Finite Group Databasebeta

← #25965025

Subgroups — #25965025

Order 11008.

2428 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583444C211yesmaximal, characteristic, complemented
2C2×#14583367C211yesmaximal, characteristic, complemented
3#19144741C214yesmaximal, complemented
4#19144714C212yesmaximal, complemented
5#19144683C212yesmaximal, complemented
6#19144650C214yesmaximal, complemented
7#19144623C212yesmaximal, complemented
8#19144592C212yesmaximal, complemented
9#19144535C211yesmaximal, characteristic, complemented
10#19144408C212yesmaximal, complemented
11#19144074C212yesmaximal, complemented
12#19143849C211yesmaximal, characteristic, complemented
13#19143845C211yesmaximal, characteristic, complemented
14#19143402C212yesmaximal, complemented
15#19143399C212yesmaximal, complemented
16#19143224C211yesmaximal, characteristic, complemented
17C43×#3094C211yesmaximal, characteristic, complemented
18C22×#10621898C2211yescharacteristic
19C22×#10621900—21no—
20C2×#13063353C2212yes—
21C2×#13063351C2212yes—
22#14583444—21no—
23#14583444—21no—
24#14583444—21no—
25#14583444—21no—
26#14583444C2212yes—
27#14583444C2212yes—
28#14583444C2212yescomplemented
29#14583444C2212yescomplemented
30C2×#13063324C2211yescharacteristic, complemented
31C2×#13063321C2211yescharacteristic, complemented
32C2×#13063311—21no—
33C2×#13063299C2211yescharacteristic
34C2×#13063297—21no—
35#14583367—21no—
36#14583367—21no—
37#14583367—21no—
38#14583367—21no—
39#14583367C2212yes—
40#14583367C2212yes—
41#14583367C2212yescomplemented
42#14583367C2212yescomplemented
43C2×#13063290C2211yescharacteristic, complemented
44C2×#13063290C2211yescharacteristic, complemented
45C2×D4×Dic43C2211yescharacteristic, complemented
46C2×#13063287C2211yescharacteristic, complemented
47C2×#13063287C2211yescharacteristic, complemented
48C2×#13063287C2211yescharacteristic, complemented
49C2×(C22⋊D43)⋊C4—21no—
50C2×(C22⋊D43)⋊C4—21no—
51C2×(C22⋊D43)⋊C4—21no—
52C2×#13063282—21no—
53C22×C4×Dic43C2211yescharacteristic
54C2×C42×D43—21no—
55#14583223C2214yescomplemented
56#14583217C2212yescomplemented
57#14583212C2212yescomplemented
58#14583193C2214yescomplemented
59#14583188C2214yescomplemented
60#14583183C2214yescomplemented
61#14583178C2214yescomplemented
62#14583098C2214yescomplemented
63#14583098C2214yescomplemented
64#14583093C2214yescomplemented
65#14583093C2214yescomplemented
66#14583046C2214yescomplemented
67#14583042C2214yescomplemented
68#14583040C2212yescomplemented
69#14583037C2212yescomplemented
70#14583035C2212yescomplemented
71#14583032C2212yescomplemented
72#14583010C2214yescomplemented
73#14583008C2214yescomplemented
74#14582998C2214yescomplemented
75#14582996C2214yescomplemented
76#14582990C2214yescomplemented
77#14582986C2214yescomplemented
78#14582981C2214yescomplemented
79#14582979C2214yescomplemented
80#14582953C2212yescomplemented
81#14582953C2212yescomplemented
82#14582949C2212yescomplemented
83#14582949C2212yescomplemented
84#14582942C2212yescomplemented
85#14582922C2212yescomplemented
86#14582903C2212yescomplemented
87#14582901C2212yes—
88#14582898C2212yes—
