Finite Group Databasebeta

← #25972536

Subgroups — #25972536

Order 11008.

2674 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583706C211yesmaximal, characteristic, complemented
2#19148389C211yesmaximal, characteristic, complemented
3#19148376C211yesmaximal, characteristic, complemented
4#19146165C214yesmaximal, complemented
5#19146144C214yesmaximal, complemented
6#19146120C214yesmaximal, complemented
7#19146099C214yesmaximal, complemented
8C2×#14583292C211yesmaximal, characteristic, complemented
9#19144246C211yesmaximal, characteristic, complemented
10#19144234C211yesmaximal, characteristic, complemented
11#19144091C211yesmaximal, characteristic, complemented
12#19144080C211yesmaximal, characteristic, complemented
13#19143890C211yesmaximal, characteristic, complemented
14#19143889C211yesmaximal, characteristic, complemented
15#19143881C211yesmaximal, characteristic, complemented
16#19143871C211yesmaximal, characteristic, complemented
17#19143396C211yesmaximal, characteristic, complemented
18#19143311C211yesmaximal, characteristic, complemented
19C2×C43×#578C211yesmaximal, characteristic, complemented
20C2×#13063372C2211yescharacteristic
21C2×#13063371C2211yescharacteristic
22#14583706—28no—
23C2×#13063357C2212yes—
24C2×#13063355C2211yescharacteristic
25C2×#13063350C2211yescharacteristic
26C2×#13063349C2212yes—
27C2×#13063346C2212yes—
28C22×#10621885C2211yescharacteristic, complemented
29C22×#10621873C2211yescharacteristic
30C22×#10621884C2211yescharacteristic
31C2×SD16×D43C2212yes—
32C2×#13063331C2211yescharacteristic
33Q8×C22⋊D43C2214yescomplemented
34#14583560C2214yes—
35#14583548—24no—
36#14583548C2214yescomplemented
37#14583537—24no—
38#14583537C2214yes—
39#14583473—21no—
40#14583473—21no—
41#14583473C2211yescharacteristic
42#14583473C2211yescharacteristic
43#14583470—21no—
44#14583470C2211yescharacteristic, complemented
45#14583463—21no—
46#14583463C2211yescharacteristic
47#14583445—21no—
48#14583445—21no—
49#14583445C2211yescharacteristic
50C2×#13063323—21no—
51C2×#13063323C2211yescharacteristic, complemented
52C2×#13063314—21no—
53C2×#13063314C2211yescharacteristic
54#41×Dic43C2211yescharacteristic
55#41×Dic43C2211yescharacteristic, complemented
56#14583292C2214yescomplemented
57#14583292C2214yescomplemented
58#14583154C2214yescomplemented
59#14583145C2214yescomplemented
60#14583137C2214yescomplemented
61#14583128C2214yescomplemented
62#14583123C2214yescomplemented
63#14583116C2214yescomplemented
64#14583107C2214yescomplemented
65#14583102C2214yescomplemented
66#14583061C2214yescomplemented
67#14583060C2214yes—
68#14583058C2214yescomplemented
69#14583055C2214yescomplemented
70#14583053C2214yescomplemented
71#14583048C2214yes—
72#14583044C2214yescomplemented
73#14583038C2214yescomplemented
74#14583011C2212yescomplemented
75#14583006C2212yescomplemented
76#14583000C2212yescomplemented
77#14583000C2212yescomplemented
78#14582970C2214yescomplemented
79#14582968C2214yescomplemented
80#14582937C2211yescharacteristic, complemented
81#14582922C2211yescharacteristic, complemented
82#14582909C2211yescharacteristic, complemented
