Finite Group Databasebeta

← #25967603

Subgroups — #25967603

Order 11008.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148268C211yesmaximal, characteristic, complemented
2#19147923C211yesmaximal, characteristic, complemented
3#19145488C212yesmaximal, complemented
4#19145476C212yesmaximal, complemented
5#19145465C212yesmaximal, complemented
6#19145444C212yesmaximal, complemented
7#19145436C212yesmaximal, complemented
8#19145422C212yesmaximal, complemented
9#19145385C212yesmaximal, complemented
10#19145379C212yesmaximal, complemented
11#19144580C211yesmaximal, characteristic, complemented
12#19144575C211yesmaximal, characteristic, complemented
13#19144525C211yesmaximal, characteristic, complemented
14C2×#14583239C211yesmaximal, characteristic, complemented
15#19144284C211yesmaximal, characteristic, complemented
16#19144280C211yesmaximal, characteristic, complemented
17#19144261C211yesmaximal, characteristic, complemented
18#19144256C211yesmaximal, characteristic, complemented
19#19143910C211yesmaximal, characteristic, complemented
20#19143851C211yesmaximal, characteristic, complemented
21#19143809C211yesmaximal, characteristic, complemented
22#19143043C211yesmaximal, characteristic, complemented
23C43×#3013C211yesmaximal, characteristic, complemented
24C2×#41×D43C2211yescharacteristic
25C2×#41×D43C2211yescharacteristic
26C2×#13063356C2211yescharacteristic, complemented
27C2×#13063345C2211yescharacteristic, complemented
28C2×#13063333C2211yescharacteristic, complemented
29C2×#13063331C2211yescharacteristic, complemented
30Q8×C22⋊D43—21no—
31#14583560—21no—
32#14583548—22no—
33#14583548—21no—
34#14583537—22no—
35#14583537—21no—
36#14583480C2211yescharacteristic
37#14583477C2211yescharacteristic
38#14583477C2212yes—
39#14583477C2211yescharacteristic
40#14583477C2211yescharacteristic, complemented
41#14583473C2212yes—
42#14583473C2211yescharacteristic, complemented
43#14583472—21no—
44#14583472C2212yes—
45#14583465—21no—
46#14583465C2212yes—
47#14583457—22no—
48#14583444—22no—
49#14583412—21no—
50#14583412C2212yes—
51#14583409—21no—
52#14583409C2212yes—
53#14583406C2211yescharacteristic
54#14583406C2212yescomplemented
55C2×#13063301C2211yescharacteristic
56C2×#13063301C2212yescomplemented
57#14583382C2211yescharacteristic, complemented
58C2×#13063283C2211yescharacteristic
59#14583241C2212yescomplemented
60#14583239C2212yescomplemented
61#14583239C2212yescomplemented
62#14583239C2212yescomplemented
63#14583239C2212yescomplemented
64#14583239C2212yescomplemented
65#14583238C2212yescomplemented
66#14583237C2212yescomplemented
67#14583235C2212yescomplemented
68#14583227C2212yescomplemented
69#14583224C2212yescomplemented
70#14583222C2212yescomplemented
71#14583221C2212yescomplemented
72#14583220C2212yescomplemented
73#14583215C2212yescomplemented
74#14583213C2212yescomplemented
75#14583156C2212yescomplemented
76#14583156C2212yescomplemented
77#14583154C2212yescomplemented
78#14583151C2212yescomplemented
79#14583148C2212yescomplemented
80#14583142C2212yescomplemented
81#14583142C2212yescomplemented
82#14583142C2212yescomplemented
83#14583139C2212yescomplemented
84#14583137C2212yescomplemented
85#14583137C2212yescomplemented
86#14583132C2212yescomplemented
87#14583131C2212yescomplemented
88#14583131C2212yescomplemented
89#14583127C2212yescomplemented
90#14583125C2212yescomplemented
91#14583061C2212yescomplemented
92#14583060C2211yescharacteristic
93#14583060C2212yes—
94#14583058C2211yescharacteristic
95#14583058C2212yes—
96#14583055C2212yescomplemented
97#14583053C2212yescomplemented
98#14583053C2211yescharacteristic, complemented
99#14583048C2211yescharacteristic, complemented
100#14583048C2212yescomplemented
101#14583044C2212yescomplemented
102#14583043C2211yescharacteristic
103#14583041C2211yescharacteristic
104#14583038C2212yescomplemented
105#14583036C2211yescharacteristic, complemented
106#14583031C2211yescharacteristic, complemented
107#14582941C2211yescharacteristic, complemented