89#14582863C2211yescharacteristic
90M16×Dic43C2212yescomplemented
91C2×#121×C43C2211yescharacteristic
92C2×#117×C43C2211yescharacteristic
93C43×#482C2214yescomplemented
94C43×#481C2212yescomplemented
95C43×#480C2212yescomplemented
96C43×#428C2212yescomplemented
97C43×#418C2212yescomplemented
98C43×#407C2211yescharacteristic
99C2×#10621898—21no—
100C2×#10621898—21no—
101C2×#10621898—28no—
102C2×#10621898C2312yes—
103C2×#10621898C2312yes—
104C2×#10621900—22no—
105C2×#10621900—22no—
106C2×#10621900—22no—
107C2×#10621900—22no—
108C2×#10621900—48no—
109C22×Dic86—21no—
110C22×Dic86C2311yescharacteristic
111C22×D172C2311yescharacteristic
112C22×D172C2311yescharacteristic
113C22×C22⋊D43—21no—
114C22×C22⋊D43—21no—
115C22×C22⋊D43—21no—
116C22×C22⋊D43—21no—
117C23×Dic43—21no—
118C23×Dic43D411yescharacteristic
119C23×Dic43D411yescharacteristic
120C22×C4×D43—21no—
121C22×C4×D43—21no—
122C22×C4×D43—21no—
123C22×C4×D43—21no—
124#13063353—28no—
125#13063351—28no—
126C2×#10621873C2314yes—
127C2×#10621883C2314yes—
128C2×D344C2314yes—
129C2×#10621882C2314yes—
130C2×#10621877C2312yes—
131#13063324—21no—
132#13063324—21no—
133#13063324C2312yes—
134#13063324C2312yes—
135#13063321—21no—
136#13063321—21no—
137#13063321C2312yes—
138#13063321C2312yes—
139#13063311—22no—
140#13063311—22no—
141#13063311—22no—
142#13063311—22no—
143#13063299—21no—
144#13063299—21no—
145#13063299C2312yes—
146#13063299C2312yes—
147#13063297—22no—
148#13063297—22no—
149#13063297—22no—
150#13063297—22no—
151#13063290—21no—
152#13063290—21no—
153#13063290—21no—
154#13063290—21no—
155#13063290C2312yes—
156#13063290C2312yes—
157#13063290C2312yes—
158#13063290C2312yes—
159D4×Dic43—21no—
160D4×Dic43—21no—
161D4×Dic43C2312yes—
162D4×Dic43C2312yes—
163#13063287—21no—
164#13063287—21no—
165#13063287—21no—
166#13063287—21no—
167#13063287—21no—
168#13063287—21no—
169#13063287C2312yes—
170#13063287C2312yes—
171#13063287C2312yes—
172#13063287C2312yes—
173#13063287C2312yes—
174#13063287C2312yes—
175(C22⋊D43)⋊C4—22no—
176(C22⋊D43)⋊C4—22no—
177(C22⋊D43)⋊C4—22no—
178(C22⋊D43)⋊C4—22no—
179(C22⋊D43)⋊C4—22no—
180(C22⋊D43)⋊C4—22no—
181(C22⋊D43)⋊C4—22no—
182(C22⋊D43)⋊C4—22no—
183(C22⋊D43)⋊C4—22no—
184(C22⋊D43)⋊C4—22no—
185(C22⋊D43)⋊C4—22no—
186(C22⋊D43)⋊C4—22no—
187#13063282—22no—
188#13063282—22no—
189#13063282—22no—
190#13063282—22no—
191C2×C4⋊Dic43C2311yescharacteristic
192C2×Dic43⋊C4—21no—
193C2×Dic43⋊C4—21no—
194C2×Dic43⋊C4—21no—
195C2×C22⋊Dic43—21no—
196C2×(C2×D43)⋊C4—21no—
197C2×(C2×D43)⋊C4—21no—
198C2×(C2×D43)⋊C4—21no—
199C2×(C2×D43)⋊C4—21no—
200C2×C4×Dic43—21no—
201C2×C4×Dic43—21no—
202C2×C4×Dic43D411yescharacteristic
203C2×C4×Dic43D411yescharacteristic
204C2×C4×Dic43D411yescharacteristic
205C2×C4×Dic43D411yescharacteristic
206C2×C4×Dic43D411yescharacteristic
207C2×C4×Dic43D411yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211C2×C4×Dic43C2311yescharacteristic
212C2×C4×Dic43C2311yescharacteristic
213C2×C4×Dic43C2311yescharacteristic
214C42×D43—22no—
215C42×D43—22no—
216C42×D43—22no—
217C42×D43—22no—
218#13063258C2314yes—
219#13063256C2314yes—
220Dic43⋊C8C2314yes—
