Finite Group Databasebeta

← #25965060

Subgroups — #25965060

Order 11008.

2180 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583435C211yesmaximal, characteristic, complemented
2C2×#41×Dic43C211yesmaximal, characteristic, complemented
3#19144767C212yesmaximal, complemented
4#19144734C212yesmaximal, complemented
5#19144705C214yesmaximal, complemented
6#19144676C212yesmaximal, complemented
7#19144643C212yesmaximal, complemented
8#19144614C214yesmaximal, complemented
9#19144539C211yesmaximal, characteristic, complemented
10#19144536C211yesmaximal, characteristic, complemented
11#19144415C212yesmaximal, complemented
12#19144091C212yesmaximal, complemented
13#19143847C211yesmaximal, characteristic
14#137×Dic43C212yesmaximal, complemented
15#19143408C212yesmaximal, complemented
16#19143224C211yesmaximal, characteristic, complemented
17C43×#3007C211yesmaximal, characteristic, complemented
18C2×#13063350C2212yes—
19#14583435—21no—
20#14583435—21no—
21#14583435—21no—
22#14583435—21no—
23#14583435C2212yes—
24#14583435C2212yes—
25#14583435C2212yescomplemented
26#14583435C2212yescomplemented
27C2×#13063320—21no—
28C2×#13063316C2211yescharacteristic, complemented
29C2×#13063314C2211yescharacteristic, complemented
30C2×#13063309—21no—
31C2×#13063299C2211yescharacteristic
32#41×Dic43—21no—
33#41×Dic43—21no—
34#41×Dic43—21no—
35#41×Dic43—21no—
36#41×Dic43C2212yes—
37#41×Dic43C2212yes—
38#41×Dic43C2212yescomplemented
39#41×Dic43C2212yescomplemented
40C2×Q8×Dic43C2211yescharacteristic, complemented
41C2×Q8×Dic43C2211yescharacteristic, complemented
42C2×Q8×Dic43C2211yescharacteristic, complemented
43C2×D4×Dic43—21no—
44C2×D4×Dic43—21no—
45C2×D4×Dic43C2211yescharacteristic, complemented
46C2×D4×Dic43C2211yescharacteristic, complemented
47C2×#13063287C2211yescharacteristic, complemented
48C2×(C22⋊D43)⋊C4—21no—
49C2×#13063284—21no—
50C2×#13063284C2211yescharacteristic
51C2×#13063283—21no—
52C22×C4×Dic43—21no—
53C22×C4×Dic43C2211yescharacteristic
54#14583237C2214yescomplemented
55#14583232C2212yescomplemented
56#14583227C2212yescomplemented
57#14583224C2214yescomplemented
58#14583218C2212yes—
59#14583213C2212yes—
60#14583208C2214yescomplemented
61#14583204C2214yescomplemented
62#14583201C2214yescomplemented
63#14583197C2214yescomplemented
64#14583123C2214yescomplemented
65#14583123C2214yescomplemented
66#14583116C2214yescomplemented
67#14583116C2214yescomplemented
68#14583044C2214yes—
69#14583038C2212yes—
70#14583033C2212yes—
71#14583008C2214yescomplemented
72#14583006C2214yescomplemented
73#14583002C2214yescomplemented
74#14583000C2214yescomplemented
75Q16×Dic43C2214yescomplemented
76SD16×Dic43C2214yescomplemented
77#14582984C2214yescomplemented
78#14582979C2214yescomplemented
79#14582953C2212yescomplemented
80#14582953C2212yescomplemented
81#14582949C2212yescomplemented
82#14582949C2212yescomplemented
83#14582941C2212yescomplemented
84#14582939C2212yescomplemented
