Finite Group Databasebeta

← C2×#19146638 #25973274

Subgroups — C2×#19146638 #25973274

Order 11008.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583622C211yesmaximal, characteristic, complemented
2C2×#14583542C211yesmaximal, characteristic
3#19146638C2116yesmaximal, direct product factor
4C2×#14583258C211yesmaximal, characteristic, complemented
5C2×#14583238C211yesmaximal, characteristic, complemented
6C2×#14583222C211yesmaximal, characteristic, complemented
7C2×#14583190C211yesmaximal, characteristic, complemented
8C2×#14583154C211yesmaximal, characteristic, complemented
9C2×#14583125C211yesmaximal, characteristic, complemented
10C2×#14583060C211yesmaximal, characteristic, complemented
11C2×#14583048C211yesmaximal, characteristic, complemented
12C2×#14582997C211yesmaximal, characteristic, complemented
13C2×#14582969C211yesmaximal, characteristic, complemented
14C2×#14582902C211yesmaximal, characteristic, complemented
15C2×#14582894C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic, complemented
22#14583622—24no—
23#14583622C2218yescomplemented
24#14583542—24no—
25#14583542C2218yes—
26C2×#13063325C2211yescharacteristic, complemented
27C2×#13063320—21no—
28C2×#13063320—21no—
29C2×#13063313—21no—
30C2×#13063307—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063301C2211yescharacteristic
33C2×#13063301C2211yescharacteristic, complemented
34C2×#13063298—21no—
35C2×#13063296C2211yescharacteristic
36C2×#13063295—21no—
37C2×C4×Dic86—21no—
38C2×C4×D172C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×#13063283C2211yescharacteristic, complemented
42C2×C22⋊C4×D43—21no—
43#14583258C2218yescomplemented
44#14583238C2218yescomplemented
45#14583222C2218yescomplemented
46#14583190C2218yescomplemented
47#14583154C2218yescomplemented
48#14583125C2218yescomplemented
49#14583060C2218yescomplemented
50#14583048C2218yescomplemented
51#14582997C2218yescomplemented
52#14582969C2218yescomplemented
53C2×#13063258C2211yescharacteristic, complemented
54C2×#13063257C2211yescharacteristic, complemented
55C2×#13063257C2211yescharacteristic, complemented
56#14582902C2218yescomplemented
57#14582894C2218yescomplemented
58C2×#13063249C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063249C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×#13063236C2211yescharacteristic, complemented
69C22×Q16×C43C2211yescharacteristic, complemented
70C22×SD16×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic, complemented
73C43×#464C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—24no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C22×Dic86—21no—
83C22×D172—21no—
84C22×D172D411yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C2×D4×D43—24no—
89C2×D4×D43—22no—
90C2×D4×D43—42no—
91C2×D4×D43C2314yes—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95C22×C4×D43C2311yescharacteristic
96C2×#10621884—24no—
97C2×#10621884C2314yes—
98C2×#10621872—42no—
99C2×#10621872C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—42no—
103C2×C8×D43C2314yescomplemented
104#13063325—22no—
105#13063325C2314yescomplemented
106#13063320—28no—
107#13063320—28no—
108#13063313—28no—
109#13063307—28no—
110#13063301—22no—
111#13063301—22no—
112#13063301—22no—
113#13063301C2314yes—
114#13063301C2314yes—
115#13063301C2314yescomplemented
116#13063298—28no—
117#13063296—22no—
118#13063296C2314yes—
119#13063295—28no—
120C4×Dic86—28no—
121C4×D172—22no—
122C4×D172D414yes—
123C4×D172C2314yes—
124C4×D172C2314yes—
125#13063283—22no—
126#13063283—22no—
127#13063283C2314yes—
128#13063283C2314yescomplemented
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43D411yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×C22⋊Dic43—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×(C2×D43)⋊C4D411yescharacteristic
146C22⋊C4×D43—28no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43—21no—
149#13063258C2314yescomplemented
150#13063257C2314yescomplemented
151#13063257C2314yescomplemented
152#13063249C2314yescomplemented
153#13063249C2314yescomplemented
154#13063249C2314yescomplemented
155#13063247C2314yes—
156#13063247C2314yes—
157#13063246C2314yes—
158#13063246C2314yes—
159#13063245C2314yes—
160(C2×D43)⋊C8C2314yes—
161(C2×D43)⋊C8C2314yescomplemented
162#13063236C2314yescomplemented
163C22×Q8×C43C2311yescharacteristic
