Finite Group Databasebeta

← C2×#19146817 #25973416

Subgroups — C2×#19146817 #25973416

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×#14583583C211yesmaximal, characteristic, complemented
2C2×#14583540C211yesmaximal, characteristic
3#19146817C2116yesmaximal, direct product factor
4C2×#14583255C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583237C211yesmaximal, characteristic, complemented
7C2×#14583198C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic, complemented
9C2×#14583123C211yesmaximal, characteristic, complemented
10C2×#14583060C211yesmaximal, characteristic, complemented
11C2×#14583049C211yesmaximal, characteristic, complemented
12C2×#14582984C211yesmaximal, characteristic, complemented
13C2×#14582975C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#14582905C211yesmaximal, characteristic, complemented
16C2×C43×#470C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621872C2211yescharacteristic, complemented
22#14583583—24no—
23#14583583C2218yescomplemented
24#14583540—24no—
25#14583540C2218yes—
26C2×#13063318—21no—
27C2×#13063316C2211yescharacteristic, complemented
28C2×#13063315—21no—
29C2×#13063314C2211yescharacteristic
30C2×#13063310—21no—
31C2×#13063307—21no—
32C2×#13063301C2211yescharacteristic, complemented
33C2×#13063300—21no—
34C2×#13063300C2211yescharacteristic
35C2×#13063295—21no—
36C2×Q8×Dic43C2211yescharacteristic, complemented
37C2×#13063287C2211yescharacteristic
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×#13063284C2211yescharacteristic
40C2×#13063283—21no—
41C2×C4⋊C4×D43C2211yescharacteristic, complemented
42C2×C22⋊C4×D43—21no—
43#14583255C2218yescomplemented
44#14583237C2218yescomplemented
45#14583219C2218yescomplemented
46#14583198C2218yescomplemented
47#14583148C2218yescomplemented
48#14583123C2218yescomplemented
49#14583060C2218yescomplemented
50#14583049C2218yescomplemented
51#14582984C2218yescomplemented
52#14582975C2218yescomplemented
53C2×#13063258C2211yescharacteristic, complemented
54C2×#13063256C2211yescharacteristic, complemented
55C2×Dic43⋊C8C2211yescharacteristic, complemented
56#14582905C2218yescomplemented
57#14582899C2218yescomplemented
58C2×#13063249C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C22×Q16×C43C2211yescharacteristic, complemented
70C22×M16×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#470C2218yescomplemented
74C2×#106×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#103×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—24no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C22×D172—24no—
83C22×D172—21no—
84C22×D172—21no—
85C22×D172—22no—
86C22×D172—21no—
87C22×D172—42no—
88C22×D172C2311yescharacteristic
89C22×D172C2314yes—
90C22×D172C2311yescharacteristic
91C22×C22⋊D43D411yescharacteristic
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43C2311yescharacteristic
96C2×#10621884—24no—
97C2×#10621884—42no—
98C2×#10621884C2314yes—
99C2×#10621884C2314yes—
100C2×#10621872—42no—
101C2×#10621872C2314yescomplemented
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104#13063318—28no—
105#13063316—22no—
106#13063316C2314yescomplemented
107#13063315—28no—
108#13063314—22no—
109#13063314C2314yes—
110#13063310—28no—
111#13063307—28no—
112#13063301—22no—
113#13063301C2314yescomplemented
114#13063300—22no—
115#13063300—28no—
116#13063300C2314yes—
117#13063295—28no—
118Q8×Dic43—22no—
119Q8×Dic43C2314yescomplemented
120#13063287—22no—
121#13063287C2314yes—
122C4×C22⋊D43D414yes—
123C4×C22⋊D43C2314yes—
124#13063284—22no—
125#13063284C2314yes—
126#13063283—28no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C4⋊C4×D43—22no—
136C4⋊C4×D43C2314yescomplemented
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43D411yescharacteristic
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
145C22⋊C4×D43—28no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yescomplemented
150#13063256C2314yescomplemented
151Dic43⋊C8C2314yescomplemented
152#13063249C2314yescomplemented
153#13063249C2314yescomplemented
154#13063247C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160C22⋊(C43⋊C8)C2314yes—
161(C2×D43)⋊C8C2314yescomplemented
162C8×Dic43C2314yescomplemented
