Finite Group Databasebeta

← #25967523

Subgroups — #25967523

Order 11008.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148267C211yesmaximal, characteristic, complemented
2#19147924C211yesmaximal, characteristic, complemented
3#19145504C212yesmaximal, complemented
4#19145494C212yesmaximal, complemented
5#19145476C212yesmaximal, complemented
6#19145474C212yesmaximal, complemented
7#19145434C212yesmaximal, complemented
8#19145423C212yesmaximal, complemented
9#19145385C212yesmaximal, complemented
10#19145374C212yesmaximal, complemented
11#19144562C211yesmaximal, characteristic, complemented
12#19144551C211yesmaximal, characteristic, complemented
13#19144544C211yesmaximal, characteristic, complemented
14#19144504C211yesmaximal, characteristic, complemented
15#19144280C211yesmaximal, characteristic, complemented
16#19144269C211yesmaximal, characteristic, complemented
17#19144249C211yesmaximal, characteristic, complemented
18#19144233C211yesmaximal, characteristic, complemented
19#19143889C211yesmaximal, characteristic, complemented
20#19143880C211yesmaximal, characteristic, complemented
21C2×#14583061C211yesmaximal, characteristic, complemented
22#19143045C211yesmaximal, characteristic, complemented
23C43×#3005C211yesmaximal, characteristic, complemented
24C2×#13063372C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26C22×#10621885C2211yescharacteristic, complemented
27C22×#10621883C2211yescharacteristic, complemented
28C2×#13063333C2211yescharacteristic
29C2×#13063333C2211yescharacteristic
30D4×Dic86—21no—
31#14583558—21no—
32#14583554—21no—
33#14583547—22no—
34#14583545—21no—
35#14583536—22no—
36#14583478C2212yescomplemented
37#14583477C2212yes—
38#14583477C2212yes—
39#14583477C2211yescharacteristic
40#14583475C2211yescharacteristic
41#14583473C2211yescharacteristic
42#14583473C2211yescharacteristic
43#14583472C2212yescomplemented
44#14583470—21no—
45#14583466C2211yescharacteristic
46#14583466C2211yescharacteristic
47#14583463—21no—
48#14583458—22no—
49#14583445—21no—
50#14583445—21no—
51#14583410—22no—
52#14583409C2212yescomplemented
53#14583406C2212yes—
54#14583406C2212yes—
55C2×#13063304C2211yescharacteristic
56C22⋊Q8×D43C2212yescomplemented
57#14583379C2211yescharacteristic
58C2×#13063284C2211yescharacteristic
59#14583241C2212yescomplemented
60#14583241C2212yescomplemented
61#14583239C2212yescomplemented
62#14583238C2212yescomplemented
63#14583237C2211yescharacteristic, complemented
64#14583237C2211yescharacteristic, complemented
65#14583235C2212yescomplemented
66#14583233C2212yescomplemented
67#14583232C2211yescharacteristic, complemented
68#14583230C2212yescomplemented
69#14583228C2212yescomplemented
70#14583227C2211yescharacteristic, complemented
71#14583222C2212yescomplemented
72#14583221C2212yescomplemented
73#14583220C2211yescharacteristic, complemented
74#14583220C2211yescharacteristic, complemented
75#14583216C2212yescomplemented
76#14583215C2211yescharacteristic, complemented
77#14583211C2212yescomplemented
78#14583210C2211yescharacteristic, complemented
79#14583156C2212yescomplemented
80#14583156C2212yescomplemented
81#14583154C2212yescomplemented
82#14583149C2212yescomplemented
83#14583144C2212yescomplemented
84#14583144C2212yescomplemented
85#14583142C2212yescomplemented
86#14583142C2212yescomplemented
87#14583139C2212yescomplemented
88#14583139C2212yescomplemented
89#14583137C2212yescomplemented
90#14583132C2212yescomplemented
91#14583127C2212yescomplemented
92#14583127C2212yescomplemented
93#14583125C2212yescomplemented
94#14583125C2212yescomplemented
95#14583061C2212yes—
96#14583061C2212yes—
97#14583061C2212yescomplemented
98#14583061C2212yescomplemented
99#14583058C2212yescomplemented
100#14583058C2212yescomplemented
101#14583053C2212yescomplemented
102#14583053C2212yescomplemented
103#14583041C2212yescomplemented
104#14583041C2212yescomplemented