108#14582939C2211yescharacteristic, complemented
109C2×#13063259C2211yescharacteristic, complemented
110C2×#13063256C2211yescharacteristic, complemented
111#14582901C2211yescharacteristic, complemented
112#14582900C2211yescharacteristic, complemented
113#14582900C2211yescharacteristic, complemented
114#14582896C2211yescharacteristic, complemented
115#14582895C2211yescharacteristic, complemented
116C2×#13063249C2211yescharacteristic, complemented
117#14582866C2211yescharacteristic, complemented
118#14582864C2212yes—
119#14582864C2212yes—
120#14582862C2211yescharacteristic
121#14582861C2212yescomplemented
122C2×(C2×D43)⋊C8C2211yescharacteristic
123C22⋊C8×D43C2212yescomplemented
124C2×2−1+4×C43C2211yescharacteristic, complemented
125C2×#137×C43C2211yescharacteristic, complemented
126C2×#135×C43C2211yescharacteristic, complemented
127C43×#537C2211yescharacteristic
128C43×#452C2212yescomplemented
129C43×#451C2212yescomplemented
130C43×#449C2212yescomplemented
131C43×#448C2212yescomplemented
132C43×#417C2211yescharacteristic, complemented
133C2×#103×C43C2211yescharacteristic, complemented
134C43×#408C2211yescharacteristic, complemented
135C2×#10621902D411yescharacteristic
136C2×#10621902C2311yescharacteristic
137C2×#10621898—21no—
138C2×#10621898C2311yescharacteristic
139C2×#10621898C2312yes—
140C2×#10621898C2311yescharacteristic
141C2×#10621900—21no—
142C2×#10621900D411yescharacteristic
143C2×#10621900D412yes—
144C2×#10621900C2311yescharacteristic
145#41×D43—42no—
146#41×D43—42no—
147#41×D43—42no—
148#41×D43—42no—
149C2×Q8×D43D411yescharacteristic
150C2×Q8×D43C2311yescharacteristic
151C2×D4×D43—21no—
152C2×D4×D43D412yes—
153C2×D4×D43D411yescharacteristic
154C2×D4×D43C2311yescharacteristic
155C22×C4×D43—21no—
156C22×C4×D43C2311yescharacteristic
157C22×C4×D43C2312yes—
158#13063356—42no—
159#13063345—42no—
160C2×#10621885C2311yescharacteristic
161C2×#10621885C2312yes—
162C2×#10621883C2311yescharacteristic
163C2×#10621884C2312yes—
164C2×#10621884C2311yescharacteristic
165C2×#10621882C2311yescharacteristic
166#13063333—42no—
167#13063331—42no—
168C2×#10621877C2311yescharacteristic
169C2×#10621872C2312yes—
170C2×#10621872C2312yes—
171C22×C43⋊C8C2311yescharacteristic
172C2×C8×D43C2312yes—
173C2×C8×D43C2312yes—
174#13063324—22no—
175#13063323—22no—
176#13063323—21no—
177#13063321—22no—
178#13063314—22no—
179#13063314—21no—
180#13063311—22no—
181#13063311—22no—
182#13063310—22no—
183#13063310—22no—
184#13063308—22no—
185#13063308—22no—
186#13063308—22no—
187#13063307—22no—
188#13063307—22no—
189#13063306—21no—
190#13063306—22no—
191#13063305—21no—
192#13063305C2312yes—
193#13063304—22no—
194#13063304—21no—
195#13063304—21no—
196#13063304C2312yes—
197#13063301—21no—
198#13063301—21no—
199#13063301—22no—
200#13063301—21no—
201#13063301—22no—
202#13063301C2312yes—
203#13063301C2311yescharacteristic
204#13063301C2312yes—
205#13063301C2311yescharacteristic
206#13063301C2312yes—
207#13063301C2312yes—
208#13063301C2312yes—
209#13063301C2312yes—
210#13063300—21no—
211#13063300C2312yes—
212#13063299—22no—
213#13063299—22no—
214#13063299—21no—
215#13063299—21no—
216#13063299C2312yes—
217#13063297—22no—
218#13063297—22no—
219#13063297—22no—
220#13063297—22no—
221#13063297—22no—
222#13063296—21no—
223#13063296C2311yescharacteristic
224#13063296C2312yes—
225#13063296C2312yes—
226#13063296C2311yescharacteristic
227#13063295—22no—
228#13063295—22no—
229#13063293—21no—
230#13063293—22no—
231#13063293—22no—
232#13063293—22no—
233Q8×Dic43—21no—
234D4×Dic43—21no—
235D4×Dic43—22no—
236D4×Dic43—22no—
237#13063287—22no—
238C4×C22⋊D43—21no—
239C4×C22⋊D43—22no—
240C4×C22⋊D43—21no—
241C4×C22⋊D43—22no—
242(C22⋊D43)⋊C4—22no—
243(C22⋊D43)⋊C4—22no—
244#13063284C2311yescharacteristic
245#13063284C2312yes—
246#13063283—21no—
247#13063283—21no—
248#13063283C2312yes—
249#13063283C2312yes—
250C2×C4⋊Dic43C2311yescharacteristic
251C2×C4⋊Dic43C2311yescharacteristic
252C2×C4⋊Dic43C2312yes—
253C2×Dic43⋊C4—21no—
