—1724no—
751C2×C4—1728no—
752C2×C4—1722no—
753C2×C4C2×D4×D4312yes—
754C2×C4C2×D4×D4311yescharacteristic
755C2×C4#41×D4312yes—
756C2×C4#41×D4312yes—
757C2×C4C24×D4311yescharacteristic
758C8—22no—
759C8—22no—
760C8—862no—
761C8—862no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—44no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—864no—
771C22—3444no—
772C22—1722no—
773C22—1722no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22—1728no—
778C22#1458340712yes—
779C22AGL(1,ℤ/8)×D4312yes—
780C22#1458369612yes—
781C22C22×D4×D4311yescharacteristic
782C4—22no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—434no—
787C4—862no—
788C4—862no—
789C4—862no—
790C4—864no—
791C4—1722no—
792C4#1458340712yes—
793C4C2×#41×D4311yescharacteristic
794C4C2×#41×D4311yescharacteristic
795C2—42no—
796C2—82no—
797C2—3442no—
798C2—1724no—
799C2#1914474114yesdirect product factor
800C2C2×#1458340711yescharacteristic
801C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
802C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#482C2
socleC23×C43C22×D4
hypercenterC2×#482D43
hypocenterC43C2×#3115
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#14583444C2semidirect
2. C2×#14583367C2semidirect
3. #19144741C2direct (N × H)
4. C2×#14583223C2semidirect
5. C2×#14583183C2semidirect
6. C2×#14583178C2semidirect
7. C2×#14583098C2semidirect
8. C2×#14583093C2semidirect
9. C2×#14583046C2semidirect
10. C2×#14583042C2semidirect
11. C2×#14583010C2semidirect
12. C2×#14583008C2semidirect
13. C2×#14582998C2semidirect
14. C2×#14582996C2semidirect
15. C2×#14582953C2semidirect
16. C2×C43×#482C2semidirect
24. #14583444C22semidirect
31. #14583367C22semidirect
44. #14583223C22semidirect
45. #14583183C22semidirect
46. #14583178C22semidirect
47. #14583098C22semidirect
48. #14583093C22semidirect
49. #14583046C22semidirect
50. #14583042C22semidirect
51. #14583010C22semidirect
52. #14583008C22semidirect
53. #14582998C22semidirect
54. #14582996C22semidirect
55. #14582953C22semidirect
71. C43×#482C22semidirect
231. C2×D172#41semidirect
246. C2×Dic86#41semidirect
347. D172C2×#41semidirect
355. Dic86C2×#41semidirect
398. C2×#482D43semidirect
412. C2×C43#3115semidirect
448. #482C2×D43semidirect
478. C43C2×#3115semidirect
799. C2#19144741direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834442
C2×#145833672
#191447412
C2×#145832232
C2×#145831832
C2×#145831782
C2×#145830982
C2×#145830932
C2×#145830462
C2×#145830422
C2×#145830102
C2×#145830082
C2×#145829982
C2×#145829962
C2×#145829532
C2×C43×#4822
C2×#311543