105#14583036C2212yescomplemented
106#14583036C2212yescomplemented
107#14582941C2211yescharacteristic, complemented
108#14582941C2211yescharacteristic, complemented
109#14582935C2211yescharacteristic, complemented
110#14582935C2211yescharacteristic, complemented
111#14582909C2211yescharacteristic, complemented
112#14582909C2211yescharacteristic, complemented
113#14582895C2211yescharacteristic, complemented
114#14582895C2211yescharacteristic, complemented
115C2×#13063249C2211yescharacteristic, complemented
116C2×#13063246C2211yescharacteristic, complemented
117#14582867C2211yescharacteristic
118#14582867C2211yescharacteristic
119#14582864C2212yescomplemented
120#14582864C2212yescomplemented
121#14582861C2212yescomplemented
122C2×C22⋊(C43⋊C8)C2211yescharacteristic
123C22⋊C8×D43C2212yescomplemented
124C22×#41×C43C2211yescharacteristic
125C2×#137×C43C2211yescharacteristic, complemented
126C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
127C43×#525C2211yescharacteristic
128C43×#452C2212yes—
129C43×#452C2212yescomplemented
130C43×#449C2212yes—
131C43×#449C2212yescomplemented
132C43×#419C2211yescharacteristic, complemented
133C43×#418C2211yescharacteristic, complemented
134C43×#407C2211yescharacteristic
135#13063372—42no—
136#13063372—42no—
137C2×#10621898—21no—
138C2×#10621898—42no—
139C2×#10621898—42no—
140C2×#10621898D411yescharacteristic
141C2×#10621898D411yescharacteristic
142C2×#10621898D412yes—
143C2×#10621898C2311yescharacteristic
144C2×#10621898C2311yescharacteristic
145C2×#10621898C2312yes—
146C2×#10621900—22no—
147C2×#10621900C2312yes—
148C22×Dic86—21no—
149C22×Dic86D411yescharacteristic
150C22×Dic86C2311yescharacteristic
151C2×Q8×D43C2312yes—
152C22×D172D411yescharacteristic
153C22×C22⋊D43D412yes—
154C22×C4×D43C2312yes—
155C2×#10621885—42no—
156C2×#10621885C2312yes—
157C2×#10621885C2312yes—
158C2×#10621883—42no—
159C2×#10621883C2312yes—
160C2×#10621883C2312yes—
161#13063333—42no—
162#13063333—42no—
163C2×#10621872C2312yes—
164C2×#10621872C2312yes—
165C22×C43⋊C8C2311yescharacteristic
166C22×C43⋊C8C2311yescharacteristic
167C2×C8×D43C2312yes—
168C2×C8×D43C2312yes—
169#13063325—21no—
170#13063324—22no—
171#13063323—21no—
172#13063323—21no—
173#13063321—21no—
174#13063321—21no—
175#13063314—21no—
176#13063314—21no—
177#13063313—21no—
178#13063312—21no—
179#13063312—21no—
180#13063311—22no—
181#13063310—22no—
182#13063309—22no—
183#13063308—22no—
184#13063308—22no—
185#13063307—22no—
186#13063307—22no—
187#13063306—22no—
188#13063306—22no—
189#13063305C2312yes—
190#13063305C2312yes—
191#13063304—21no—
192#13063304—21no—
193#13063304—21no—
194#13063304—22no—
195#13063304—22no—
196#13063304C2312yes—
197#13063304C2312yes—
198#13063303—22no—
199#13063302—22no—
200#13063302—22no—
201#13063301C2312yes—
202#13063301C2312yes—
203#13063301C2312yes—
204#13063301C2312yes—
205#13063301C2312yes—
206#13063299—21no—
207#13063299—22no—
208#13063299—22no—
209#13063298—22no—
210#13063297—22no—
211#13063297—22no—
212#13063297—22no—
213#13063297—22no—
214#13063297—22no—
215#13063297—22no—
216#13063296—22no—
217#13063296C2312yes—
218#13063296C2312yes—
219#13063296C2312yes—
220#13063296C2312yes—
221#13063296C2312yes—
222#13063294—22no—
223#13063294—22no—
224#13063293—22no—
225#13063293—22no—
226#13063293—22no—
227C4×Dic86—21no—
228C4×D172—21no—
229D4×Dic43—22no—
230C4×C22⋊D43—22no—
231C4×C22⋊D43—22no—
232C4×C22⋊D43—22no—
233C4×C22⋊D43—22no—
234(C22⋊D43)⋊C4—22no—
235(C22⋊D43)⋊C4—22no—
236#13063284—21no—
237#13063284—21no—
238#13063284C2311yescharacteristic
239#13063284C2311yescharacteristic
240#13063284C2311yescharacteristic
241#13063284C2311yescharacteristic
242#13063283C2312yes—
243C2×C4⋊Dic43C2311yescharacteristic
244C2×C4⋊Dic43C2311yescharacteristic
245C2×C4⋊Dic43C2311yescharacteristic
246C2×Dic43⋊C4—21no—
247C4⋊C4×D43—22no—
248C4⋊C4×D43C2312yes—
249C2×C22⋊Dic43—21no—