83#14582908C2211yescharacteristic, complemented
84#14582908C2211yescharacteristic, complemented
85#14582905C2211yescharacteristic
86#14582895C2211yescharacteristic
87#14582895C2211yescharacteristic, complemented
88#14582867C2211yescharacteristic
89#14582866C2211yescharacteristic, complemented
90C2×#13063235C2211yescharacteristic, complemented
91C2×2−1+4×C43C2211yescharacteristic
92C2×2−1+4×C43C2211yescharacteristic, complemented
93C43×#578—28no—
94C2×#137×C43C2211yescharacteristic
95C2×#137×C43C2212yescomplemented
96C2×#137×C43C2211yescharacteristic, complemented
97C2×#137×C43C2212yescomplemented
98C2×#135×C43C2211yescharacteristic
99C2×#135×C43C2212yescomplemented
100C22×Q16×C43C2211yescharacteristic, complemented
101C22×Q16×C43C2212yescomplemented
102C2×#131×C43C2211yescharacteristic, complemented
103#13063372—24no—
104#13063372—42no—
105#13063371—24no—
106#13063371—42no—
107C2×#10621902C2312yes—
108C2×#10621898—21no—
109C2×#10621898—21no—
110C2×#10621898C2311yescharacteristic
111C2×#10621900—22no—
112C2×#10621900C2312yes—
113C22×Dic86—21no—
114C22×Dic86C2311yescharacteristic
115C2×Q8×D43C2312yes—
116C22×D172—21no—
117C22×D172C2311yescharacteristic
118C2×D4×D43—22no—
119C2×D4×D43C2312yes—
120#13063357—28no—
121#13063355—24no—
122#13063350—24no—
123#13063349—28no—
124#13063346—28no—
125C2×#10621885—42no—
126C2×#10621885C2312yes—
127C2×#10621885C2314yes—
128C2×#10621873—24no—
129C2×#10621873C2312yes—
130C2×#10621873C2312yes—
131C2×#10621883C2312yes—
132C2×#10621884—42no—
133C2×#10621884C2312yes—
134C2×#10621884C2314yes—
135SD16×D43—28no—
136C2×#10621882C2312yes—
137#13063331—24no—
138C2×#10621877C2311yescharacteristic
139C2×#10621872C2312yes—
140C22×C43⋊C8C2311yescharacteristic
141C2×C8×D43C2312yes—
142#13063323—21no—
143#13063323—21no—
144#13063323—21no—
145#13063323—24no—
146#13063323—21no—
147#13063323—21no—
148#13063323D411yescharacteristic
149#13063323C2314yes—
150#13063321—21no—
151#13063321D411yescharacteristic
152#13063314—21no—
153#13063314—21no—
154#13063314—21no—
155#13063314—24no—
156#13063314—21no—
157#13063314—21no—
158#13063314D411yescharacteristic
159#13063314C2314yes—
160#13063312—21no—
161#13063312D411yescharacteristic
162#13063308—22no—
163#13063308—22no—
164#13063308—24no—
165#13063308—24no—
166#13063306—22no—
167#13063306—24no—
168#13063304—24no—
169#13063304C2314yes—
170#13063301—24no—
171#13063301—24no—
172#13063301C2314yes—
173#13063301C2314yes—
174#13063299—24no—
175#13063299C2314yes—
176#13063297—24no—
177#13063297—24no—
178#13063297D414yes—
179#13063293—22no—
180#13063293—24no—
181Q8×Dic43C2312yes—
182Q8×Dic43C2312yes—
183D4×Dic43—22no—
184D4×Dic43—22no—
185D4×Dic43C2312yes—
186D4×Dic43C2312yes—
187C4×C22⋊D43—24no—
188C4×C22⋊D43—24no—
189C4×C22⋊D43C2314yes—
190#13063284—21no—
191#13063284—21no—
192#13063284C2311yescharacteristic
193#13063284C2311yescharacteristic
194C2×Dic43⋊C4—22no—
195C2×Dic43⋊C4—24no—
196C2×(C2×D43)⋊C4—22no—
197C2×(C2×D43)⋊C4—24no—
198C2×C4×Dic43—21no—
199C2×C4×Dic43—21no—
200C2×C4×Dic43C2311yescharacteristic
201#13063259C2312yes—
202#13063257C2312yes—
203Dic43⋊C8C2314yes—
204#13063250C2314yes—