221Dic43⋊C8C2314yes—
222#13063250C2314yes—
223#13063248C2314yes—
224#13063247C2314yes—
225#13063245C2314yes—
226#13063245C2314yes—
227#13063245C2314yes—
228C22⋊(C43⋊C8)C2312yes—
229C22⋊(C43⋊C8)C2312yes—
230#13063235C2314yes—
231C8×Dic43C2314yes—
232C22×D4×C43—21no—
233C22×D4×C43C2311yescharacteristic
234C23×C4×C43C2311yescharacteristic
235C2×M16×C43C2312yes—
236#121×C43—21no—
237#121×C43—21no—
238#121×C43C2312yes—
239#121×C43C2312yes—
240#117×C43—21no—
241#117×C43—21no—
242#117×C43C2312yes—
243#117×C43C2312yes—
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C4⋊C4×C43C2311yescharacteristic
246C2×C4⋊C4×C43C2311yescharacteristic
247C2×C22⋊C4×C43—21no—
248C2×C22⋊C4×C43—21no—
249C2×C42×C43—21no—
250#107×C43C2314yes—
251#106×C43C2314yes—
252#102×C43C2314yes—
253#102×C43C2314yes—
254C22⋊C8×C43C2312yes—
255C22⋊C8×C43C2312yes—
256C24×C43—21no—
257C24×C43C2×D411yescharacteristic
258C23×D43—21no—
259C23×D43—21no—
260C2×D4×C43—21no—
261C2×D4×C43—22no—
262C2×D4×C43—22no—
263C2×D4×C43—24no—
264C2×D4×C43—44no—
265C2×D4×C43C2412yes—
266C22×C4×C43—24no—
267C22×C4×C43—21no—
268C22×C4×C43—21no—
269C22×C4×C43—21no—
270C22×C4×C43C2×D411yescharacteristic
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2×D411yescharacteristic
273C22×C4×C43C2411yescharacteristic
274C22×C4×C43C2411yescharacteristic
275C22×C4×C43C2411yescharacteristic
276C2×C22⋊D43—28no—
277C2×C22⋊D43—22no—
278C2×C22⋊D43—22no—
279C2×C22⋊D43—22no—
280C2×C22⋊D43—22no—
281C2×C22⋊D43—22no—
282C2×C22⋊D43—22no—
283C2×C22⋊D43—22no—
284C2×C22⋊D43—22no—
285C2×C22⋊D43—44no—
286C2×C22⋊D43—44no—
287C2×C22⋊D43—44no—
288C22×Dic43—24no—
289C22×Dic43—22no—
290C22×Dic43—22no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—42no—
294C22×Dic43—44no—
295C22×Dic43C2×D411yescharacteristic
296C22×Dic43C2×D411yescharacteristic
297C22×Dic43C2×D411yescharacteristic
298C22×Dic43C2×D411yescharacteristic
299C22×Dic43C2×D411yescharacteristic
300C22×Dic43C2×D411yescharacteristic
301C22×Dic43C2×D411yescharacteristic
302C22×Dic43C2×D411yescharacteristic
303C22×Dic43C2×D411yescharacteristic
304C22×Dic43C2×D411yescharacteristic
305C22×Dic43C2×D411yescharacteristic
306C22×Dic43C2×D411yescharacteristic
307#10621900—48no—
308#10621900—48no—
309#10621900—48no—
310#10621900—48no—
311#10621898—28no—
312#10621898—28no—
313#10621898—24no—
314#10621898—24no—
315#10621898—24no—
316#10621898#4118yescomplemented
317C2×D172—21no—
318C2×D172—24no—
319C2×D172—21no—
320C2×D172—24no—
321C2×D172C2412yes—
322C2×D172C2412yes—
323C2×C4×D43—28no—
324C2×C4×D43—22no—
325C2×C4×D43—22no—
326C2×C4×D43—22no—
327C2×C4×D43—22no—
328C2×C4×D43—22no—
329C2×C4×D43—22no—
330C2×C4×D43—22no—
331C2×C4×D43—22no—
332C2×C4×D43—44no—
333C2×C4×D43—44no—
334C2×C4×D43—44no—
335C2×Dic86—21no—
336C2×Dic86—24no—
337C2×Dic86—22no—
338C2×Dic86—22no—
339C2×Dic86—44no—
340C2×Dic86C2412yes—
341M16×C43—24no—
342C2×C8×C43C2414yes—
343C4⋊C4×C43—21no—
344C4⋊C4×C43—21no—
345C4⋊C4×C43—21no—
346C4⋊C4×C43C2412yes—
347C4⋊C4×C43C2412yes—
348C4⋊C4×C43C2412yes—
349C22⋊C4×C43—22no—
350C22⋊C4×C43—22no—
351C22⋊C4×C43—22no—
352C22⋊C4×C43—22no—
353C42×C43—22no—
354C42×C43—22no—