250C2×C22⋊Dic43—21no—
251C22⋊C4×D43—22no—
252C2×C4×Dic43—21no—
253#13063259C2312yes—
254#13063259C2312yes—
255#13063258C2311yescharacteristic
256#13063258C2311yescharacteristic
257#13063258C2311yescharacteristic
258#13063258C2311yescharacteristic
259#13063257C2312yes—
260#13063257C2312yes—
261#13063256C2311yescharacteristic
262#13063256C2311yescharacteristic
263#13063256C2311yescharacteristic
264#13063256C2311yescharacteristic
265#13063250C2312yes—
266#13063250C2312yes—
267#13063250C2312yes—
268#13063250C2312yes—
269#13063249C2311yescharacteristic
270#13063249C2311yescharacteristic
271#13063249C2312yes—
272#13063249C2312yes—
273#13063249C2311yescharacteristic
274#13063249C2311yescharacteristic
275#13063246C2311yescharacteristic
276#13063246C2311yescharacteristic
277#13063246C2311yescharacteristic
278#13063246C2311yescharacteristic
279#13063246C2312yes—
280#13063246C2312yes—
281C22⋊(C43⋊C8)C2311yescharacteristic
282C22⋊(C43⋊C8)C2311yescharacteristic
283C22⋊(C43⋊C8)C2311yescharacteristic
284C22⋊(C43⋊C8)C2311yescharacteristic
285(C2×D43)⋊C8C2312yes—
286(C2×D43)⋊C8C2312yes—
287(C2×D43)⋊C8C2312yes—
288(C2×D43)⋊C8C2312yes—
289C2×#41×C43—21no—
290C2×#41×C43—21no—
291C2×#41×C43—42no—
292C2×#41×C43—42no—
293C2×#41×C43C2311yescharacteristic
294C2×#41×C43C2312yes—
295C2×#41×C43C2312yes—
296C22×Q8×C43C2311yescharacteristic
297C22×D4×C43—21no—
298C22×D4×C43C2311yescharacteristic
299C23×C4×C43—21no—
300C23×C4×C43C2311yescharacteristic
301#137×C43—42no—
302AGL(1,ℤ/8)×C43—42no—
303C2×Q16×C43C2312yes—
304C2×SD16×C43C2312yes—
305C2×SD16×C43C2312yes—
306C2×D8×C43C2312yes—
307C2×M16×C43C2311yescharacteristic
308C2×M16×C43C2311yescharacteristic
309#123×C43—21no—
310C22⋊Q8×C43C2311yescharacteristic
311C22⋊Q8×C43C2311yescharacteristic
312#121×C43C2311yescharacteristic
313#121×C43C2311yescharacteristic
314#120×C43—21no—
315C4×D4×C43—21no—
316C4×D4×C43—21no—
317#117×C43C2311yescharacteristic
318#103×C43C2312yes—
319#103×C43C2312yes—
320#102×C43C2312yes—
321#102×C43C2312yes—
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C24×C43—21no—
325C24×C43C2×D411yescharacteristic
326C23×D43C2×D412yes—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—42no—
330#41×C43—42no—
331#41×C43—42no—
332#41×C43—42no—
333#41×C43—44no—
334#41×C43—44no—
335C2×Q8×C43—21no—
336C2×Q8×C43—22no—
337C2×Q8×C43—22no—
338C2×Q8×C43C2412yes—
339C2×Q8×C43C2411yescharacteristic
340C2×D4×C43—21no—
341C2×D4×C43—21no—
342C2×D4×C43—21no—
343C2×D4×C43—22no—
344C2×D4×C43—22no—
345C2×D4×C43—21no—
346C2×D4×C43—22no—
347C2×D4×C43—22no—
348C2×D4×C43—44no—
349C2×D4×C43C2412yes—
350C2×D4×C43C2411yescharacteristic
351C22×C4×C43—22no—
352C22×C4×C43—22no—
353C22×C4×C43—21no—
354C22×C4×C43—22no—
355C22×C4×C43—22no—
356C22×C4×C43—21no—
357C22×C4×C43—44no—
358C22×C4×C43C2×D411yescharacteristic
359C22×C4×C43C2×D411yescharacteristic
360C22×C4×C43C2×D411yescharacteristic
361C22×C4×C43C2411yescharacteristic
362C22×C4×C43C2411yescharacteristic
363C22×C4×C43C2411yescharacteristic
364C2×C22⋊D43—22no—
365C2×C22⋊D43—22no—
366C2×C22⋊D43—22no—
367C2×C22⋊D43—22no—
368C2×C22⋊D43—22no—
369C2×C22⋊D43—22no—
370C2×C22⋊D43—44no—
371C2×C22⋊D43C2×D412yes—
372C2×C22⋊D43C2×D412yes—
373C2×C22⋊D43C2×D412yes—
374C2×C22⋊D43C2×D412yes—
375C22×Dic43—22no—
376C22×Dic43—21no—
377C22×Dic43—21no—
378C22×Dic43—21no—
379C22×Dic43—21no—
380C22×Dic43C2×D412yes—
381Q8×D43—42no—
382Q8×D43—42no—
383#10621900—42no—
384#10621900—42no—
385#10621900—48no—
386#10621898—22no—
387#10621898—22no—
388#10621898—22no—
389#10621898—22no—
390#10621898—42no—
391#10621898—42no—
392#10621898—42no—
393#10621898—42no—
394#10621898—44no—
395#10621898—44no—
396C2×D172—42no—
397C2×D172C2×D411yescharacteristic
398C2×D172C2×D411yescharacteristic
399C2×D172C2×D412yes—
400C2×C4×D43—22no—
401C2×C4×D43—22no—
402C2×C4×D43—42no—
403C2×C4×D43—42no—
404C2×C4×D43C2×D412yes—
405C2×C4×D43C2×D412yes—