205#13063249C2314yes—
206#13063249C2312yes—
207#13063249C2312yes—
208#13063249C2314yes—
209#13063247C2314yes—
210#13063246C2312yes—
211#13063246C2312yes—
212C22⋊(C43⋊C8)C2314yes—
213(C2×D43)⋊C8C2314yes—
214#13063235C2312yes—
215#13063235C2312yes—
2162−1+4×C43—24no—
2172−1+4×C43—24no—
2182−1+4×C43—42no—
2192−1+4×C43—42no—
220C2×#41×C43—21no—
221C2×#41×C43—22no—
222C2×#41×C43—21no—
223C2×#41×C43—22no—
224C2×#41×C43C2312yes—
225C2×#41×C43C2312yes—
226C2×#41×C43C2311yescharacteristic
227C2×#41×C43C2311yescharacteristic
228C2×#41×C43C2311yescharacteristic
229C22×Q8×C43—21no—
230C22×Q8×C43—21no—
231C22×Q8×C43C2311yescharacteristic
232C22×Q8×C43C2311yescharacteristic
233C22×Q8×C43C2312yes—
234C22×Q8×C43C2312yes—
235#137×C43—24no—
236#137×C43—24no—
237#137×C43—28no—
238#137×C43—28no—
239#135×C43—28no—
240#135×C43D418yescomplemented
241C2×Q16×C43—28no—
242C2×Q16×C43—24no—
243C2×Q16×C43C2312yes—
244C2×Q16×C43C2312yes—
245C2×Q16×C43C2312yes—
246C2×Q16×C43C2312yes—
247C2×Q16×C43C2311yescharacteristic
248C2×SD16×C43C2312yes—
249C2×SD16×C43C2312yes—
250C2×SD16×C43C2311yescharacteristic
251C2×SD16×C43C2311yescharacteristic
252C2×D8×C43C2311yescharacteristic
253#131×C43—24no—
254C2×M16×C43C2311yescharacteristic
255C2×M16×C43C2312yes—
256C22×C8×C43C2312yes—
257C22×C8×C43C2311yescharacteristic
258C23×D43—21no—
259C23×D43—22no—
260#41×C43—22no—
261#41×C43—22no—
262#41×C43—22no—
263#41×C43—22no—
264#41×C43—24no—
265#41×C43—24no—
266#41×C43—42no—
267#41×C43—42no—
268#41×C43—44no—
269#41×C43—44no—
270#41×C43—48no—
271#41×C43—48no—
272#41×C43C2×D414yes—
273#41×C43C2×D414yes—
274C2×Q8×C43—22no—
275C2×Q8×C43—22no—
276C2×Q8×C43—21no—
277C2×Q8×C43—21no—
278C2×Q8×C43—24no—
279C2×Q8×C43—24no—
280C2×Q8×C43—22no—
281C2×Q8×C43—22no—
282C2×Q8×C43—22no—
283C2×Q8×C43—22no—
284C2×Q8×C43—42no—
285C2×Q8×C43—42no—
286C2×Q8×C43—44no—
287C2×Q8×C43—44no—
288C2×Q8×C43C2×D411yescharacteristic
289C2×Q8×C43C2412yes—
290C2×Q8×C43C2412yes—
291C2×Q8×C43C2411yescharacteristic
292C2×Q8×C43C2411yescharacteristic
293C2×D4×C43—21no—
294C2×D4×C43—21no—
295C2×D4×C43—22no—
296C2×D4×C43—22no—
297C2×D4×C43C2×D412yes—
298C2×D4×C43C2×D411yescharacteristic
299C2×D4×C43C2411yescharacteristic
300C2×D4×C43C2411yescharacteristic
301C22×C4×C43—21no—
302C22×C4×C43—21no—
303C22×C4×C43—22no—
304C22×C4×C43—22no—
305C22×C4×C43—21no—
306C22×C4×C43—21no—
307C22×C4×C43—22no—
308C22×C4×C43—22no—
309C22×C4×C43C2412yes—
310C22×C4×C43C2411yescharacteristic
311C2×C22⋊D43—22no—
312C2×C22⋊D43—24no—
313C2×C22⋊D43—22no—
314C2×C22⋊D43C2×D412yes—
315C2×C22⋊D43C2×D414yes—
316C22×Dic43—22no—
317C22×Dic43—22no—
318C22×Dic43—22no—
319C22×Dic43—21no—
320C22×Dic43C2×D412yes—
321#10621902—24no—
322#10621902—42no—
323Q8×D43—24no—
324Q8×D43—42no—
325#10621900—24no—
326#10621900—42no—
327#10621900—48no—
328D4×D43—24no—
329D4×D43—42no—
330D4×D43—48no—
331#10621898—22no—
332#10621898—22no—
333#10621898—44no—
334#10621898—44no—
335C2×D172—21no—
336C2×D172—22no—
337C2×D172—22no—
338C2×D172—22no—
339C2×D172—44no—
340C2×D172C2×D411yescharacteristic
341C2×D172C2412yes—
342C2×C4×D43—22no—
343C2×C4×D43—22no—
344C2×C4×D43C2412yes—
345C2×Dic86—22no—