254C2×Dic43⋊C4—22no—
255C2×(C2×D43)⋊C4—21no—
256C2×(C2×D43)⋊C4—21no—
257C2×(C2×D43)⋊C4—22no—
258C2×C4×Dic43—21no—
259#13063259C2312yes—
260#13063259C2312yes—
261#13063259C2312yes—
262#13063258C2312yes—
263#13063257C2312yes—
264#13063256C2312yes—
265#13063256C2312yes—
266#13063256C2312yes—
267#13063250C2311yescharacteristic
268#13063250C2312yes—
269#13063250C2311yescharacteristic
270#13063249C2311yescharacteristic
271#13063249C2312yes—
272#13063249C2312yes—
273#13063249C2312yes—
274#13063249C2311yescharacteristic
275#13063249C2312yes—
276#13063247C2311yescharacteristic
277#13063247C2312yes—
278#13063247C2311yescharacteristic
279#13063246C2311yescharacteristic
280#13063246C2312yes—
281#13063246C2312yes—
282#13063246C2311yescharacteristic
283C22⋊(C43⋊C8)C2312yes—
284C22⋊(C43⋊C8)C2312yes—
285(C2×D43)⋊C8C2311yescharacteristic
286(C2×D43)⋊C8C2311yescharacteristic
287(C2×D43)⋊C8C2312yes—
288(C2×D43)⋊C8C2311yescharacteristic
289(C2×D43)⋊C8C2311yescharacteristic
290(C2×D43)⋊C8C2312yes—
2912−1+4×C43—42no—
2922−1+4×C43—42no—
293C2×#41×C43—21no—
294C2×#41×C43—22no—
295C2×#41×C43C2311yescharacteristic
296C2×#41×C43C2311yescharacteristic
297C2×#41×C43C2312yes—
298C2×#41×C43C2311yescharacteristic
299C22×Q8×C43—21no—
300C22×Q8×C43C2311yescharacteristic
301C22×Q8×C43C2312yes—
302#137×C43—42no—
303#135×C43—42no—
304C2×Q16×C43C2311yescharacteristic
305C2×Q16×C43C2312yes—
306C2×SD16×C43C2311yescharacteristic
307C2×SD16×C43C2311yescharacteristic
308C2×SD16×C43C2312yes—
309C2×D8×C43C2311yescharacteristic
310C2×M16×C43C2311yescharacteristic
311C22×C8×C43C2311yescharacteristic
312C22⋊Q8×C43—21no—
313C22⋊Q8×C43C2312yes—
314#121×C43—21no—
315#121×C43—22no—
316#121×C43C2312yes—
317C2×C4⋊C4×C43C2311yescharacteristic
318#103×C43C2312yes—
319#103×C43C2312yes—
320#103×C43C2312yes—
321#102×C43C2312yes—
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C23×D43—21no—
325C23×D43C2×D411yescharacteristic
326C23×D43C2×D412yes—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—22no—
332#41×C43—22no—
333#41×C43—42no—
334#41×C43—42no—
335#41×C43—48no—
336#41×C43—44no—
337C2×Q8×C43—22no—
338C2×Q8×C43—21no—
339C2×Q8×C43—22no—
340C2×Q8×C43—22no—
341C2×Q8×C43—42no—
342C2×Q8×C43—42no—
343C2×Q8×C43—44no—
344C2×Q8×C43C2×D411yescharacteristic
345C2×Q8×C43C2412yes—
346C2×Q8×C43C2411yescharacteristic
347C2×Q8×C43C2411yescharacteristic
348C2×D4×C43—21no—
349C2×D4×C43—22no—
350C2×D4×C43—21no—
351C2×D4×C43—22no—
352C2×D4×C43C2×D411yescharacteristic
353C2×D4×C43C2×D412yes—
354C2×D4×C43C2411yescharacteristic
355C2×D4×C43C2411yescharacteristic
356C22×C4×C43—21no—
357C22×C4×C43—22no—
358C22×C4×C43—21no—
359C22×C4×C43—22no—
360C22×C4×C43—21no—
361C22×C4×C43—21no—
362C22×C4×C43C2412yes—
363C22×C4×C43C2411yescharacteristic
364C2×C22⋊D43—21no—
365C2×C22⋊D43—21no—
366C2×C22⋊D43—22no—
367C2×C22⋊D43—21no—
368C2×C22⋊D43—21no—
369C2×C22⋊D43—22no—
370C2×C22⋊D43—21no—
371C2×C22⋊D43—22no—
372C2×C22⋊D43C2×D412yes—
373C2×C22⋊D43C2×D412yes—
374C2×C22⋊D43C2×D412yes—
375C22×Dic43—21no—
376C22×Dic43—21no—
377C22×Dic43—22no—
378C22×Dic43—21no—
379C22×Dic43C2×D411yescharacteristic
380C22×Dic43C2×D412yes—
381#10621902—42no—
382#10621902—41no—
383#10621902—41no—
384Q8×D43—42no—
385Q8×D43—41no—
386Q8×D43—41no—
387#10621900—42no—
388#10621900—41no—
389#10621900—41no—
390#10621900—44no—
391#10621900—44no—
392D4×D43—44no—
393D4×D43—44no—
394D4×D43—42no—
395D4×D43—41no—
396D4×D43—41no—
397#10621898—22no—
398#10621898—22no—
399#10621898—22no—
400#10621898—22no—
401#10621898—42no—
402#10621898—42no—
403#10621898—44no—
404C2×D172—21no—
405C2×D172—22no—
406C2×D172C2×D411yescharacteristic
407C2×D172C2×D412yes—
408C2×D172C2411yescharacteristic
409C2×C4×D43—22no—
410C2×C4×D43—22no—
411C2×C4×D43—21no—
412C2×C4×D43—21no—
413C2×C4×D43—21no—
414C2×C4×D43—42no—
415C2×C4×D43—42no—
416C2×C4×D43—44no—
417C2×C4×D43C2×D411yescharacteristic
418C2×C4×D43C2×D411yescharacteristic
419C2×C4×D43C2×D412yes—
420C2×C4×D43C2×D412yes—
421C2×C4×D43C2411yescharacteristic