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C2×Q16×C43—42no—
167C2×Q16×C43C2314yescomplemented
168C2×SD16×C43—42no—
169C2×SD16×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172#124×C43—22no—
173#124×C43C2314yes—
174C4×Q8×C43—22no—
175C4×Q8×C43C2314yescomplemented
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C42×C43—21no—
181C2×C42×C43C2311yescharacteristic
182C4⋊C8×C43C2314yescomplemented
183#103×C43C2314yescomplemented
184#102×C43C2314yes—
185C24×C43—21no—
186C23×D43—21no—
187C23×D43—24no—
188C23×D43—44no—
189C23×D43—44no—
190C23×D43—82no—
191C23×D43C2×D411yescharacteristic
192C23×D43C2×D411yescharacteristic
193C2×Q8×C43—21no—
194C2×Q8×C43—21no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43C2412yes—
200C2×Q8×C43C2412yes—
201C2×D4×C43—21no—
202C2×D4×C43—22no—
203C2×D4×C43—22no—
204C2×D4×C43C2412yes—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2411yescharacteristic
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—82no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220#10621902—28no—
221#10621902—44no—
222#10621902—48no—
223D4×D43—28no—
224D4×D43—44no—
225D4×D43—48no—
226C2×D172—21no—
227C2×D172—22no—
228C2×D172—24no—
229C2×D172—42no—
230C2×D172—44no—
231C2×D172C2×D414yes—
232C2×D172#4114yes—
233C2×D172C2412yes—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—44no—
241C2×C4×D43—82no—
242C2×C4×D43C2×D412yes—
243C2×C4×D43C2×D412yes—
244C2×C4×D43C2412yes—
245C2×C4×D43C2412yes—
246C2×Dic86—24no—
247C2×Dic86—44no—
248Q16×C43—44no—
249SD16×C43—44no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2412yes—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—24no—
259C42×C43—24no—
260C42×C43C2×D412yes—
261C42×C43C2412yes—
262C22⋊Dic43—24no—
263#10621884—28no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4C2×D414yes—
271(C2×D43)⋊C4C2×D414yes—
272C4⋊Dic43—24no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43C2×D414yes—
277C4⋊Dic43C2412yes—
278C4⋊Dic43C2412yes—
279C4⋊Dic43C2412yes—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283C4×Dic43—24no—
284C4×Dic43—24no—
285C2×C43⋊C8—22no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289#10621872—44no—
290C8×D43—44no—
291C23×C43—22no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—24no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—48no—
305C22×D43—48no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—84no—
309C22×D43—816no—
310C22×D43C22×D412yes—
311C22×D43C22×D412yes—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—42no—
317Q8×C43—42no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—42no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43C22×D412yes—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4112yes—
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43C2511yescharacteristic
335C22⋊D43—48no—
336C22⋊D43—84no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43C22×D412yes—
346C2×Dic43C22×D412yes—
347D172—24no—
348D172—22no—
349D172—44no—
350D172—48no—
351D172C2×#4114yes—
352C4×D43—24no—
353C4×D43—24no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—48no—
359C4×D43—84no—
360Dic86—48no—
361C8×C43—22no—
362C8×C43—22no—
363C43⋊C8—22no—
364C43⋊C8—22no—
365C2×#3311—431nomaximal, Sylow
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—84no—
370C22×C43#54612yes—
371C22×C43#57512yes—
372C22×C43#57712yes—
373C22×C43C23×D411yescharacteristic
374C2×D43—24no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—44no—
382C2×D43—44no—
383C2×D43—48no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—816no—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43#54612yes—
393C4×C43C22×#4111yescharacteristic
394C4×C43C2×H(5,𝔽2)11yescharacteristic
395Dic43—22no—
396Dic43—22no—
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400C2×#556—431no—
401C2×#546—431no—
402#3311—4316no—
403C2×#489—431no—
404C2×#485—431no—
405C2×#482—431no—
406C2×#476—431no—
407C2×#470—431no—
408C2×#465—431no—
409C2×#464D4311yescharacteristic, complemented
410C2×#452—431no—
411C2×#450—431no—
412C2×#440—431no—
413C2×#435—431no—
414C2×#418—431no—
415C2×#416—431no—
416C2×C43—82no—
417C2×C43#331114yescomplemented
418C2×C43C2×#54611yescharacteristic
419C2×C43C2×#57511yescharacteristic
420C2×C43C2×#57711yescharacteristic
421D43—42no—
422D43—42no—
423D43—44no—
424C22×#41—431no—
425C23×D4—431no—
426C22×Q16C2×D4311yescharacteristic, complemented