346C2×Dic86—22no—
347C2×Dic86—21no—
348C2×Dic86—22no—
349C2×Dic86—44no—
350C2×Dic86C2×D411yescharacteristic
351C2×Dic86C2412yes—
352Q16×C43—24no—
353Q16×C43—24no—
354Q16×C43—24no—
355Q16×C43—24no—
356Q16×C43C2×D414yes—
357SD16×C43—24no—
358SD16×C43—24no—
359SD16×C43C2×D414yes—
360SD16×C43C2×D414yes—
361D8×C43C2×D414yes—
362M16×C43—22no—
363M16×C43—24no—
364C2×C8×C43—24no—
365C2×C8×C43C2×D414yes—
366C2×C8×C43C2412yes—
367C2×C8×C43C2411yescharacteristic
368C2×C8×C43C2411yescharacteristic
369C22⋊Dic43—22no—
370C22⋊Dic43—22no—
371C22⋊Dic43—21no—
372C22⋊Dic43—21no—
373C22⋊Dic43—24no—
374C22⋊Dic43C2×D414yes—
375#10621885—24no—
376#10621885—44no—
377#10621884—24no—
378#10621884—44no—
379#10621883—24no—
380#10621882—24no—
381(C2×D43)⋊C4—24no—
382(C2×D43)⋊C4—24no—
383(C2×D43)⋊C4—24no—
384(C2×D43)⋊C4—24no—
385(C2×D43)⋊C4—24no—
386(C2×D43)⋊C4C2×D414yes—
387C4⋊Dic43—22no—
388C4⋊Dic43—22no—
389C4⋊Dic43C2412yes—
390C4⋊Dic43C2412yes—
391Dic43⋊C4—24no—
392Dic43⋊C4—24no—
393Dic43⋊C4—24no—
394Dic43⋊C4—24no—
395Dic43⋊C4—24no—
396Dic43⋊C4C2×D414yes—
397C4×Dic43—21no—
398C4×Dic43—21no—
399C4×Dic43—22no—
400C4×Dic43—22no—
401C4×Dic43C2×D411yescharacteristic
402C4×Dic43C2×D411yescharacteristic
403C4×Dic43C2412yes—
404#10621877—22no—
405C2×C43⋊C8—22no—
406C2×C43⋊C8C2412yes—
407C2×C43⋊C8C2412yes—
408#10621873—24no—
409#10621873—24no—
410#10621872—24no—
411C8×D43—24no—
412C23×C43—21no—
413C23×C43—21no—
414C23×C43C22×D412yes—
415C23×C43C22×D411yescharacteristic
416C22×D43—22no—
417C22×D43—44no—
418C22×D43—42no—
419C22×D43—84no—
420C22×D43—82no—
421C22×D43C22×D412yes—
422Q8×C43—22no—
423Q8×C43—21no—
424Q8×C43—21no—
425Q8×C43—22no—
426Q8×C43—22no—
427Q8×C43—22no—
428Q8×C43—22no—
429Q8×C43—44no—
430Q8×C43—44no—
431Q8×C43—42no—
432Q8×C43—42no—
433Q8×C43C22×D412yes—
434Q8×C43C22×D412yes—
435D4×C43—24no—
436D4×C43—24no—
437D4×C43—24no—
438D4×C43—22no—
439D4×C43—21no—
440D4×C43—21no—
441D4×C43—44no—
442D4×C43—44no—
443D4×C43C22×D412yes—
444D4×C43C22×D412yes—
445C2×C4×C43—21no—
446C2×C4×C43—21no—
447C2×C4×C43—24no—
448C2×C4×C43—24no—
449C2×C4×C43—22no—
450C2×C4×C43—22no—
451C2×C4×C43—22no—
452C2×C4×C43—22no—
453C2×C4×C43—44no—
454C2×C4×C43—44no—
455C2×C4×C43—44no—
456C2×C4×C43—44no—
457C2×C4×C43—42no—
458C2×C4×C43—42no—
459C2×C4×C43C22×D412yes—
460C2×C4×C43C22×D411yescharacteristic
461C2×C4×C43C22×D412yes—
462C2×C4×C43H(5,𝔽2)12yes—
463C2×C4×C43C2511yescharacteristic
464C22⋊D43—24no—
465C22⋊D43—44no—
466C22⋊D43—44no—
467C22⋊D43—44no—
468C22⋊D43—84no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—42no—
473C2×Dic43—44no—
474C2×Dic43—44no—
475C2×Dic43—42no—
476C2×Dic43—82no—
477C2×Dic43C22×D412yes—
478C2×Dic43C22×D412yes—
479C2×Dic43C22×D412yes—
480D172—22no—
481D172—22no—
482D172—22no—
483D172—44no—
484D172—42no—
485C4×D43—22no—
486C4×D43—22no—
487C4×D43—44no—
488C4×D43—44no—
489Dic86—22no—
490Dic86—22no—
491Dic86—22no—
492Dic86—44no—
493Dic86—42no—
494C8×C43—22no—
495C8×C43C22×D412yes—
496C8×C43C22×D412yes—
497C43⋊C8—22no—
498C43⋊C8—22no—
499#61083—431nomaximal, Sylow
500C22×C43—22no—
501C22×C43—24no—
502C22×C43—22no—
503C22×C43—22no—
504C22×C43—22no—
505C22×C43—42no—
