Finite Group Databasebeta

← C2×#19145950 #25969434

Subgroups — C2×#19145950 #25969434

Order 11008.

2178 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583444C211yesmaximal, characteristic, complemented
2C2×#14583430C211yesmaximal, characteristic, complemented
3#19145950C2116yesmaximal, direct product factor
4C2×#14583183C211yesmaximal, characteristic, complemented
5C2×#14583198C211yesmaximal, characteristic, complemented
6C2×#14583197C211yesmaximal, characteristic, complemented
7C2×#14583177C211yesmaximal, characteristic, complemented
8C2×#14583150C211yesmaximal, characteristic, complemented
9C2×#14583145C211yesmaximal, characteristic, complemented
10C2×#14583143C211yesmaximal, characteristic, complemented
11C2×#14583098C211yesmaximal, characteristic, complemented
12C2×#14583113C211yesmaximal, characteristic, complemented
13C2×#14583112C211yesmaximal, characteristic, complemented
14C2×#14583092C211yesmaximal, characteristic, complemented
15C2×#14582922C211yesmaximal, characteristic, complemented
16C2×C43×#469C211yesmaximal, characteristic, complemented
17C22×#10621900—21no—
18C22×#10621873C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22#14583444—24no—
23#14583444C2218yescomplemented
24C2×#13063324C2211yescharacteristic
25C2×#13063321C2211yescharacteristic
26#14583430—24no—
27#14583430C2218yescomplemented
28C2×#13063318—21no—
29C2×#13063316C2211yescharacteristic
30C2×#13063312C2211yescharacteristic
31C2×#13063311—21no—
32C2×#13063306—21no—
33C2×#13063304C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35C2×#13063297—21no—
36C2×#13063290C2211yescharacteristic
37C2×D4×Dic43—21no—
38C2×D4×Dic43C2211yescharacteristic
39C2×D4×Dic43C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×(C22⋊D43)⋊C4—21no—
42C2×#13063281—21no—
43C22×C4×Dic43C2211yescharacteristic
44#14583198C2218yescomplemented
45#14583197C2218yescomplemented
46#14583183C2218yescomplemented
47#14583177C2218yescomplemented
48#14583150C2218yescomplemented
49#14583145C2218yescomplemented
50#14583143C2218yescomplemented
51#14583113C2218yescomplemented
52#14583112C2218yescomplemented
53#14583098C2218yescomplemented
54#14583092C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58#14582922C2218yescomplemented
59C2×Dic43⋊C8C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×#13063246C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C2×#121×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#469C2218yescomplemented
74C2×#106×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—28no—
78C2×#10621900—48no—
79C22×Dic86—21no—
80C22×Dic86C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C23×Dic43—21no—
86C23×Dic43—21no—
87C23×Dic43D411yescharacteristic
88C23×Dic43D411yescharacteristic
89C22×C4×D43—21no—
90C2×#10621873—42no—
91C2×#10621873C2314yes—
92C2×#10621883—42no—
93C2×#10621883C2314yes—
94C2×#10621882—42no—
95C2×#10621882C2314yes—
96C2×#10621877—42no—
97C2×#10621877C2314yes—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100#13063324—22no—
101#13063324C2314yes—
102#13063321—22no—
103#13063321C2314yes—
104#13063318—28no—
105#13063316—22no—
106#13063316C2314yes—
107#13063312—22no—
108#13063312C2314yes—
109#13063311—28no—
110#13063306—28no—
111#13063304—22no—
112#13063304C2314yes—
113#13063299—22no—
114#13063299C2314yes—
115#13063297—28no—
116#13063290—22no—
117#13063290C2314yes—
118D4×Dic43—28no—
119D4×Dic43—22no—
120D4×Dic43—22no—
121D4×Dic43C2314yes—
122D4×Dic43C2314yes—
123#13063287—22no—
124#13063287C2314yes—
125(C22⋊D43)⋊C4—28no—
126#13063281—28no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D414yes—
145C2×C4×Dic43C2311yescharacteristic
146C2×C4×Dic43C2311yescharacteristic
147C2×C4×Dic43C2314yes—
148#13063259C2314yes—
149#13063258C2314yes—
150#13063256C2314yes—
151Dic43⋊C8C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154Dic43⋊C8C2314yes—
155#13063250C2314yes—
156#13063248C2314yes—
