Finite Group Databasebeta

← #25966737

Subgroups — #25966737

Order 11008.

2008 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147891C211yesmaximal, characteristic, complemented
2C2×#14583433C211yesmaximal, characteristic, complemented
3#19145324C214yesmaximal, complemented
4#19145304C212yesmaximal, complemented
5#19145293C212yesmaximal, complemented
6#19145201C212yesmaximal, complemented
7#19145190C212yesmaximal, complemented
8#19145165C214yesmaximal, complemented
9#19145147C211yesmaximal, characteristic, complemented
10#19145061C211yesmaximal, characteristic, complemented
11#19144996C211yesmaximal, characteristic, complemented
12#19144982C211yesmaximal, characteristic, complemented
13#19144225C212yesmaximal, complemented
14#19144214C212yesmaximal, complemented
15C4×#13063358C212yesmaximal, complemented
16C4×#13063353C212yesmaximal, complemented
17C2×C4×M16×C43C211yesmaximal, characteristic, complemented
18C2×#13063358C2212yes—
19C2×#13063353C2212yes—
20#14583456C2211yescharacteristic
21#14583456C2211yescharacteristic, complemented
22#14583456C2211yescharacteristic, complemented
23#14583449C2211yescharacteristic
24#14583449C2211yescharacteristic, complemented
25#14583449C2211yescharacteristic, complemented
26#14583433—21no—
27#14583433—21no—
28#14583433—21no—
29#14583433—21no—
30#14583433—21no—
31#14583433—21no—
32#14583433—21no—
33#14583433—21no—
34#14583433C2212yes—
35#14583433C2212yes—
36#14583433C2212yes—
37#14583433C2212yes—
38#14583433C2212yescomplemented
39#14583433C2212yescomplemented
40C2×#13063319—21no—
41C2×#13063317C2211yescharacteristic
42C2×#13063313C2211yescharacteristic
43#14583410—21no—
44#14583410—21no—
45#14583410C2212yes—
46C2×#13063308—21no—
47C2×#13063304C2211yescharacteristic
48C2×#13063299C2211yescharacteristic
49C4×#10621898—21no—
50C4×#10621898—21no—
51C4×#10621898C2212yes—
52C2×C4×Dic86C2211yescharacteristic
53C2×C4×D172C2211yescharacteristic
54C2×C4×C22⋊D43—21no—
55C2×#13063282—21no—
56#14583308C2212yescomplemented
57#14583308C2212yescomplemented
58#14583301C2214yescomplemented
59#14583293C2212yescomplemented
60#14583288C2212yescomplemented
61#14583283C2214yescomplemented
62#14583268C2212yescomplemented
63#14583264C2212yescomplemented
64#14583259C2212yescomplemented
65#14583259C2212yescomplemented
66#14583254C2214yescomplemented
67#14583254C2214yescomplemented
68#14583157C2214yescomplemented
69#14583152C2214yes—
70#14583145C2214yes—
71#14583145C2214yescomplemented
72#14583140C2214yescomplemented
73#14583135C2214yes—
74#14583128C2214yes—
75#14583128C2214yescomplemented
76#14583012C2214yescomplemented
77#14583007C2214yescomplemented
78#14583001C2214yescomplemented
79#14583001C2214yescomplemented
80C4×Dic172C2214yescomplemented
81C4×#10621873C2214yescomplemented
82C4×#10621873C2214yescomplemented
83C4×D344C2214yescomplemented
84#14582941C2212yes—