506C22×C43—42no—
507C22×C43D4212yes—
508C22×C43C23×D411yescharacteristic
509C2×D43—24no—
510C2×D43—22no—
511C2×D43—44no—
512C2×D43—42no—
513C2×D43—164no—
514C2×D43—162no—
515C4×C43—22no—
516C4×C43—22no—
517C4×C43—22no—
518C4×C43—42no—
519C4×C43—42no—
520C4×C43D4212yes—
521C4×C43C23×D411yescharacteristic
522C4×C43C2×H(5,𝔽2)11yescharacteristic
523Dic43—22no—
524Dic43—22no—
525Dic43—22no—
526Dic43—42no—
527Dic43—42no—
528Dic43—42no—
529C2×#578D4311yescharacteristic, complemented
530C2×#577—431no—
531#3500—431no—
532#3499—431no—
533#3270—434no—
534#3269—434no—
535#3267—434no—
536#3266—434no—
537C2×#497—431no—
538#3059—431no—
539#3057—431no—
540#3040—431no—
541#3039—431no—
542#3011—431no—
543#3011—431no—
544#3010—431no—
545#3009—431no—
546#2943—431no—
547#2932—431no—
548C2×C43—22no—
549C2×C43—42no—
550C2×C43—42no—
551C2×C43—42no—
552C2×C43C2×D4211yescharacteristic
553C2×C43#358612yes—
554D43—42no—
555D43—82no—
556C2×2−1+4—431no—
557C2×2−1+4C2×D4311yescharacteristic
558C2×2−1+4C2×D4311yescharacteristic, complemented
559C2×H(5,𝔽2)—431no—
560#578—28no—
561#577—868no—
562C2×#137—431no—
563C2×#137—432no—
564C2×#137C2×D4311yescharacteristic
565C2×#137C2×D4312yescomplemented
566C2×#137C2×D4311yescharacteristic, complemented
567C2×#137C2×D4312yescomplemented
568C2×AGL(1,ℤ/8)—431no—
569C2×AGL(1,ℤ/8)—432no—
570C2×#135—432no—
571C2×#135C2×D4311yescharacteristic
572C2×#135C2×D4312yescomplemented
573C22×Q16—431no—
574C22×Q16C2×D4311yescharacteristic, complemented
575C22×Q16C2×D4312yescomplemented
576C22×SD16—431no—
577C22×SD16—432no—
578C22×SD16—431no—
579C2×#131—431no—
580C2×#131C2×D4311yescharacteristic, complemented
581D4×Q8—434no—
582#548—434no—
583#547—434no—
584#547—864no—
585#546—434no—
586#546—864no—
587#536—431no—
588#536—431no—
589#536—431no—
590#536—861no—
591#536—861no—
592#536—861no—
593#535—431no—
594#535—861no—
595#532—431no—
596#532—861no—
597#532—861no—
598C2×C4⋊Q8—431no—
599C2×C4⋊Q8—861no—
600C2×#124—431no—
601C2×#124—861no—
602C4×#41—431no—
603C4×#41—431no—
604#497—434no—
605#497—434no—
606#470—434no—
607#468—434no—
608#467—434no—
609#465—434no—
610#464—434no—
611#463—434no—
612#462—434no—
613#461—434no—
614#452—434no—
615#452—434no—
616#452—434no—
617#451—434no—
618#451—434no—
619#450—434no—
620#449—434no—
621#448—434no—
622#442—432no—
623#441—432no—
624#440—432no—
625#440—432no—
626#435—434no—
627#435—434no—
628#427—431no—
629#423—431no—
630#419—431no—
631#419—431no—
632#419—431no—
633#418—431no—
634#416—431no—
635#416—431no—
636#408—431no—
637#408—431no—
638C2×#97—431no—
639C43#6108311yescharacteristic, complemented, Sylow
6402−1+4—24no—
6412−1+4—24no—
6422−1+4—42no—
6432−1+4—42no—
6442−1+4—864no—
6452−1+4—1722no—
646H(5,𝔽2)—864no—
647H(5,𝔽2)—1722no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—22no—
651C2×#41—22no—
652C2×#41—431no—
653C2×#41—432no—
654C2×#41—432no—
655C2×#41—861no—
656C2×#41—861no—
657C2×#41—862no—
658C2×#41C22×D4312yes—
659C2×#41C22×D4312yes—
660C2×#41C22×D4311yescharacteristic
661C2×#41C22×D4311yescharacteristic
662C2×#41C22×D4311yescharacteristic
663C22×Q8—21no—
664C22×Q8—21no—
665C22×Q8—432no—