355C22⋊Dic43—22no—
356C22⋊Dic43—22no—
357#10621883—28no—
358#10621882—28no—
359(C2×D43)⋊C4—22no—
360(C2×D43)⋊C4—22no—
361(C2×D43)⋊C4—22no—
362(C2×D43)⋊C4—22no—
363(C2×D43)⋊C4—22no—
364(C2×D43)⋊C4—22no—
365(C2×D43)⋊C4—22no—
366(C2×D43)⋊C4—22no—
367C4⋊Dic43—21no—
368C4⋊Dic43C2412yes—
369Dic43⋊C4—22no—
370Dic43⋊C4—22no—
371Dic43⋊C4—22no—
372Dic43⋊C4—22no—
373Dic43⋊C4—22no—
374Dic43⋊C4—22no—
375C4×Dic43—22no—
376C4×Dic43—22no—
377C4×Dic43—22no—
378C4×Dic43—22no—
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2×D411yescharacteristic
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2×D411yescharacteristic
384C4×Dic43C2×D411yescharacteristic
385C4×Dic43C2×D411yescharacteristic
386C4×Dic43C2×D411yescharacteristic
387C4×Dic43C2×D411yescharacteristic
388C4×Dic43C2×D411yescharacteristic
389C4×Dic43C2×D411yescharacteristic
390C4×Dic43C2×D411yescharacteristic
391C4×Dic43C2411yescharacteristic
392C4×Dic43C2411yescharacteristic
393C4×Dic43C2411yescharacteristic
394C4×Dic43C2411yescharacteristic
395#10621877—24no—
396C2×C43⋊C8C2414yes—
397D344—28no—
398#10621873—28no—
399C23×C43—22no—
400C23×C43—22no—
401C23×C43—22no—
402C23×C43—41no—
403C23×C43—42no—
404C23×C43—42no—
405C23×C43—42no—
406C23×C43C22×D411yescharacteristic
407C23×C43C22×D411yescharacteristic
408C23×C43C22×D411yescharacteristic
409C22×D43—24no—
410C22×D43—22no—
411C22×D43—22no—
412C22×D43—42no—
413C22×D43—42no—
414C22×D43—42no—
415C22×D43—42no—
416C22×D43—42no—
417D4×C43—24no—
418D4×C43—44no—
419D4×C43—44no—
420D4×C43—42no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—42no—
430C2×C4×C43—42no—
431C2×C4×C43—42no—
432C2×C4×C43C22×D411yescharacteristic
433C2×C4×C43C22×D411yescharacteristic
434C2×C4×C43C22×D411yescharacteristic
435C2×C4×C43C2×#4114yes—
436C2×C4×C43C2511yescharacteristic
437C22⋊D43—28no—
438C22⋊D43—28no—
439C22⋊D43—44no—
440C22⋊D43—44no—
441C22⋊D43—44no—
442C22⋊D43—44no—
443C22⋊D43—44no—
444C22⋊D43—44no—
445C2×Dic43—24no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—41no—
459C2×Dic43—44no—
460C2×Dic43—42no—
461C2×Dic43—44no—
462C2×Dic43AGL(1,ℤ/8)14yescomplemented
463C2×Dic43C22×D411yescharacteristic
464C2×Dic43C22×D411yescharacteristic
465C2×Dic43C22×D411yescharacteristic
466C2×Dic43C22×D411yescharacteristic
467C2×Dic43C22×D411yescharacteristic
468C2×Dic43C22×D411yescharacteristic
469C2×Dic43C22×D411yescharacteristic
470C2×Dic43C22×D411yescharacteristic
471D172—24no—
472D172—22no—
473D172—24no—
474D172—42no—
475D172C2×#4114yescomplemented
476C4×D43—28no—
477C4×D43—28no—
478C4×D43—44no—
479C4×D43—44no—
480C4×D43—44no—
481C4×D43—44no—
482C4×D43—44no—
483C4×D43—44no—
484Dic86—24no—
485Dic86—22no—
486Dic86—44no—
487Dic86—44no—
488Dic86C2×#4114yescomplemented
489C8×C43—24no—
490C43⋊C8—24no—
491#60561—431nomaximal, Sylow
492C22×C43—21no—
493C22×C43—21no—
494C22×C43—21no—
495C22×C43—21no—
496C22×C43—21no—
497C22×C43—21no—
498C22×C43—21no—
499C22×C43—44no—
500C22×C43—42no—
501C22×C43—42no—
502C22×C43—42no—
503C22×C43—84no—
504C22×C43#52512yes—
505C22×C43C2×AGL(1,ℤ/8)12yes—
506C22×C43C23×D411yescharacteristic
507C2×D43—24no—
508C2×D43—48no—
