Finite Group Databasebeta

← #25967501

Subgroups — #25967501

Order 11008.

2208 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148265C211yesmaximal, characteristic, complemented
2#19147926C211yesmaximal, characteristic, complemented
3#19145508C212yesmaximal, complemented
4#19145495C212yesmaximal, complemented
5#19145445C212yesmaximal, complemented
6#19145445C212yesmaximal, complemented
7#19145435C212yesmaximal, complemented
8#19145408C212yesmaximal, complemented
9#19145386C212yesmaximal, complemented
10#19145359C212yesmaximal, complemented
11#19144564C211yesmaximal, characteristic, complemented
12#19144537C211yesmaximal, characteristic, complemented
13#19144512C211yesmaximal, characteristic, complemented
14#19144287C211yesmaximal, characteristic, complemented
15#19144273C211yesmaximal, characteristic, complemented
16#19144242C211yesmaximal, characteristic, complemented
17#19144235C211yesmaximal, characteristic, complemented
18#19143874C211yesmaximal, characteristic, complemented
19#19143861C211yesmaximal, characteristic, complemented
20#19143839C211yesmaximal, characteristic, complemented
21C2×#14583045C211yesmaximal, characteristic, complemented
22#19143043C211yesmaximal, characteristic, complemented
23C43×#3096C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C22×#10621900C2211yescharacteristic, complemented
26C2×#41×D43C2211yescharacteristic
27C2×#13063358C2211yescharacteristic, complemented
28C2×#13063351C2211yescharacteristic, complemented
29C22×#10621873C2211yescharacteristic, complemented
30C22×#10621882C2211yescharacteristic, complemented
31C2×#13063333C2211yescharacteristic, complemented
32C2×#13063331C2211yescharacteristic, complemented
33#14583571—21no—
34#14583561—21no—
35#14583544—22no—
36#14583544—21no—
37D4×D172—21no—
38D4×D172—22no—
39#14583480C2211yescharacteristic
40#14583480C2212yescomplemented
41#14583478C2212yescomplemented
42#14583478C2212yescomplemented
43#14583475C2211yescharacteristic, complemented
44#14583470C2211yescharacteristic
45#14583469—21no—
46#14583468C2211yescharacteristic
47#14583468C2212yescomplemented
48#14583466C2211yescharacteristic, complemented
49#14583462—21no—
50#14583459—22no—
51#14583448—21no—
52#14583447—21no—
53#14583411C2211yescharacteristic
54#14583411C2212yescomplemented
55#14583409C2212yescomplemented
56#14583409C2212yescomplemented
57#14583405—22no—
58C2×#13063300C2211yescharacteristic
59C2×#13063300C2212yescomplemented
60#117×D43C2211yescharacteristic, complemented
61#14583243C2211yescharacteristic, complemented
62#14583242C2211yescharacteristic, complemented
63#14583240C2212yescomplemented
64#14583240C2212yescomplemented
65#14583236C2211yescharacteristic, complemented
66#14583234C2212yescomplemented
67#14583231C2211yescharacteristic, complemented
68#14583229C2212yescomplemented
69#14583226C2211yescharacteristic, complemented
70#14583226C2212yescomplemented
71#14583225C2211yescharacteristic, complemented
72#14583225C2212yescomplemented
73#14583219C2212yescomplemented
74#14583219C2211yescharacteristic, complemented
75#14583214C2212yescomplemented
76#14583214C2211yescharacteristic, complemented
77#14583158C2212yescomplemented
78#14583151C2212yescomplemented
79#14583151C2212yescomplemented
80#14583151C2212yescomplemented
81#14583146C2212yescomplemented
82#14583146C2212yescomplemented
83#14583146C2212yescomplemented
84#14583144C2212yescomplemented
85#14583141C2212yescomplemented
86#14583134C2212yescomplemented
87#14583134C2212yescomplemented
