Finite Group Databasebeta

← C2×#19144065 #25963434

Subgroups — C2×#19144065 #25963434

Order 11008.

2810 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C22×#13063354C211yesmaximal, characteristic, complemented
3C2×#14583448C211yesmaximal, characteristic
4C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
5#19144065C2116yesmaximal, direct product factor
6C2×#14583122C211yesmaximal, characteristic, complemented
7C2×#14583121C211yesmaximal, characteristic, complemented
8C2×#14583118C211yesmaximal, characteristic, complemented
9C2×#14583108C211yesmaximal, characteristic, complemented
10C2×#14583107C211yesmaximal, characteristic, complemented
11C2×#14583098C211yesmaximal, characteristic, complemented
12C2×#14583097C211yesmaximal, characteristic, complemented
13C2×#14582921C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#14582897C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C2×#13063357—28no—
21C2×#13063357C2218yescomplemented
22C2×#13063354—28no—
23C2×#13063354C2218yescomplemented
24C22×Dic172C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621873C2211yescharacteristic
28C22×#10621883C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621872C2211yescharacteristic
31C22×#10621872C2211yescharacteristic
32#14583448—24no—
33#14583448C2218yes—
34C2×#13063323C2211yescharacteristic
35C2×#13063321C2211yescharacteristic
36C2×#13063313C2211yescharacteristic
37C2×#13063298—21no—
38C2×#13063298—21no—
39C2×Q8×Dic43C2211yescharacteristic
40C2×C4×Dic86—21no—
41C2×C4×Dic86C2211yescharacteristic
42C2×#13063290—21no—
43C2×#13063290C2211yescharacteristic
44C4×Q8×D43—24no—
45C4×Q8×D43C2218yescomplemented
46C2×(C22⋊D43)⋊C4—21no—
47C2×(C22⋊D43)⋊C4—21no—
48C2×C4⋊C4×D43—21no—
49C2×C4⋊C4×D43C2211yescharacteristic
50C2×C42×D43—21no—
51C2×C42×D43C2211yescharacteristic
52#14583122C2218yescomplemented
53#14583121C2218yescomplemented
54#14583118C2218yescomplemented
55#14583108C2218yescomplemented
56#14583107C2218yescomplemented
57#14583098C2218yescomplemented
58#14583097C2218yescomplemented
59#14582921C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63#14582899C2218yescomplemented
64#14582897C2218yescomplemented
65C2×#13063250C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063248C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×#13063246C2211yescharacteristic
70C2×#13063245C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic
73C2×#124×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C43×#464C2218yescomplemented
76C2×C4⋊C8×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×#102×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—24no—
81C2×#10621902—24no—
82C2×#10621902C2314yes—
83C2×#10621900—24no—
84C2×#10621900—22no—
85C2×#10621900—24no—
86C2×#10621900C2314yes—
87C22×Dic86—21no—
88C22×Dic86C2311yescharacteristic
89C22×Dic86C2311yescharacteristic
90C2×Q8×D43—22no—
91C2×Q8×D43—24no—
92C2×Q8×D43D418yescomplemented
93C2×Q8×D43C2314yes—
94C22×D172—21no—
95C22×D172C2311yescharacteristic
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C23×Dic43—21no—