85#14582941C2212yes—
86#14582909C2212yes—
87#14582905C2212yes—
88#14582901C2212yes—
89#14582901C2212yes—
90C22×M16×C43C2212yes—
91C22×C42×C43C2211yescharacteristic
92C4×M16×C43C2211yescharacteristic
93C4×M16×C43C2211yescharacteristic
94C4×M16×C43C2212yes—
95C4×M16×C43C2212yescomplemented
96C4×M16×C43C2212yescomplemented
97C2×#97×C43C2212yescomplemented
98C2×C4×C8×C43C2212yescomplemented
99C2×#10621898—21no—
100C2×#10621898—21no—
101C2×#10621898C2312yes—
102C22×Dic86C2311yescharacteristic
103C22×D172C2311yescharacteristic
104C22×C22⋊D43—21no—
105C22×C4×D43—21no—
106#13063358—28no—
107#13063353—28no—
108C2×Dic172C2314yes—
109C2×#10621873C2314yes—
110C2×#10621873C2314yes—
111C2×D344C2314yes—
112#13063325C2311yescharacteristic
113#13063325C2311yescharacteristic
114#13063325C2311yescharacteristic
115#13063322C2311yescharacteristic
116#13063319—22no—
117#13063319—22no—
118#13063319—22no—
119#13063319—22no—
120#13063319—22no—
121#13063319—22no—
122#13063317—21no—
123#13063317—21no—
124#13063317—21no—
125#13063317—21no—
126#13063317C2312yes—
127#13063317C2312yes—
128#13063317C2312yes—
129#13063313—21no—
130#13063313—21no—
131#13063313—21no—
132#13063313—21no—
133#13063313C2312yes—
134#13063313C2312yes—
135#13063313C2312yes—
136#13063308—22no—
137#13063308—22no—
138#13063308—22no—
139#13063308—22no—
140#13063308—22no—
141#13063308—22no—
142#13063308—22no—
143#13063304—21no—
144#13063304—21no—
145#13063304—21no—
146#13063304—21no—
147#13063304—21no—
148#13063304—21no—
149#13063304C2312yes—
150#13063304C2312yes—
151#13063304C2312yes—
152#13063304C2312yes—
153#13063299—21no—
154#13063299—21no—
155#13063299—21no—
156#13063299—21no—
157#13063299—21no—
158#13063299—21no—
159#13063299C2312yes—
160#13063299C2312yes—
161#13063299C2312yes—
162#13063299C2312yes—
163#13063294—22no—
164C4×Dic86—21no—
165C4×Dic86—21no—
166C4×Dic86—21no—
167C4×Dic86—21no—
168C4×Dic86—21no—
169C4×Dic86—21no—
170C4×Dic86C2312yes—
171C4×Dic86C2312yes—
172C4×Dic86C2312yes—
173C4×Dic86C2312yes—
174C4×D172—21no—
175C4×D172—21no—
176C4×D172—21no—
177C4×D172—21no—
178C4×D172—21no—
179C4×D172—21no—
180C4×D172C2312yes—
181C4×D172C2312yes—
182C4×D172C2312yes—
183C4×D172C2312yes—
184C4×C22⋊D43—22no—
185C4×C22⋊D43—22no—
186C4×C22⋊D43—22no—
187C4×C22⋊D43—22no—
188C4×C22⋊D43—22no—
189C4×C22⋊D43—22no—
190C4×C22⋊D43—22no—
191C4×C22⋊D43—22no—
192C4×C22⋊D43—22no—
193C4×C22⋊D43—22no—
194#13063284—21no—
195#13063284—21no—
196#13063284C2312yes—
197#13063282—22no—
198#13063282—22no—
199#13063282—22no—
200#13063282—22no—
201#13063282—22no—
202#13063282—22no—
203#13063282—22no—
204C2×C4⋊Dic43C2311yescharacteristic
205C2×C4⋊Dic43C2311yescharacteristic
206C2×Dic43⋊C4—21no—
207C2×Dic43⋊C4—21no—
208C2×Dic43⋊C4—21no—
209C2×Dic43⋊C4—21no—
210C2×C22⋊Dic43—21no—
211C2×(C2×D43)⋊C4—21no—
212C2×(C2×D43)⋊C4—21no—
213C2×(C2×D43)⋊C4—21no—