157#13063247C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160#13063245C2314yes—
161C22×D4×C43—21no—
162C22×D4×C43—21no—
163C22×D4×C43C2311yescharacteristic
164C22×D4×C43C2311yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C2×D8×C43—42no—
167C2×D8×C43C2314yes—
168C2×M16×C43—42no—
169C2×M16×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172#121×C43—22no—
173#121×C43—22no—
174#121×C43C2314yes—
175#121×C43C2314yes—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180#106×C43C2314yes—
181#102×C43C2314yes—
182#102×C43C2314yes—
183C24×C43—21no—
184C24×C43—21no—
185C24×C43C2×D411yescharacteristic
186C23×D43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—24no—
190C2×D4×C43—24no—
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—44no—
196C2×D4×C43—44no—
197C2×D4×C43C2412yes—
198C2×D4×C43C2412yes—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—44no—
211C2×C22⋊D43—44no—
212C2×C22⋊D43—44no—
213C22×Dic43—24no—
214C22×Dic43—24no—
215C22×Dic43—24no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—42no—
220C22×Dic43—44no—
221C22×Dic43—44no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D414yes—
226C22×Dic43C2×D414yes—
227C22×Dic43C2×D411yescharacteristic
228#10621900—432no—
229C2×D172—21no—
230C2×D172—22no—
231C2×D172—22no—
232C2×D172C2412yes—
233C2×C4×D43—24no—
234C2×C4×D43—44no—
235C2×Dic86—22no—
236C2×Dic86—22no—
237C2×Dic86—21no—
238C2×Dic86—24no—
239C2×Dic86—44no—
240C2×Dic86C2412yes—
241D8×C43—44no—
242M16×C43—44no—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C2×C8×C43C2412yes—
246C2×C8×C43C2412yes—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43C2412yes—
250C4⋊C4×C43C2412yes—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—24no—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257C22⋊Dic43—24no—
258#10621883—44no—
259#10621882—44no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—24no—
265C4⋊Dic43C2412yes—
266C4⋊Dic43C2412yes—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271C4×Dic43—24no—
272C4×Dic43C2×D414yes—
273C4×Dic43C2×D414yes—
274C4×Dic43C2×D412yes—
275C4×Dic43C2×D412yes—
276C4×Dic43C2412yes—
277C4×Dic43C2412yes—
278#10621877—44no—
279C2×C43⋊C8—22no—
280C2×C43⋊C8—22no—
281C2×C43⋊C8C2412yes—
282C2×C43⋊C8C2412yes—
283#10621873—44no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43C22×D412yes—
296C23×C43C22×D411yescharacteristic
297C22×D43—22no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—22no—
305D4×C43—48no—
306D4×C43—48no—
307D4×C43—42no—
308D4×C43—42no—
309C2×C4×C43—22no—
310C2×C4×C43—24no—
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×C43C22×D412yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43H(5,𝔽2)12yes—
320C2×C4×C432−1+412yes—
321C2×C4×C43C2511yescharacteristic
322C22⋊D43—48no—
323C22⋊D43—48no—
324C22⋊D43—48no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—28no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—44no—
333C2×Dic43—48no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—48no—
338C2×Dic43AGL(1,ℤ/8)14yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C2×Dic43C22×D412yes—
342C2×Dic43C22×D412yes—
343D172—22no—
344D172—22no—
345D172—42no—
346C4×D43—48no—
347Dic86—22no—
348Dic86—22no—
349Dic86—42no—
350Dic86—48no—
351C8×C43—22no—
352C8×C43—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C2×#3251—431nomaximal, Sylow
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—44no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—84no—
367C22×C43—84no—
368C22×C43#53712yes—
369C22×C43C2×AGL(1,ℤ/8)12yes—
370C22×C43#57512yes—
371C22×C43C23×D411yescharacteristic
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—84no—
376C4×C43—22no—
377C4×C43—42no—
378C4×C43—42no—
379C4×C43#53712yes—
380C4×C43C2×H(5,𝔽2)11yescharacteristic
381C4×C43C2×2−1+411yescharacteristic
382Dic43—22no—
383Dic43—22no—
384Dic43—22no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388Dic43C2×AGL(1,ℤ/8)14yes—