85#14582922C2212yescomplemented
86#14582908C2212yescomplemented
87#14582905C2212yescomplemented
88#14582900C2212yes—
89#14582863C2211yescharacteristic
90M16×Dic43C2212yescomplemented
91C22×#41×C43C2211yescharacteristic
92C2×#137×C43C2212yes—
93C2×C22⋊Q8×C43C2211yescharacteristic
94C43×#452C2214yescomplemented
95C43×#451C2212yescomplemented
96C43×#450C2212yescomplemented
97C43×#417C2212yes—
98C43×#407C2211yescharacteristic
99C22×D172C2311yescharacteristic
100C22×C22⋊D43—21no—
101C23×Dic43—21no—
102C23×Dic43—21no—
103C23×Dic43D411yescharacteristic
104C23×Dic43D411yescharacteristic
105C22×C4×D43—21no—
106#13063350—28no—
107C2×#10621884C2314yes—
108C2×#10621882C2314yes—
109C2×#10621877C2312yes—
110#13063320—22no—
111#13063320—22no—
112#13063320—22no—
113#13063320—22no—
114#13063316—21no—
115#13063316—21no—
116#13063316C2312yes—
117#13063316C2312yes—
118#13063314—21no—
119#13063314—21no—
120#13063314C2312yes—
121#13063314C2312yes—
122#13063309—22no—
123#13063309—22no—
124#13063309—22no—
125#13063309—22no—
126#13063299—21no—
127#13063299—21no—
128#13063299C2312yes—
129#13063299C2312yes—
130Q8×Dic43—21no—
131Q8×Dic43—21no—
132Q8×Dic43—21no—
133Q8×Dic43—21no—
134Q8×Dic43—21no—
135Q8×Dic43—21no—
136Q8×Dic43C2312yes—
137Q8×Dic43C2312yes—
138Q8×Dic43C2312yes—
139Q8×Dic43C2312yes—
140Q8×Dic43C2312yes—
141Q8×Dic43C2312yes—
142D4×Dic43—22no—
143D4×Dic43—22no—
144D4×Dic43—22no—
145D4×Dic43—22no—
146D4×Dic43—22no—
147D4×Dic43—22no—
148D4×Dic43—22no—
149D4×Dic43—22no—
150D4×Dic43—21no—
151D4×Dic43—21no—
152D4×Dic43—21no—
153D4×Dic43—21no—
154D4×Dic43C2312yes—
155D4×Dic43C2312yes—
156D4×Dic43C2312yes—
157D4×Dic43C2312yes—
158#13063287—21no—
159#13063287—21no—
160#13063287C2312yes—
161#13063287C2312yes—
162(C22⋊D43)⋊C4—22no—
163(C22⋊D43)⋊C4—22no—
164(C22⋊D43)⋊C4—22no—
165(C22⋊D43)⋊C4—22no—
166#13063284—21no—
167#13063284—21no—
168#13063284—22no—
169#13063284—22no—
170#13063284—22no—
171#13063284—22no—
172#13063284C2312yes—
173#13063284C2312yes—
174#13063283—22no—
175#13063283—22no—
176#13063283—22no—
177#13063283—22no—
178C2×C4⋊Dic43—21no—
179C2×C4⋊Dic43—21no—
180C2×C4⋊Dic43—21no—
181C2×C4⋊Dic43—21no—
182C2×C4⋊Dic43C2311yescharacteristic
183C2×C4⋊Dic43C2311yescharacteristic
184C2×C4⋊Dic43C2311yescharacteristic
185C2×Dic43⋊C4—21no—
186C2×C22⋊Dic43—21no—
187C2×C22⋊Dic43—21no—
188C2×C22⋊Dic43—21no—
189C2×(C2×D43)⋊C4—21no—
190C2×(C2×D43)⋊C4—21no—
191C2×(C2×D43)⋊C4—21no—
192C2×(C2×D43)⋊C4—21no—
193C2×C4×Dic43—21no—
194C2×C4×Dic43—21no—
195C2×C4×Dic43—21no—
196C2×C4×Dic43—21no—
197C2×C4×Dic43—22no—
198C2×C4×Dic43—22no—
199C2×C4×Dic43—22no—
200C2×C4×Dic43—22no—
201C2×C4×Dic43D411yescharacteristic
202C2×C4×Dic43D411yescharacteristic
203C2×C4×Dic43D411yescharacteristic
204C2×C4×Dic43D411yescharacteristic
205C2×C4×Dic43D411yescharacteristic
206C2×C4×Dic43D411yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211C2×C4×Dic43C2311yescharacteristic
212C2×C4×Dic43C2311yescharacteristic