214C2×(C2×D43)⋊C4—21no—
215C2×C4×Dic43—21no—
216C42×D43—22no—
217#13063259C2314yes—
218#13063259C2314yes—
219#13063257C2314yes—
220#13063257C2314yes—
221#13063250C2314yes—
222#13063250C2314yes—
223#13063250C2314yes—
224#13063250C2314yes—
225#13063247C2314yes—
226#13063247C2314yes—
227#13063247C2314yes—
228#13063247C2314yes—
229C23×C4×C43D411yescharacteristic
230C23×C4×C43D411yescharacteristic
231C23×C4×C43C2311yescharacteristic
232C2×M16×C43—28no—
233C2×M16×C43C2314yes—
234C2×M16×C43C2312yes—
235C2×M16×C43C2312yes—
236C22×C8×C43C2314yes—
237C2×C42×C43D411yescharacteristic
238C2×C42×C43D411yescharacteristic
239C2×C42×C43D411yescharacteristic
240C2×C42×C43D411yescharacteristic
241C2×C42×C43D411yescharacteristic
242C2×C42×C43D411yescharacteristic
243C2×C42×C43C2311yescharacteristic
244C2×C42×C43C2311yescharacteristic
245C2×C42×C43C2311yescharacteristic
246C2×C42×C43C2311yescharacteristic
247C2×C42×C43C2311yescharacteristic
248C2×C42×C43C2311yescharacteristic
249#97×C43C2312yes—
250#97×C43C2314yes—
251#97×C43C2312yes—
252C4×C8×C43C2312yes—
253C4×C8×C43C2314yes—
254C4×C8×C43C2312yes—
255C24×C43C2×D411yescharacteristic
256C23×D43—21no—
257C22×C4×C43—24no—
258C22×C4×C43—42no—
259C22×C4×C43—42no—
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2×D411yescharacteristic
266C22×C4×C43C2×D411yescharacteristic
267C22×C4×C43C2×D411yescharacteristic
268C22×C4×C43C2×D411yescharacteristic
269C22×C4×C43C2×D411yescharacteristic
270C22×C4×C43C2×D411yescharacteristic
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2×D411yescharacteristic
273C22×C4×C43C2×D411yescharacteristic
274C22×C4×C43C2×D411yescharacteristic
275C22×C4×C43C2411yescharacteristic
276C22×C4×C43C2411yescharacteristic
277C22×C4×C43C2411yescharacteristic
278C2×C22⋊D43—22no—
279C2×C22⋊D43—22no—
280C2×C22⋊D43—22no—
281C2×C22⋊D43—22no—
282C2×C22⋊D43—22no—
283C2×C22⋊D43—44no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43—21no—
287#10621898—24no—
288#10621898—24no—
289#10621898—44no—
290#10621898—44no—
291C2×D172—21no—
292C2×D172—21no—
293C2×D172—21no—
294C2×D172—24no—
295C2×D172C2412yes—
296C2×D172C2412yes—
297C2×C4×D43—22no—
298C2×C4×D43—22no—
299C2×C4×D43—22no—
300C2×C4×D43—22no—
301C2×C4×D43—22no—
302C2×C4×D43—44no—
303C2×Dic86—24no—
304C2×Dic86—21no—
305C2×Dic86—21no—
306C2×Dic86—21no—
307C2×Dic86C2412yes—
308C2×Dic86C2412yes—
309M16×C43—24no—
310M16×C43—28no—
311M16×C43#4118yescomplemented
312C2×C8×C43—28no—
313C2×C8×C43C2414yes—
314C2×C8×C43C2414yes—
315C42×C43C2×D411yescharacteristic
316C42×C43C2×D411yescharacteristic
317C42×C43C2×D411yescharacteristic
318C42×C43C2×D411yescharacteristic
319C42×C43C2×D411yescharacteristic
320C42×C43C2×D411yescharacteristic
321C42×C43C2×D411yescharacteristic
322C42×C43C2×D411yescharacteristic
323C42×C43C2×D411yescharacteristic
324C42×C43C2×D411yescharacteristic
325C42×C43C2×D411yescharacteristic