422C2×C4×D43C2411yescharacteristic
423C2×C4×D43C2412yes—
424C2×Dic86—21no—
425C2×Dic86C2×D411yescharacteristic
426C2×Dic86C2×D412yes—
427C2×Dic86C2411yescharacteristic
428Q16×C43—41no—
429Q16×C43—42no—
430SD16×C43—41no—
431SD16×C43—41no—
432SD16×C43—42no—
433D8×C43—41no—
434M16×C43—22no—
435C2×C8×C43—22no—
436C2×C8×C43C2412yes—
437C2×C8×C43C2411yescharacteristic
438C2×C8×C43C2411yescharacteristic
439C4⋊C4×C43—21no—
440C4⋊C4×C43—22no—
441C4⋊C4×C43C2412yes—
442C22⋊C4×C43—22no—
443C22⋊C4×C43—22no—
444C22⋊Dic43—21no—
445C22⋊Dic43—21no—
446C22⋊Dic43—22no—
447C22⋊Dic43—22no—
448C22⋊Dic43—22no—
449C22⋊Dic43—21no—
450C22⋊Dic43—22no—
451#10621885—41no—
452#10621885—42no—
453#10621884—41no—
454#10621884—42no—
455#10621883—41no—
456#10621882—41no—
457(C2×D43)⋊C4—22no—
458(C2×D43)⋊C4—22no—
459(C2×D43)⋊C4—22no—
460(C2×D43)⋊C4—21no—
461(C2×D43)⋊C4—22no—
462(C2×D43)⋊C4—22no—
463(C2×D43)⋊C4—22no—
464(C2×D43)⋊C4—22no—
465(C2×D43)⋊C4—22no—
466(C2×D43)⋊C4—22no—
467(C2×D43)⋊C4—21no—
468(C2×D43)⋊C4—22no—
469(C2×D43)⋊C4—22no—
470C4⋊Dic43—21no—
471C4⋊Dic43—22no—
472C4⋊Dic43—21no—
473C4⋊Dic43—22no—
474C4⋊Dic43C2412yes—
475C4⋊Dic43C2411yescharacteristic
476C4⋊Dic43C2411yescharacteristic
477C4⋊Dic43C2412yes—
478Dic43⋊C4—22no—
479Dic43⋊C4—22no—
480Dic43⋊C4—21no—
481Dic43⋊C4—22no—
482Dic43⋊C4—22no—
483Dic43⋊C4—22no—
484Dic43⋊C4—22no—
485Dic43⋊C4—21no—
486Dic43⋊C4—22no—
487C4×Dic43—22no—
488C4×Dic43—21no—
489C4×Dic43—22no—
490C4×Dic43—22no—
491#10621877—22no—
492C2×C43⋊C8—22no—
493C2×C43⋊C8C2412yes—
494C2×C43⋊C8C2411yescharacteristic
495C2×C43⋊C8C2411yescharacteristic
496#10621872—42no—
497#10621872—42no—
498C8×D43—42no—
499C8×D43—42no—
500C23×C43—21no—
501C23×C43—21no—
502C23×C43C22×D412yes—
503C23×C43C22×D411yescharacteristic
504C22×D43—22no—
505C22×D43—21no—
506C22×D43—42no—
507C22×D43—41no—
508C22×D43—42no—
509C22×D43—41no—
510C22×D43—42no—
511C22×D43—42no—
512C22×D43—81no—
513C22×D43—81no—
514C22×D43C22×D411yescharacteristic
515C22×D43C22×D411yescharacteristic
516C22×D43C22×D412yes—
517Q8×C43—22no—
518Q8×C43—22no—
519Q8×C43—21no—
520Q8×C43—21no—
521Q8×C43—22no—
522Q8×C43—21no—
523Q8×C43—21no—
524Q8×C43—44no—
525Q8×C43—42no—
526D4×C43—24no—
527D4×C43—22no—
528D4×C43—21no—
529D4×C43—21no—
530D4×C43—21no—
531D4×C43—21no—
532D4×C43—44no—
533D4×C43—42no—
534D4×C43—42no—
535D4×C43—82no—
536C2×C4×C43—22no—
537C2×C4×C43—22no—
538C2×C4×C43—22no—
539C2×C4×C43—22no—
540C2×C4×C43—21no—
541C2×C4×C43—21no—
542C2×C4×C43—44no—
543C2×C4×C43—44no—
544C2×C4×C43—42no—
545C2×C4×C43—42no—
546C2×C4×C43—42no—
547C2×C4×C43—81no—
548C2×C4×C43C22×D412yes—
549C2×C4×C43C22×D411yescharacteristic
550C2×C4×C43H(5,𝔽2)12yes—
551C2×C4×C43H(5,𝔽2)12yes—
552C2×C4×C43C2511yescharacteristic
553C22⋊D43—24no—
554C22⋊D43—42no—
555C22⋊D43—42no—
556C22⋊D43—42no—
557C22⋊D43—42no—
558C22⋊D43—42no—
559C22⋊D43—42no—
560C22⋊D43—81no—
561C22⋊D43—82no—
562C22⋊D43—82no—
563C22⋊D43—82no—
564C2×Dic43—22no—
565C2×Dic43—21no—
566C2×Dic43—22no—
567C2×Dic43—22no—
568C2×Dic43—21no—
569C2×Dic43—21no—
570C2×Dic43—42no—
571C2×Dic43—42no—
572C2×Dic43—81no—
573C2×Dic43—82no—
574C2×Dic43—81no—
575C2×Dic43C22×D411yescharacteristic
576C2×Dic43C22×D411yescharacteristic
577C2×Dic43C22×D412yes—
578D172—22no—
579D172—21no—
580D172—21no—
581D172—42no—
582D172—42no—
583D172—82no—
584C4×D43—22no—
585C4×D43—22no—
586C4×D43—22no—
587C4×D43—22no—
588C4×D43—21no—
589C4×D43—21no—
590C4×D43—21no—
591C4×D43—21no—
592C4×D43—42no—
593C4×D43—42no—
594C4×D43—42no—
595C4×D43—42no—
596C4×D43—42no—
597Dic86—22no—
598Dic86—21no—
599Dic86—21no—
600Dic86—42no—
601Dic86—42no—
602C8×C43—21no—
603C8×C43—22no—
604C8×C43—21no—
605C43⋊C8—21no—
606C43⋊C8—22no—
607C43⋊C8—21no—
608#60766—431nomaximal, Sylow
609C22×C43—21no—
610C22×C43—21no—
611C22×C43—22no—
612C22×C43—22no—
613C22×C43—22no—
614C22×C43—41no—
615C22×C43—41no—
616C22×C43—41no—
617C22×C43—41no—
618C22×C43—41no—
619C22×C43—41no—
620C22×C43#53412yes—
621C22×C43C23×D411yescharacteristic
622C2×D43—21no—
623C2×D43—21no—
624C2×D43—22no—