509C2×D43—42no—
510C2×D43—42no—
511C2×D43—42no—
512C2×D43—42no—
513C2×D43—42no—
514C2×D43—84no—
515C4×C43—21no—
516C4×C43—21no—
517C4×C43—42no—
518C4×C43—42no—
519C4×C43—42no—
520C4×C43#52512yes—
521C4×C43C22×#4112yes—
522Dic43—24no—
523Dic43—21no—
524Dic43—21no—
525Dic43—21no—
526Dic43—21no—
527Dic43—21no—
528Dic43—42no—
529Dic43C2×AGL(1,ℤ/8)12yes—
530Dic43C2×AGL(1,ℤ/8)12yes—
531Dic43#57512yes—
532C2×#532—431no—
533C2×C4×#41—431no—
534#3115—434no—
535#3112—432no—
536#3109—432no—
537#3106—434no—
538#3103—432no—
539#3100—432no—
540#3094—431no—
541#3094D4311yescharacteristic, complemented
542#3079—432no—
543#3038—432no—
544#3006—431no—
545#3006—431no—
546C4×AGL(1,ℤ/8)—432no—
547C4×AGL(1,ℤ/8)—432no—
548#2920—431no—
549C2×C43—22no—
550C2×C43—22no—
551C2×C43—41no—
552C2×C43—82no—
553C2×C43C2×#52511yescharacteristic
554C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
555C2×C43C2×#57511yescharacteristic
556D43—44no—
557D43—82no—
558C22×#41—431no—
559C22×#41—861no—
560C2×AGL(1,ℤ/8)—432no—
561C2×AGL(1,ℤ/8)—432no—
562#532—432no—
563#532—432no—
564#532—432no—
565#532—432no—
566#532—861no—
567#532—861no—
568#532—861no—
569#532—861no—
570C2×C4⋊Q8—431no—
571C2×#127—431no—
572C2×#124—861no—
573C2×#121—431no—
574C2×#121—861no—
575C2×#121C2×D4311yescharacteristic
576C4×#41—432no—
577C4×#41—432no—
578C4×#41—432no—
579C4×#41—432no—
580C4×#41—861no—
581C4×#41—861no—
582C4×#41—861no—
583C4×#41—861no—
584C2×C4×Q8—431no—
585C2×C4×Q8—431no—
586C2×C4×D4—431no—
587C2×C4×D4—431no—
588C2×C4×D4—431no—
589C2×C4×D4—431no—
590C2×C4×D4—861no—
591C2×C4×D4—861no—
592C2×C4×D4—861no—
593C2×#117—861no—
594C2×#117C2×D4311yescharacteristic
595C22×C42—431no—
596C22×C42—861no—
597#482—434no—
598#482C2×D4314yescomplemented
599#481—432no—
600#481C2×D4312yescomplemented
601#480—432no—
602#480C2×D4312yescomplemented
603#477—434no—
604#476—434no—
605#475—434no—
606#474—434no—
607#460—434no—
608#460—434no—
609#459—434no—
610#459—434no—
611#449—434no—
612#449—434no—
613#448—432no—
614#448—432no—
615#447—432no—
616#447—432no—
617#442—434no—
618#442—434no—
619#440—434no—
620#440—434no—
621C4×SD16—434no—
622C4×SD16—434no—
623C4×D8—434no—
624C4×D8—434no—
625#432—432no—
626#432—432no—
627#431—432no—
628#431—432no—
629#428—432no—
630#428C2×D4312yescomplemented
631#423—432no—
632#418—432no—
633#418C2×D4312yescomplemented
634#417—432no—
635#417—432no—
636#407—431no—
637#407C2×D4311yescharacteristic
638C4×M16—432no—
639C43#6056111yescharacteristic, complemented, Sylow
640C2×#41—432no—
641C2×#41—432no—
642C2×#41—868no—
643C2×#41—862no—
644C2×#41—862no—
645C2×#41—862no—
646C2×#41—862no—
647C2×#41—861no—
648C2×#41—861no—
649C2×#41—1728no—
650C22×Q8—431no—
651C22×Q8—861no—
652C22×D4—21no—
653C22×D4—431no—
654C22×D4—431no—
655C22×D4—861no—
656C22×D4—861no—
657C22×D4—861no—
658C22×D4—861no—
659C22×D4C22×D4311yescharacteristic
660C23×C4—431no—
661C23×C4—431no—
662C23×C4—861no—
663C23×C4—861no—
664C23×C4—861no—
665C23×C4—861no—
666C23×C4—861no—
667C23×C4C22×D4311yescharacteristic
668AGL(1,ℤ/8)—868no—
669AGL(1,ℤ/8)—868no—
670C2×SD16—434no—
671C2×SD16—434no—
672C2×D8—434no—
673C2×D8—434no—