100C22×C4×D43—21no—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43D411yescharacteristic
104C22×C4×D43D411yescharacteristic
105C22×C4×D43C2311yescharacteristic
106#13063357—232no—
107#13063354—232no—
108C2×Dic172—24no—
109C2×Dic172C2314yes—
110C2×#10621885—24no—
111C2×#10621885—24no—
112C2×#10621885C2314yes—
113C2×#10621885C2314yes—
114C2×#10621873—24no—
115C2×#10621873C2314yes—
116C2×#10621883—24no—
117C2×#10621883C2314yes—
118C2×#10621884—24no—
119C2×#10621884C2314yes—
120C2×#10621872—24no—
121C2×#10621872—24no—
122C2×#10621872C2314yes—
123C2×#10621872C2314yes—
124C22×C43⋊C8C2311yescharacteristic
125C22×C43⋊C8C2311yescharacteristic
126#13063323—22no—
127#13063323C2314yes—
128#13063321—22no—
129#13063321C2314yes—
130#13063313—22no—
131#13063313C2314yes—
132#13063298—28no—
133#13063298—28no—
134Q8×Dic43—22no—
135Q8×Dic43C2314yes—
136C4×Dic86—22no—
137C4×Dic86—28no—
138C4×Dic86C2314yes—
139#13063290—22no—
140#13063290—28no—
141#13063290C2314yes—
142(C22⋊D43)⋊C4—28no—
143(C22⋊D43)⋊C4—28no—
144C2×C4⋊Dic43—21no—
145C2×C4⋊Dic43C2311yescharacteristic
146C2×Dic43⋊C4—21no—
147C2×Dic43⋊C4—21no—
148C2×Dic43⋊C4—21no—
149C2×Dic43⋊C4—21no—
150C2×Dic43⋊C4—21no—
151C4⋊C4×D43—28no—
152C4⋊C4×D43—22no—
153C4⋊C4×D43C2314yes—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×C4×Dic43—21no—
157C2×C4×Dic43—21no—
158C2×C4×Dic43—21no—
159C2×C4×Dic43D411yescharacteristic
160C2×C4×Dic43D411yescharacteristic
161C2×C4×Dic43C2311yescharacteristic
162C42×D43—28no—
163C42×D43D414yes—
164C42×D43C2314yes—
165C4⋊(C43⋊C8)C2314yes—
166Dic43⋊C8C2314yes—
167Dic43⋊C8C2314yes—
168#13063250C2314yes—
169#13063249C2314yes—
170#13063248C2314yes—
171#13063247C2314yes—
172#13063246C2314yes—
173#13063245C2314yes—
174C22×Q8×C43C2311yescharacteristic
175C22×Q8×C43C2311yescharacteristic
176C22×D4×C43C2311yescharacteristic
177C2×Q16×C43—24no—
178C2×Q16×C43C2314yes—
179C2×SD16×C43—24no—
180C2×SD16×C43C2314yes—
181C22×C8×C43C2311yescharacteristic
182C22×C8×C43C2311yescharacteristic
183#124×C43—22no—
184#124×C43C2314yes—
185C4×Q8×C43—22no—
186C4×Q8×C43C2314yes—
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43C2311yescharacteristic
189C2×C22⋊C4×C43—21no—
190C2×C22⋊C4×C43—21no—
191C2×C42×C43—21no—
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43C2314yes—
194#103×C43C2314yes—
195#102×C43C2314yes—
196C24×C43—21no—
197C23×D43—21no—
198C23×D43C2×D411yescharacteristic
199C2×Q8×C43—21no—
200C2×Q8×C43—21no—
201C2×Q8×C43—22no—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43C2×D414yes—
205C2×Q8×C43C2412yes—
206C2×Q8×C43C2412yes—
207C2×D4×C43—21no—
208C2×D4×C43—22no—
209C2×D4×C43—22no—
210C2×D4×C43C2412yes—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—44no—
221C2×C22⋊D43—44no—
222C2×C22⋊D43—44no—
223C22×Dic43—24no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—44no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231#10621902—28no—
232#10621902—28no—
233#10621902—48no—
234Q8×D43—216no—
235Q8×D43—28no—
236Q8×D43C2×D4116yescomplemented
237#10621900—28no—
238#10621900—28no—
239#10621900—48no—
240C2×D172—21no—
241C2×D172—24no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—44no—