427C22×SD16—431no—
428C22×SD16C2×D4311yescharacteristic
429C22×M16—431no—
430C23×C8—431no—
431#556—438no—
432#556—864no—
433#546—438no—
434#546—864no—
435C2×C4⋊Q8—431no—
436C2×#126—861no—
437C2×#126—861no—
438C2×#124—861no—
439C2×#124C2×D4311yescharacteristic
440C2×#123—861no—
441C2×C22⋊Q8—431no—
442C2×C22⋊Q8—431no—
443C2×C22⋊Q8—431no—
444C2×#121—431no—
445C2×#121—861no—
446C2×#120—861no—
447C2×C4×Q8—861no—
448C2×C4×Q8C2×D4311yescharacteristic, complemented
449C2×C4×D4—431no—
450C2×C4×D4—431no—
451C2×#117—431no—
452C2×#117—431no—
453C22×C22⋊C4—861no—
454#489—438no—
455#485—438no—
456#482—438no—
457#476—438no—
458#470—438no—
459#465—438no—
460#464C2×D4318yescomplemented
461#452—438no—
462#450—438no—
463#440—438no—
464#435—438no—
465C2×#107—431no—
466C2×#106—431no—
467C2×#106—431no—
468C2×C4⋊C8C2×D4311yescharacteristic, complemented
469#418—438no—
470#416—438no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103C2×D4311yescharacteristic, complemented
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102C2×D4311yescharacteristic
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×#97—431no—
484C43C2×#331111yescharacteristic, complemented, Sylow
485C25—861no—
486C2×#41—434no—
487C2×#41—862no—
488C2×#41—864no—
489C2×#41—1722no—
490C22×Q8—861no—
491C22×Q8C22×D4311yescharacteristic
492C22×Q8C22×D4311yescharacteristic
493C22×D4—434no—
494C22×D4—431no—
495C22×D4—431no—
496C22×D4—861no—
497C22×D4—862no—
498C22×D4—861no—
499C22×D4—864no—
500C22×D4—861no—
501C22×D4—1722no—
502C22×D4C22×D4311yescharacteristic
503C23×C4—431no—
504C23×C4—431no—
505C23×C4—861no—
506C23×C4—861no—
507C2×Q16—42no—
508C2×Q16C22×D4314yescomplemented
509C2×SD16—42no—
510C2×SD16—434no—
511C2×SD16—864no—
512C2×SD16C22×D4314yes—
513C2×M16—434no—
514C2×M16—1722no—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8—434no—
518C22×C8—1722no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521C4⋊Q8—434no—
522C4⋊Q8—862no—
523#126—868no—
524#126—868no—
525#124—22no—
526#124—868no—
527#124C22×D4314yes—
528#123—868no—
529C22⋊Q8—434no—
530C22⋊Q8—434no—
531C22⋊Q8—434no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534C22⋊Q8—862no—
535#121—434no—
536#121—868no—
537#121—862no—
538#120—868no—
539C4×Q8—22no—
540C4×Q8—868no—
541C4×Q8C22×D4314yescomplemented
542C4×D4—434no—
543C4×D4—434no—
544C4×D4—434no—
545C4×D4—862no—
546#117—434no—
547#117—434no—
548#117—862no—
549#117—862no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4C22×D4311yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—431no—
563C2×C22⋊C4—431no—
564C2×C22⋊C4—868no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C42—21no—
573C2×C42—861no—
574C2×C42—861no—
575C2×C42C22×D4311yescharacteristic
576#107—434no—
577#106—434no—
578#106—434no—
579C4⋊C8C22×D4314yescomplemented
580#103—434no—
581#103—434no—
582#103—434no—
583#103C22×D4314yescomplemented
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588#102—434no—
589#102C22×D4314yes—
590C22⋊C8—434no—
591C22⋊C8—434no—
592#97—434no—
593C24—21no—
594C24—431no—
595C24—431no—
596C24—864no—
597C24—861no—
598C24—3442no—
599C24—1724no—
600C24—1724no—
601#41—868no—
602#41—1724no—
603#41—1728no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—864no—
611C2×Q8—1724no—
612C2×Q8C23×D4312yes—
613C2×Q8C23×D4312yes—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—434no—
618C2×D4—434no—
619C2×D4—432no—
620C2×D4—864no—
621C2×D4—864no—
622C2×D4—868no—
623C2×D4—864no—
624C2×D4—861no—
625C2×D4—862no—
626C2×D4—3442no—
627C2×D4—1722no—
628C2×D4—1724no—
629C2×D4—1724no—
630C2×D4—1728no—
631C2×D4—1724no—
632C2×D4C23×D4312yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—432no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—864no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—864no—
651C22×C4—3442no—
652C22×C4—1724no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656Q16—44no—
657SD16—44no—
658SD16—868no—
659M16—1724no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—862no—
665C2×C8—862no—
666C2×C8—1724no—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—434no—
672C4⋊C4—432no—
673C4⋊C4—432no—
674C4⋊C4—432no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—864no—
682C4⋊C4C23×D4312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—434no—
686C22⋊C4—434no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C42—24no—