389C2×#532—431no—
390C2×#529—431no—
391#3251—4316no—
392C2×#475—431no—
393C2×#478—431no—
394C2×#478—431no—
395C2×#474—431no—
396C2×#469—431no—
397C2×#469D4311yescharacteristic, complemented
398C2×#468—431no—
399C2×#468—431no—
400C2×#460—431no—
401C2×#463—431no—
402C2×#463—431no—
403C2×#459—431no—
404C2×#423—431no—
405C2×C43—42no—
406C2×C43—82no—
407C2×C43—82no—
408C2×C43#325114yescomplemented
409C2×C43C2×#53711yescharacteristic
410C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
411C2×C43C2×#57511yescharacteristic
412D43—82no—
413C22×#41—861no—
414C22×SD16—431no—
415C22×SD16—431no—
416C22×D8—431no—
417C22×D8C2×D4311yescharacteristic
418C22×M16—431no—
419C22×M16C2×D4311yescharacteristic
420#532—438no—
421#532—864no—
422C2×C4⋊Q8—431no—
423C2×#127—431no—
424#529—438no—
425#529—864no—
426C2×#126—861no—
427C2×#125—431no—
428C2×#124—431no—
429C2×#124—861no—
430C2×#123—861no—
431C2×C22⋊Q8—431no—
432C2×#121—431no—
433C2×#121—861no—
434C2×#121C2×D4311yescharacteristic
435C2×#121C2×D4311yescharacteristic
436C2×C4×Q8—431no—
437C2×C4×D4—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—861no—
441C2×C4×D4—861no—
442C2×#117—861no—
443C22×C42—431no—
444#478—438no—
445#478—438no—
446#475—438no—
447#474—438no—
448#469—438no—
449#469C2×D4318yescomplemented
450#468—438no—
451#468—438no—
452#463—438no—
453#463—438no—
454#460—438no—
455#459—438no—
456C2×#107—431no—
457C2×#107—431no—
458C2×#106—431no—
459C2×#106C2×D4311yescharacteristic
460#423—438no—
461C2×C4⋊C8—431no—
462C2×C4⋊C8—431no—
463C2×C4⋊C8—431no—
464C2×C4⋊C8—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102C2×D4311yescharacteristic
472C2×#102C2×D4311yescharacteristic
473C43C2×#325111yescharacteristic, complemented, Sylow
474C2×#41—868no—
475C2×#41—1728no—
476C22×Q8—431no—
477C22×Q8—861no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—431no—
481C22×D4—861no—
482C22×D4—861no—
483C22×D4—861no—
484C22×D4C22×D4311yescharacteristic
485C22×D4C22×D4311yescharacteristic
486C23×C4—431no—
487C23×C4—431no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492C2×SD16—434no—
493C2×SD16—434no—
494C2×SD16—1722no—
495C2×SD16—1722no—
496C2×D8—42no—
497C2×D8—434no—
498C2×D8—1722no—
499C2×D8C22×D4314yes—
500C2×M16—42no—
501C2×M16—434no—
502C2×M16—1722no—
503C2×M16C22×D4314yes—
504C22×C8—431no—
505C22×C8—431no—
506C22×C8C22×D4311yescharacteristic
507C22×C8C22×D4311yescharacteristic
508C4⋊Q8—434no—
509C4⋊Q8—862no—
510#127—434no—
511#127—862no—
512#126—868no—
513#125—434no—
514#125—862no—
515#124—434no—
516#124—868no—
517#124—862no—
518#123—868no—
519C22⋊Q8—434no—
520C22⋊Q8—862no—
521#121—22no—
522#121—22no—
523#121—434no—
524#121—868no—
525#121—862no—
526#121C22×D4314yes—
527#121C22×D4314yes—
528C4×Q8—434no—
529C4×Q8—862no—
530C4×D4—434no—
531C4×D4—434no—
532C4×D4—434no—
533C4×D4—868no—
534C4×D4—862no—
535C4×D4—862no—
536C4×D4—862no—
537C4×D4—868no—
538#117—868no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
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—434no—
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—434no—
563C2×C42—861no—
564#107—434no—
565#107—434no—
566#106—434no—
567#106C22×D4314yes—
568C4⋊C8—434no—
569C4⋊C8—434no—
570C4⋊C8—434no—
571C4⋊C8—434no—
572#103—434no—
573#103—434no—
574#102—434no—
575#102—434no—
576#102—434no—
577#102—434no—
578#102C22×D4314yes—
579#102C22×D4314yes—
580C24—21no—
581C24—21no—
582C24—861no—
583C24D4×D4311yescharacteristic
584#41—17232no—
585C2×Q8—432no—
586C2×Q8—864no—
587C2×Q8—861no—
588C2×Q8—862no—
589C2×Q8—862no—
590C2×Q8—1724no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—432no—
602C2×D4—864no—
603C2×D4—864no—
604C2×D4—864no—
605C2×D4—861no—
606C2×D4—862no—
607C2×D4—862no—
608C2×D4—1724no—
609C2×D4—1724no—
610C2×D4—1724no—
611C2×D4C23×D4312yes—
612C2×D4C23×D4312yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—431no—