213#13063259C2314yes—
214#13063258C2314yes—
215#13063257C2314yes—
216#13063256C2314yes—
217Dic43⋊C8C2314yes—
218Dic43⋊C8C2314yes—
219#13063249C2314yes—
220#13063249C2314yes—
221#13063249C2314yes—
222#13063247C2314yes—
223#13063247C2314yes—
224#13063246C2314yes—
225C22⋊(C43⋊C8)C2312yes—
226C22⋊(C43⋊C8)C2312yes—
227#13063235C2314yes—
228C8×Dic43C2314yes—
229C2×#41×C43—28no—
230C2×#41×C43—21no—
231C2×#41×C43—21no—
232C2×#41×C43C2312yes—
233C2×#41×C43C2312yes—
234C22×Q8×C43C2311yescharacteristic
235C22×Q8×C43C2311yescharacteristic
236C22×D4×C43—21no—
237C22×D4×C43C2311yescharacteristic
238C23×C4×C43—21no—
239C23×C4×C43C2311yescharacteristic
240#137×C43—28no—
241C2×Q16×C43C2314yes—
242C2×SD16×C43C2314yes—
243C2×M16×C43C2312yes—
244C22⋊Q8×C43—21no—
245C22⋊Q8×C43—21no—
246C22⋊Q8×C43C2312yes—
247C22⋊Q8×C43C2312yes—
248C2×C4⋊C4×C43—21no—
249C2×C4⋊C4×C43C2311yescharacteristic
250C2×C22⋊C4×C43—21no—
251#103×C43C2314yes—
252#102×C43C2314yes—
253C22⋊C8×C43C2312yes—
254C22⋊C8×C43C2312yes—
255C24×C43—21no—
256C24×C43C2×D411yescharacteristic
257C23×D43—21no—
258#41×C43—28no—
259#41×C43—28no—
260#41×C43—24no—
261#41×C43—24no—
262#41×C43—24no—
263#41×C43#4118yes—
264C2×Q8×C43—24no—
265C2×Q8×C43—21no—
266C2×Q8×C43—21no—
267C2×Q8×C43—24no—
268C2×Q8×C43C2412yes—
269C2×Q8×C43C2412yes—
270C2×D4×C43—28no—
271C2×D4×C43—24no—
272C2×D4×C43—21no—
273C2×D4×C43—22no—
274C2×D4×C43—22no—
275C2×D4×C43C2412yes—
276C22×C4×C43—28no—
277C22×C4×C43—22no—
278C22×C4×C43—22no—
279C22×C4×C43—24no—
280C22×C4×C43—21no—
281C22×C4×C43—21no—
282C22×C4×C43—21no—
283C22×C4×C43C2×D411yescharacteristic
284C22×C4×C43C2×D411yescharacteristic
285C22×C4×C43C2×D411yescharacteristic
286C22×C4×C43C2411yescharacteristic
287C22×C4×C43C2411yescharacteristic
288C22×C4×C43C2411yescharacteristic
289C2×C22⋊D43—22no—
290C2×C22⋊D43—22no—
291C2×C22⋊D43—44no—
292C22×Dic43—22no—
293C22×Dic43—22no—
294C22×Dic43—22no—
295C22×Dic43—22no—
296C22×Dic43—21no—
297C22×Dic43—21no—
298C22×Dic43—21no—
299C22×Dic43—42no—
300C22×Dic43—42no—
301C22×Dic43—44no—
302C22×Dic43—44no—
303C22×Dic43C2×D411yescharacteristic
304C22×Dic43C2×D411yescharacteristic
305C22×Dic43C2×D411yescharacteristic
306C22×Dic43C2×D411yescharacteristic
307C22×Dic43C2×D411yescharacteristic
308C22×Dic43C2×D411yescharacteristic
309C22×Dic43C2×D411yescharacteristic
310C22×Dic43C2×D411yescharacteristic
311C22×Dic43C2×D411yescharacteristic
312C22×Dic43C2×D411yescharacteristic
313C22×Dic43C2×D411yescharacteristic
314C22×Dic43C2×D411yescharacteristic
315C2×D172—21no—
316C2×D172—24no—
317C2×D172C2412yes—
318C2×C4×D43—22no—
319C2×C4×D43—22no—
320C2×C4×D43—44no—
321Q16×C43—28no—
322SD16×C43—28no—
323M16×C43—24no—
324C2×C8×C43C2414yes—
325C4⋊C4×C43—22no—
326C4⋊C4×C43—22no—
327C4⋊C4×C43—21no—
328C4⋊C4×C43C2412yes—
329C22⋊C4×C43—22no—
330C22⋊C4×C43—22no—
331C22⋊Dic43—22no—
332C22⋊Dic43—22no—
333C22⋊Dic43—22no—
334C22⋊Dic43—22no—
335C22⋊Dic43—22no—
336C22⋊Dic43—22no—
337#10621884—28no—