695C42—864no—
696C42—864no—
697C42D4×D4312yes—
698C42C23×D4312yes—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—432no—
704C23—432no—
705C23—862no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—862no—
712C23—864no—
713C23—3444no—
714C23—34416no—
715C23—1728no—
716C23—1728no—
717C23—1722no—
718C23—1722no—
719C23C2×D4×D4311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726Q8—1728no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—434no—
731D4—862no—
732D4—864no—
733D4—3444no—
734D4—1724no—
735D4—1728no—
736D4—1728no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—432no—
746C2×C4—432no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—864no—
754C2×C4—864no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—3444no—
759C2×C4—1728no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4C2×D4×D4312yes—
764C2×C4C2×D4×D4312yes—
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4#41×D4312yes—
767C2×C4#1306337012yes—
768C2×C4C24×D4311yescharacteristic
769C8—22no—
770C8—22no—
771C8—862no—
772C8—862no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—862no—
778C22—862no—
779C22—864no—
780C22—862no—
781C22—862no—
782C22—862no—
783C22—862no—
784C22—34416no—
785C22—1722no—
786C22—1722no—
787C22—1724no—
788C22—1724no—
789C22—1728no—
790C22#1458354612yes—
791C22#1458369812yes—
792C22#1458370612yes—
793C22C22×D4×D4311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—862no—
800C4—862no—
801C4—1722no—
802C4—1722no—
803C4—1722no—
804C4#1458354612yes—
805C4C2×#41×D4311yescharacteristic
806C4C2×#1306337011yescharacteristic
807C2—82no—
808C2—1722no—
809C2—1722no—
810C2—1724no—
811C2#1914663814yesdirect product factor
812C2C2×#1458354611yescharacteristic
813C2C2×#1458369811yescharacteristic
814C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#14583542C2
hypercenterC2×#464D43
hypocenterC43C2×#3311
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#14583622C2semidirect
3. #19146638C2direct (N × H)
4. C2×#14583258C2semidirect
5. C2×#14583238C2semidirect
6. C2×#14583222C2semidirect
7. C2×#14583190C2semidirect
8. C2×#14583154C2semidirect
9. C2×#14583125C2semidirect
10. C2×#14583060C2semidirect
11. C2×#14583048C2semidirect
12. C2×#14582997C2semidirect
13. C2×#14582969C2semidirect
14. C2×#14582902C2semidirect
15. C2×#14582894C2semidirect
16. C2×C43×#464C2semidirect
21. C22×C8×D43C22semidirect
23. #14583622C22semidirect
26. C2×#13063325C22semidirect
33. C2×#13063301C22semidirect
41. C2×#13063283C22semidirect
43. #14583258C22semidirect
44. #14583238C22semidirect
45. #14583222C22semidirect
46. #14583190C22semidirect
47. #14583154C22semidirect
48. #14583125C22semidirect
49. #14583060C22semidirect
50. #14583048C22semidirect
51. #14582997C22semidirect
52. #14582969C22semidirect
53. C2×#13063258C22semidirect
54. C2×#13063257C22semidirect
55. C2×#13063257C22semidirect
56. #14582902C22semidirect
57. #14582894C22semidirect
58. C2×#13063249C22semidirect
59. C2×#13063249C22semidirect
60. C2×#13063249C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×#13063236C22semidirect
69. C22×Q16×C43C22semidirect
72. C2×C4×Q8×C43C22semidirect
73. C43×#464C22semidirect
74. C2×C4⋊C8×C43C22semidirect
75. C2×#103×C43C22semidirect
103. C2×C8×D43C23semidirect
105. #13063325C23semidirect
115. #13063301C23semidirect
128. #13063283C23semidirect
149. #13063258C23semidirect
150. #13063257C23semidirect
151. #13063257C23semidirect
152. #13063249C23semidirect
153. #13063249C23semidirect
154. #13063249C23semidirect
161. (C2×D43)⋊C8C23semidirect
162. #13063236C23semidirect
167. C2×Q16×C43C23semidirect
175. C4×Q8×C43C23semidirect
182. C4⋊C8×C43C23semidirect
183. #103×C43C23semidirect
409. C2×#464D43semidirect
417. C2×C43#3311semidirect
426. C22×Q16C2×D43semidirect
448. C2×C4×Q8C2×D43semidirect
460. #464C2×D43semidirect
468. C2×C4⋊C8C2×D43semidirect
474. C2×#103C2×D43semidirect
484. C43C2×#3311semidirect
508. C2×Q16C22×D43semidirect
541. C4×Q8C22×D43semidirect
579. C4⋊C8C22×D43semidirect
583. #103C22×D43semidirect
811. C2#19146638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836222
C2×#145835422
#191466382
C2×#145832582
C2×#145832382
C2×#145832222
C2×#145831902
C2×#145831542
C2×#145831252
C2×#145830602
C2×#145830482
C2×#145829972
C2×#145829692
C2×#145829022
C2×#145828942
C2×C43×#4642
C2×#331143