618C22×C4—434no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—434no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—864no—
626C22×C4—864no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—1724no—
631C22×C4—1724no—
632C22×C4—1722no—
633C22×C4—1724no—
634C22×C4D4×D4312yes—
635C22×C4D4×D4311yescharacteristic
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638SD16—1724no—
639SD16—1724no—
640D8—44no—
641D8—1724no—
642M16—44no—
643M16—1724no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—432no—
647C2×C8—432no—
648C2×C8—862no—
649C2×C8—862no—
650C2×C8C23×D4312yes—
651C2×C8C23×D4312yes—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—432no—
655C4⋊C4—432no—
656C4⋊C4—864no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—864no—
663C4⋊C4C23×D4312yes—
664C4⋊C4C23×D4312yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C42—434no—
675C42—432no—
676C42—434no—
677C42—432no—
678C42—432no—
679C42—432no—
680C42—864no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—862no—
693C23—1722no—
694C23—1722no—
695C23—1722no—
696C23C2×D4×D4312yes—
697C23C2×D4×D4311yescharacteristic
698Q8—862no—
699Q8—862no—
700Q8—1728no—
701Q8—1722no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—48no—
707D4—48no—
708D4—42no—
709D4—42no—
710D4—862no—
711D4—862no—
712D4—1728no—
713D4—1728no—
714D4—1728no—
715D4—1722no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—434no—
725C2×C4—432no—
726C2×C4—432no—
727C2×C4—432no—
728C2×C4—432no—
729C2×C4—868no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—1728no—
737C2×C4—1728no—
738C2×C4—1724no—
739C2×C4—1728no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4C2×D4×D4312yes—
744C2×C4C2×D4×D4311yescharacteristic
745C2×C4#1306337012yes—
746C2×C4#1306337212yes—
747C2×C4C24×D4311yescharacteristic
748C8—22no—
749C8—22no—
750C8—862no—
751C8—862no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—84no—
763C22—84no—
764C22—3444no—
765C22—1722no—
766C22—1722no—
767C22—1722no—
768C22#1458347612yes—
769C22AGL(1,ℤ/8)×D4312yes—
770C22#1458369512yes—
771C22C22×D4×D4311yescharacteristic
772C4—22no—
773C4—42no—
774C4—42no—
775C4—434no—
776C4—862no—
777C4—862no—
778C4—862no—
779C4—1722no—
780C4—1722no—
781C4—1722no—
782C4#1458347612yes—
783C4C2×#1306337011yescharacteristic
784C4C2×#1306337211yescharacteristic
785C2—42no—
786C2—82no—
787C2—82no—
788C2—3442no—
789C2#1914595014yesdirect product factor
790C2C2×#1458347611yescharacteristic
791C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
792C2C2×#1458369511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#469C2
socleC23×C43C22×D4
hypercenterC2×#469D43
hypocenterC43C2×#3251
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#14583444C2semidirect
2. C2×#14583430C2semidirect
3. #19145950C2direct (N × H)
4. C2×#14583183C2semidirect
5. C2×#14583198C2semidirect
6. C2×#14583197C2semidirect
7. C2×#14583177C2semidirect
8. C2×#14583150C2semidirect
9. C2×#14583145C2semidirect
10. C2×#14583143C2semidirect
11. C2×#14583098C2semidirect
12. C2×#14583113C2semidirect
13. C2×#14583112C2semidirect
14. C2×#14583092C2semidirect
15. C2×#14582922C2semidirect
16. C2×C43×#469C2semidirect
23. #14583444C22semidirect
27. #14583430C22semidirect
44. #14583198C22semidirect
45. #14583197C22semidirect
46. #14583183C22semidirect
47. #14583177C22semidirect
48. #14583150C22semidirect
49. #14583145C22semidirect
50. #14583143C22semidirect
51. #14583113C22semidirect
52. #14583112C22semidirect
53. #14583098C22semidirect
54. #14583092C22semidirect
58. #14582922C22semidirect
73. C43×#469C22semidirect
397. C2×#469D43semidirect
408. C2×C43#3251semidirect
449. #469C2×D43semidirect
473. C43C2×#3251semidirect
789. C2#19145950direct (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×#145834302
#191459502
C2×#145831832
C2×#145831982
C2×#145831972
C2×#145831772
C2×#145831502
C2×#145831452
C2×#145831432
C2×#145830982
C2×#145831132
C2×#145831122
C2×#145830922
C2×#145829222
C2×C43×#4692
C2×#325143