674C2×M16—432no—
675C2×M16C22×D4312yes—
676C4⋊Q8—432no—
677C4⋊Q8—432no—
678C4⋊Q8—861no—
679C4⋊Q8—861no—
680#127—432no—
681#127—432no—
682#127—861no—
683#127—861no—
684#124—862no—
685#124—862no—
686#124—862no—
687#124—862no—
688#121—21no—
689#121—21no—
690#121—432no—
691#121—432no—
692#121—862no—
693#121—862no—
694#121—862no—
695#121—862no—
696#121—861no—
697#121—861no—
698#121C22×D4312yes—
699#121C22×D4312yes—
700C4×Q8—432no—
701C4×Q8—432no—
702C4×Q8—432no—
703C4×Q8—432no—
704C4×Q8—861no—
705C4×Q8—861no—
706C4×Q8—861no—
707C4×Q8—861no—
708C4×D4—432no—
709C4×D4—432no—
710C4×D4—432no—
711C4×D4—432no—
712C4×D4—432no—
713C4×D4—432no—
714C4×D4—432no—
715C4×D4—432no—
716C4×D4—862no—
717C4×D4—862no—
718C4×D4—862no—
719C4×D4—862no—
720C4×D4—861no—
721C4×D4—861no—
722C4×D4—861no—
723C4×D4—861no—
724C4×D4—861no—
725C4×D4—861no—
726C4×D4—861no—
727C4×D4—861no—
728C4×D4—862no—
729C4×D4—862no—
730C4×D4—862no—
731C4×D4—862no—
732C4×D4—862no—
733C4×D4—862no—
734C4×D4—862no—
735C4×D4—862no—
736#117—21no—
737#117—21no—
738#117—862no—
739#117—862no—
740#117—862no—
741#117—862no—
742#117C22×D4312yes—
743#117C22×D4312yes—
744C2×C4⋊C4—431no—
745C2×C4⋊C4—861no—
746C2×C4⋊C4—861no—
747C2×C4⋊C4—861no—
748C2×C4⋊C4C22×D4311yescharacteristic
749C2×C4⋊C4C22×D4311yescharacteristic
750C2×C4⋊C4C22×D4311yescharacteristic
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—861no—
754C2×C22⋊C4—861no—
755C2×C22⋊C4—861no—
756C2×C22⋊C4—861no—
757C2×C22⋊C4—861no—
758C2×C42—21no—
759C2×C42—431no—
760C2×C42—431no—
761C2×C42—431no—
762C2×C42—431no—
763C2×C42—431no—
764C2×C42—431no—
765C2×C42—431no—
766C2×C42—431no—
767C2×C42—431no—
768C2×C42—431no—
769C2×C42—431no—
770C2×C42—431no—
771C2×C42—862no—
772C2×C42—862no—
773C2×C42—862no—
774C2×C42—862no—
775C2×C42—861no—
776C2×C42—861no—
777#107—434no—
778#107C22×D4314yes—
779#106—434no—
780#106C22×D4314yes—
781C4⋊C8—434no—
782C4⋊C8—434no—
783#103—434no—
784#103—434no—
785#102—434no—
786#102—434no—
787#102—434no—
788#102—434no—
789#102C22×D4314yes—
790#102C22×D4314yes—
791C22⋊C8—432no—
792C22⋊C8—432no—
793C22⋊C8C22×D4312yes—
794C22⋊C8C22×D4312yes—
795#97—434no—
796C4×C8—434no—
797C24—21no—
798C24—861no—
799C24—861no—
800C24D4×D4311yescharacteristic
801#41—438no—
802#41—864no—
803#41—864no—
804#41—868no—
805#41—868no—
806#41—864no—
807#41—1728no—
808#41—1728no—
809#41—1728no—
810#41—1728no—
811C2×Q8—432no—
812C2×Q8—862no—
813C2×Q8—862no—
814C2×Q8—864no—
815C2×Q8—861no—
816C2×Q8—1724no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—21no—
820C2×D4—24no—
821C2×D4—44no—
822C2×D4—432no—
823C2×D4—432no—
824C2×D4—864no—
825C2×D4—862no—
826C2×D4—862no—
827C2×D4—862no—
828C2×D4—862no—
829C2×D4—868no—
830C2×D4—862no—
831C2×D4—862no—
832C2×D4—862no—
833C2×D4—862no—
834C2×D4—861no—
835C2×D4—861no—
836C2×D4—864no—
837C2×D4—1724no—
838C2×D4—1724no—
839C2×D4—1724no—
840C2×D4C23×D4312yes—
841C22×C4—24no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—431no—
846C22×C4—431no—
847C22×C4—431no—
848C22×C4—431no—
849C22×C4—431no—
850C22×C4—431no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—431no—
855C22×C4—431no—