666C22×Q8—431no—
667C22×Q8—861no—
668C22×Q8C22×D4311yescharacteristic
669C22×Q8C22×D4311yescharacteristic
670C22×Q8C22×D4312yes—
671C22×Q8C22×D4312yes—
672C22×D4—432no—
673C22×D4—431no—
674C22×D4—861no—
675C22×D4—862no—
676#137—24no—
677#137—24no—
678#137—28no—
679#137—28no—
680#137—864no—
681#137—868no—
682AGL(1,ℤ/8)—864no—
683AGL(1,ℤ/8)—868no—
684#135—28no—
685#135—868no—
686#135C22⋊D4318yescomplemented
687C2×Q16—28no—
688C2×Q16—24no—
689C2×Q16—432no—
690C2×Q16—434no—
691C2×Q16—1722no—
692C2×Q16C22×D4312yes—
693C2×Q16C22×D4312yes—
694C2×Q16C22×D4312yes—
695C2×Q16C22×D4312yes—
696C2×Q16C22×D4311yescharacteristic
697C2×SD16—432no—
698C2×SD16—432no—
699C2×SD16—434no—
700C2×SD16—432no—
701C2×SD16—432no—
702C2×SD16—868no—
703C2×SD16—864no—
704C2×SD16—1722no—
705C2×SD16C22×D4312yes—
706C2×SD16C22×D4312yes—
707C2×SD16C22×D4311yescharacteristic
708C2×SD16C22×D4311yescharacteristic
709C2×D8—432no—
710C2×D8C22×D4311yescharacteristic
711#131—24no—
712#131—864no—
713C2×M16—431no—
714C2×M16—432no—
715C2×M16C22×D4311yescharacteristic
716C2×M16C22×D4312yes—
717C22×C8—431no—
718C22×C8—432no—
719C22×C8C22×D4312yes—
720C22×C8C22×D4311yescharacteristic
721C4⋊Q8—431no—
722C4⋊Q8—434no—
723C4⋊Q8—861no—
724C4⋊Q8—861no—
725C4⋊Q8—864no—
726C4⋊Q8—861no—
727C4⋊Q8—861no—
728C4⋊Q8—861no—
729#127—431no—
730#127—861no—
731#124—431no—
732#124—431no—
733#124—434no—
734#124—861no—
735#124—861no—
736#124—864no—
737#124—861no—
738#124—861no—
739#124—861no—
740#124—861no—
741#123—864no—
742#123—864no—
743#123—864no—
744#123—862no—
745#123—862no—
746#123—862no—
747C22⋊Q8—434no—
748C22⋊Q8—434no—
749C22⋊Q8—434no—
750C22⋊Q8—864no—
751C22⋊Q8—864no—
752C22⋊Q8—864no—
753#121—434no—
754#121—434no—
755#121—864no—
756#121—864no—
757#121—864no—
758#120—864no—
759#120—862no—
760C4×Q8—432no—
761C4×Q8—432no—
762C4×D4—434no—
763C4×D4—432no—
764C4×D4—432no—
765C4×D4—864no—
766C4×D4—864no—
767C4×D4—862no—
768C4×D4—862no—
769#117—431no—
770#117—431no—
771#117—861no—
772#117—861no—
773C2×C4⋊C4—864no—
774C2×C4⋊C4—862no—
775C2×C22⋊C4—864no—
776C2×C22⋊C4—862no—
777C2×C42—431no—
778C2×C42—861no—
779C2×C42—861no—
780#107—432no—
781#106—432no—
782C4⋊C8—434no—
783#103—432no—
784#103—432no—
785#103—434no—
786#103—434no—
787#103—434no—
788#102—432no—
789#102—432no—
790#102—434no—
791C22⋊C8—434no—
792C22⋊C8—434no—
793#97—432no—
794#97—432no—
795C24—862no—
796C24—861no—
797#41—22no—
798#41—22no—
799#41—22no—
800#41—22no—
801#41—24no—
802#41—24no—
803#41—42no—
804#41—42no—
805#41—44no—
806#41—44no—
807#41—48no—
808#41—48no—
809#41—862no—
810#41—862no—
811#41—864no—
812#41—864no—
813#41—1724no—
814#41—1724no—
815#41—1722no—
816#41—1722no—
817#41—1728no—
818#41C2×C22⋊D4314yes—
819#41C2×C22⋊D4314yes—
820C2×Q8—22no—
821C2×Q8—22no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—24no—
825C2×Q8—24no—
826C2×Q8—22no—
827C2×Q8—22no—
828C2×Q8—22no—
829C2×Q8—22no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×Q8—44no—
833C2×Q8—44no—
834C2×Q8—431no—
835C2×Q8—432no—
836C2×Q8—862no—
837C2×Q8—861no—
838C2×Q8—864no—
839C2×Q8—862no—
840C2×Q8—862no—
841C2×Q8—1724no—
842C2×Q8—1722no—
843C2×Q8D4×D4311yescharacteristic