163C22×Q8×C43C2311yescharacteristic
164C22×Q8×C43C2311yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C2×Q16×C43—42no—
167C2×Q16×C43C2314yescomplemented
168C2×M16×C43—42no—
169C2×M16×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22⋊Q8×C43—22no—
173C22⋊Q8×C43—22no—
174C22⋊Q8×C43C2314yes—
175C22⋊Q8×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182#106×C43C2314yescomplemented
183#103×C43C2314yescomplemented
184#103×C43C2314yescomplemented
185C24×C43C2×D411yescharacteristic
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—24no—
189C23×D43—44no—
190C23×D43—44no—
191C23×D43—82no—
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—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2412yes—
210C22×C4×C43C2411yescharacteristic
211C2×C22⋊D43—42no—
212C2×C22⋊D43C2×D414yes—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218#10621902—28no—
219#10621902—44no—
220#10621902—48no—
221C2×D172—21no—
222C2×D172—22no—
223C2×D172—24no—
224C2×D172—21no—
225C2×D172—24no—
226C2×D172—24no—
227C2×D172—22no—
228C2×D172—22no—
229C2×D172—28no—
230C2×D172—44no—
231C2×D172—44no—
232C2×D172—44no—
233C2×D172—48no—
234C2×D172—82no—
235C2×D172#4114yes—
236C2×D172C2412yes—
237C2×D172C2412yes—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43—24no—
241C2×C4×D43—24no—
242C2×C4×D43—24no—
243C2×C4×D43—44no—
244C2×C4×D43—44no—
245C2×C4×D43—82no—
246C2×C4×D43C2×D412yes—
247C2×C4×D43C2412yes—
248Q16×C43—44no—
249M16×C43—44no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43C2412yes—
259C4⋊C4×C43C2412yes—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊Dic43—24no—
263C22⋊Dic43C2×D414yes—
264#10621884—28no—
265#10621884—44no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4C2×D414yes—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—24no—
275C4⋊Dic43—24no—
276C4⋊Dic43C2412yes—
277C4⋊Dic43C2412yes—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4C2×D414yes—
282C4×Dic43—24no—
283C4×Dic43—24no—
284C4×Dic43C2×D412yes—
285C4×Dic43C2412yes—
286C2×C43⋊C8—22no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8C2412yes—
289C2×C43⋊C8C2412yes—
290#10621872—44no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43C22×D412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—24no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—48no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—48no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—84no—
310C22×D43—816no—
311C22×D43C22×D412yes—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—42no—
317Q8×C43—42no—
318C2×C4×C43—22no—
319C2×C4×C43—24no—
320C2×C4×C43—22no—
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×C43—42no—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4112yes—
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43C2511yescharacteristic
335C22⋊D43—44no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345C2×Dic43C22×D412yes—
346D172—24no—
347D172—22no—
348D172—22no—
349D172—22no—
350D172—48no—
351D172—48no—
352D172—42no—
353D172—84no—
354D172C2×#4114yes—
355C4×D43—24no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—48no—
359C4×D43—48no—
360C4×D43—84no—
361C8×C43—22no—
362C8×C43—22no—
363C43⋊C8—22no—
364C43⋊C8—22no—
365C2×#3323—431nomaximal, Sylow
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—44no—
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—44no—
379C2×D43—48no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—816no—
386C2×D43—84no—
387C4×C43—22no—
388C4×C43—42no—
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—22no—
398Dic43—42no—
399Dic43—42no—
400C2×#552—431no—
401C2×#546—431no—
402#3323—4316no—
403C2×#488—431no—
404C2×#481—431no—
405C2×#485—431no—
406C2×#478—431no—
407C2×#470D4311yescharacteristic, complemented
408C2×#468—431no—
409C2×#464—431no—
410C2×#452—431no—
411C2×#450—431no—
412C2×C4×SD16—431no—
413C2×#436—431no—
414C2×#417—431no—
415C2×#418—431no—
416C2×C43—42no—
417C2×C43#332314yescomplemented
418C2×C43C2×#54611yescharacteristic
419C2×C43C2×#57511yescharacteristic
420C2×C43C2×#57711yescharacteristic
421D43—42no—
422D43—44no—
423D43—82no—
424C22×#41—431no—
425C23×D4—431no—
426C22×Q16C2×D4311yescharacteristic, complemented
427C22×SD16—431no—