856C22×C4—431no—
857C22×C4—862no—
858C22×C4—862no—
859C22×C4—862no—
860C22×C4—862no—
861C22×C4—862no—
862C22×C4—862no—
863C22×C4—868no—
864C22×C4—864no—
865C22×C4—862no—
866C22×C4—862no—
867C22×C4—861no—
868C22×C4—862no—
869C22×C4—862no—
870C22×C4—861no—
871C22×C4—1724no—
872C22×C4—1724no—
873C22×C4—1724no—
874C22×C4—1722no—
875C22×C4—1724no—
876C22×C4D4×D4311yescharacteristic
877C22×C4D4×D4311yescharacteristic
878C22×C4D4×D4311yescharacteristic
879C22×C4C23×D4311yescharacteristic
880C22×C4C23×D4311yescharacteristic
881C22×C4C23×D4311yescharacteristic
882SD16—868no—
883SD16—868no—
884D8—868no—
885D8—868no—
886M16—24no—
887M16—864no—
888C2×C8—434no—
889C2×C8C23×D4314yes—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—432no—
894C4⋊C4—862no—
895C4⋊C4—862no—
896C4⋊C4—862no—
897C4⋊C4—862no—
898C4⋊C4—862no—
899C4⋊C4—862no—
900C4⋊C4—861no—
901C4⋊C4C23×D4312yes—
902C4⋊C4C23×D4312yes—
903C4⋊C4C23×D4312yes—
904C22⋊C4—22no—
905C22⋊C4—22no—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—862no—
909C22⋊C4—862no—
910C22⋊C4—862no—
911C22⋊C4—862no—
912C22⋊C4—862no—
913C22⋊C4—862no—
914C22⋊C4—862no—
915C22⋊C4—862no—
916C22⋊C4—862no—
917C22⋊C4—862no—
918C42—22no—
919C42—22no—
920C42—431no—
921C42—431no—
922C42—431no—
923C42—431no—
924C42—431no—
925C42—431no—
926C42—431no—
927C42—431no—
928C42—431no—
929C42—431no—
930C42—431no—
931C42—431no—
932C42—431no—
933C42—431no—
934C42—431no—
935C42—431no—
936C42—862no—
937C42—862no—
938C42—862no—
939C42—862no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—41no—
944C23—42no—
945C23—42no—
946C23—42no—
947C23—864no—
948C23—862no—
949C23—862no—
950C23—1722no—
951C23—1722no—
952C23—1722no—
953C23—1722no—
954C23—1722no—
955C23C2×D4×D4311yescharacteristic
956C23C2×D4×D4311yescharacteristic
957C23C2×D4×D4311yescharacteristic
958Q8—434no—
959Q8—864no—
960Q8—862no—
961Q8—1724no—
962Q8—1724no—
963D4—24no—
964D4—44no—
965D4—44no—
966D4—42no—
967D4—434no—
968D4—864no—
969D4—868no—
970D4—868no—
971D4—862no—
972D4—864no—
973D4—1724no—
974D4—1724no—
975D4—1724no—
976D4—1724no—
977D4—1724no—
978D4—1724no—
979D4—1722no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—434no—
992C2×C4—431no—
993C2×C4—431no—
994C2×C4—431no—
995C2×C4—431no—
996C2×C4—431no—
997C2×C4—431no—
998C2×C4—431no—
999C2×C4—431no—
1000C2×C4—868no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—864no—
1009C2×C4—862no—
1010C2×C4—862no—
1011C2×C4—868no—
1012C2×C4—862no—
1013C2×C4—1724no—
1014C2×C4—1724no—
1015C2×C4—1724no—
1016C2×C4—1724no—
1017C2×C4—1724no—
1018C2×C4—1724no—
1019C2×C4—1724no—
1020C2×C4—1721no—
1021C2×C4—1721no—
1022C2×C4—1721no—
1023C2×C4—1724no—
1024C2×C4—1722no—
1025C2×C4C2×D4×D4311yescharacteristic
1026C2×C4C2×D4×D4311yescharacteristic
1027C2×C4C2×D4×D4311yescharacteristic
1028C2×C4#41×D4314yes—
1029C2×C4C24×D4311yescharacteristic
1030C8—24no—
1031C8—864no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—21no—
1038C22—21no—
1039C22—44no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—84no—
1044C22—864no—
1045C22—3444no—
1046C22—1728no—
1047C22—1722no—
1048C22—1722no—
1049C22—1722no—
1050C22—1722no—