844C2×Q8C23×D4312yes—
845C2×Q8C23×D4312yes—
846C2×Q8C23×D4311yescharacteristic
847C2×Q8C23×D4311yescharacteristic
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—432no—
853C2×D4—434no—
854C2×D4—431no—
855C2×D4—432no—
856C2×D4—862no—
857C2×D4—862no—
858C2×D4—864no—
859C2×D4—864no—
860C2×D4—862no—
861C2×D4—861no—
862C2×D4—862no—
863C2×D4—862no—
864C2×D4—1724no—
865C2×D4—1722no—
866C2×D4—1728no—
867C2×D4D4×D4312yes—
868C2×D4D4×D4311yescharacteristic
869C2×D4C23×D4311yescharacteristic
870C2×D4C23×D4311yescharacteristic
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—432no—
880C22×C4—432no—
881C22×C4—862no—
882C22×C4—862no—
883C22×C4—862no—
884C22×C4—862no—
885C22×C4—862no—
886C22×C4—861no—
887C22×C4C23×D4312yes—
888C22×C4C23×D4311yescharacteristic
889Q16—24no—
890Q16—24no—
891Q16—24no—
892Q16—24no—
893Q16—864no—
894Q16—1724no—
895Q16C2×C22⋊D4314yes—
896SD16—24no—
897SD16—24no—
898SD16—864no—
899SD16—864no—
900SD16—864no—
901SD16—864no—
902SD16—1724no—
903SD16C2×C22⋊D4314yes—
904SD16C2×C22⋊D4314yes—
905D8—864no—
906D8C2×C22⋊D4314yes—
907M16—22no—
908M16—24no—
909M16—862no—
910M16—864no—
911C2×C8—24no—
912C2×C8—432no—
913C2×C8—432no—
914C2×C8—862no—
915C2×C8—864no—
916C2×C8C2×C22⋊D4314yes—
917C2×C8C23×D4312yes—
918C2×C8C23×D4311yescharacteristic
919C2×C8C23×D4311yescharacteristic
920C4⋊C4—434no—
921C4⋊C4—432no—
922C4⋊C4—432no—
923C4⋊C4—864no—
924C4⋊C4—864no—
925C4⋊C4—864no—
926C4⋊C4—862no—
927C4⋊C4—862no—
928C4⋊C4—864no—
929C4⋊C4—864no—
930C22⋊C4—434no—
931C22⋊C4—434no—
932C22⋊C4—864no—
933C22⋊C4—864no—
934C22⋊C4—864no—
935C22⋊C4—864no—
936C22⋊C4—862no—
937C22⋊C4—862no—
938C22⋊C4—861no—
939C22⋊C4—861no—
940C22⋊C4—864no—
941C22⋊C4—864no—
942C42—431no—
943C42—431no—
944C42—432no—
945C42—862no—
946C42—862no—
947C42—861no—
948C42—861no—
949C23—21no—
950C23—21no—
951C23—432no—
952C23—862no—
953C23—3442no—
954C23—3444no—
955C23—1724no—
956C23—1722no—
957C23C2×D4×D4312yes—
958C23C2×D4×D4311yescharacteristic
959Q8—21no—
960Q8—21no—
961Q8—22no—
962Q8—22no—
963Q8—22no—
964Q8—22no—
965Q8—22no—
966Q8—44no—
967Q8—44no—
968Q8—42no—
969Q8—42no—
970Q8—862no—
971Q8—862no—
972Q8—862no—
973Q8—1724no—
974Q8—1722no—
975Q8C22×C22⋊D4312yes—
976Q8C22×C22⋊D4312yes—
977D4—24no—
978D4—24no—
979D4—24no—
980D4—21no—
981D4—21no—
982D4—22no—
983D4—44no—
984D4—44no—
985D4—864no—
986D4—862no—
987D4—862no—
988D4—862no—
989D4—3444no—
990D4—1724no—
991D4—1724no—
992D4—1724no—
993D4—1724no—
994D4—1722no—
995D4C22×C22⋊D4312yes—
996D4C22×C22⋊D4312yes—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—44no—
1006C2×C4—44no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—432no—
1012C2×C4—432no—
1013C2×C4—432no—
1014C2×C4—862no—
1015C2×C4—862no—
1016C2×C4—862no—
1017C2×C4—862no—
1018C2×C4—862no—
1019C2×C4—3442no—
1020C2×C4—1724no—
1021C2×C4—1724no—
1022C2×C4—1722no—
1023C2×C4—1724no—
1024C2×C4—1724no—
1025C2×C4—1722no—
1026C2×C4C2×D4×D4312yes—
1027C2×C4C2×D4×D4311yescharacteristic
1028C2×C4C22×C22⋊D4312yes—
1029C2×C4#1306337012yes—
1030C2×C4C24×D4311yescharacteristic
1031C8—22no—
1032C8—862no—
1033C8—862no—
1034C8C22×C22⋊D4312yes—