428C22×SD16—431no—
429C22×M16—431no—
430C22×M16C2×D4311yescharacteristic
431#552—438no—
432#552—864no—
433#546—438no—
434#546—864no—
435C2×#126—861no—
436C2×#125—431no—
437C2×#125—861no—
438C2×#124—431no—
439C2×#123—861no—
440C2×#123—861no—
441C2×C22⋊Q8—431no—
442C2×C22⋊Q8C2×D4311yescharacteristic
443C2×C22⋊Q8C2×D4311yescharacteristic
444C2×#121—431no—
445C2×#121—861no—
446C2×#120—861no—
447C2×C4×Q8—431no—
448C2×C4×D4—431no—
449C2×C4×D4—431no—
450C2×#117—431no—
451C2×#117—861no—
452C22×C4⋊C4—431no—
453C22×C22⋊C4—861no—
454#488—438no—
455#485—438no—
456#481—438no—
457#478—438no—
458#470C2×D4318yescomplemented
459#468—438no—
460#464—438no—
461#452—438no—
462#450—438no—
463C4×SD16—438no—
464#436—438no—
465C2×#107—431no—
466C2×#106—431no—
467C2×#106C2×D4311yescharacteristic, complemented
468C2×C4⋊C8—431no—
469#418—438no—
470#417—438no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103C2×D4311yescharacteristic, complemented
474C2×#103C2×D4311yescharacteristic, complemented
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×C4×C8—431no—
484C43C2×#332311yescharacteristic, complemented, Sylow
485C25—861no—
486C2×#41—434no—
487C2×#41—862no—
488C2×#41—864no—
489C2×#41—1722no—
490C22×Q8C22×D4311yescharacteristic
491C22×Q8C22×D4311yescharacteristic
492C22×D4—431no—
493C22×D4—431no—
494C22×D4—431no—
495C22×D4—434no—
496C22×D4—864no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4—862no—
501C22×D4—1722no—
502C23×C4—431no—
503C23×C4—861no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4C22×D4311yescharacteristic
507C2×Q16—42no—
508C2×Q16C22×D4314yescomplemented
509C2×SD16—434no—
510C2×SD16—434no—
511C2×SD16—864no—
512C2×SD16—1722no—
513C2×M16—42no—
514C2×M16—434no—
515C2×M16—1722no—
516C2×M16C22×D4314yes—
517C22×C8—431no—
518C22×C8—431no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521#126—868no—
522#125—434no—
523#125—862no—
524#125—868no—
525#124—434no—
526#124—862no—
527#123—868no—
528#123—868no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—434no—
532C22⋊Q8—862no—
533C22⋊Q8C22×D4314yes—
534C22⋊Q8C22×D4314yes—
535#121—434no—
536#121—868no—
537#121—862no—
538#120—868no—
539C4×Q8—434no—
540C4×Q8—862no—
541C4×D4—434no—
542C4×D4—434no—
543C4×D4—434no—
544C4×D4—862no—
545#117—434no—
546#117—868no—
547#117—862no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—434no—
554C2×C4⋊C4—862no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—431no—
565C2×C22⋊C4—431no—
566C2×C22⋊C4—868no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C42—431no—
574C2×C42—861no—
575C2×C42—861no—
576#107—434no—
577#106—434no—
578#106C22×D4314yescomplemented
579C4⋊C8—434no—
580#103—434no—
581#103—434no—
582#103C22×D4314yescomplemented
583#103C22×D4314yescomplemented
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588#102—434no—
589#102—434no—
590C22⋊C8—434no—
591C22⋊C8—434no—
592C4×C8—434no—
593C24—431no—
594C24—861no—
595C24—864no—
596C24—861no—
597C24—3442no—
598C24—1724no—
599C24—1724no—
600C24D4×D4311yescharacteristic
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×Q8C23×D4312yes—
611C2×Q8C23×D4312yes—
612C2×D4—434no—
613C2×D4—434no—
614C2×D4—432no—
615C2×D4—432no—
616C2×D4—868no—
617C2×D4—864no—
618C2×D4—864no—
619C2×D4—861no—
620C2×D4—864no—
621C2×D4—861no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—3442no—
626C2×D4—1724no—
627C2×D4—1728no—
628C2×D4—1724no—
629C2×D4—1724no—
630C2×D4—1722no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—864no—
643C22×C4—864no—
644C22×C4—864no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—3442no—
650C22×C4—1724no—
651C22×C4—1724no—
652C22×C4D4×D4312yes—
653C22×C4D4×D4311yescharacteristic
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656Q16—44no—
657SD16—868no—
658SD16—1724no—
659M16—44no—
660M16—1724no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—432no—
664C2×C8—432no—
665C2×C8—862no—
666C2×C8—862no—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—434no—
674C4⋊C4—432no—
675C4⋊C4—432no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4C23×D4312yes—
684C4⋊C4C23×D4312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—434no—
688C22⋊C4—434no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C22⋊C4—864no—
