Finite Group Databasebeta

← C2×#19144651 #25964654

Subgroups — C2×#19144651 #25964654

Order 11008.

2450 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×#14583446C211yesmaximal, characteristic, complemented
2C2×C4×#10621900C211yesmaximal, characteristic, complemented
3#19144651C2116yesmaximal, direct product factor
4C2×#14583226C211yesmaximal, characteristic, complemented
5C2×#14583222C211yesmaximal, characteristic, complemented
6C2×#14583193C211yesmaximal, characteristic, complemented
7C2×#14583187C211yesmaximal, characteristic, complemented
8C2×#14583098C211yesmaximal, characteristic, complemented
9C2×#14583092C211yesmaximal, characteristic, complemented
10C2×#14583045C211yesmaximal, characteristic, complemented
11C2×#14583041C211yesmaximal, characteristic, complemented
12C2×C4×#10621873C211yesmaximal, characteristic, complemented
13C2×C4×#10621883C211yesmaximal, characteristic, complemented
14C2×C4×#10621882C211yesmaximal, characteristic, complemented
15C2×#14582950C211yesmaximal, characteristic, complemented
16C2×C4×D8×C43C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×#10621900C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22#14583446—24no—
23#14583446C2218yescomplemented
24C2×#13063324C2211yescharacteristic
25C2×#13063321C2211yescharacteristic
26C2×#13063311—21no—
27C2×#13063300C2211yescharacteristic
28C2×#13063298—21no—
29C2×#13063296C2211yescharacteristic
30C4×#10621900—24no—
31C4×#10621900C2218yescomplemented
32C2×C4×Dic86C2211yescharacteristic
33C2×#13063290C2211yescharacteristic
34C2×C4×D172C2211yescharacteristic
35C2×D4×Dic43C2211yescharacteristic
36C2×C4×C22⋊D43—21no—
37C2×C4×C22⋊D43—21no—
38C2×(C22⋊D43)⋊C4—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063281—21no—
41C22×C4×Dic43—21no—
42C2×C42×D43C2211yescharacteristic
43#14583226C2218yescomplemented
44#14583222C2218yescomplemented
45#14583193C2218yescomplemented
46#14583187C2218yescomplemented
47#14583098C2218yescomplemented
48#14583092C2218yescomplemented
49#14583045C2218yescomplemented
50#14583041C2218yescomplemented
51C4×#10621873C2218yescomplemented
52C4×#10621883C2218yescomplemented
53C4×#10621882C2218yescomplemented
54#14582950C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C4×D8×C43C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C2×#10621900—24no—
80C2×#10621900—22no—
81C2×#10621900—24no—
82C2×#10621900C2314yes—
83C22×Dic86—21no—
84C22×Dic86C2311yescharacteristic
85C22×D172—21no—
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C23×Dic43—21no—
93C22×C4×D43—21no—
94C22×C4×D43D411yescharacteristic
95C22×C4×D43D411yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C2×#10621873—24no—
98C2×#10621873C2314yes—
99C2×#10621883—24no—
100C2×#10621883C2314yes—
101C2×#10621882—24no—
102C2×#10621882C2314yes—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105#13063324—22no—
106#13063324C2314yes—
107#13063321—22no—
108#13063321C2314yes—
109#13063311—28no—
110#13063300—22no—
111#13063300C2314yes—
112#13063298—28no—
113#13063296—22no—
114#13063296C2314yes—
115C4×Dic86—22no—
116C4×Dic86C2314yes—
117#13063290—22no—
118#13063290C2314yes—
119C4×D172—22no—
120C4×D172C2314yes—
121D4×Dic43—22no—
122D4×Dic43C2314yes—
123C4×C22⋊D43—28no—
124C4×C22⋊D43—28no—
125(C22⋊D43)⋊C4—28no—
126#13063283—22no—
127#13063283C2314yes—
128#13063281—28no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43—28no—
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43C2311yescharacteristic
146C42×D43D414yes—
147C42×D43C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151Dic43⋊C8C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063248C2314yes—
155#13063247C2314yes—
156#13063246C2314yes—
157#13063246C2314yes—
158#13063245C2314yes—
159(C2×D43)⋊C8C2314yes—
160(C2×D43)⋊C8C2314yes—
161C4×C43⋊C8C2314yes—
162C22×D4×C43C2311yescharacteristic
163C22×D4×C43C2311yescharacteristic
164C23×C4×C43—21no—
165C23×C4×C43—21no—
166C2×D8×C43—24no—