88#14583134C2212yescomplemented
89#14583129C2212yescomplemented
90#14583129C2212yescomplemented
91#14583129C2212yescomplemented
92#14583127C2212yescomplemented
93#14583063C2212yescomplemented
94#14583063C2212yescomplemented
95#14583062C2212yescomplemented
96#14583062C2212yescomplemented
97#14583052C2212yescomplemented
98#14583052C2212yescomplemented
99#14583045C2212yescomplemented
100#14583045C2212yescomplemented
101#14583045C2212yescomplemented
102#14583045C2212yescomplemented
103#14583045C2212yescomplemented
104#14583045C2212yescomplemented
105#14583042C2212yescomplemented
106#14583042C2212yescomplemented
107#14583032C2212yescomplemented
108#14583032C2212yescomplemented
109#14582939C2211yescharacteristic, complemented
110#14582935C2211yescharacteristic, complemented
111#14582907C2211yescharacteristic, complemented
112#14582905C2211yescharacteristic, complemented
113#14582903C2211yescharacteristic, complemented
114#14582896C2211yescharacteristic, complemented
115#14582893C2211yescharacteristic, complemented
116C2×#13063248C2211yescharacteristic, complemented
117#14582866C2211yescharacteristic
118#14582864C2212yescomplemented
119#14582864C2212yescomplemented
120#14582862C2211yescharacteristic, complemented
121#14582861C2212yescomplemented
122C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
123C22⋊C8×D43C2212yescomplemented
124C43×#535C2211yescharacteristic
125C43×#520C2211yescharacteristic
126C43×#482C2212yescomplemented
127C43×#482C2212yescomplemented
128C43×#481C2212yescomplemented
129C43×#480C2212yescomplemented
130C43×#428C2211yescharacteristic, complemented
131C43×#427C2211yescharacteristic, complemented
132C43×#418C2211yescharacteristic, complemented
133C2×#102×C43C2211yescharacteristic, complemented
134C43×#408C2211yescharacteristic
135#13063371—42no—
136#13063371—42no—
137C2×#10621902—21no—
138C2×#10621902D411yescharacteristic
139C2×#10621898C2311yescharacteristic
140C2×#10621898C2312yes—
141C2×#10621898C2311yescharacteristic
142C2×#10621898C2312yes—
143C2×#10621900—21no—
144C2×#10621900—21no—
145C2×#10621900—42no—
146C2×#10621900—42no—
147C2×#10621900D412yes—
148C2×#10621900D411yescharacteristic
149C2×#10621900C2312yes—
150C2×#10621900C2312yes—
151#41×D43—42no—
152#41×D43—42no—
153C22×Dic86C2311yescharacteristic
154C2×Q8×D43D411yescharacteristic
155C22×D172—21no—
156C22×D172—22no—
157C22×D172C2311yescharacteristic
158C22×D172C2312yes—
159C22×C22⋊D43—21no—
160C2×D4×D43—22no—
161C2×D4×D43—21no—
162C2×D4×D43D412yes—
163C2×D4×D43D411yescharacteristic
164C23×Dic43—21no—
165C22×C4×D43C2311yescharacteristic
166C22×C4×D43C2312yes—
167#13063358—42no—
168#13063351—42no—
169C2×Dic172C2312yes—
170C2×#10621873—42no—
171C2×#10621873C2312yes—
172C2×#10621873C2312yes—
173C2×#10621873C2312yes—
174C2×#10621883C2312yes—
175C2×#10621882—42no—
176C2×#10621882C2312yes—
177C2×#10621882C2312yes—
178C2×#10621882C2312yes—
179#13063333—42no—
180#13063331—42no—
181C2×#10621877C2311yescharacteristic
182C2×#10621872C2312yes—
183C2×#10621872C2312yes—
184C22×C43⋊C8C2311yescharacteristic
185C2×C8×D43C2312yes—
186C2×C8×D43C2312yes—
187#13063325—21no—
188#13063323—21no—
189#13063322—21no—
190#13063322—22no—
191#13063321—21no—
192#13063313—21no—
193#13063313—21no—
194#13063313—22no—
195#13063312—21no—
196#13063312—21no—
197#13063309—22no—
198#13063309—21no—
199#13063309—22no—
200#13063307—22no—
201#13063307—22no—
202#13063306—22no—
203#13063305—21no—
204#13063305—22no—
205#13063305C2311yescharacteristic