695C42—432no—
696C42—432no—
697C42—864no—
698C42—864no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—432no—
703C23—862no—
704C23—862no—
705C23—862no—
706C23—862no—
707C23—864no—
708C23—862no—
709C23—3444no—
710C23—34416no—
711C23—1728no—
712C23—1728no—
713C23—1722no—
714C23—1722no—
715C23—1722no—
716C23—1722no—
717C23—1722no—
718C23C2×D4×D4312yes—
719C23C2×D4×D4311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726D4—434no—
727D4—862no—
728D4—862no—
729D4—862no—
730D4—864no—
731D4—3444no—
732D4—1728no—
733D4—1728no—
734D4—1724no—
735D4—1722no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—432no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—864no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—3444no—
760C2×C4—1728no—
761C2×C4—1728no—
762C2×C4—1722no—
763C2×C4—1722no—
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—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—862no—
778C22—864no—
779C22—862no—
780C22—862no—
781C22—34416no—
782C22—3444no—
783C22—1722no—
784C22—1722no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1724no—
789C22—1728no—
790C22#1458353812yes—
791C22#1458369812yes—
792C22#1458370812yes—
793C22C22×D4×D4311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—862no—
800C4—862no—
801C4—862no—
802C4—1722no—
803C4—1722no—
804C4#1458353812yes—
805C4C2×#41×D4311yescharacteristic
806C4C2×#1306337011yescharacteristic
807C2—42no—
808C2—3442no—
809C2—1722no—
810C2—1724no—
811C2#1914681714yesdirect product factor
812C2C2×#1458353811yescharacteristic
813C2C2×#1458369811yescharacteristic
814C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#470C2
socleC23×C43C22×D4
prime radicalC2×#14583540C2
hypercenterC2×#470D43
hypocenterC43C2×#3323
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C2×#14583583C2semidirect
3. #19146817C2direct (N × H)
4. C2×#14583255C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583237C2semidirect
7. C2×#14583198C2semidirect
8. C2×#14583148C2semidirect
9. C2×#14583123C2semidirect
10. C2×#14583060C2semidirect
11. C2×#14583049C2semidirect
12. C2×#14582984C2semidirect
13. C2×#14582975C2semidirect
14. C2×#14582899C2semidirect
15. C2×#14582905C2semidirect
16. C2×C43×#470C2semidirect
21. C22×#10621872C22semidirect
23. #14583583C22semidirect
27. C2×#13063316C22semidirect
32. C2×#13063301C22semidirect
36. C2×Q8×Dic43C22semidirect
41. C2×C4⋊C4×D43C22semidirect
43. #14583255C22semidirect
44. #14583237C22semidirect
45. #14583219C22semidirect
46. #14583198C22semidirect
47. #14583148C22semidirect
48. #14583123C22semidirect
49. #14583060C22semidirect
50. #14583049C22semidirect
51. #14582984C22semidirect
52. #14582975C22semidirect
53. C2×#13063258C22semidirect
54. C2×#13063256C22semidirect
55. C2×Dic43⋊C8C22semidirect
56. #14582905C22semidirect
57. #14582899C22semidirect
58. C2×#13063249C22semidirect
59. C2×#13063249C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×C8×Dic43C22semidirect
69. C22×Q16×C43C22semidirect
73. C43×#470C22semidirect
74. C2×#106×C43C22semidirect
75. C2×#103×C43C22semidirect
76. C2×#103×C43C22semidirect
101. C2×#10621872C23semidirect
106. #13063316C23semidirect
113. #13063301C23semidirect
119. Q8×Dic43C23semidirect
136. C4⋊C4×D43C23semidirect
149. #13063258C23semidirect
150. #13063256C23semidirect
151. Dic43⋊C8C23semidirect
152. #13063249C23semidirect
153. #13063249C23semidirect
161. (C2×D43)⋊C8C23semidirect
162. C8×Dic43C23semidirect
167. C2×Q16×C43C23semidirect
182. #106×C43C23semidirect
183. #103×C43C23semidirect
184. #103×C43C23semidirect
407. C2×#470D43semidirect
417. C2×C43#3323semidirect
426. C22×Q16C2×D43semidirect
458. #470C2×D43semidirect
467. C2×#106C2×D43semidirect
473. C2×#103C2×D43semidirect
474. C2×#103C2×D43semidirect
484. C43C2×#3323semidirect
508. C2×Q16C22×D43semidirect
578. #106C22×D43semidirect
582. #103C22×D43semidirect
583. #103C22×D43semidirect
811. C2#19146817direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835832
C2×#145835402
#191468172
C2×#145832552
C2×#145832192
C2×#145832372
C2×#145831982
C2×#145831482
C2×#145831232
C2×#145830602
C2×#145830492
C2×#145829842
C2×#145829752
C2×#145828992
C2×#145829052
C2×C43×#4702
C2×#332343