245C2×D172C2412yes—
246C2×C4×D43—24no—
247C2×C4×D43—24no—
248C2×C4×D43—28no—
249C2×C4×D43—24no—
250C2×C4×D43—24no—
251C2×C4×D43—42no—
252C2×C4×D43—44no—
253C2×C4×D43—44no—
254C2×C4×D43C2×D414yes—
255C2×C4×D43C2×D414yes—
256C2×C4×D43C2×D414yes—
257C2×C4×D43C2×D412yes—
258C2×C4×D43#4114yes—
259C2×C4×D43C2412yes—
260C2×Dic86—21no—
261C2×Dic86—22no—
262C2×Dic86—28no—
263C2×Dic86—24no—
264C2×Dic86—22no—
265C2×Dic86—22no—
266C2×Dic86—21no—
267C2×Dic86C2×D414yes—
268C2×Dic86C2412yes—
269C2×Dic86C2412yes—
270Q16×C43—28no—
271SD16×C43—28no—
272C2×C8×C43—22no—
273C2×C8×C43—22no—
274C2×C8×C43C2412yes—
275C2×C8×C43C2412yes—
276C4⋊C4×C43—24no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43C2412yes—
279C22⋊C4×C43—24no—
280C22⋊C4×C43—24no—
281C42×C43—24no—
282C42×C43C2×D412yes—
283C42×C43C2412yes—
284#10621885—28no—
285#10621885—28no—
286#10621884—28no—
287#10621883—28no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—24no—
290C4⋊Dic43—21no—
291C4⋊Dic43—24no—
292C4⋊Dic43C2412yes—
293Dic43⋊C4—24no—
294Dic43⋊C4—24no—
295Dic43⋊C4—24no—
296Dic43⋊C4—24no—
297Dic43⋊C4—24no—
298C4×Dic43—24no—
299C4×Dic43—24no—
300C4×Dic43—24no—
301C4×Dic43C2×D412yes—
302C4×Dic43C2×D414yes—
303C4×Dic43C2×D414yes—
304C4×Dic43C2412yes—
305C2×C43⋊C8—22no—
306C2×C43⋊C8—22no—
307C2×C43⋊C8C2412yes—
308C2×C43⋊C8C2412yes—
309Dic172—28no—
310#10621873—28no—
311#10621872—28no—
312#10621872—28no—
313C23×C43—22no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43C22×D411yescharacteristic
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43—42no—
324C22×D43#12114yes—
325C22×D43C22×D412yes—
326Q8×C43—24no—
327Q8×C43—22no—
328Q8×C43—22no—
329Q8×C43—22no—
330Q8×C43—42no—
331Q8×C43C22×D414yes—
332D4×C43—22no—
333D4×C43—22no—
334D4×C43—42no—
335C2×C4×C43—24no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43C22×D412yes—
344C2×C4×C43C22×D412yes—
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D412yes—
347C2×C4×C43C2×#4112yes—
348C2×C4×C43C2511yescharacteristic
349C22⋊D43—48no—
350C22⋊D43—48no—
351C22⋊D43—48no—
352C2×Dic43—24no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—42no—
358C2×Dic43—42no—
359C2×Dic43—48no—
360C2×Dic43#12114yes—
361C2×Dic43#13714yescomplemented
362C2×Dic43C22×D412yes—
363C2×Dic43C22×D412yes—
364C2×Dic43C22×D412yes—
365D172—22no—
366D172—22no—
367D172—48no—
368D172—42no—
369C4×D43—216no—
370C4×D43—28no—
371C4×D43—44no—
372C4×D43—48no—
373C4×D43—48no—
374C4×D43#12118yes—
375C4×D43C22×D414yes—
376C4×D43C2×#4114yes—
377Dic86—24no—
378Dic86—22no—
379Dic86—216no—
380Dic86—22no—
381Dic86—22no—
382Dic86—42no—
383Dic86C22×D414yes—
384C8×C43—22no—
385C8×C43—22no—
386C43⋊C8—22no—
387C43⋊C8—22no—
388C2×#3037—431nomaximal, Sylow
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43—84no—
393C22×C43C2×#12112yes—
394C22×C43C2×#13712yes—
395C22×C43#57512yes—
396C22×C43C23×D411yescharacteristic
397C2×D43—28no—
398C2×D43—22no—
399C2×D43—22no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—84no—
404C2×D43C2×#12114yes—
405C4×C43—24no—
406C4×C43—22no—
407C4×C43—22no—
408C4×C43—42no—
409C4×C43—42no—
410C4×C43C2×#12112yes—
