Finite Group Databasebeta

← C2×#19146683 #25973130

Subgroups — C2×#19146683 #25973130

Order 11008.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583609C211yesmaximal, characteristic, complemented
2C2×#14583542C211yesmaximal, characteristic
3#19146683C2116yesmaximal, direct product factor
4C2×#14583258C211yesmaximal, characteristic, complemented
5C2×#14583233C211yesmaximal, characteristic, complemented
6C2×#14583211C211yesmaximal, characteristic, complemented
7C2×#14583180C211yesmaximal, characteristic, complemented
8C2×#14583142C211yesmaximal, characteristic, complemented
9C2×#14583137C211yesmaximal, characteristic, complemented
10C2×#14583060C211yesmaximal, characteristic, complemented
11C2×#14583048C211yesmaximal, characteristic, complemented
12C2×#14582997C211yesmaximal, characteristic, complemented
13C2×#14582969C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621872C2211yescharacteristic, complemented
21C22×C8×D43C2211yescharacteristic
22#14583609—24no—
23#14583609C2218yescomplemented
24#14583542—24no—
25#14583542C2218yes—
26C2×#13063325C2211yescharacteristic, complemented
27C2×#13063317—21no—
28C2×#13063307—21no—
29C2×#13063303—21no—
30C2×#13063303—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063301C2211yescharacteristic
33C2×#13063301C2211yescharacteristic, complemented
34C2×#13063298—21no—
35C2×#13063296C2211yescharacteristic
36C2×#13063295—21no—
37C2×C4×D172—21no—
38C2×C4×D172C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic, complemented
42C2×C22⋊C4×D43—21no—
43#14583258C2218yescomplemented
44#14583233C2218yescomplemented
45#14583211C2218yescomplemented
46#14583180C2218yescomplemented
47#14583142C2218yescomplemented
48#14583137C2218yescomplemented
49#14583060C2218yescomplemented
50#14583048C2218yescomplemented
51#14582997C2218yescomplemented
52#14582969C2218yescomplemented
53C2×#13063259C2211yescharacteristic, complemented
54C2×#13063259C2211yescharacteristic, complemented
55C2×#13063258C2211yescharacteristic, complemented
56#14582899C2218yescomplemented
57C2×#13063249C2211yescharacteristic, complemented
58C2×#13063249C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65#102×D43C2218yescomplemented
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×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×#10621884—24no—
99C2×#10621884C2314yes—
100C2×#10621872—42no—
101C2×#10621872C2314yescomplemented
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C2×C8×D43—42no—
105C2×C8×D43C2314yes—
106#13063325—22no—
107#13063325C2314yescomplemented
108#13063317—28no—
109#13063307—28no—
110#13063303—28no—
111#13063303—28no—
112#13063301—22no—
113#13063301—22no—
114#13063301—22no—
115#13063301C2314yes—
116#13063301C2314yes—
117#13063301C2314yescomplemented
118#13063298—28no—
119#13063296—22no—
120#13063296C2314yes—
121#13063295—28no—
122C4×D172—28no—
123C4×D172—22no—
124C4×D172D414yes—
125C4×D172C2314yes—
126C4×D172C2314yes—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43D411yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C4⋊C4×D43—22no—
138C4⋊C4×D43—22no—
139C4⋊C4×D43C2314yes—
140C4⋊C4×D43C2314yescomplemented
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4D411yescharacteristic
147C2×(C2×D43)⋊C4D411yescharacteristic
148C22⋊C4×D43—28no—
149#13063259C2314yescomplemented
150#13063259C2314yescomplemented
151#13063258C2314yescomplemented
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—24no—
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—24no—
241C2×C4×D43—24no—
242C2×C4×D43—44no—
243C2×C4×D43—82no—
244C2×C4×D43—82no—
245C2×C4×D43—82no—
246C2×C4×D43C2×D412yes—
247C2×C4×D43C2×D412yes—
248C2×C4×D43C2412yes—
249C2×C4×D43C2412yes—
250C2×Dic86—24no—
251C2×Dic86—82no—
252Q16×C43—44no—
253SD16×C43—44no—
254C2×C8×C43—22no—
255C2×C8×C43—22no—