625C2×D43—21no—
626C2×D43—21no—
627C2×D43—22no—
628C2×D43—21no—
629C2×D43—21no—
630C2×D43—22no—
631C2×D43—41no—
632C2×D43—41no—
633C2×D43—41no—
634C2×D43—82no—
635C2×D43—84no—
636C2×D43—84no—
637C4×C43—22no—
638C4×C43—42no—
639C4×C43—41no—
640C4×C43—42no—
641C4×C43—41no—
642C4×C43#53412yes—
643C4×C43C2×H(5,𝔽2)11yescharacteristic
644C4×C43C2×H(5,𝔽2)11yescharacteristic
645Dic43—22no—
646Dic43—21no—
647Dic43—21no—
648Dic43—42no—
649Dic43—41no—
650Dic43—42no—
651Dic43—41no—
652Dic43—41no—
653#3489—431no—
654#3449—431no—
655#3202—432no—
656#3201—432no—
657#3200—432no—
658#3198—432no—
659#3197—432no—
660#3196—432no—
661#3191—432no—
662#3190—432no—
663#3099—431no—
664#3098—431no—
665#3093—431no—
666C2×#485—431no—
667#3063—431no—
668#3063—431no—
669#3061—431no—
670#3060—431no—
671#3013—431no—
672#3013D4311yescharacteristic, complemented
673#3007—431no—
674#3002—431no—
675#2880—431no—
676C2×C43—22no—
677C2×C43—42no—
678C2×C43—81no—
679C2×C43—81no—
680C2×C43C2×#53411yescharacteristic
681C2×C43#358411yescharacteristic
682C2×C43#358611yescharacteristic
683D43—42no—
684D43—41no—
685D43—41no—
686D43—81no—
687C2×2−1+4C2×D4311yescharacteristic, complemented
688C22×#41—431no—
689C22×#41—431no—
690C2×#137—431no—
691C2×#137C2×D4311yescharacteristic, complemented
692C2×#135—431no—
693C2×#135C2×D4311yescharacteristic, complemented
694C2×#131—431no—
695C2×#131—431no—
696D4×Q8—861no—
697#548—861no—
698#547—861no—
699#547—862no—
700#546—862no—
701#546—861no—
702#537—431no—
703#537—432no—
704#537—431no—
705#537—431no—
706#537—431no—
707#537C2×D4311yescharacteristic
708#536—432no—
709#536—431no—
710#536—432no—
711#536—861no—
712#535—432no—
713#535—861no—
714#534—862no—
715#532—862no—
716#525—431no—
717#525—432no—
718#525—432no—
719#525—432no—
720#525—861no—
721#525—861no—
722C2×C22⋊Q8—431no—
723C2×C22⋊Q8—432no—
724#520—431no—
725C2×#117—431no—
726#485—432no—
727#485—432no—
728#485—432no—
729#485—432no—
730#485—432no—
731#485—432no—
732#485—432no—
733#485—432no—
734#484—432no—
735#483—432no—
736#482—432no—
737#482—432no—
738#482—432no—
739#482—432no—
740#481—432no—
741#480—432no—
742#470—432no—
743#470—432no—
744#470—432no—
745#469—432no—
746#468—432no—
747#468—432no—
748#468—432no—
749#468—432no—
750#467—432no—
751#467—432no—
752#467—432no—
753#466—432no—
754#465—432no—
755#465—432no—
756#465—432no—
757#465—432no—
758#452—432no—
759#452—431no—
760#452—432no—
761#452—432no—
762#452—431no—
763#452C2×D4312yescomplemented
764#451—432no—
765#451—432no—
766#451—431no—
767#451C2×D4312yescomplemented
768#450—432no—
769#450—431no—
770#449—432no—
771#449—431no—
772#449—431no—
773#449C2×D4312yescomplemented
774#448—432no—
775#448—431no—
776#448C2×D4312yescomplemented
777#447—431no—
778#428—431no—
779#428—431no—
780C2×#107—431no—
781C2×#106—431no—
782#417—431no—
783#417—431no—
784#417—431no—
785#417C2×D4311yescharacteristic, complemented
786#416—431no—
787#416—431no—
788C2×#103—431no—
789C2×#103C2×D4311yescharacteristic, complemented
790#408—431no—
791#408—432no—
792#408—432no—
793#408C2×D4311yescharacteristic, complemented
794#407—431no—
795#407—432no—
796C2×C22⋊C8—431no—
797C2×C22⋊C8—432no—
798C43#6076611yescharacteristic, complemented, Sylow
7992−1+4—42no—
8002−1+4—42no—
801C2×#41—21no—
802C2×#41—22no—
803C2×#41—431no—
804C2×#41—431no—
805C2×#41—432no—
806C2×#41—431no—
807C2×#41—432no—
808C2×#41—431no—
809C2×#41—431no—
810C2×#41—431no—
811C2×#41—861no—
812C2×#41—861no—
813C2×#41—1722no—
814C2×#41—1722no—
815C2×#41—1722no—
816C2×#41—1722no—
817C2×#41C22×D4311yescharacteristic
818C2×#41C22×D4311yescharacteristic
819C2×#41C22×D4312yes—
820C2×#41C22×D4311yescharacteristic
821C22×Q8—21no—
822C22×Q8—431no—
823C22×Q8—431no—
824C22×Q8C22×D4311yescharacteristic
825C22×Q8C22×D4312yes—
826C22×D4—432no—
827C22×D4—431no—
828C22×D4—431no—
829C22×D4—861no—
830C23×C4—431no—
831C23×C4—432no—
832C23×C4—861no—
833#137—42no—
834#137—1722no—
835#135—42no—
836#135—1722no—
837C2×Q16—431no—
838C2×Q16—432no—