1035C8C22×C22⋊D4312yes—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—24no—
1041C22—42no—
1042C22—42no—
1043C22—862no—
1044C22—864no—
1045C22—1722no—
1046C22—1724no—
1047C22—6882no—
1048C22—6884no—
1049C22D4×C22⋊D4312yes—
1050C22C22×D4×D4311yescharacteristic
1051C4—22no—
1052C4—22no—
1053C4—22no—
1054C4—42no—
1055C4—42no—
1056C4—862no—
1057C4—862no—
1058C4—862no—
1059C4—1722no—
1060C4—1722no—
1061C4—1722no—
1062C4D4×C22⋊D4312yes—
1063C4C23×C22⋊D4311yescharacteristic
1064C4C2×#1306337011yescharacteristic
1065C2—22no—
1066C2—42no—
1067C2—42no—
1068C2—42no—
1069C2—3442no—
1070C2—1722no—
1071C2C2×D4×C22⋊D4311yescharacteristic
1072C2#1914938012yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#578C2
socleC22×C43C23×D4
hypercenterC2×#578D43
hypocenterC43#61083
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×#14583706C2semidirect
2. #19148389C2semidirect
3. #19148376C2semidirect
4. #19146165C2semidirect
5. #19146144C2semidirect
6. #19146120C2semidirect
7. #19146099C2semidirect
8. C2×#14583292C2semidirect
9. #19144246C2semidirect
10. #19144234C2semidirect
11. #19144091C2semidirect
12. #19144080C2semidirect
13. #19143890C2semidirect
14. #19143889C2semidirect
15. #19143881C2semidirect
16. #19143871C2semidirect
17. #19143396C2semidirect
18. #19143311C2semidirect
19. C2×C43×#578C2semidirect
28. C22×#10621885C22semidirect
33. Q8×C22⋊D43C22semidirect
36. #14583548C22semidirect
44. #14583470C22semidirect
51. C2×#13063323C22semidirect
55. #41×Dic43C22semidirect
56. #14583292C22semidirect
57. #14583292C22semidirect
58. #14583154C22semidirect
59. #14583145C22semidirect
60. #14583137C22semidirect
61. #14583128C22semidirect
62. #14583123C22semidirect
63. #14583116C22semidirect
64. #14583107C22semidirect
65. #14583102C22semidirect
66. #14583061C22semidirect
68. #14583058C22semidirect
69. #14583055C22semidirect
70. #14583053C22semidirect
72. #14583044C22semidirect
73. #14583038C22semidirect
74. #14583011C22semidirect
75. #14583006C22semidirect
76. #14583000C22semidirect
77. #14583000C22semidirect
78. #14582970C22semidirect
79. #14582968C22semidirect
80. #14582937C22semidirect
81. #14582922C22semidirect
82. #14582909C22semidirect
83. #14582908C22semidirect
84. #14582908C22semidirect
87. #14582895C22semidirect
89. #14582866C22semidirect
90. C2×#13063235C22semidirect
92. C2×2−1+4×C43C22semidirect
95. C2×#137×C43C22semidirect
96. C2×#137×C43C22semidirect
97. C2×#137×C43C22semidirect
99. C2×#135×C43C22semidirect
100. C22×Q16×C43C22semidirect
101. C22×Q16×C43C22semidirect
102. C2×#131×C43C22semidirect
240. #135×C43D4semidirect
529. C2×#578D43semidirect
558. C2×2−1+4C2×D43semidirect
565. C2×#137C2×D43semidirect
566. C2×#137C2×D43semidirect
567. C2×#137C2×D43semidirect
572. C2×#135C2×D43semidirect
574. C22×Q16C2×D43semidirect
575. C22×Q16C2×D43semidirect
580. C2×#131C2×D43semidirect
639. C43#61083semidirect
686. #135C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145837062
#191483892
#191483762
#191461652
#191461442
#191461202
#191460992
C2×#145832922
#191442462
#191442342
#191440912
#191440802
#191438902
#191438892
#191438812
#191438712
#191433962
#191433112
C2×C43×#5782
#6108343