406C2×C4×D43C2412yes—
407C2×C4×D43C2412yes—
408C2×Dic86—22no—
409C2×Dic86—22no—
410C2×Dic86—21no—
411C2×Dic86—22no—
412C2×Dic86—42no—
413C2×Dic86—44no—
414C2×Dic86C2×D411yescharacteristic
415C2×Dic86C2×D411yescharacteristic
416C2×Dic86C2×D412yes—
417C2×Dic86C2412yes—
418Q16×C43—42no—
419SD16×C43—42no—
420SD16×C43—42no—
421D8×C43—42no—
422M16×C43—22no—
423M16×C43—22no—
424C2×C8×C43C2412yes—
425C2×C8×C43C2412yes—
426C4⋊C4×C43—21no—
427C4⋊C4×C43—21no—
428C4⋊C4×C43C2411yescharacteristic
429C4⋊C4×C43C2411yescharacteristic
430C22⋊C4×C43—21no—
431C22⋊C4×C43—21no—
432C22⋊C4×C43—21no—
433C22⋊C4×C43—21no—
434C22⋊C4×C43—21no—
435C42×C43—21no—
436C22⋊Dic43—22no—
437C22⋊Dic43—22no—
438C22⋊Dic43—22no—
439C22⋊Dic43—22no—
440C22⋊Dic43—22no—
441C22⋊Dic43—22no—
442C22⋊Dic43—21no—
443C22⋊Dic43—21no—
444C22⋊Dic43—21no—
445C22⋊Dic43—21no—
446C22⋊Dic43—22no—
447#10621885—42no—
448#10621885—42no—
449#10621883—42no—
450#10621883—42no—
451(C2×D43)⋊C4—22no—
452(C2×D43)⋊C4—22no—
453(C2×D43)⋊C4—22no—
454(C2×D43)⋊C4—22no—
455(C2×D43)⋊C4—22no—
456(C2×D43)⋊C4—22no—
457(C2×D43)⋊C4—22no—
458(C2×D43)⋊C4—22no—
459C4⋊Dic43—21no—
460C4⋊Dic43—21no—
461C4⋊Dic43—21no—
462C4⋊Dic43—22no—
463C4⋊Dic43—22no—
464C4⋊Dic43C2412yes—
465C4⋊Dic43C2411yescharacteristic
466C4⋊Dic43C2411yescharacteristic
467C4⋊Dic43C2411yescharacteristic
468C4⋊Dic43C2411yescharacteristic
469Dic43⋊C4—22no—
470Dic43⋊C4—22no—
471Dic43⋊C4—22no—
472Dic43⋊C4—22no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—22no—
476Dic43⋊C4—22no—
477C4×Dic43—21no—
478C4×Dic43—21no—
479C4×Dic43—21no—
480C4×Dic43—21no—
481C4×Dic43—22no—
482C2×C43⋊C8—22no—
483C2×C43⋊C8—22no—
484C2×C43⋊C8C2411yescharacteristic
485C2×C43⋊C8C2411yescharacteristic
486C2×C43⋊C8C2411yescharacteristic
487C2×C43⋊C8C2411yescharacteristic
488#10621872—42no—
489#10621872—42no—
490C8×D43—42no—
491C8×D43—42no—
492C23×C43—22no—
493C23×C43—22no—
494C23×C43—21no—
495C23×C43—41no—
496C23×C43—41no—
497C23×C43—42no—
498C23×C43—81no—
499C23×C43—81no—
500C23×C43C22×D411yescharacteristic
501C23×C43C22×D411yescharacteristic
502C23×C43C22×D411yescharacteristic
503C22×D43—42no—
504C22×D43—42no—
505C22×D43—42no—
506C22×D43C22×D412yes—
507C22×D43C22×D412yes—
508Q8×C43—22no—
509Q8×C43—21no—
510Q8×C43—22no—
511Q8×C43—21no—
512Q8×C43—42no—
513D4×C43—22no—
514D4×C43—21no—
515D4×C43—22no—
516D4×C43—21no—
517D4×C43—42no—
518D4×C43—44no—
519D4×C43—44no—
520D4×C43—42no—
521D4×C43—42no—
522D4×C43—81no—
523C2×C4×C43—22no—
524C2×C4×C43—22no—
525C2×C4×C43—22no—
526C2×C4×C43—21no—
527C2×C4×C43—21no—
528C2×C4×C43—21no—
529C2×C4×C43—21no—
530C2×C4×C43—21no—
531C2×C4×C43—22no—
532C2×C4×C43—21no—
533C2×C4×C43—21no—
534C2×C4×C43—44no—
535C2×C4×C43—44no—
536C2×C4×C43—42no—
537C2×C4×C43—42no—
538C2×C4×C43C22×D411yescharacteristic
539C2×C4×C43C22×D411yescharacteristic
540C2×C4×C43C22×D411yescharacteristic
541C2×C4×C43H(5,𝔽2)12yes—
542C2×C4×C43H(5,𝔽2)12yes—
543C2×C4×C43C2511yescharacteristic
544C22⋊D43—24no—
545C22⋊D43—24no—
546C22⋊D43—42no—
547C22⋊D43—42no—
548C22⋊D43—44no—
549C22⋊D43—82no—
550C22⋊D43—82no—
551C22⋊D43—82no—
552C22⋊D43—82no—
553C22⋊D43—82no—
554C2×Dic43—21no—
555C2×Dic43—21no—
556C2×Dic43—21no—
557C2×Dic43—21no—
558C2×Dic43—22no—
559C2×Dic43—22no—
560C2×Dic43—42no—
561C2×Dic43—44no—
562C2×Dic43—42no—
563C2×Dic43—81no—
564C2×Dic43—81no—
565C2×Dic43—81no—
566C2×Dic43C22×D412yes—
567C2×Dic43C22×D412yes—
568D172—22no—
569D172—22no—
570D172—42no—
571C4×D43—22no—
572C4×D43—22no—
573C4×D43—22no—
574C4×D43—22no—
575C4×D43—42no—
576C4×D43—42no—
577C4×D43—44no—
578C4×D43—82no—
579Dic86—22no—
580Dic86—22no—
581Dic86—22no—
582Dic86—22no—
583Dic86—42no—
584Dic86—44no—
585Dic86—42no—
586C8×C43—22no—
587C8×C43—22no—
588C43⋊C8—21no—
589C43⋊C8—21no—
590C43⋊C8—21no—
591C43⋊C8—21no—
592#60761—431nomaximal, Sylow
593C22×C43—21no—
594C22×C43—21no—
595C22×C43—21no—
596C22×C43—21no—
597C22×C43—21no—
598C22×C43—21no—