1051C22—1722no—
1052C22#1458340712yes—
1053C22AGL(1,ℤ/8)×D4312yes—
1054C22C22×D4×D4311yescharacteristic
1055C4—21no—
1056C4—21no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—432no—
1061C4—432no—
1062C4—432no—
1063C4—861no—
1064C4—861no—
1065C4—861no—
1066C4—861no—
1067C4—861no—
1068C4—864no—
1069C4—1722no—
1070C4#1458340712yes—
1071C4C2×#41×D4312yes—
1072C2—22no—
1073C2—22no—
1074C2—41no—
1075C2—82no—
1076C2—3442no—
1077C2—1724no—
1078C2C2×#1458340711yescharacteristic
1079C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1080C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
hypercenter#3094D43
hypocenterC43#60561
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. C2×#14583444C2semidirect
2. C2×#14583367C2semidirect
3. #19144741C2semidirect
4. #19144714C2semidirect
5. #19144683C2semidirect
6. #19144650C2semidirect
7. #19144623C2semidirect
8. #19144592C2semidirect
9. #19144535C2semidirect
10. #19144408C2semidirect
11. #19144074C2semidirect
12. #19143849C2semidirect
13. #19143845C2semidirect
14. #19143402C2semidirect
15. #19143399C2semidirect
16. #19143224C2semidirect
17. C43×#3094C2semidirect
28. #14583444C22semidirect
29. #14583444C22semidirect
30. C2×#13063324C22semidirect
31. C2×#13063321C22semidirect
41. #14583367C22semidirect
42. #14583367C22semidirect
43. C2×#13063290C22semidirect
44. C2×#13063290C22semidirect
45. C2×D4×Dic43C22semidirect
46. C2×#13063287C22semidirect
47. C2×#13063287C22semidirect
48. C2×#13063287C22semidirect
55. #14583223C22semidirect
56. #14583217C22semidirect
57. #14583212C22semidirect
58. #14583193C22semidirect
59. #14583188C22semidirect
60. #14583183C22semidirect
61. #14583178C22semidirect
62. #14583098C22semidirect
63. #14583098C22semidirect
64. #14583093C22semidirect
65. #14583093C22semidirect
66. #14583046C22semidirect
67. #14583042C22semidirect
68. #14583040C22semidirect
69. #14583037C22semidirect
70. #14583035C22semidirect
71. #14583032C22semidirect
72. #14583010C22semidirect
73. #14583008C22semidirect
74. #14582998C22semidirect
75. #14582996C22semidirect
76. #14582990C22semidirect
77. #14582986C22semidirect
78. #14582981C22semidirect
79. #14582979C22semidirect
80. #14582953C22semidirect
81. #14582953C22semidirect
82. #14582949C22semidirect
83. #14582949C22semidirect
84. #14582942C22semidirect
85. #14582922C22semidirect
86. #14582903C22semidirect
90. M16×Dic43C22semidirect
93. C43×#482C22semidirect
94. C43×#481C22semidirect
95. C43×#480C22semidirect
96. C43×#428C22semidirect
97. C43×#418C22semidirect
316. #10621898#41semidirect
462. C2×Dic43AGL(1,ℤ/8)semidirect
475. D172C2×#41semidirect
488. Dic86C2×#41semidirect
541. #3094D43semidirect
598. #482C2×D43semidirect
600. #481C2×D43semidirect
602. #480C2×D43semidirect
630. #428C2×D43semidirect
633. #418C2×D43semidirect
639. C43#60561semidirect

Maximal subgroups

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

subgroupindex
C2×#145834442
C2×#145833672
#191447412
#191447142
#191446832
#191446502
#191446232
#191445922
#191445352
#191444082
#191440742
#191438492
#191438452
#191434022
#191433992
#191432242
C43×#30942
#6056143