256C2×C8×C43C2412yes—
257C2×C8×C43C2412yes—
258C4⋊C4×C43—24no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43C2412yes—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C42×C43—24no—
264C42×C43C2×D412yes—
265C42×C43C2412yes—
266C22⋊Dic43—24no—
267#10621884—28no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4C2×D414yes—
273(C2×D43)⋊C4C2×D414yes—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—24no—
277C4⋊Dic43—21no—
278C4⋊Dic43C2×D414yes—
279C4⋊Dic43C2412yes—
280C4⋊Dic43C2412yes—
281C4⋊Dic43C2412yes—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291#10621872—44no—
292C8×D43—44no—
293C23×C43—22no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—24no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—48no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—48no—
309C22×D43—84no—
310C22×D43—816no—
311C22×D43#13714yes—
312C22×D43C22×D412yes—
313C22×D43C22×D412yes—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—42no—
319Q8×C43—42no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—42no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43C22×D412yes—
332C2×C4×C43C22×D412yes—
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C2×#4112yes—
335C2×C4×C43H(5,𝔽2)12yes—
336C2×C4×C43C2511yescharacteristic
337C22⋊D43—48no—
338C22⋊D43—84no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43C22×D412yes—
348C2×Dic43C22×D412yes—
349D172—28no—
350D172—24no—
351D172—22no—
352D172—48no—
353D172C2×#4114yes—
354C4×D43—24no—
355C4×D43—24no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—48no—
361C4×D43—84no—
362C4×D43—84no—
363C4×D43—84no—
364Dic86—84no—
365C8×C43—22no—
366C8×C43—22no—
367C43⋊C8—22no—
368C43⋊C8—22no—
369C2×#3314—431nomaximal, Sylow
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—84no—
374C22×C43#54612yes—
375C22×C43C2×#13712yes—
376C22×C43#57612yes—
377C22×C43C23×D411yescharacteristic
378C2×D43—22no—
379C2×D43—28no—
380C2×D43—22no—
381C2×D43—24no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—44no—
386C2×D43—48no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—816no—
390C2×D43C2×#13714yes—
391C4×C43—22no—
392C4×C43—22no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43#54612yes—
397C4×C43C22×#4111yescharacteristic
398C4×C43C2×H(5,𝔽2)11yescharacteristic
399Dic43—22no—
400Dic43—22no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C2×#554—431no—
405C2×#546—431no—
406#3314—4316no—
407C2×#489—431no—
408C2×#484—431no—
409C2×#480—431no—
410C2×#474—431no—
411C2×#468—431no—
412C2×#467—431no—
413C2×#464D4311yescharacteristic, complemented
414C2×#452—431no—
415C2×#450—431no—
416C2×#440—431no—
417C2×#435—431no—
418C2×#417—431no—
419C22×#102—431no—
420C2×C43—82no—
421C2×C43#331414yescomplemented
422C2×C43C2×#54611yescharacteristic
423C2×C43C22×#13711yescharacteristic
424C2×C43C2×#57611yescharacteristic
425D43—24no—
426D43—42no—
427D43—44no—
428C22×#41—431no—
429C23×D4—431no—
430C22×Q16C2×D4311yescharacteristic, complemented
431C22×SD16—431no—
432C22×SD16C2×D4311yescharacteristic
433C22×M16—431no—
434C23×C8—431no—
435#554—438no—
436#554—864no—
437#546—438no—
438#546—864no—
439C2×C4⋊Q8—431no—
440C2×#125—861no—
441C2×#124C2×D4311yescharacteristic
442C2×#123—861no—
443C2×C22⋊Q8—431no—
444C2×C22⋊Q8—431no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—861no—
447C2×C22⋊Q8—861no—
448C2×#121—431no—
449C2×#121—861no—
450C2×#120—861no—
451C2×C4×Q8C2×D4311yescharacteristic, complemented
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C2×C4×D4—861no—
455C22×C4⋊C4—431no—
456C22×C4⋊C4—431no—
457C22×C22⋊C4—861no—
458#489—438no—
459#484—438no—
460#480—438no—
461#474—438no—
462#468—438no—
463#467—438no—
464#464C2×D4318yescomplemented
465#452—438no—
466#450—438no—
467#440—438no—
468#435—438no—
469C2×#107—431no—
470C2×#107—431no—
471C2×#107—431no—