167C2×D8×C43C2314yes—
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C4×D4×C43—22no—
171C4×D4×C43—22no—
172C4×D4×C43C2314yes—
173C4×D4×C43C2314yes—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43—21no—
178C2×C42×C43C2311yescharacteristic
179#107×C43C2314yes—
180#102×C43C2314yes—
181#102×C43C2314yes—
182C4×C8×C43C2314yes—
183C24×C43—21no—
184C24×C43—21no—
185C23×D43—21no—
186C23×D43C2×D411yescharacteristic
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43#4114yescomplemented
193C2×D4×C43C2412yes—
194C2×D4×C43C2412yes—
195C22×C4×C43—24no—
196C22×C4×C43—24no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—44no—
200C22×C4×C43—44no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—28no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—44no—
210C2×C22⋊D43—44no—
211C2×C22⋊D43—44no—
212C22×Dic43—28no—
213C22×Dic43—24no—
214C22×Dic43—24no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—44no—
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222#10621900—216no—
223#10621900—28no—
224#10621900—28no—
225#10621898—432no—
226C2×D172—21no—
227C2×D172—24no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172—44no—
231C2×D172C2412yes—
232C2×C4×D43—24no—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—24no—
236C2×C4×D43—24no—
237C2×C4×D43—44no—
238C2×C4×D43C2×D412yes—
239C2×C4×D43C2×D414yes—
240C2×C4×D43C2×D414yes—
241C2×C4×D43C2412yes—
242C2×Dic86—21no—
243C2×Dic86—22no—
244C2×Dic86—24no—
245C2×Dic86—44no—
246C2×Dic86#4114yescomplemented
247C2×Dic86C2412yes—
248D8×C43—28no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43C2412yes—
252C2×C8×C43C2412yes—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C2412yes—
256C4⋊C4×C43C2412yes—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—24no—
259C42×C43C2×D412yes—
260C42×C43C2412yes—
261C22⋊Dic43—24no—
262C22⋊Dic43—24no—
263#10621883—28no—
264#10621882—28no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43C2412yes—
271C4⋊Dic43C2412yes—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275C4×Dic43—24no—
276C4×Dic43—24no—
277C4×Dic43—24no—
278C4×Dic43C2×D412yes—
279C4×Dic43C2×D414yes—
280C4×Dic43C2×D414yes—
281C4×Dic43C2412yes—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286#10621873—28no—
287C23×C43—24no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43C22×D412yes—
304D4×C43—24no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—42no—
309D4×C43C2×#4114yescomplemented
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—48no—
316C2×C4×C43—48no—
317C2×C4×C43AGL(1,ℤ/8)14yes—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D412yes—
321C2×C4×C43C2×#4112yes—
322C2×C4×C43C2×#4112yes—
323C2×C4×C43C2511yescharacteristic
324C22⋊D43—216no—
325C22⋊D43—48no—
326C22⋊D43—48no—
327C22⋊D43—48no—
328C2×Dic43—216no—
329C2×Dic43—24no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—48no—
338C2×Dic43#13514yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C2×Dic43C22×D412yes—
342D172—22no—
343D172—22no—
344D172—48no—
345D172—42no—
346C4×D43—24no—
347C4×D43—28no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—28no—
351C4×D43—48no—
352Dic86—24no—
353Dic86—22no—
354Dic86—48no—
355Dic86C2×#4114yescomplemented
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C2×#3106—431nomaximal, Sylow
361C22×C43—24no—
362C22×C43—48no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—84no—
369C22×C43#52512yes—
370C22×C43C2×#13512yes—
371C22×C43C2×AGL(1,ℤ/8)12yes—
372C22×C43C23×D411yescharacteristic
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—44no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—84no—
381C4×C43—22no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43#52512yes—
385C4×C43C2×AGL(1,ℤ/8)14yes—
386C4×C43C22×#4111yescharacteristic
387C4×C43C22×#4111yescharacteristic
388Dic43—24no—
389Dic43—22no—
390Dic43—22no—
391Dic43—42no—
392Dic43—42no—
393Dic43C2×#13514yes—
394C2×#532—431no—
395C2×C4×#41—431no—