839C2×Q16C22×D4311yescharacteristic
840C2×Q16C22×D4312yes—
841C2×SD16—431no—
842C2×SD16—432no—
843C2×SD16—431no—
844C2×SD16C22×D4311yescharacteristic
845C2×SD16C22×D4311yescharacteristic
846C2×SD16C22×D4312yes—
847C2×D8—431no—
848C2×D8C22×D4311yescharacteristic
849#131—1722no—
850#131—1722no—
851C2×M16—431no—
852C2×M16—432no—
853C2×M16—432no—
854C2×M16C22×D4311yescharacteristic
855C22×C8—431no—
856C22×C8—432no—
857C22×C8—432no—
858C22×C8C22×D4311yescharacteristic
859C4⋊Q8—862no—
860C4⋊Q8—861no—
861C4⋊Q8—862no—
862#127—862no—
863#124—862no—
864#124—862no—
865#124—861no—
866#124—862no—
867#123—862no—
868#123—862no—
869#123—862no—
870#123—862no—
871#123—862no—
872#123—862no—
873#123—862no—
874#123—861no—
875#123—862no—
876C22⋊Q8—21no—
877C22⋊Q8—432no—
878C22⋊Q8—431no—
879C22⋊Q8—432no—
880C22⋊Q8—432no—
881C22⋊Q8—432no—
882C22⋊Q8—431no—
883C22⋊Q8—432no—
884C22⋊Q8—432no—
885C22⋊Q8—432no—
886C22⋊Q8—432no—
887C22⋊Q8—861no—
888C22⋊Q8—861no—
889C22⋊Q8—861no—
890C22⋊Q8—862no—
891C22⋊Q8—861no—
892C22⋊Q8—862no—
893C22⋊Q8—861no—
894C22⋊Q8—862no—
895C22⋊Q8—861no—
896C22⋊Q8C22×D4312yes—
897#121—21no—
898#121—22no—
899#121—431no—
900#121—432no—
901#121—431no—
902#121—432no—
903#121—432no—
904#121—432no—
905#121—861no—
906#121—861no—
907#121—862no—
908#121—861no—
909#121—862no—
910#121—862no—
911#121—862no—
912#121—862no—
913#121—862no—
914#121—861no—
915#121—862no—
916#121C22×D4312yes—
917#120—862no—
918#120—862no—
919#120—862no—
920#120—862no—
921#120—861no—
922#120—862no—
923C4×Q8—861no—
924C4×D4—862no—
925C4×D4—862no—
926C4×D4—862no—
927C4×D4—861no—
928C4×D4—862no—
929C4×D4—861no—
930C4×D4—862no—
931C4×D4—862no—
932C4×D4—862no—
933C4×D4—861no—
934#117—431no—
935#117—432no—
936#117—432no—
937#117—432no—
938#117—861no—
939#117—861no—
940C2×C4⋊C4—431no—
941C2×C4⋊C4—431no—
942C2×C4⋊C4—432no—
943C2×C4⋊C4—861no—
944C2×C4⋊C4—862no—
945C2×C4⋊C4C22×D4311yescharacteristic
946C2×C22⋊C4—861no—
947C2×C22⋊C4—861no—
948C2×C22⋊C4—862no—
949C2×C42—861no—
950#107—432no—
951#107—432no—
952#107—432no—
953#107—432no—
954#106—432no—
955#106—432no—
956#106—432no—
957#106—432no—
958#103—432no—
959#103—432no—
960#103—431no—
961#103—431no—
962#103—432no—
963#103—432no—
964#103—431no—
965#103—431no—
966#103—432no—
967#103C22×D4312yes—
968#103C22×D4312yes—
969#103C22×D4312yes—
970#102—431no—
971#102—431no—
972#102—432no—
973#102—432no—
974#102—431no—
975#102—431no—
976#102—432no—
977#102C22×D4312yes—
978C22⋊C8—432no—
979C22⋊C8—432no—
980C22⋊C8—431no—
981C22⋊C8—431no—
982C22⋊C8—432no—
983C22⋊C8—431no—
984C22⋊C8—431no—
985C22⋊C8—432no—
986C22⋊C8C22×D4312yes—
987C22⋊C8C22×D4312yes—
988C24—431no—
989C24—432no—
990C24—861no—
991#41—22no—
992#41—22no—
993#41—22no—
994#41—22no—
995#41—22no—
996#41—22no—
997#41—42no—
998#41—42no—
999#41—48no—
1000#41—44no—
1001#41—862no—
1002#41—862no—
1003#41—862no—
1004#41—862no—
1005#41—1722no—
1006#41—1722no—
1007#41—1724no—
1008#41—1724no—
1009#41—1722no—
1010#41—1721no—
1011#41—1721no—
1012#41—1724no—
1013#41—1722no—
1014#41—1721no—
1015#41—1721no—
1016C2×Q8—22no—
1017C2×Q8—21no—
1018C2×Q8—22no—
1019C2×Q8—22no—
1020C2×Q8—42no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×Q8—431no—
1024C2×Q8—432no—
1025C2×Q8—431no—
1026C2×Q8—861no—
1027C2×Q8—1722no—
1028C2×Q8—1721no—
1029C2×Q8—1721no—
1030C2×Q8D4×D4311yescharacteristic
1031C2×Q8C23×D4311yescharacteristic
1032C2×Q8C23×D4312yes—
1033C2×Q8C23×D4311yescharacteristic
1034C2×D4—22no—
1035C2×D4—21no—
1036C2×D4—21no—
1037C2×D4—22no—
1038C2×D4—432no—
1039C2×D4—432no—
1040C2×D4—432no—
1041C2×D4—431no—
1042C2×D4—432no—
1043C2×D4—431no—
1044C2×D4—862no—
1045C2×D4—861no—
1046C2×D4—861no—
1047C2×D4—862no—
1048C2×D4—861no—
1049C2×D4—862no—
1050C2×D4—862no—
1051C2×D4—861no—
1052C2×D4—861no—
1053C2×D4—861no—
1054C2×D4—1722no—
1055C2×D4—1721no—
1056C2×D4—1721no—
1057C2×D4—1724no—
1058C2×D4—1724no—
1059C2×D4D4×D4312yes—
1060C2×D4D4×D4311yescharacteristic
1061C2×D4C23×D4311yescharacteristic
1062C2×D4C23×D4311yescharacteristic
1063C22×C4—22no—
1064C22×C4—21no—