472C2×C4⋊C8C2×D4311yescharacteristic, complemented
473#417—438no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103C2×D4311yescharacteristic, complemented
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—438no—
484C2×#102C2×D4311yescharacteristic
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×#97—431no—
488C43C2×#331411yescharacteristic, complemented, Sylow
489C25—861no—
490C2×#41—434no—
491C2×#41—862no—
492C2×#41—864no—
493C2×#41—1722no—
494C22×Q8—861no—
495C22×Q8C22×D4311yescharacteristic
496C22×Q8C22×D4311yescharacteristic
497C22×D4—434no—
498C22×D4—431no—
499C22×D4—431no—
500C22×D4—861no—
501C22×D4—862no—
502C22×D4—861no—
503C22×D4—864no—
504C22×D4—861no—
505C22×D4—1722no—
506C22×D4C22×D4311yescharacteristic
507C23×C4—431no—
508C23×C4—431no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512C23×C4—861no—
513C2×Q16—42no—
514C2×Q16C22×D4314yescomplemented
515C2×SD16—42no—
516C2×SD16—434no—
517C2×SD16—864no—
518C2×SD16C22×D4314yes—
519C2×M16—434no—
520C2×M16—1722no—
521C22×C8—431no—
522C22×C8—431no—
523C22×C8—434no—
524C22×C8—1722no—
525C22×C8C22×D4311yescharacteristic
526C22×C8C22×D4311yescharacteristic
527C4⋊Q8—434no—
528C4⋊Q8—862no—
529#125—868no—
530#124—22no—
531#124C22×D4314yes—
532#123—868no—
533C22⋊Q8—434no—
534C22⋊Q8—434no—
535C22⋊Q8—434no—
536C22⋊Q8—868no—
537C22⋊Q8—868no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
541#121—434no—
542#121—868no—
543#121—862no—
544#120—868no—
545C4×Q8—22no—
546C4×Q8C22×D4314yescomplemented
547C4×D4—434no—
548C4×D4—434no—
549C4×D4—434no—
550C4×D4—868no—
551C4×D4—862no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—434no—
558C2×C4⋊C4—434no—
559C2×C4⋊C4—862no—
560C2×C4⋊C4—862no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—868no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C42—21no—
579C2×C42C22×D4311yescharacteristic
580#107—434no—
581#107—434no—
582#107—434no—
583C4⋊C8C22×D4314yescomplemented
584#103—434no—
585#103—434no—
586#103—434no—
587#103C22×D4314yescomplemented
588#102—434no—
589#102—434no—
590#102—434no—
591#102—434no—
592#102—434no—
593#102C22×D4314yes—
594C22⋊C8—434no—
595C22⋊C8—434no—
596#97—434no—
597C24—21no—
598C24—431no—
599C24—431no—
600C24—864no—
601C24—861no—
602C24—3442no—
603C24—1724no—
604C24—1724no—
605#41—868no—
606#41—1724no—
607#41—1728no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—864no—
615C2×Q8—3442no—
616C2×Q8C23×D4312yes—
617C2×Q8C23×D4312yes—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—434no—
622C2×D4—434no—
623C2×D4—432no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—868no—
628C2×D4—864no—
629C2×D4—861no—
630C2×D4—862no—
631C2×D4—3442no—
632C2×D4—1724no—
633C2×D4—1724no—
634C2×D4—1728no—
635C2×D4—1724no—
636C2×D4C23×D4312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—432no—
643C22×C4—432no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—864no—
647C22×C4—864no—
648C22×C4—864no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—864no—
657C22×C4—3442no—
658C22×C4—3442no—
659C22×C4—3442no—
660C22×C4—1724no—
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4C23×D4311yescharacteristic
664Q16—44no—
665SD16—44no—
666SD16—868no—
667M16—1724no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—432no—
671C2×C8—432no—
672C2×C8—862no—
673C2×C8—862no—
674C2×C8—1724no—
675C2×C8C23×D4312yes—
676C2×C8C23×D4312yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—434no—
680C4⋊C4—432no—
681C4⋊C4—432no—
682C4⋊C4—432no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—864no—
692C4⋊C4C23×D4312yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—434no—
696C22⋊C4—434no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C42—24no—
703C42D4×D4312yes—
704C42C23×D4312yes—
705C23—22no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—434no—
710C23—432no—