326C42×C43C2×D411yescharacteristic
327C42×C43C2411yescharacteristic
328C42×C43C2411yescharacteristic
329C42×C43C2411yescharacteristic
330C42×C43C2411yescharacteristic
331C22⋊Dic43—22no—
332C22⋊Dic43—22no—
333C22⋊Dic43—22no—
334C22⋊Dic43—22no—
335C22⋊Dic43—22no—
336(C2×D43)⋊C4—22no—
337(C2×D43)⋊C4—22no—
338(C2×D43)⋊C4—22no—
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—
347(C2×D43)⋊C4—22no—
348(C2×D43)⋊C4—22no—
349(C2×D43)⋊C4—22no—
350C4⋊Dic43—21no—
351C4⋊Dic43—21no—
352C4⋊Dic43—21no—
353C4⋊Dic43—21no—
354C4⋊Dic43—21no—
355C4⋊Dic43—21no—
356C4⋊Dic43C2412yes—
357C4⋊Dic43C2412yes—
358C4⋊Dic43C2412yes—
359C4⋊Dic43C2412yes—
360Dic43⋊C4—22no—
361Dic43⋊C4—22no—
362Dic43⋊C4—22no—
363Dic43⋊C4—22no—
364Dic43⋊C4—22no—
365Dic43⋊C4—22no—
366Dic43⋊C4—22no—
367Dic43⋊C4—22no—
368Dic43⋊C4—22no—
369Dic43⋊C4—22no—
370Dic43⋊C4—22no—
371Dic43⋊C4—22no—
372Dic43⋊C4—22no—
373Dic43⋊C4—22no—
374C4×Dic43—22no—
375C4×Dic43—22no—
376C4×Dic43—22no—
377C4×Dic43—22no—
378C4×Dic43—22no—
379Dic172—28no—
380D344—28no—
381#10621873—28no—
382#10621873—28no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—41no—
386C23×C43C22×D411yescharacteristic
387C23×C43C22×D411yescharacteristic
388C23×C43C22×D411yescharacteristic
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—42no—
392C22×D43—42no—
393C22×D43—42no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43C22×D411yescharacteristic
412C2×C4×C43C22×D411yescharacteristic
413C2×C4×C43C22×D411yescharacteristic
414C2×C4×C43C22×D411yescharacteristic
415C2×C4×C43C22×D411yescharacteristic
416C2×C4×C43C22×D411yescharacteristic
417C2×C4×C43C22×D411yescharacteristic
418C2×C4×C43C22×D411yescharacteristic
419C2×C4×C43C22×D411yescharacteristic
420C2×C4×C43C22×D411yescharacteristic
421C2×C4×C43C22×D411yescharacteristic
422C2×C4×C43C2×#4114yes—
423C2×C4×C43C2511yescharacteristic
424C22⋊D43—44no—
425C22⋊D43—44no—
426C22⋊D43—44no—
427C22⋊D43—44no—
428C22⋊D43—44no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—22no—
433C2×Dic43—22no—
434C2×Dic43—22no—
435C2×Dic43—42no—
436C2×Dic43—42no—
437C2×Dic43—42no—
438D172—22no—
439D172—24no—
440D172—22no—
441D172—42no—
442D172—42no—
443D172—42no—
444C4×D43—44no—
445C4×D43—44no—
446C4×D43—44no—
447C4×D43—44no—
448C4×D43—44no—
449Dic86—22no—
450Dic86—24no—
451Dic86—22no—
452Dic86—42no—
453Dic86—42no—
454Dic86—42no—
455C8×C43—24no—
456C8×C43C2×#4118yes—
457#60702—431nomaximal, Sylow
458C22×C43—21no—
459C22×C43—21no—
460C22×C43—21no—
461C22×C43—21no—
462C22×C43—21no—
463C22×C43—21no—
464C22×C43—21no—
465C22×C43—44no—
466C22×C43#53212yes—
467C22×C43#57512yes—
468C22×C43C23×D411yescharacteristic
469C2×D43—42no—
470C2×D43—42no—
471C2×D43—42no—
472C2×D43—42no—
473C2×D43—42no—
474C2×D43—42no—
475C2×D43—84no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43—21no—
485C4×C43#53212yes—
486C4×C43#57512yes—
487C4×C43C22×#4112yes—