599C22×C43—21no—
600C22×C43—21no—
601C22×C43—42no—
602C22×C43—41no—
603C22×C43—42no—
604C22×C43—41no—
605C22×C43—42no—
606C22×C43—41no—
607C22×C43—82no—
608C22×C43—84no—
609C22×C43#53412yes—
610C22×C43C23×D411yescharacteristic
611C2×D43—22no—
612C2×D43—22no—
613C2×D43—22no—
614C2×D43—22no—
615C2×D43—22no—
616C2×D43—22no—
617C2×D43—84no—
618C4×C43—21no—
619C4×C43—21no—
620C4×C43—41no—
621C4×C43—41no—
622C4×C43—41no—
623C4×C43—42no—
624C4×C43#53412yes—
625C4×C43C2×H(5,𝔽2)11yescharacteristic
626C4×C43C2×H(5,𝔽2)11yescharacteristic
627Dic43—22no—
628Dic43—22no—
629Dic43—42no—
630Dic43—41no—
631Dic43—41no—
632Dic43—41no—
633Dic43—41no—
634Dic43—42no—
635#3489—431no—
636#3449—431no—
637#3204—432no—
638#3203—432no—
639#3201—432no—
640#3201—432no—
641#3197—432no—
642#3196—432no—
643#3191—432no—
644#3190—432no—
645#3097—431no—
646#3096—431no—
647#3095—431no—
648#3091—431no—
649#3063—431no—
650#3062—431no—
651#3059—431no—
652#3057—431no—
653#3011—431no—
654#3010—431no—
655#3005D4311yescharacteristic, complemented
656C2×#452—431no—
657#2880—431no—
658C2×C43—22no—
659C2×C43—41no—
660C2×C43—41no—
661C2×C43—81no—
662C2×C43—82no—
663C2×C43C2×#53411yescharacteristic
664C2×C43#358411yescharacteristic
665C2×C43#358611yescharacteristic
666D43—42no—
667D43—42no—
668C2×2−1+4—431no—
669C22×#41—431no—
670C22×#41C2×D4311yescharacteristic
671C2×#137C2×D4311yescharacteristic, complemented
672C2×AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
673C22×Q16—431no—
674C22×SD16—431no—
675C2×#131—431no—
676C2×#131—431no—
677D4×Q8—861no—
678#548—861no—
679#547—861no—
680#547—862no—
681#546—861no—
682#546—862no—
683#537—432no—
684#537—432no—
685#537—431no—
686#537—432no—
687#536—431no—
688#536—431no—
689#536—432no—
690#536—431no—
691#536—861no—
692#535—431no—
693#535—431no—
694#535—861no—
695#534—862no—
696#532—861no—
697#532—861no—
698#525—432no—
699#525—432no—
700#525—432no—
701#525—862no—
702#525C2×D4311yescharacteristic
703C2×C22⋊Q8—431no—
704C2×C22⋊Q8—432no—
705#520—431no—
706C2×#117—431no—
707#485—431no—
708#485—431no—
709#485—432no—
710#485—432no—
711#485—432no—
712#485—432no—
713#484—431no—
714#484—432no—
715#484—432no—
716#483—431no—
717#483—432no—
718#483—432no—
719#482—431no—
720#482—431no—
721#482—432no—
722#482—432no—
723#481—431no—
724#481—432no—
725#480—431no—
726#480—432no—
727#470—432no—
728#470—432no—
729#470—432no—
730#469—432no—
731#468—432no—
732#468—432no—
733#468—432no—
734#468—432no—
735#467—432no—
736#467—432no—
737#467—432no—
738#466—432no—
739#465—432no—
740#465—432no—
741#465—432no—
742#465—432no—
743#452—432no—
744#452—432no—
745#452—432no—
746#452—432no—
747#452—432no—
748#452—432no—
749#452C2×D4312yes—
750#452C2×D4312yescomplemented
751#451—432no—
752#451—432no—
753#449—432no—
754#449—432no—
755#449C2×D4312yes—
756#449C2×D4312yescomplemented
757#448—432no—
758#448—432no—
759#428—431no—
760#428—431no—
761#427—431no—
762#427—431no—
763#419—431no—
764#419—431no—
765#419C2×D4311yescharacteristic, complemented
766#418C2×D4311yescharacteristic, complemented
767#416—431no—
768#416—431no—
769C2×#103—431no—
770C2×#102—431no—
771#408—431no—
772#408—431no—
773#408—432no—
774#408—432no—
775#407—432no—
776#407C2×D4311yescharacteristic
777C2×C22⋊C8—431no—
778C2×C22⋊C8—432no—
779C43#6076111yescharacteristic, complemented, Sylow
7802−1+4—1722no—
7812−1+4—1722no—
782C2×#41—21no—
783C2×#41—21no—
784C2×#41—42no—
785C2×#41—42no—
786C2×#41—432no—
787C2×#41—431no—
788C2×#41—431no—
789C2×#41—431no—
790C2×#41—431no—
791C2×#41—432no—
792C2×#41—432no—
793C2×#41—861no—
794C2×#41—862no—
795C2×#41—1722no—
796C2×#41—1722no—
797C2×#41C22×D4311yescharacteristic
798C2×#41C22×D4312yes—
799C2×#41C22×D4312yes—
800C22×Q8—431no—
801C22×Q8—432no—
802C22×Q8—431no—
803C22×Q8—861no—
804C22×Q8C22×D4311yescharacteristic
805C22×D4—21no—
806C22×D4—432no—
807C22×D4—431no—
808C22×D4C22×D4311yescharacteristic