711C23—432no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—864no—
719C23—3444no—
720C23—34416no—
721C23—1728no—
722C23—1728no—
723C23—1722no—
724C23—1722no—
725C23C2×D4×D4311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—3444no—
733D4—22no—
734D4—22no—
735D4—42no—
736D4—434no—
737D4—868no—
738D4—862no—
739D4—864no—
740D4—3444no—
741D4—1728no—
742D4—1728no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—432no—
752C2×C4—432no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—864no—
760C2×C4—864no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—3444no—
765C2×C4—3444no—
766C2×C4—3444no—
767C2×C4—1728no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4C2×D4×D4312yes—
772C2×C4C2×D4×D4312yes—
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4#41×D4312yes—
775C2×C4#1306337012yes—
776C2×C4C24×D4311yescharacteristic
777C8—22no—
778C8—22no—
779C8—862no—
780C8—862no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—434no—
786C22—862no—
787C22—862no—
788C22—868no—
789C22—862no—
790C22—864no—
791C22—862no—
792C22—862no—
793C22—34416no—
794C22—1722no—
795C22—1722no—
796C22—1724no—
797C22—1728no—
798C22#1458354612yes—
799C22#137×D4312yes—
800C22#1458370112yes—
801C22C22×D4×D4311yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—862no—
808C4—862no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4#1458354612yes—
813C4C2×#41×D4311yescharacteristic
814C4C2×#1306337011yescharacteristic
815C2—82no—
816C2—864no—
817C2—1722no—
818C2—1724no—
819C2#1914668314yesdirect product factor
820C2C2×#1458354611yescharacteristic
821C2C2×#137×D4311yescharacteristic
822C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#14583542C2
hypercenterC2×#464D43
hypocenterC43C2×#3314
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×#14583609C2semidirect
3. #19146683C2direct (N × H)
4. C2×#14583258C2semidirect
5. C2×#14583233C2semidirect
6. C2×#14583211C2semidirect
7. C2×#14583180C2semidirect
8. C2×#14583142C2semidirect
9. C2×#14583137C2semidirect
10. C2×#14583060C2semidirect
11. C2×#14583048C2semidirect
12. C2×#14582997C2semidirect
13. C2×#14582969C2semidirect
14. C2×#14582899C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#464C2semidirect
20. C22×#10621872C22semidirect
23. #14583609C22semidirect
26. C2×#13063325C22semidirect
33. C2×#13063301C22semidirect
41. C2×C4⋊C4×D43C22semidirect
43. #14583258C22semidirect
44. #14583233C22semidirect
45. #14583211C22semidirect
46. #14583180C22semidirect
47. #14583142C22semidirect
48. #14583137C22semidirect
49. #14583060C22semidirect
50. #14583048C22semidirect
51. #14582997C22semidirect
52. #14582969C22semidirect
53. C2×#13063259C22semidirect
54. C2×#13063259C22semidirect
55. C2×#13063258C22semidirect
56. #14582899C22semidirect
57. C2×#13063249C22semidirect
58. C2×#13063249C22semidirect
59. C2×#13063249C22semidirect
65. #102×D43C22semidirect
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
101. C2×#10621872C23semidirect
107. #13063325C23semidirect
117. #13063301C23semidirect
140. C4⋊C4×D43C23semidirect
149. #13063259C23semidirect
150. #13063259C23semidirect
151. #13063258C23semidirect
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
413. C2×#464D43semidirect
421. C2×C43#3314semidirect
430. C22×Q16C2×D43semidirect
451. C2×C4×Q8C2×D43semidirect
464. #464C2×D43semidirect
472. C2×C4⋊C8C2×D43semidirect
477. C2×#103C2×D43semidirect
488. C43C2×#3314semidirect
514. C2×Q16C22×D43semidirect
546. C4×Q8C22×D43semidirect
583. C4⋊C8C22×D43semidirect
587. #103C22×D43semidirect
819. C2#19146683direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836092
C2×#145835422
#191466832
C2×#145832582
C2×#145832332
C2×#145832112
C2×#145831802
C2×#145831422
C2×#145831372
C2×#145830602
C2×#145830482
C2×#145829972
C2×#145829692
C2×#145828992
C2×#102×D432
C2×C43×#4642
C2×#331443