488Dic43—42no—
489Dic43—42no—
490Dic43—42no—
491Dic43—42no—
492Dic43—42no—
493Dic43—42no—
494#3444—431no—
495C2×#529—431no—
496#3183—434no—
497#3181—432no—
498#3180—432no—
499#3172—432no—
500#3171—432no—
501#3168—434no—
502#3166—431no—
503#3153—431no—
504#3142—431no—
505#3140—431no—
506#3056—432no—
507#3055—432no—
508C4×#137—432no—
509C4×AGL(1,ℤ/8)—432no—
510C2×C4×M16D4311yescharacteristic, complemented
511C2×C43—22no—
512C2×C43—22no—
513C2×C43—41no—
514C2×C43C2×#53211yescharacteristic
515C2×C43C2×#57511yescharacteristic
516C2×C43C2×#57511yescharacteristic
517D43—82no—
518D43—82no—
519C2×#137—432no—
520C2×AGL(1,ℤ/8)—432no—
521C22×M16C2×D4312yes—
522#533—431no—
523#533—431no—
524#533—431no—
525#532—431no—
526#532—431no—
527#532—431no—
528#529—432no—
529#529—432no—
530#529—432no—
531#529—432no—
532#529—432no—
533#529—432no—
534#529—861no—
535#529—861no—
536#529—861no—
537#529—861no—
538#529—861no—
539#529—861no—
540#529—861no—
541#529—861no—
542C2×#126—861no—
543C2×#125—431no—
544C2×#124—431no—
545#525—432no—
546#525—861no—
547#525—861no—
548C2×#123—861no—
549C2×C22⋊Q8—431no—
550C2×#121—431no—
551C4×#41—432no—
552C4×#41—861no—
553C4×#41—861no—
554C2×C4×Q8—431no—
555C2×C4×D4—431no—
556C2×C4×D4—861no—
557C2×#117—861no—
558C22×C42C2×D4311yescharacteristic
559#501—432no—
560#501—432no—
561#499—434no—
562#497—432no—
563#496—432no—
564#495—434no—
565#491—432no—
566#490—432no—
567#489—432no—
568#489—432no—
569#488—434no—
570#488—434no—
571#470—434no—
572#469—434no—
573#468—434no—
574#468—434no—
575#467—434no—
576#466—434no—
577#465—434no—
578#465—434no—
579#442—434no—
580#441—434no—
581#440—434no—
582#440—434no—
583C4×Q16—434no—
584C4×SD16—434no—
585C4×SD16—434no—
586C4×D8—434no—
587#428—432no—
588#428—432no—
589#419—432no—
590#418—432no—
591#417—432no—
592#417—432no—
593C4×M16C2×D4311yescharacteristic
594C4×M16C2×D4311yescharacteristic
595C4×M16C2×D4312yes—
596C4×M16C2×D4312yescomplemented
597C4×M16C2×D4312yescomplemented
598C2×#97C2×D4312yescomplemented
599C2×C4×C8C2×D4312yescomplemented
600C43#6070211yescharacteristic, complemented, Sylow
601C2×#41—432no—
602C2×#41—861no—
603C2×#41—861no—
604C22×Q8—431no—
605C22×D4—431no—
606C22×D4—861no—
607C23×C4—861no—
608C23×C4D17211yescharacteristic
609C23×C4D17211yescharacteristic
610C23×C4C22×D4311yescharacteristic
611#137—868no—
612AGL(1,ℤ/8)—868no—
613C2×Q16—434no—
614C2×SD16—434no—
615C2×SD16—434no—
616C2×D8—434no—
617C2×M16—28no—
618C2×M16C22×D4312yes—
619C2×M16C22×D4314yes—
620C2×M16C22×D4312yes—
621C22×C8C22×D4314yes—
622C4⋊Q8—431no—
623C4⋊Q8—431no—
624C4⋊Q8—431no—
625#127—431no—
626#126—862no—
627#126—862no—
628#126—862no—
629#126—862no—
630#126—862no—
631#126—862no—
632#125—432no—
633#125—432no—
634#125—432no—
635#125—861no—
636#125—861no—
637#125—861no—
638#125—861no—
639#124—432no—
640#124—432no—
641#124—432no—
642#124—861no—