411C4×C43C23×D411yescharacteristic
412C4×C43C22×#4111yescharacteristic
413Dic43—24no—
414Dic43—22no—
415Dic43—42no—
416Dic43—42no—
417Dic43C2×#12114yes—
418Dic43C2×#13714yescomplemented
419C22×#137—431no—
420C22×#137—431no—
421C2×#532—431no—
422C22×C4×Q8—431no—
423#3037—4316no—
424C2×#464—431no—
425C2×#464—431no—
426C2×#464—431no—
427C2×#464D4311yescharacteristic, complemented
428C2×#462—431no—
429C2×#462—431no—
430C2×#460—431no—
431C2×#460—431no—
432C2×#423—431no—
433C2×#417—431no—
434C2×#417—431no—
435C2×C43—82no—
436C2×C43#303714yescomplemented
437C2×C43C22×#12111yescharacteristic
438C2×C43C22×#13711yescharacteristic
439C2×C43C2×#57511yescharacteristic
440D43—24no—
441D43—82no—
442C22×#41—431no—
443C22×#41—431no—
444C23×Q8—431no—
445C2×#137—438no—
446C2×#137—438no—
447C2×#137—868no—
448C2×#137—868no—
449C22×Q16—431no—
450C22×Q16—431no—
451C22×Q16—431no—
452C22×Q16C2×D4311yescharacteristic
453C22×SD16—431no—
454C22×SD16—431no—
455C22×SD16—431no—
456C22×SD16C2×D4311yescharacteristic
457C22×M16—431no—
458C22×M16—431no—
459#532—438no—
460#532—864no—
461C2×C4⋊Q8—431no—
462C2×#127—431no—
463C2×#124—431no—
464C2×#124C2×D4311yescharacteristic
465C2×#121—861no—
466C2×#121—861no—
467C2×C4×Q8—431no—
468C2×C4×Q8—438no—
469C2×C4×Q8—431no—
470C2×C4×Q8—431no—
471C2×C4×Q8—861no—
472C2×C4×Q8—861no—
473C2×C4×Q8—864no—
474C2×C4×Q8C2×D4311yescharacteristic
475C2×C4×D4—861no—
476C2×C4×D4—861no—
477C22×C4⋊C4—431no—
478C22×C4⋊C4—861no—
479C22×C42—431no—
480C22×C42—861no—
481#464—438no—
482#464—438no—
483#464—438no—
484#464C2×D4318yescomplemented
485#462—438no—
486#462—438no—
487#460—438no—
488#460—438no—
489#423—438no—
490C2×C4⋊C8—431no—
491C2×C4⋊C8—431no—
492C2×C4⋊C8—431no—
493C2×C4⋊C8C2×D4311yescharacteristic
494#417—438no—
495#417—438no—
496C2×#103—431no—
497C2×#103—431no—
498C2×#103—431no—
499C2×#103C2×D4311yescharacteristic
500C2×#102—431no—
501C2×#102—431no—
502C2×#102—431no—
503C2×#102C2×D4311yescharacteristic
504C43C2×#303711yescharacteristic, complemented, Sylow
505C2×#41—434no—
506C2×#41—434no—
507C2×#41—862no—
508C2×#41—862no—
509C2×#41—864no—
510C2×#41—864no—
511C2×#41—864no—
512C2×#41—864no—
513C22×Q8—438no—
514C22×Q8—434no—
515C22×Q8—431no—
516C22×Q8—431no—
517C22×Q8—861no—
518C22×Q8—862no—
519C22×Q8—864no—
520C22×Q8C22×D4311yescharacteristic
521C22×Q8C22×D4311yescharacteristic
522C22×D4—431no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4—861no—
527C22×D4C22×D4311yescharacteristic
528C23×C4—431no—
529C23×C4—431no—
530C23×C4—431no—
531C23×C4—861no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4—861no—
535#137—8632no—
536#137—8632no—
537C2×Q16—24no—
538C2×Q16—434no—
539C2×Q16—434no—
540C2×Q16—434no—
541C2×Q16—864no—
542C2×Q16—864no—
543C2×Q16—864no—
544C2×Q16C22×D4314yes—
545C2×SD16—24no—
546C2×SD16—434no—
547C2×SD16—434no—
548C2×SD16—434no—
549C2×SD16—864no—
550C2×SD16—864no—
551C2×SD16—864no—
552C2×SD16C22×D4314yes—
553C2×M16—434no—
554C2×M16—434no—
555C2×M16—864no—
556C2×M16—864no—
557C22×C8—431no—
558C22×C8—431no—
559C22×C8C22×D4311yescharacteristic
560C22×C8C22×D4311yescharacteristic
561C4⋊Q8—434no—