338#10621882—28no—
339(C2×D43)⋊C4—22no—
340(C2×D43)⋊C4—22no—
341(C2×D43)⋊C4—22no—
342(C2×D43)⋊C4—22no—
343(C2×D43)⋊C4—22no—
344(C2×D43)⋊C4—22no—
345(C2×D43)⋊C4—22no—
346(C2×D43)⋊C4—22no—
347C4⋊Dic43—21no—
348C4⋊Dic43—21no—
349C4⋊Dic43—21no—
350C4⋊Dic43—22no—
351C4⋊Dic43—22no—
352C4⋊Dic43—22no—
353C4⋊Dic43—22no—
354C4⋊Dic43—22no—
355C4⋊Dic43—22no—
356C4⋊Dic43—22no—
357C4⋊Dic43—22no—
358C4⋊Dic43C2412yes—
359C4⋊Dic43C2412yes—
360C4⋊Dic43C2412yes—
361Dic43⋊C4—22no—
362Dic43⋊C4—22no—
363C4×Dic43—22no—
364C4×Dic43—22no—
365C4×Dic43—22no—
366C4×Dic43—22no—
367C4×Dic43—22no—
368C4×Dic43—22no—
369C4×Dic43—22no—
370C4×Dic43—22no—
371C4×Dic43C2×D411yescharacteristic
372C4×Dic43C2×D411yescharacteristic
373C4×Dic43C2×D411yescharacteristic
374C4×Dic43C2×D411yescharacteristic
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2×D411yescharacteristic
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2411yescharacteristic
384C4×Dic43C2411yescharacteristic
385C4×Dic43C2411yescharacteristic
386C4×Dic43C2411yescharacteristic
387#10621877—24no—
388C2×C43⋊C8C2414yes—
389C23×C43—24no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—22no—
393C23×C43—41no—
394C23×C43—42no—
395C23×C43—42no—
396C23×C43C22×D411yescharacteristic
397C23×C43C22×D411yescharacteristic
398C23×C43C22×D411yescharacteristic
399C22×D43—22no—
400C22×D43—42no—
401C22×D43—42no—
402C22×D43—42no—
403Q8×C43—24no—
404Q8×C43—22no—
405Q8×C43—24no—
406Q8×C43—42no—
407Q8×C43C2×#4114yes—
408D4×C43—28no—
409D4×C43—24no—
410D4×C43—28no—
411D4×C43—22no—
412D4×C43C2×#4114yes—
413C2×C4×C43—24no—
414C2×C4×C43—28no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—28no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—42no—
425C2×C4×C43—42no—
426C2×C4×C43C22×D411yescharacteristic
427C2×C4×C43C22×D411yescharacteristic
428C2×C4×C43C22×D411yescharacteristic
429C2×C4×C43C2×#4114yes—
430C2×C4×C43C2511yescharacteristic
431C22⋊D43—44no—
432C22⋊D43—44no—
433C2×Dic43—22no—
434C2×Dic43—22no—
435C2×Dic43—22no—
436C2×Dic43—22no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—41no—
442C2×Dic43—41no—
443C2×Dic43—41no—
444C2×Dic43—41no—
445C2×Dic43—41no—
446C2×Dic43—41no—
447C2×Dic43—41no—
448C2×Dic43—44no—
449C2×Dic43—44no—
450C2×Dic43—44no—
451C2×Dic43—42no—
452C2×Dic43—42no—
453C2×Dic43—42no—
454C2×Dic43—44no—
455C2×Dic43C22×D411yescharacteristic
456C2×Dic43C22×D411yescharacteristic
457C2×Dic43C22×D411yescharacteristic
458C2×Dic43C22×D411yescharacteristic
459C2×Dic43C22×D411yescharacteristic
460C2×Dic43C22×D411yescharacteristic
461C2×Dic43C22×D411yescharacteristic
462C2×Dic43C22×D411yescharacteristic
463D172—24no—
464D172—42no—
465C4×D43—44no—
466C4×D43—44no—
467C8×C43—24no—
468C43⋊C8—24no—
469#60563—431nomaximal, Sylow
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—24no—
475C22×C43—21no—
476C22×C43—21no—
477C22×C43—21no—
478C22×C43—44no—
479C22×C43—48no—
480C22×C43—42no—
481C22×C43—42no—
482C22×C43#52512yes—