809C23×C4—21no—
810C23×C4—432no—
811C23×C4C22×D4311yescharacteristic
812#137—42no—
813AGL(1,ℤ/8)—42no—
814C2×Q16—432no—
815C2×Q16—432no—
816C2×Q16—1722no—
817C2×Q16C22×D4312yes—
818C2×SD16—432no—
819C2×SD16—432no—
820C2×SD16—1722no—
821C2×SD16C22×D4312yes—
822C2×SD16C22×D4312yes—
823C2×D8C22×D4312yes—
824#131—1722no—
825#131—1722no—
826C2×M16—432no—
827C2×M16—432no—
828C2×M16C22×D4311yescharacteristic
829C2×M16C22×D4311yescharacteristic
830C22×C8—431no—
831C22×C8—431no—
832C22×C8—432no—
833C22×C8—432no—
834C4⋊Q8—861no—
835C4⋊Q8—862no—
836C4⋊Q8—861no—
837C4⋊Q8—861no—
838#127—861no—
839#127—861no—
840#124—861no—
841#124—862no—
842#124—861no—
843#124—861no—
844#124—861no—
845#124—861no—
846#123—21no—
847#123—862no—
848#123—862no—
849#123—862no—
850#123—862no—
851#123—862no—
852#123—862no—
853#123—862no—
854#123—862no—
855C22⋊Q8—432no—
856C22⋊Q8—432no—
857C22⋊Q8—432no—
858C22⋊Q8—432no—
859C22⋊Q8—432no—
860C22⋊Q8—432no—
861C22⋊Q8—432no—
862C22⋊Q8—432no—
863C22⋊Q8—432no—
864C22⋊Q8—862no—
865C22⋊Q8—862no—
866C22⋊Q8—862no—
867C22⋊Q8—862no—
868C22⋊Q8—862no—
869C22⋊Q8—861no—
870C22⋊Q8—861no—
871C22⋊Q8—861no—
872C22⋊Q8C22×D4311yescharacteristic
873C22⋊Q8C22×D4311yescharacteristic
874#121—432no—
875#121—432no—
876#121—432no—
877#121—432no—
878#121—432no—
879#121—862no—
880#121—862no—
881#121—862no—
882#121—861no—
883#121—862no—
884#121—862no—
885#121—862no—
886#121—862no—
887#121—862no—
888#121—862no—
889#121—862no—
890#121C22×D4311yescharacteristic
891#121C22×D4311yescharacteristic
892#120—21no—
893#120—862no—
894#120—862no—
895#120—862no—
896#120—862no—
897#120—862no—
898C4×Q8—861no—
899C4×D4—21no—
900C4×D4—21no—
901C4×D4—861no—
902C4×D4—862no—
903C4×D4—862no—
904C4×D4—862no—
905C4×D4—862no—
906C4×D4—862no—
907C4×D4—862no—
908C4×D4—862no—
909#117—431no—
910#117—431no—
911#117—431no—
912#117—431no—
913#117—432no—
914#117—861no—
915#117—861no—
916#117C22×D4311yescharacteristic
917C2×C4⋊C4—431no—
918C2×C4⋊C4—431no—
919C2×C4⋊C4—431no—
920C2×C4⋊C4—432no—
921C2×C4⋊C4—862no—
922C2×C4⋊C4—861no—
923C2×C22⋊C4—862no—
924C2×C22⋊C4—861no—
925C2×C22⋊C4—861no—
926C2×C42—861no—
927#107—432no—
928#107—432no—
929#107—431no—
930#107—431no—
931#107—431no—
932#107—431no—
933#106—432no—
934#106—432no—
935#106—431no—
936#106—431no—
937#106—431no—
938#106—431no—
939#103—432no—
940#103—432no—
941#103—431no—
942#103—431no—
943#103—431no—
944#103—431no—
945#103—432no—
946#103—432no—
947#103—432no—
948#103—432no—
949#103C22×D4312yes—
950#103C22×D4312yes—
951#102—432no—
952#102—432no—
953#102—431no—
954#102—431no—
955#102—431no—
956#102—431no—
957#102C22×D4312yes—
958#102C22×D4312yes—
959C22⋊C8—431no—
960C22⋊C8—431no—
961C22⋊C8—431no—
962C22⋊C8—431no—
963C22⋊C8—432no—
964C22⋊C8—432no—
965C22⋊C8—432no—
966C22⋊C8—432no—
967C22⋊C8C22×D4312yes—
968C22⋊C8C22×D4312yes—
969C24—21no—
970C24—432no—
971C24D4×D4311yescharacteristic
972#41—22no—
973#41—22no—
974#41—42no—
975#41—42no—
976#41—42no—
977#41—42no—
978#41—44no—
979#41—44no—
980#41—862no—
981#41—862no—
982#41—862no—
983#41—862no—
984#41—1722no—
985#41—1722no—
986#41—1724no—
987#41—1722no—
988#41—1722no—
989#41—1724no—
990#41—1722no—
991#41—1722no—
992#41—1728no—
993C2×Q8—21no—
994C2×Q8—22no—
995C2×Q8—22no—
996C2×Q8—431no—
997C2×Q8—431no—
998C2×Q8—432no—
999C2×Q8—432no—
1000C2×Q8—862no—
1001C2×Q8—861no—
1002C2×Q8—862no—
1003C2×Q8—862no—
1004C2×Q8—1722no—
1005C2×Q8—1724no—
1006C2×Q8—1722no—
1007C2×Q8—1722no—
1008C2×Q8C23×D4311yescharacteristic
1009C2×Q8C23×D4312yes—
1010C2×D4—21no—
1011C2×D4—21no—
1012C2×D4—22no—
1013C2×D4—22no—
1014C2×D4—21no—
1015C2×D4—21no—
1016C2×D4—22no—
1017C2×D4—22no—
1018C2×D4—44no—
1019C2×D4—432no—
1020C2×D4—432no—
1021C2×D4—432no—
1022C2×D4—432no—
1023C2×D4—431no—
1024C2×D4—431no—
1025C2×D4—432no—
1026C2×D4—862no—
1027C2×D4—862no—
1028C2×D4—862no—
1029C2×D4—862no—
1030C2×D4—862no—
1031C2×D4—862no—
1032C2×D4—1722no—
1033C2×D4—1724no—