396#3106—4316no—
397C2×#482—431no—
398C2×#482—431no—
399C2×#477—431no—
400C2×#476—431no—
401C2×#460—431no—
402C2×#459—431no—
403C2×#449—431no—
404C2×#449—431no—
405C2×C4×SD16—431no—
406C2×C4×SD16—431no—
407C2×C4×D8—431no—
408C2×C4×D8D4311yescharacteristic, complemented
409C2×#431—431no—
410C2×C43—44no—
411C2×C43—82no—
412C2×C43#310614yescomplemented
413C2×C43C2×#52511yescharacteristic
414C2×C43C22×#13511yescharacteristic
415C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
416D43—42no—
417D43—82no—
418C22×#41—431no—
419C22×#41—861no—
420C22×SD16—431no—
421C22×SD16—431no—
422C22×D8—431no—
423C22×D8C2×D4311yescharacteristic
424#532—438no—
425#532—864no—
426C2×C4⋊Q8—431no—
427C2×#127—431no—
428C2×#124—861no—
429C2×#121—431no—
430C2×#121—431no—
431C2×#121—861no—
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—861no—
439C2×C4×D4—861no—
440C2×C4×D4—861no—
441C2×C4×D4C2×D4311yescharacteristic
442C2×C4×D4C2×D4311yescharacteristic
443C2×#117—431no—
444C2×#117—861no—
445C22×C42—431no—
446C22×C42—861no—
447#482—438no—
448#482—438no—
449#477—438no—
450#476—438no—
451#460—438no—
452#459—438no—
453#449—438no—
454#449—438no—
455C4×SD16—438no—
456C4×SD16—438no—
457C4×D8—438no—
458C4×D8C2×D4318yescomplemented
459#431—438no—
460C2×#107—431no—
461C2×#107C2×D4311yescharacteristic
462C2×#106—431no—
463C2×#106—431no—
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⋊C8—431no—
476C2×C4×C8—431no—
477C2×C4×C8C2×D4311yescharacteristic
478C43C2×#310611yescharacteristic, complemented, Sylow
479C2×#41—434no—
480C2×#41—868no—
481C2×#41—862no—
482C2×#41—864no—
483C2×#41—864no—
484C2×#41—1728no—
485C22×Q8—431no—
486C22×Q8—861no—
487C22×D4—431no—
488C22×D4—861no—
489C22×D4—861no—
490C22×D4—861no—
491C22×D4—861no—
492C22×D4—861no—
493C22×D4C22×D4311yescharacteristic
494C22×D4C22×D4311yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—431no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—861no—
501C23×C4—861no—
502C23×C4—861no—
503C2×SD16—434no—
504C2×SD16—434no—
505C2×SD16—864no—
506C2×SD16—864no—
507C2×D8—24no—
508C2×D8—434no—
509C2×D8—864no—
510C2×D8C22×D4314yes—
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—434no—
521#121—434no—
522#121—868no—
523#121—862no—
524#121—862no—
525C4×Q8—434no—
526C4×Q8—434no—
527C4×Q8—862no—
528C4×Q8—862no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—434no—
532C4×D4—434no—
533C4×D4—868no—
534C4×D4—862no—
535C4×D4—868no—
536C4×D4—868no—
537C4×D4—862no—
538C4×D4C22×D4314yes—
539C4×D4C22×D4314yes—
540#117—434no—
541#117—868no—
542#117—862no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
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—431no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—434no—
561C2×C42—434no—
562C2×C42—868no—
563C2×C42—861no—
564C2×C42—861no—
565C2×C42—861no—
566C2×C42C22×D4311yescharacteristic
567#107—434no—
568#107C22×D4314yes—
569#106—434no—
570#106—434no—
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⋊C8—434no—
583C4×C8—434no—
584C4×C8C22×D4314yes—
585C24—21no—
586C24—21no—
587C24—431no—
588C24—861no—
589#41—868no—
590#41—8616no—
591#41—868no—
592#41—17232no—
593C2×Q8—434no—
594C2×Q8—432no—
595C2×Q8—864no—
596C2×Q8—861no—
597C2×Q8—862no—
598C2×Q8—1724no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—432no—
605C2×D4—864no—
606C2×D4—864no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—868no—
610C2×D4—864no—
611C2×D4—861no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—1724no—
615C2×D4—1724no—
616C2×D4—1724no—
617C2×D4—1724no—
618C2×D4#1062189814yescomplemented
619C2×D4C23×D4312yes—
620C2×D4C23×D4312yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—432no—
631C22×C4—434no—
632C22×C4—434no—
633C22×C4—432no—
634C22×C4—864no—
635C22×C4—864no—
636C22×C4—864no—
637C22×C4—868no—
638C22×C4—861no—
639C22×C4—864no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—864no—
645C22×C4—1724no—
646C22×C4—1724no—