562C4⋊Q8—862no—
563#127—434no—
564#127—862no—
565#124—22no—
566#124—434no—
567#124—862no—
568#124C22×D4314yes—
569#121—868no—
570#121—868no—
571C4×Q8—22no—
572C4×Q8—434no—
573C4×Q8—434no—
574C4×Q8—434no—
575C4×Q8—868no—
576C4×Q8—868no—
577C4×Q8—862no—
578C4×Q8—862no—
579C4×Q8—862no—
580C4×Q8C22×D4314yes—
581C4×D4—868no—
582C4×D4—868no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—431no—
585C2×C4⋊C4—434no—
586C2×C4⋊C4—862no—
587C2×C4⋊C4—868no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4C22×D4311yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C42—21no—
600C2×C42—431no—
601C2×C42—431no—
602C2×C42—431no—
603C2×C42—434no—
604C2×C42—434no—
605C2×C42—868no—
606C2×C42—861no—
607C2×C42—861no—
608C2×C42—861no—
609C2×C42C22×D4311yescharacteristic
610C4⋊C8—434no—
611C4⋊C8—434no—
612C4⋊C8—434no—
613C4⋊C8C22×D4314yes—
614#103—434no—
615#103—434no—
616#103—434no—
617#103C22×D4314yes—
618#102—434no—
619#102—434no—
620#102—434no—
621#102C22×D4314yes—
622C24—21no—
623C24—431no—
624C24—861no—
625#41—868no—
626#41—868no—
627#41—868no—
628#41—868no—
629#41—1728no—
630#41—1728no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—4316no—
637C2×Q8—434no—
638C2×Q8—432no—
639C2×Q8—432no—
640C2×Q8—864no—
641C2×Q8—868no—
642C2×Q8—8616no—
643C2×Q8—868no—
644C2×Q8—861no—
645C2×Q8—861no—
646C2×Q8—862no—
647C2×Q8—862no—
648C2×Q8—862no—
649C2×Q8D4×D4314yes—
650C2×Q8C23×D4312yes—
651C2×Q8C23×D4312yes—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—22no—
655C2×D4—432no—
656C2×D4—864no—
657C2×D4—864no—
658C2×D4—864no—
659C2×D4—864no—
660C2×D4—862no—
661C2×D4—861no—
662C2×D4—862no—
663C2×D4—1724no—
664C2×D4—1724no—
665C2×D4—1724no—
666C2×D4—1724no—
667C2×D4C23×D4312yes—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—432no—
674C22×C4—434no—
675C22×C4—434no—
676C22×C4—432no—
677C22×C4—431no—
678C22×C4—434no—
679C22×C4—434no—
680C22×C4—864no—
681C22×C4—864no—
682C22×C4—864no—
683C22×C4—868no—
684C22×C4—864no—
685C22×C4—864no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—1722no—
690C22×C4—1724no—
691C22×C4—1724no—
692C22×C4—1724no—
693C22×C4D4×D4311yescharacteristic
694C22×C4D4×D4311yescharacteristic
695C22×C4C23×D4311yescharacteristic
696Q16—28no—
697Q16—868no—
698Q16—868no—
699Q16—868no—
700SD16—28no—
701SD16—868no—
702SD16—868no—
703SD16—868no—
704M16—868no—
705M16—868no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—432no—
709C2×C8—432no—
710C2×C8—862no—
711C2×C8—862no—
712C2×C8C23×D4312yes—
713C2×C8C23×D4312yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—432no—
717C4⋊C4—864no—
718C4⋊C4—864no—
719C4⋊C4—864no—
720C4⋊C4—864no—
721C4⋊C4—864no—
722C4⋊C4—861no—
723C4⋊C4—864no—
724C4⋊C4C23×D4312yes—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—864no—
728C22⋊C4—864no—
729C42—24no—
730C42—434no—
731C42—434no—
732C42—432no—
733C42—432no—
734C42—864no—
735C42—864no—
736C42—864no—
737C42D4×D4312yes—
738C42C23×D4312yes—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—434no—
744C23—432no—
745C23—862no—
746C23—862no—
747C23—862no—
748C23—1722no—
749C23—1722no—
750C23—1722no—
751C23C2×D4×D4311yescharacteristic