1034C2×D4C23×D4311yescharacteristic
1035C2×D4C23×D4312yes—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—44no—
1043C22×C4—432no—
1044C22×C4—432no—
1045C22×C4—432no—
1046C22×C4—432no—
1047C22×C4—432no—
1048C22×C4—862no—
1049C22×C4—862no—
1050C22×C4—862no—
1051C22×C4—861no—
1052C22×C4—861no—
1053C22×C4—861no—
1054C22×C4—861no—
1055C22×C4—1722no—
1056C22×C4—1722no—
1057C22×C4D4×D4311yescharacteristic
1058C22×C4D4×D4311yescharacteristic
1059C22×C4D4×D4311yescharacteristic
1060C22×C4C23×D4311yescharacteristic
1061C22×C4C23×D4311yescharacteristic
1062C22×C4C23×D4311yescharacteristic
1063Q16—42no—
1064Q16—1722no—
1065Q16—1722no—
1066SD16—42no—
1067SD16—42no—
1068SD16—1722no—
1069SD16—1722no—
1070D8—42no—
1071M16—22no—
1072M16—22no—
1073M16—1722no—
1074M16—1722no—
1075C2×C8—431no—
1076C2×C8—431no—
1077C2×C8—431no—
1078C2×C8—431no—
1079C2×C8—862no—
1080C2×C8—862no—
1081C2×C8—1722no—
1082C2×C8—1722no—
1083C2×C8C23×D4312yes—
1084C2×C8C23×D4312yes—
1085C4⋊C4—21no—
1086C4⋊C4—21no—
1087C4⋊C4—432no—
1088C4⋊C4—431no—
1089C4⋊C4—431no—
1090C4⋊C4—431no—
1091C4⋊C4—431no—
1092C4⋊C4—862no—
1093C4⋊C4—862no—
1094C4⋊C4—862no—
1095C4⋊C4—862no—
1096C4⋊C4—862no—
1097C4⋊C4—862no—
1098C4⋊C4—862no—
1099C4⋊C4—862no—
1100C4⋊C4—861no—
1101C4⋊C4—861no—
1102C4⋊C4—861no—
1103C4⋊C4—862no—
1104C4⋊C4—862no—
1105C4⋊C4C23×D4311yescharacteristic
1106C4⋊C4C23×D4311yescharacteristic
1107C22⋊C4—21no—
1108C22⋊C4—21no—
1109C22⋊C4—21no—
1110C22⋊C4—21no—
1111C22⋊C4—21no—
1112C22⋊C4—862no—
1113C22⋊C4—862no—
1114C22⋊C4—862no—
1115C22⋊C4—862no—
1116C22⋊C4—862no—
1117C22⋊C4—862no—
1118C22⋊C4—862no—
1119C22⋊C4—862no—
1120C22⋊C4—862no—
1121C22⋊C4—862no—
1122C22⋊C4—862no—
1123C22⋊C4—862no—
1124C22⋊C4—862no—
1125C22⋊C4—862no—
1126C22⋊C4—861no—
1127C22⋊C4—861no—
1128C22⋊C4—861no—
1129C22⋊C4—861no—
1130C22⋊C4—862no—
1131C42—21no—
1132C42—862no—
1133C42—861no—
1134C42—861no—
1135C42—861no—
1136C42—861no—
1137C23—22no—
1138C23—21no—
1139C23—22no—
1140C23—41no—
1141C23—41no—
1142C23—42no—
1143C23—81no—
1144C23—81no—
1145C23—432no—
1146C23—432no—
1147C23—1722no—
1148C23—1722no—
1149C23—1722no—
1150C23C2×D4×D4311yescharacteristic
1151C23C2×D4×D4311yescharacteristic
1152C23C2×D4×D4311yescharacteristic
1153Q8—21no—
1154Q8—22no—
1155Q8—21no—
1156Q8—22no—
1157Q8—42no—
1158Q8—862no—
1159Q8—862no—
1160Q8—862no—
1161Q8—862no—
1162Q8—1722no—
1163Q8—1724no—
1164Q8—1722no—
1165D4—21no—
1166D4—22no—
1167D4—21no—
1168D4—22no—
1169D4—44no—
1170D4—44no—
1171D4—42no—
1172D4—42no—
1173D4—42no—
1174D4—81no—
1175D4—864no—
1176D4—864no—
1177D4—862no—
1178D4—862no—
1179D4—3442no—
1180D4—3442no—
1181D4—3442no—
1182D4—3442no—
1183D4—3442no—
1184D4—1722no—
1185D4—1722no—
1186D4—1722no—
1187D4—1724no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—44no—
1200C2×C4—44no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—432no—
1204C2×C4—432no—
1205C2×C4—862no—
1206C2×C4—862no—
1207C2×C4—862no—
1208C2×C4—862no—
1209C2×C4—861no—
1210C2×C4—861no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—862no—
1214C2×C4—862no—
1215C2×C4—3442no—
1216C2×C4—3441no—
1217C2×C4—3441no—
1218C2×C4—3441no—
1219C2×C4—1722no—
1220C2×C4—1722no—
1221C2×C4—1724no—
1222C2×C4—1722no—
1223C2×C4—1724no—
1224C2×C4—1722no—
1225C2×C4C2×D4×D4311yescharacteristic
1226C2×C4C2×D4×D4311yescharacteristic
1227C2×C4C2×D4×D4311yescharacteristic
1228C2×C4#1306337012yes—
1229C2×C4#1306337012yes—
1230C2×C4C24×D4311yescharacteristic
1231C8—22no—
1232C8—22no—
1233C8—861no—
1234C8—861no—
1235C8—861no—
1236C8—861no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—41no—
1246C22—42no—
1247C22—41no—
1248C22—42no—
1249C22—42no—
1250C22—41no—
1251C22—82no—
1252C22—84no—
1253C22—862no—
1254C22—862no—
1255C22—862no—
1256C22—862no—
1257C22—862no—
1258C22—862no—
1259C22—3444no—
1260C22#1458345912yes—
1261C22C22×D4×D4311yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—41no—
1265C4—41no—