1065C22×C4—21no—
1066C22×C4—22no—
1067C22×C4—21no—
1068C22×C4—21no—
1069C22×C4—431no—
1070C22×C4—432no—
1071C22×C4—431no—
1072C22×C4—431no—
1073C22×C4—431no—
1074C22×C4—431no—
1075C22×C4—432no—
1076C22×C4—432no—
1077C22×C4—432no—
1078C22×C4—861no—
1079C22×C4—861no—
1080C22×C4—861no—
1081C22×C4—862no—
1082C22×C4—862no—
1083C22×C4—861no—
1084C22×C4—862no—
1085C22×C4—861no—
1086C22×C4—861no—
1087C22×C4—1722no—
1088C22×C4—1722no—
1089C22×C4—1724no—
1090C22×C4C23×D4312yes—
1091C22×C4C23×D4311yescharacteristic
1092Q16—41no—
1093Q16—42no—
1094Q16—1721no—
1095Q16—1722no—
1096SD16—41no—
1097SD16—41no—
1098SD16—42no—
1099SD16—1721no—
1100SD16—1721no—
1101SD16—1722no—
1102D8—41no—
1103D8—1721no—
1104M16—22no—
1105M16—862no—
1106M16—1722no—
1107M16—1722no—
1108C2×C8—22no—
1109C2×C8—432no—
1110C2×C8—431no—
1111C2×C8—431no—
1112C2×C8—862no—
1113C2×C8—1722no—
1114C2×C8—1722no—
1115C2×C8C23×D4312yes—
1116C2×C8C23×D4311yescharacteristic
1117C2×C8C23×D4311yescharacteristic
1118C4⋊C4—21no—
1119C4⋊C4—22no—
1120C4⋊C4—431no—
1121C4⋊C4—432no—
1122C4⋊C4—431no—
1123C4⋊C4—432no—
1124C4⋊C4—862no—
1125C4⋊C4—861no—
1126C4⋊C4—862no—
1127C4⋊C4—862no—
1128C4⋊C4—862no—
1129C4⋊C4—862no—
1130C4⋊C4—862no—
1131C4⋊C4—861no—
1132C4⋊C4—862no—
1133C4⋊C4—861no—
1134C4⋊C4—862no—
1135C4⋊C4—861no—
1136C4⋊C4—862no—
1137C4⋊C4C23×D4312yes—
1138C22⋊C4—22no—
1139C22⋊C4—22no—
1140C22⋊C4—862no—
1141C22⋊C4—862no—
1142C22⋊C4—861no—
1143C22⋊C4—862no—
1144C22⋊C4—862no—
1145C22⋊C4—862no—
1146C22⋊C4—862no—
1147C22⋊C4—862no—
1148C22⋊C4—862no—
1149C22⋊C4—862no—
1150C22⋊C4—861no—
1151C22⋊C4—862no—
1152C22⋊C4—861no—
1153C22⋊C4—862no—
1154C22⋊C4—861no—
1155C22⋊C4—862no—
1156C22⋊C4—862no—
1157C22⋊C4—861no—
1158C22⋊C4—862no—
1159C22⋊C4—862no—
1160C42—862no—
1161C42—862no—
1162C42—862no—
1163C42—861no—
1164C23—21no—
1165C23—21no—
1166C23—431no—
1167C23—431no—
1168C23—432no—
1169C23—862no—
1170C23—861no—
1171C23—3441no—
1172C23—3441no—
1173C23—1722no—
1174C23—1721no—
1175C23—1721no—
1176C23—1722no—
1177C23—1722no—
1178C23—1722no—
1179C23C2×D4×D4312yes—
1180C23C2×D4×D4311yescharacteristic
1181Q8—22no—
1182Q8—22no—
1183Q8—21no—
1184Q8—21no—
1185Q8—22no—
1186Q8—21no—
1187Q8—21no—
1188Q8—44no—
1189Q8—42no—
1190Q8—862no—
1191Q8—861no—
1192Q8—861no—
1193Q8—1722no—
1194Q8—1722no—
1195D4—24no—
1196D4—22no—
1197D4—21no—
1198D4—21no—
1199D4—21no—
1200D4—21no—
1201D4—44no—
1202D4—42no—
1203D4—42no—
1204D4—82no—
1205D4—864no—
1206D4—862no—
1207D4—861no—
1208D4—861no—
1209D4—3442no—
1210D4—3442no—
1211D4—3442no—
1212D4—3441no—
1213D4—3442no—
1214D4—1722no—
1215D4—1722no—
1216D4—1722no—
1217D4—1722no—
1218D4—1722no—
1219D4—1722no—
1220D4—1722no—
1221D4—1722no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—44no—
1229C2×C4—44no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—81no—
1234C2×C4—431no—
1235C2×C4—431no—
1236C2×C4—432no—
1237C2×C4—862no—
1238C2×C4—862no—
1239C2×C4—862no—
1240C2×C4—862no—
1241C2×C4—862no—
1242C2×C4—861no—
1243C2×C4—861no—
1244C2×C4—861no—
1245C2×C4—861no—
1246C2×C4—861no—
1247C2×C4—862no—
1248C2×C4—862no—
1249C2×C4—861no—
1250C2×C4—861no—
1251C2×C4—3441no—
1252C2×C4—3442no—
1253C2×C4—3441no—
1254C2×C4—1722no—
1255C2×C4—1722no—
1256C2×C4—1722no—
1257C2×C4—1722no—
1258C2×C4—1722no—
1259C2×C4—1722no—
1260C2×C4—1722no—
1261C2×C4C2×D4×D4312yes—
1262C2×C4C2×D4×D4311yescharacteristic
1263C2×C4#1306337012yes—
1264C2×C4#1306337012yes—
1265C2×C4C24×D4311yescharacteristic
1266C8—21no—
1267C8—21no—
1268C8—22no—
1269C8—861no—
1270C8—861no—
1271C8—862no—
1272C22—21no—
1273C22—21no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—862no—
1284C22—861no—
1285C22—861no—
1286C22—862no—
1287C22—861no—
1288C22—861no—
1289C22—861no—
1290C22—861no—
1291C22—862no—
1292C22—3442no—
1293C22—3444no—
1294C22—3444no—
1295C22—1721no—
1296C22—1721no—
1297C22—1721no—
1298C22#1458345912yes—
1299C22C22×D4×D4311yescharacteristic
1300C4—22no—
1301C4—42no—
1302C4—42no—
1303C4—41no—
1304C4—41no—
1305C4—861no—
1306C4—861no—
1307C4—862no—
1308C4—1722no—