483C22×C43#57512yes—
484C22×C43C23×D411yescharacteristic
485C2×D43—42no—
486C2×D43—42no—
487C2×D43—42no—
488C2×D43—84no—
489C4×C43—21no—
490C4×C43—24no—
491C4×C43—21no—
492C4×C43—42no—
493C4×C43—42no—
494C4×C43#52512yes—
495C4×C43C22×#4112yes—
496Dic43—21no—
497Dic43—21no—
498Dic43—21no—
499Dic43—21no—
500Dic43—21no—
501Dic43—21no—
502Dic43—21no—
503Dic43—42no—
504Dic43—42no—
505Dic43—42no—
506Dic43#57512yes—
507C2×#529—431no—
508C2×C4×#41—431no—
509#3117—432no—
510#3114—432no—
511#3111—434no—
512#3108—432no—
513#3105—432no—
514#3102—434no—
515#3095—431no—
516#3094—431no—
517#3080—432no—
518#3040—432no—
519#3007D4311yescharacteristic, complemented
520#3006—431no—
521C4×#137—432no—
522C4×AGL(1,ℤ/8)—432no—
523#2920—431no—
524C2×C43—22no—
525C2×C43—22no—
526C2×C43—41no—
527C2×C43—44no—
528C2×C43C2×#52511yescharacteristic
529C2×C43C2×#57511yescharacteristic
530C2×C43C2×#57511yescharacteristic
531D43—82no—
532C22×#41C2×D4311yescharacteristic
533C2×#137C2×D4312yes—
534C2×AGL(1,ℤ/8)—432no—
535#529—432no—
536#529—432no—
537#529—432no—
538#529—432no—
539#529—861no—
540#529—861no—
541#529—861no—
542#529—861no—
543C2×#126—861no—
544C2×#125—431no—
545C2×#124—431no—
546C2×#123—861no—
547C2×C22⋊Q8C2×D4311yescharacteristic
548C2×#121—431no—
549C4×#41—432no—
550C4×#41—432no—
551C4×#41—432no—
552C4×#41—432no—
553C4×#41—861no—
554C4×#41—861no—
555C4×#41—861no—
556C4×#41—861no—
557C2×C4×Q8—431no—
558C2×C4×Q8—431no—
559C2×C4×Q8—431no—
560C2×C4×D4—431no—
561C2×C4×D4—431no—
562C2×C4×D4—431no—
563C2×C4×D4—861no—
564C2×C4×D4—861no—
565C2×C4×D4—861no—
566C2×#117—431no—
567C2×#117—861no—
568C2×#117—861no—
569C22×C42—431no—
570C22×C42—861no—
571#485—434no—
572#484—432no—
573#483—432no—
574#482—434no—
575#481—432no—
576#480—432no—
577#479—434no—
578#479—434no—
579#478—434no—
580#478—434no—
581#464—434no—
582#464—434no—
583#463—434no—
584#463—434no—
585#452C2×D4314yescomplemented
586#451C2×D4312yescomplemented
587#450C2×D4312yescomplemented
588#449—434no—
589#448—432no—
590#447—432no—
591#442—434no—
592#441—434no—
593#440—434no—
594#440—434no—
595C4×Q16—434no—
596C4×SD16—434no—
597C4×SD16—434no—
598C4×D8—434no—
599#432—432no—
600#432—432no—
601#431—432no—
602#431—432no—
603#428—432no—
604#428—432no—
605#423—432no—
606#419—432no—
607#418—432no—
608#417—432no—
609#417C2×D4312yes—
610#407—431no—
611#407C2×D4311yescharacteristic
612C4×M16—432no—
613C43#6056311yescharacteristic, complemented, Sylow
614C2×#41—28no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41C22×D4312yes—
618C2×#41C22×D4312yes—
619C22×Q8C22×D4311yescharacteristic
620C22×Q8C22×D4311yescharacteristic
621C22×D4—21no—
622C22×D4—431no—
623C22×D4—861no—
624C22×D4C22×D4311yescharacteristic
625C23×C4—21no—
626C23×C4—431no—
627C23×C4—431no—
628C23×C4—861no—
629C23×C4—861no—
630C23×C4—861no—
631C23×C4C22×D4311yescharacteristic
632#137—28no—
633AGL(1,ℤ/8)—868no—
634C2×Q16C22×D4314yes—
635C2×SD16—434no—
636C2×SD16C22×D4314yes—