643#124—861no—
644#124—861no—
645#124—861no—
646#123—862no—
647#123—862no—
648#123—862no—
649#123—862no—
650#123—862no—
651#123—862no—
652#123—862no—
653C22⋊Q8—432no—
654C22⋊Q8—432no—
655C22⋊Q8—432no—
656C22⋊Q8—432no—
657C22⋊Q8—861no—
658C22⋊Q8—861no—
659C22⋊Q8—861no—
660C22⋊Q8—861no—
661C22⋊Q8—861no—
662C22⋊Q8—861no—
663#121—432no—
664#121—432no—
665#121—432no—
666#121—432no—
667#121—861no—
668#121—861no—
669#121—861no—
670#121—861no—
671#121—861no—
672#121—861no—
673#120—862no—
674C4×Q8—432no—
675C4×Q8—432no—
676C4×Q8—432no—
677C4×Q8—432no—
678C4×Q8—861no—
679C4×Q8—861no—
680C4×Q8—861no—
681C4×Q8—861no—
682C4×Q8—861no—
683C4×Q8—861no—
684C4×D4—432no—
685C4×D4—432no—
686C4×D4—432no—
687C4×D4—432no—
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—861no—
699C4×D4—861no—
700C4×D4—861no—
701C4×D4—861no—
702C4×D4—861no—
703C4×D4—861no—
704#117—432no—
705#117—861no—
706#117—861no—
707#117—862no—
708#117—862no—
709#117—862no—
710#117—862no—
711#117—862no—
712#117—862no—
713#117—862no—
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×C22⋊C4—861no—
721C2×C22⋊C4—861no—
722C2×C22⋊C4—861no—
723C2×C22⋊C4—861no—
724C2×C22⋊C4—861no—
725C2×C42—861no—
726C2×C42—862no—
727C2×C42D17211yescharacteristic
728C2×C42D17211yescharacteristic
729C2×C42D17211yescharacteristic
730C2×C42D17211yescharacteristic
731C2×C42D17211yescharacteristic
732C2×C42D17211yescharacteristic
733C2×C42C22×D4311yescharacteristic
734C2×C42C22×D4311yescharacteristic
735C2×C42C22×D4311yescharacteristic
736C2×C42C22×D4311yescharacteristic
737C2×C42C22×D4311yescharacteristic
738C2×C42C22×D4311yescharacteristic
739#107—434no—
740#107—434no—
741#106—434no—
742#106—434no—
743#103—434no—
744#103—434no—
745#103—434no—
746#103—434no—
747#102—434no—
748#102—434no—
749#102—434no—
750#102—434no—
751#97C22×D4314yes—
752#97C22×D4312yes—
753#97C22×D4312yes—
754C4×C8C22×D4314yes—
755C4×C8C22×D4312yes—
756C4×C8C22×D4312yes—
757C24—861no—
758C24C2×D17211yescharacteristic
759#41—864no—
760#41—864no—
761#41—1724no—
762#41—1724no—
763C2×Q8—432no—
764C2×Q8—432no—
765C2×Q8—861no—
766C2×Q8—861no—
767C2×Q8—861no—
768C2×Q8—864no—
769C2×D4—432no—
770C2×D4—432no—
771C2×D4—862no—
772C2×D4—862no—
773C2×D4—862no—
774C2×D4—862no—
775C2×D4—862no—
776C2×D4—861no—
777C2×D4—861no—
778C2×D4—861no—
779C2×D4—864no—
780C2×D4—1724no—
781C22×C4—24no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—861no—
785C22×C4—861no—
786C22×C4—861no—
787C22×C4—862no—
788C22×C4—862no—
789C22×C4—862no—
790C22×C4—862no—
791C22×C4—862no—
792C22×C4—1724no—
793C22×C4C2×D17211yescharacteristic
794C22×C4C2×D17211yescharacteristic
795C22×C4C2×D17211yescharacteristic
796C22×C4C2×D17211yescharacteristic
797C22×C4C2×D17211yescharacteristic
798C22×C4C2×D17211yescharacteristic
799C22×C4C2×D17211yescharacteristic
800C22×C4C2×D17211yescharacteristic
801C22×C4C2×D17211yescharacteristic