752Q8—24no—
753Q8—22no—
754Q8—22no—
755Q8—22no—
756Q8—42no—
757Q8—434no—
758Q8—8616no—
759Q8—864no—
760Q8—862no—
761Q8—862no—
762Q8—862no—
763Q8—1722no—
764Q8C2×D4×D4314yes—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—862no—
769D4—862no—
770D4—1728no—
771D4—1728no—
772D4—1728no—
773D4—1728no—
774D4—1722no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—434no—
784C2×C4—434no—
785C2×C4—432no—
786C2×C4—432no—
787C2×C4—438no—
788C2×C4—434no—
789C2×C4—434no—
790C2×C4—432no—
791C2×C4—868no—
792C2×C4—8616no—
793C2×C4—864no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—1724no—
799C2×C4—1728no—
800C2×C4—1728no—
801C2×C4—1728no—
802C2×C4—1722no—
803C2×C4—1722no—
804C2×C4C2×D4×D4312yes—
805C2×C4C2×D4×D4312yes—
806C2×C4C2×D4×D4311yescharacteristic
807C2×C4C2×D4×D4312yes—
808C2×C4#41×D4312yes—
809C2×C4C24×D4311yescharacteristic
810C8—22no—
811C8—22no—
812C8—862no—
813C8—862no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—84no—
818C22—434no—
819C22—862no—
820C22—862no—
821C22—868no—
822C22—3444no—
823C22—1722no—
824C22—1722no—
825C22—1722no—
826C22#121×D4312yes—
827C22#137×D4312yes—
828C22#1458369612yes—
829C22C22×D4×D4311yescharacteristic
830C4—22no—
831C4—22no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—434no—
836C4—434no—
837C4—862no—
838C4—864no—
839C4—1722no—
840C4—1722no—
841C4#121×D4312yes—
842C4C22×D4×D4311yescharacteristic
843C4C2×#41×D4311yescharacteristic
844C2—82no—
845C2—864no—
846C2—3442no—
847C2#1914406514yesdirect product factor
848C2C2×#121×D4311yescharacteristic
849C2C2×#137×D4311yescharacteristic
850C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#14583448C2
hypercenterC2×#464D43
hypocenterC43C2×#3037
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. C22×#13063357C2semidirect
2. C22×#13063354C2semidirect
4. C2×C4×Q8×D43C2semidirect
5. #19144065C2direct (N × H)
6. C2×#14583122C2semidirect
7. C2×#14583121C2semidirect
8. C2×#14583118C2semidirect
9. C2×#14583108C2semidirect
10. C2×#14583107C2semidirect
11. C2×#14583098C2semidirect
12. C2×#14583097C2semidirect
13. C2×#14582921C2semidirect
14. C2×#14582899C2semidirect
15. C2×#14582897C2semidirect
16. C2×C43×#464C2semidirect
21. C2×#13063357C22semidirect
23. C2×#13063354C22semidirect
45. C4×Q8×D43C22semidirect
52. #14583122C22semidirect
53. #14583121C22semidirect
54. #14583118C22semidirect
55. #14583108C22semidirect
56. #14583107C22semidirect
57. #14583098C22semidirect
58. #14583097C22semidirect
59. #14582921C22semidirect
63. #14582899C22semidirect
64. #14582897C22semidirect
75. C43×#464C22semidirect
92. C2×Q8×D43D4semidirect
236. Q8×D43C2×D4semidirect
361. C2×Dic43#137semidirect
418. Dic43C2×#137semidirect
427. C2×#464D43semidirect
436. C2×C43#3037semidirect
484. #464C2×D43semidirect
504. C43C2×#3037semidirect
847. C2#19144065direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633572
C22×#130633542
C2×#145834482
C2×C4×Q8×D432
#191440652
C2×#145831222
C2×#145831212
C2×#145831182
C2×#145831082
C2×#145831072
C2×#145830982
C2×#145830972
C2×#145829212
C2×#145828992
C2×#145828972
C2×C43×#4642
C2×#303743