637C2×D8—434no—
638C2×M16—432no—
639C2×M16C22×D4312yes—
640#126—862no—
641#126—862no—
642#126—862no—
643#126—862no—
644#125—432no—
645#125—432no—
646#125—861no—
647#125—861no—
648#124—432no—
649#124—432no—
650#124—861no—
651#124—861no—
652#123—862no—
653#123—862no—
654#123—862no—
655#123—862no—
656C22⋊Q8—21no—
657C22⋊Q8—21no—
658C22⋊Q8C22×D4312yes—
659C22⋊Q8C22×D4312yes—
660#121—432no—
661#121—432no—
662#121—861no—
663#121—861no—
664C4×Q8—432no—
665C4×Q8—432no—
666C4×Q8—432no—
667C4×Q8—432no—
668C4×Q8—432no—
669C4×Q8—432no—
670C4×Q8—861no—
671C4×Q8—861no—
672C4×Q8—861no—
673C4×Q8—861no—
674C4×Q8—861no—
675C4×Q8—861no—
676C4×D4—432no—
677C4×D4—432no—
678C4×D4—432no—
679C4×D4—432no—
680C4×D4—432no—
681C4×D4—432no—
682C4×D4—861no—
683C4×D4—861no—
684C4×D4—861no—
685C4×D4—861no—
686C4×D4—861no—
687C4×D4—861no—
688C4×D4—862no—
689C4×D4—862no—
690C4×D4—862no—
691C4×D4—862no—
692C4×D4—862no—
693C4×D4—862no—
694C4×D4—862no—
695C4×D4—862no—
696C4×D4—862no—
697C4×D4—862no—
698C4×D4—862no—
699C4×D4—862no—
700#117—432no—
701#117—432no—
702#117—862no—
703#117—862no—
704#117—862no—
705#117—862no—
706#117—862no—
707#117—862no—
708#117—862no—
709#117—862no—
710#117—861no—
711#117—861no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—431no—
714C2×C4⋊C4—431no—
715C2×C4⋊C4—431no—
716C2×C4⋊C4—861no—
717C2×C4⋊C4—861no—
718C2×C4⋊C4—861no—
719C2×C4⋊C4—861no—
720C2×C4⋊C4—861no—
721C2×C4⋊C4C22×D4311yescharacteristic
722C2×C22⋊C4—21no—
723C2×C22⋊C4—861no—
724C2×C22⋊C4—861no—
725C2×C22⋊C4—861no—
726C2×C22⋊C4—861no—
727C2×C22⋊C4—861no—
728C2×C22⋊C4—861no—
729C2×C22⋊C4—861no—
730C2×C42—431no—
731C2×C42—431no—
732C2×C42—431no—
733C2×C42—431no—
734C2×C42—431no—
735C2×C42—431no—
736C2×C42—431no—
737C2×C42—431no—
738C2×C42—431no—
739C2×C42—431no—
740C2×C42—431no—
741C2×C42—431no—
742C2×C42—862no—
743C2×C42—862no—
744C2×C42—862no—
745C2×C42—862no—
746C2×C42—861no—
747C2×C42—861no—
748C2×C42—861no—
749C2×C42—861no—
750#107—434no—
751#107—434no—
752#106—434no—
753#106—434no—
754C4⋊C8—434no—
755C4⋊C8—434no—
756#103—434no—
757#103—434no—
758#103—434no—
759#103C22×D4314yes—
760#102—434no—
761#102—434no—
762#102—434no—
763#102C22×D4314yes—
764C22⋊C8—432no—
765C22⋊C8—432no—
766C22⋊C8C22×D4312yes—
767C22⋊C8C22×D4312yes—
768#97—434no—
769C4×C8—434no—
770C24—21no—
771C24—861no—
772C24D4×D4311yescharacteristic
773#41—28no—
774#41—28no—
775#41—24no—
776#41—24no—
777#41—24no—
778#41#1062190018yes—
779C2×Q8—24no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—24no—
783C2×Q8C23×D4312yes—
784C2×Q8C23×D4312yes—
785C2×D4—28no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—24no—
789C2×D4—21no—
790C2×D4—432no—
791C2×D4—862no—
792C2×D4—862no—
793C2×D4—861no—
794C2×D4—864no—
795C2×D4—1724no—
796C2×D4C23×D4312yes—
797C22×C4—28no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—431no—
805C22×C4—431no—
806C22×C4—431no—
807C22×C4—431no—
808C22×C4—431no—
809C22×C4—431no—
810C22×C4—431no—
811C22×C4—431no—