802C22×C4C2×D17211yescharacteristic
803C22×C4C2×D17211yescharacteristic
804C22×C4C2×D17211yescharacteristic
805C22×C4C2×D17211yescharacteristic
806C22×C4C2×D17211yescharacteristic
807C22×C4C2×D17211yescharacteristic
808C22×C4C23×D4311yescharacteristic
809C22×C4C23×D4311yescharacteristic
810C22×C4C23×D4311yescharacteristic
811Q16—868no—
812SD16—868no—
813SD16—868no—
814D8—868no—
815M16—24no—
816M16—28no—
817M16#1062189818yescomplemented
818C2×C8—28no—
819C2×C8C23×D4314yes—
820C2×C8C23×D4314yes—
821C4⋊C4—432no—
822C4⋊C4—432no—
823C4⋊C4—432no—
824C4⋊C4—432no—
825C4⋊C4—861no—
826C4⋊C4—861no—
827C4⋊C4—862no—
828C4⋊C4—862no—
829C4⋊C4—862no—
830C4⋊C4—862no—
831C4⋊C4—862no—
832C4⋊C4—862no—
833C4⋊C4—862no—
834C4⋊C4—862no—
835C4⋊C4—862no—
836C4⋊C4—862no—
837C4⋊C4—861no—
838C4⋊C4—861no—
839C4⋊C4—861no—
840C4⋊C4—861no—
841C4⋊C4—862no—
842C4⋊C4—862no—
843C4⋊C4—862no—
844C4⋊C4—862no—
845C22⋊C4—862no—
846C22⋊C4—862no—
847C22⋊C4—862no—
848C22⋊C4—862no—
849C22⋊C4—862no—
850C22⋊C4—862no—
851C22⋊C4—862no—
852C22⋊C4—862no—
853C22⋊C4—862no—
854C22⋊C4—862no—
855C22⋊C4—862no—
856C22⋊C4—862no—
857C22⋊C4—862no—
858C22⋊C4—862no—
859C22⋊C4—862no—
860C22⋊C4—862no—
861C22⋊C4—862no—
862C22⋊C4—862no—
863C22⋊C4—862no—
864C42—862no—
865C42—862no—
866C42—862no—
867C42—862no—
868C42—862no—
869C42C2×D17211yescharacteristic
870C42C2×D17211yescharacteristic
871C42C2×D17211yescharacteristic
872C42C2×D17211yescharacteristic
873C42C2×D17211yescharacteristic
874C42C2×D17211yescharacteristic
875C42C2×D17211yescharacteristic
876C42C2×D17211yescharacteristic
877C42C2×D17211yescharacteristic
878C42C2×D17211yescharacteristic
879C42C2×D17211yescharacteristic
880C42C2×D17211yescharacteristic
881C42C23×D4311yescharacteristic
882C42C23×D4311yescharacteristic
883C42C23×D4311yescharacteristic
884C42C23×D4311yescharacteristic
885C23—22no—
886C23—22no—
887C23—41no—
888C23—862no—
889C23—862no—
890C23—1722no—
891C23—1722no—
892C23—1722no—
893C23C22×D17211yescharacteristic
894C23C22×D17211yescharacteristic
895C23C22×D17211yescharacteristic
896Q8—862no—
897Q8—864no—
898Q8—862no—
899Q8—1722no—
900Q8—1722no—
901Q8—1722no—
902D4—862no—
903D4—864no—
904D4—862no—
905D4—1722no—
906D4—1722no—
907D4—1724no—
908D4—1724no—
909D4—1724no—
910D4—1724no—
911D4—1724no—
912D4—1722no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—862no—
935C2×C4—862no—
936C2×C4—1724no—
937C2×C4—1724no—
938C2×C4—1722no—
939C2×C4—1722no—
940C2×C4—1722no—
941C2×C4—1724no—
942C2×C4—1724no—
943C2×C4—1724no—
944C2×C4C22×D17211yescharacteristic
945C2×C4C22×D17211yescharacteristic
946C2×C4C22×D17211yescharacteristic
947C2×C4C22×D17211yescharacteristic
948C2×C4C22×D17211yescharacteristic
949C2×C4C22×D17211yescharacteristic
950C2×C4C22×D17211yescharacteristic
951C2×C4C22×D17211yescharacteristic
952C2×C4C22×D17211yescharacteristic
953C2×C4C22×D17211yescharacteristic