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4C23×D4311yescharacteristic
650SD16—868no—
651SD16—868no—
652D8—28no—
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—432no—
665C4⋊C4—432no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—864no—
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—434no—
681C42—434no—
682C42—432no—
683C42—432no—
684C42—864no—
685C42—864no—
686C42—864no—
687C42D4×D4312yes—
688C42C23×D4312yes—
689C23—24no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—432no—
698C23—862no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—1722no—
703C23—1722no—
704C23—1722no—
705C23C2×D4×D4311yescharacteristic
706Q8—434no—
707Q8—864no—
708Q8—862no—
709Q8—1728no—
710D4—24no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—8616no—
716D4—862no—
717D4—862no—
718D4—1728no—
719D4—1728no—
720D4—1728no—
721D4—1728no—
722D4—1722no—
723D4C2×#1062189814yescomplemented
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—48no—
730C2×C4—48no—
731C2×C4—434no—
732C2×C4—432no—
733C2×C4—432no—
734C2×C4—432no—
735C2×C4—868no—
736C2×C4—8616no—
737C2×C4—862no—
738C2×C4—864no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—864no—
742C2×C4—868no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—1728no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4—1728no—
751C2×C4#1306334914yes—
752C2×C4C2×D4×D4312yes—
753C2×C4C2×D4×D4311yescharacteristic
754C2×C4C2×D4×D4312yes—
755C2×C4#41×D4312yes—
756C2×C4C2×#1062189812yes—
757C2×C4C24×D4311yescharacteristic
758C8—22no—
759C8—22no—
760C8—862no—
761C8—862no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—48no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—862no—
771C22—862no—
772C22—862no—
773C22—3444no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22—1724no—
778C22#1458340812yes—
779C22#135×D4312yes—
780C22C2×#1306334912yes—
781C22C22×D4×D4311yescharacteristic
782C4—22no—
783C4—42no—
784C4—42no—
785C4—434no—
786C4—862no—
787C4—862no—
788C4—864no—
789C4—1722no—
790C4—1722no—
791C4#1458340812yes—
792C4C2×#1306334914yes—
793C4C2×#41×D4311yescharacteristic
794C4C22×#1062189811yescharacteristic
795C2—44no—
796C2—82no—
797C2—3442no—
798C2—1722no—
799C2#1914465114yesdirect product factor
800C2C2×#1458340811yescharacteristic
801C2C2×#135×D4311yescharacteristic
802C2C22×#1306334911yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
hypercenterC2×C4×D8D43
hypocenterC43C2×#3106
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583446C2semidirect
2. C2×C4×#10621900C2semidirect
3. #19144651C2direct (N × H)
4. C2×#14583226C2semidirect
5. C2×#14583222C2semidirect
6. C2×#14583193C2semidirect
7. C2×#14583187C2semidirect
8. C2×#14583098C2semidirect
9. C2×#14583092C2semidirect
10. C2×#14583045C2semidirect
11. C2×#14583041C2semidirect
12. C2×C4×#10621873C2semidirect
13. C2×C4×#10621883C2semidirect
14. C2×C4×#10621882C2semidirect
15. C2×#14582950C2semidirect
16. C2×C4×D8×C43C2semidirect
23. #14583446C22semidirect
31. C4×#10621900C22semidirect
43. #14583226C22semidirect
44. #14583222C22semidirect
45. #14583193C22semidirect
46. #14583187C22semidirect
47. #14583098C22semidirect
48. #14583092C22semidirect
49. #14583045C22semidirect
50. #14583041C22semidirect
51. C4×#10621873C22semidirect
52. C4×#10621883C22semidirect
53. C4×#10621882C22semidirect
54. #14582950C22semidirect
72. C4×D8×C43C22semidirect
192. C2×D4×C43#41semidirect
246. C2×Dic86#41semidirect
309. D4×C43C2×#41semidirect
355. Dic86C2×#41semidirect
408. C2×C4×D8D43semidirect
412. C2×C43#3106semidirect
458. C4×D8C2×D43semidirect
478. C43C2×#3106semidirect
618. C2×D4#10621898semidirect
723. D4C2×#10621898semidirect
799. C2#19144651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834462
C2×C4×#106219002
#191446512
C2×#145832262
C2×#145832222
C2×#145831932
C2×#145831872
C2×#145830982
C2×#145830922
C2×#145830452
C2×#145830412
C2×C4×#106218732
C2×C4×#106218832
C2×C4×#106218822
C2×#145829502
C2×C4×D8×C432
C2×#310643