812C22×C4—431no—
813C22×C4—431no—
814C22×C4—431no—
815C22×C4—431no—
816C22×C4—862no—
817C22×C4—862no—
818C22×C4—862no—
819C22×C4—862no—
820C22×C4—862no—
821C22×C4—862no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—1724no—
826C22×C4—1722no—
827C22×C4—1722no—
828C22×C4—1724no—
829C22×C4—1724no—
830C22×C4D4×D4311yescharacteristic
831C22×C4D4×D4311yescharacteristic
832C22×C4D4×D4311yescharacteristic
833C22×C4C23×D4311yescharacteristic
834C22×C4C23×D4311yescharacteristic
835C22×C4C23×D4311yescharacteristic
836Q16—28no—
837SD16—28no—
838SD16—868no—
839D8—868no—
840M16—24no—
841M16—864no—
842C2×C8—434no—
843C2×C8C23×D4314yes—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—21no—
847C4⋊C4—432no—
848C4⋊C4—432no—
849C4⋊C4—432no—
850C4⋊C4—862no—
851C4⋊C4—862no—
852C4⋊C4—862no—
853C4⋊C4—862no—
854C4⋊C4—862no—
855C4⋊C4—862no—
856C4⋊C4—862no—
857C4⋊C4—862no—
858C4⋊C4—862no—
859C4⋊C4—862no—
860C4⋊C4—861no—
861C4⋊C4—861no—
862C4⋊C4—861no—
863C4⋊C4C23×D4312yes—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—862no—
867C22⋊C4—862no—
868C22⋊C4—862no—
869C22⋊C4—862no—
870C22⋊C4—862no—
871C22⋊C4—862no—
872C22⋊C4—862no—
873C22⋊C4—862no—
874C22⋊C4—862no—
875C22⋊C4—862no—
876C22⋊C4—862no—
877C22⋊C4—862no—
878C22⋊C4—862no—
879C22⋊C4—862no—
880C42—431no—
881C42—431no—
882C42—431no—
883C42—431no—
884C42—431no—
885C42—431no—
886C42—431no—
887C42—431no—
888C42—431no—
889C42—431no—
890C42—431no—
891C42—431no—
892C42—431no—
893C42—431no—
894C42—431no—
895C42—431no—
896C42—862no—
897C42—862no—
898C42—862no—
899C42—862no—
900C42—862no—
901C42—862no—
902C42—862no—
903C42—862no—
904C23—24no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—42no—
911C23—862no—
912C23—1722no—
913C23—1722no—
914C23—1722no—
915C23C2×D4×D4311yescharacteristic
916C23C2×D4×D4311yescharacteristic
917C23C2×D4×D4311yescharacteristic
918Q8—24no—
919Q8—22no—
920Q8—24no—
921Q8—42no—
922Q8C2×#1062190014yes—
923D4—28no—
924D4—24no—
925D4—28no—
926D4—22no—
927D4—864no—
928D4—1724no—
929D4—1724no—
930D4—1722no—
931D4C2×#1062190014yes—
932C2×C4—24no—
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—28no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—431no—
946C2×C4—431no—
947C2×C4—431no—
948C2×C4—431no—
949C2×C4—431no—
950C2×C4—431no—
951C2×C4—431no—
952C2×C4—431no—
953C2×C4—862no—
954C2×C4—862no—
955C2×C4—862no—
956C2×C4—862no—
957C2×C4—862no—
958C2×C4—862no—
959C2×C4—862no—
960C2×C4—862no—
961C2×C4—1724no—
962C2×C4—1724no—
963C2×C4—1724no—
964C2×C4—1721no—
965C2×C4—1721no—
966C2×C4—1721no—
967C2×C4—1721no—
968C2×C4—1721no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1724no—
972C2×C4—1724no—
973C2×C4—1724no—
974C2×C4—1722no—
975C2×C4—1722no—
976C2×C4—1722no—
977C2×C4C2×D4×D4311yescharacteristic
978C2×C4C2×D4×D4311yescharacteristic
979C2×C4C2×D4×D4311yescharacteristic
980C2×C4C2×#1062190014yes—
981C2×C4C24×D4311yescharacteristic
982C8—24no—
983C8—864no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—24no—