954C2×C4C22×D17211yescharacteristic
955C2×C4C2×#1062189814yes—
956C2×C4C24×D4311yescharacteristic
957C8—24no—
958C8C2×#1062189818yes—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—44no—
967C22—3444no—
968C22—1722no—
969C22—1722no—
970C22—1722no—
971C22—1722no—
972C22—1722no—
973C22—1722no—
974C22#1458344912yes—
975C22#1458369912yes—
976C22C23×D17211yescharacteristic
977C4—21no—
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—1722no—
987C4—1722no—
988C4—1722no—
989C4—1722no—
990C4—1722no—
991C4—1722no—
992C4#1458344912yes—
993C4#1458369912yes—
994C4C22×#1062189812yes—
995C2—22no—
996C2—22no—
997C2—41no—
998C2—3442no—
999C2—3442no—
1000C2C2×#1458344911yescharacteristic
1001C2C2×#1458369911yescharacteristic
1002C2C2×#1458369911yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×M16×C43C2
socleC22×C43C23×D4
hypercenterC2×C4×M16D43
hypocenterC43#60702
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
1. #19147891C2semidirect
2. C2×#14583433C2semidirect
3. #19145324C2semidirect
4. #19145304C2semidirect
5. #19145293C2semidirect
6. #19145201C2semidirect
7. #19145190C2semidirect
8. #19145165C2semidirect
9. #19145147C2semidirect
10. #19145061C2semidirect
11. #19144996C2semidirect
12. #19144982C2semidirect
13. #19144225C2semidirect
14. #19144214C2semidirect
15. C4×#13063358C2semidirect
16. C4×#13063353C2semidirect
17. C2×C4×M16×C43C2semidirect
21. #14583456C22semidirect
22. #14583456C22semidirect
24. #14583449C22semidirect
25. #14583449C22semidirect
38. #14583433C22semidirect
39. #14583433C22semidirect
56. #14583308C22semidirect
57. #14583308C22semidirect
58. #14583301C22semidirect
59. #14583293C22semidirect
60. #14583288C22semidirect
61. #14583283C22semidirect
62. #14583268C22semidirect
63. #14583264C22semidirect
64. #14583259C22semidirect
65. #14583259C22semidirect
66. #14583254C22semidirect
67. #14583254C22semidirect
68. #14583157C22semidirect
71. #14583145C22semidirect
72. #14583140C22semidirect
75. #14583128C22semidirect
76. #14583012C22semidirect
77. #14583007C22semidirect
78. #14583001C22semidirect
79. #14583001C22semidirect
80. C4×Dic172C22semidirect
81. C4×#10621873C22semidirect
82. C4×#10621873C22semidirect
83. C4×D344C22semidirect
95. C4×M16×C43C22semidirect
96. C4×M16×C43C22semidirect
97. C2×#97×C43C22semidirect
98. C2×C4×C8×C43C22semidirect
311. M16×C43#41semidirect
510. C2×C4×M16D43semidirect
596. C4×M16C2×D43semidirect
597. C4×M16C2×D43semidirect
598. C2×#97C2×D43semidirect
599. C2×C4×C8C2×D43semidirect
600. C43#60702semidirect
817. M16#10621898semidirect

Maximal subgroups

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

subgroupindex
#191478912
C2×#145834332
#191453242
#191453042
#191452932
#191452012
#191451902
#191451652
#191451472
#191450612
#191449962
#191449822
#191442252
#191442142
C4×#130633582
C4×#130633532
C2×C4×M16×C432
#6070243