1266C4—42no—
1267C4—41no—
1268C4—862no—
1269C4—862no—
1270C4—1722no—
1271C4—1721no—
1272C4—1721no—
1273C4—1721no—
1274C4—1721no—
1275C4—1722no—
1276C4#1458345912yes—
1277C4C2×#1306337011yescharacteristic
1278C4C2×#1306337011yescharacteristic
1279C2—22no—
1280C2—41no—
1281C2—41no—
1282C2—82no—
1283C2—81no—
1284C2—1722no—
1285C2—1722no—
1286C2C2×#1458345911yescharacteristic
1287C2#1914936811yescharacteristic
1288C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3005C2
socleC22×C43C23×D4
hypercenter#3005D43
hypocenterC43#60761
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3005

Complements

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

NH ≅ G/Ntype
1. #19148267C2semidirect
2. #19147924C2semidirect
3. #19145504C2semidirect
4. #19145494C2semidirect
5. #19145476C2semidirect
6. #19145474C2semidirect
7. #19145434C2semidirect
8. #19145423C2semidirect
9. #19145385C2semidirect
10. #19145374C2semidirect
11. #19144562C2semidirect
12. #19144551C2semidirect
13. #19144544C2semidirect
14. #19144504C2semidirect
15. #19144280C2semidirect
16. #19144269C2semidirect
17. #19144249C2semidirect
18. #19144233C2semidirect
19. #19143889C2semidirect
20. #19143880C2semidirect
21. C2×#14583061C2semidirect
22. #19143045C2semidirect
23. C43×#3005C2semidirect
26. C22×#10621885C22semidirect
27. C22×#10621883C22semidirect
36. #14583478C22semidirect
43. #14583472C22semidirect
52. #14583409C22semidirect
56. C22⋊Q8×D43C22semidirect
59. #14583241C22semidirect
60. #14583241C22semidirect
61. #14583239C22semidirect
62. #14583238C22semidirect
63. #14583237C22semidirect
64. #14583237C22semidirect
65. #14583235C22semidirect
66. #14583233C22semidirect
67. #14583232C22semidirect
68. #14583230C22semidirect
69. #14583228C22semidirect
70. #14583227C22semidirect
71. #14583222C22semidirect
72. #14583221C22semidirect
73. #14583220C22semidirect
74. #14583220C22semidirect
75. #14583216C22semidirect
76. #14583215C22semidirect
77. #14583211C22semidirect
78. #14583210C22semidirect
79. #14583156C22semidirect
80. #14583156C22semidirect
81. #14583154C22semidirect
82. #14583149C22semidirect
83. #14583144C22semidirect
84. #14583144C22semidirect
85. #14583142C22semidirect
86. #14583142C22semidirect
87. #14583139C22semidirect
88. #14583139C22semidirect
89. #14583137C22semidirect
90. #14583132C22semidirect
91. #14583127C22semidirect
92. #14583127C22semidirect
93. #14583125C22semidirect
94. #14583125C22semidirect
97. #14583061C22semidirect
98. #14583061C22semidirect
99. #14583058C22semidirect
100. #14583058C22semidirect
101. #14583053C22semidirect
102. #14583053C22semidirect
103. #14583041C22semidirect
104. #14583041C22semidirect
105. #14583036C22semidirect
106. #14583036C22semidirect
107. #14582941C22semidirect
108. #14582941C22semidirect
109. #14582935C22semidirect
110. #14582935C22semidirect
111. #14582909C22semidirect
112. #14582909C22semidirect
113. #14582895C22semidirect
114. #14582895C22semidirect
115. C2×#13063249C22semidirect
116. C2×#13063246C22semidirect
119. #14582864C22semidirect
120. #14582864C22semidirect
121. #14582861C22semidirect
123. C22⋊C8×D43C22semidirect
125. C2×#137×C43C22semidirect
126. C2×AGL(1,ℤ/8)×C43C22semidirect
129. C43×#452C22semidirect
131. C43×#449C22semidirect
132. C43×#419C22semidirect
133. C43×#418C22semidirect
655. #3005D43semidirect
671. C2×#137C2×D43semidirect
672. C2×AGL(1,ℤ/8)C2×D43semidirect
750. #452C2×D43semidirect
756. #449C2×D43semidirect
765. #419C2×D43semidirect
766. #418C2×D43semidirect
779. C43#60761semidirect

Maximal subgroups

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

subgroupindex
#191482672
#191479242
#191455042
#191454942
#191454762
#191454742
#191454342
#191454232
#191453852
#191453742
#191445622
#191445512
#191445442
#191445042
#191442802
#191442692
#191442492
#191442332
#191438892
#191438802
C2×#145830612
#191430452
C43×#30052
#6076143