992C22—44no—
993C22—48no—
994C22—42no—
995C22—42no—
996C22—3444no—
997C22—1722no—
998C22—1722no—
999C22—1722no—
1000C22#1458340512yes—
1001C22#1458369812yes—
1002C22C22×D4×D4311yescharacteristic
1003C4—21no—
1004C4—24no—
1005C4—21no—
1006C4—42no—
1007C4—42no—
1008C4—432no—
1009C4—861no—
1010C4—861no—
1011C4—861no—
1012C4—861no—
1013C4—861no—
1014C4—861no—
1015C4—861no—
1016C4—1722no—
1017C4—1722no—
1018C4—1722no—
1019C4#1458340512yes—
1020C4C22×#1062190012yes—
1021C2—22no—
1022C2—22no—
1023C2—41no—
1024C2—44no—
1025C2—3442no—
1026C2C2×#1458340511yescharacteristic
1027C2#575×D4311yescharacteristic
1028C2C2×#1458369811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3007C2
socleC22×C43C23×D4
prime radical#19143847C2
hypercenter#3007D43
hypocenterC43#60563
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. C2×#14583435C2semidirect
2. C2×#41×Dic43C2semidirect
3. #19144767C2semidirect
4. #19144734C2semidirect
5. #19144705C2semidirect
6. #19144676C2semidirect
7. #19144643C2semidirect
8. #19144614C2semidirect
9. #19144539C2semidirect
10. #19144536C2semidirect
11. #19144415C2semidirect
12. #19144091C2semidirect
14. #137×Dic43C2semidirect
15. #19143408C2semidirect
16. #19143224C2semidirect
17. C43×#3007C2semidirect
25. #14583435C22semidirect
26. #14583435C22semidirect
28. C2×#13063316C22semidirect
29. C2×#13063314C22semidirect
38. #41×Dic43C22semidirect
39. #41×Dic43C22semidirect
40. C2×Q8×Dic43C22semidirect
41. C2×Q8×Dic43C22semidirect
42. C2×Q8×Dic43C22semidirect
45. C2×D4×Dic43C22semidirect
46. C2×D4×Dic43C22semidirect
47. C2×#13063287C22semidirect
54. #14583237C22semidirect
55. #14583232C22semidirect
56. #14583227C22semidirect
57. #14583224C22semidirect
60. #14583208C22semidirect
61. #14583204C22semidirect
62. #14583201C22semidirect
63. #14583197C22semidirect
64. #14583123C22semidirect
65. #14583123C22semidirect
66. #14583116C22semidirect
67. #14583116C22semidirect
71. #14583008C22semidirect
72. #14583006C22semidirect
73. #14583002C22semidirect
74. #14583000C22semidirect
75. Q16×Dic43C22semidirect
76. SD16×Dic43C22semidirect
77. #14582984C22semidirect
78. #14582979C22semidirect
79. #14582953C22semidirect
80. #14582953C22semidirect
81. #14582949C22semidirect
82. #14582949C22semidirect
83. #14582941C22semidirect
84. #14582939C22semidirect
85. #14582922C22semidirect
86. #14582908C22semidirect
87. #14582905C22semidirect
90. M16×Dic43C22semidirect
94. C43×#452C22semidirect
95. C43×#451C22semidirect
96. C43×#450C22semidirect
519. #3007D43semidirect
585. #452C2×D43semidirect
586. #451C2×D43semidirect
587. #450C2×D43semidirect
613. C43#60563semidirect

Maximal subgroups

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

subgroupindex
C2×#145834352
C2×#41×Dic432
#191447672
#191447342
#191447052
#191446762
#191446432
#191446142
#191445392
#191445362
#191444152
#191440912
#191438472
#137×Dic432
#191434082
#191432242
C43×#30072
#6056343