1309C4—1721no—
1310C4—1722no—
1311C4—1721no—
1312C4—1721no—
1313C4#1458345912yes—
1314C4C2×#1306337011yescharacteristic
1315C4C2×#1306337011yescharacteristic
1316C2—22no—
1317C2—42no—
1318C2—81no—
1319C2—81no—
1320C2—3441no—
1321C2—1721no—
1322C2—1721no—
1323C2—1722no—
1324C2C2×#1458345911yescharacteristic
1325C2#1914936511yescharacteristic
1326C2#1914937711yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3013C2
socleC22×C43C23×D4
hypercenter#3013D43
hypocenterC43#60766
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3013

Complements

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

NH ≅ G/Ntype
1. #19148268C2semidirect
2. #19147923C2semidirect
3. #19145488C2semidirect
4. #19145476C2semidirect
5. #19145465C2semidirect
6. #19145444C2semidirect
7. #19145436C2semidirect
8. #19145422C2semidirect
9. #19145385C2semidirect
10. #19145379C2semidirect
11. #19144580C2semidirect
12. #19144575C2semidirect
13. #19144525C2semidirect
14. C2×#14583239C2semidirect
15. #19144284C2semidirect
16. #19144280C2semidirect
17. #19144261C2semidirect
18. #19144256C2semidirect
19. #19143910C2semidirect
20. #19143851C2semidirect
21. #19143809C2semidirect
22. #19143043C2semidirect
23. C43×#3013C2semidirect
26. C2×#13063356C22semidirect
27. C2×#13063345C22semidirect
28. C2×#13063333C22semidirect
29. C2×#13063331C22semidirect
40. #14583477C22semidirect
42. #14583473C22semidirect
54. #14583406C22semidirect
56. C2×#13063301C22semidirect
57. #14583382C22semidirect
59. #14583241C22semidirect
60. #14583239C22semidirect
61. #14583239C22semidirect
62. #14583239C22semidirect
63. #14583239C22semidirect
64. #14583239C22semidirect
65. #14583238C22semidirect
66. #14583237C22semidirect
67. #14583235C22semidirect
68. #14583227C22semidirect
69. #14583224C22semidirect
70. #14583222C22semidirect
71. #14583221C22semidirect
72. #14583220C22semidirect
73. #14583215C22semidirect
74. #14583213C22semidirect
75. #14583156C22semidirect
76. #14583156C22semidirect
77. #14583154C22semidirect
78. #14583151C22semidirect
79. #14583148C22semidirect
80. #14583142C22semidirect
81. #14583142C22semidirect
82. #14583142C22semidirect
83. #14583139C22semidirect
84. #14583137C22semidirect
85. #14583137C22semidirect
86. #14583132C22semidirect
87. #14583131C22semidirect
88. #14583131C22semidirect
89. #14583127C22semidirect
90. #14583125C22semidirect
91. #14583061C22semidirect
96. #14583055C22semidirect
97. #14583053C22semidirect
98. #14583053C22semidirect
99. #14583048C22semidirect
100. #14583048C22semidirect
101. #14583044C22semidirect
104. #14583038C22semidirect
105. #14583036C22semidirect
106. #14583031C22semidirect
107. #14582941C22semidirect
108. #14582939C22semidirect
109. C2×#13063259C22semidirect
110. C2×#13063256C22semidirect
111. #14582901C22semidirect
112. #14582900C22semidirect
113. #14582900C22semidirect
114. #14582896C22semidirect
115. #14582895C22semidirect
116. C2×#13063249C22semidirect
117. #14582866C22semidirect
121. #14582861C22semidirect
123. C22⋊C8×D43C22semidirect
124. C2×2−1+4×C43C22semidirect
125. C2×#137×C43C22semidirect
126. C2×#135×C43C22semidirect
128. C43×#452C22semidirect
129. C43×#451C22semidirect
130. C43×#449C22semidirect
131. C43×#448C22semidirect
132. C43×#417C22semidirect
133. C2×#103×C43C22semidirect
134. C43×#408C22semidirect
672. #3013D43semidirect
687. C2×2−1+4C2×D43semidirect
691. C2×#137C2×D43semidirect
693. C2×#135C2×D43semidirect
763. #452C2×D43semidirect
767. #451C2×D43semidirect
773. #449C2×D43semidirect
776. #448C2×D43semidirect
785. #417C2×D43semidirect
789. C2×#103C2×D43semidirect
793. #408C2×D43semidirect
798. C43#60766semidirect

Maximal subgroups

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

subgroupindex
#191482682
#191479232
#191454882
#191454762
#191454652
#191454442
#191454362
#191454222
#191453852
#191453792
#191445802
#191445752
#191445252
C2×#145832392
#191442842
#191442802
#191442612
#191442562
#191439102
#191438512
#191438092
#191430432
C43×#30132
#6076643