206#13063305C2311yescharacteristic
207#13063305C2312yes—
208#13063305C2312yes—
209#13063305C2312yes—
210#13063304C2312yes—
211#13063304C2312yes—
212#13063302—22no—
213#13063302—22no—
214#13063300—21no—
215#13063300—22no—
216#13063300—21no—
217#13063300—22no—
218#13063300—21no—
219#13063300—22no—
220#13063300C2312yes—
221#13063300C2312yes—
222#13063300C2311yescharacteristic
223#13063300C2311yescharacteristic
224#13063300C2312yes—
225#13063300C2312yes—
226#13063300C2312yes—
227#13063299—22no—
228#13063299—22no—
229#13063299—22no—
230#13063298—22no—
231#13063298—22no—
232#13063297—22no—
233#13063297—22no—
234#13063296—22no—
235#13063296—22no—
236#13063296C2312yes—
237#13063296C2312yes—
238#13063295—21no—
239#13063295—22no—
240#13063295—22no—
241#13063295—22no—
242#13063295—22no—
243#13063294—22no—
244#13063293—22no—
245#13063293—22no—
246C4×D172—21no—
247C4×D172—22no—
248C4×D172—21no—
249C4×D172—22no—
250D4×Dic43—22no—
251D4×Dic43—22no—
252(C22⋊D43)⋊C4—22no—
253(C22⋊D43)⋊C4—22no—
254#13063284C2311yescharacteristic
255#13063283C2311yescharacteristic
256#13063283C2311yescharacteristic
257#13063282—21no—
258#13063281—21no—
259C4⋊C4×D43C2311yescharacteristic
260C4⋊C4×D43C2311yescharacteristic
261C2×(C2×D43)⋊C4—21no—
262C2×(C2×D43)⋊C4—22no—
263C22⋊C4×D43—21no—
264C42×D43—21no—
265#13063258C2311yescharacteristic
266#13063258C2311yescharacteristic
267#13063258C2312yes—
268#13063256C2312yes—
269#13063256C2311yescharacteristic
270#13063256C2311yescharacteristic
271#13063250C2311yescharacteristic
272#13063250C2311yescharacteristic
273#13063248C2311yescharacteristic
274#13063248C2311yescharacteristic
275#13063248C2312yes—
276#13063248C2312yes—
277#13063248C2312yes—
278#13063248C2312yes—
279#13063247C2311yescharacteristic
280#13063247C2311yescharacteristic
281#13063247C2312yes—
282#13063247C2312yes—
283#13063245C2312yes—
284#13063245C2312yes—
285#13063245C2311yescharacteristic
286#13063245C2311yescharacteristic
287C22⋊(C43⋊C8)C2312yes—
288C22⋊(C43⋊C8)C2312yes—
289(C2×D43)⋊C8C2311yescharacteristic
290(C2×D43)⋊C8C2311yescharacteristic
291(C2×D43)⋊C8C2311yescharacteristic
292(C2×D43)⋊C8C2311yescharacteristic
293(C2×D43)⋊C8C2312yes—
294(C2×D43)⋊C8C2312yes—
295C2×#41×C43C2311yescharacteristic
296C22×D4×C43C2311yescharacteristic
297C2×M16×C43C2311yescharacteristic
298C22×C8×C43C2311yescharacteristic
299#127×C43—21no—
300#124×C43—21no—
301#121×C43C2312yes—
302#121×C43C2312yes—
303#120×C43—22no—
304C4×Q8×C43—21no—
305C4×D4×C43—22no—
306C4×D4×C43—21no—
307#117×C43C2311yescharacteristic
308#117×C43C2312yes—
309#117×C43C2311yescharacteristic
310C2×C4⋊C4×C43C2311yescharacteristic
311C2×C4⋊C4×C43C2312yes—
312#107×C43C2312yes—
313#107×C43C2311yescharacteristic
314#107×C43C2311yescharacteristic
315#106×C43C2311yescharacteristic
316#106×C43C2311yescharacteristic
317#106×C43C2312yes—
318#102×C43C2312yes—
319#102×C43C2312yes—
320#102×C43C2312yes—
321#102×C43C2312yes—
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C24×C43—21no—
325C23×D43—22no—
326C23×D43—21no—
327C23×D43C2×D411yescharacteristic
328C23×D43C2×D412yes—
329#41×C43—22no—
330#41×C43—22no—
331C2×Q8×C43C2×D411yescharacteristic
332C2×D4×C43—21no—
333C2×D4×C43—22no—
334C2×D4×C43—22no—
335C2×D4×C43—22no—
336C2×D4×C43—22no—
337C2×D4×C43C2×D412yes—
338C2×D4×C43C2×D411yescharacteristic
339C2×D4×C43C2412yes—
340C22×C4×C43—22no—
341C22×C4×C43—21no—
342C22×C4×C43C2412yes—
343C22×C4×C43C2411yescharacteristic
344C2×C22⋊D43—22no—
345C2×C22⋊D43—21no—
346C2×C22⋊D43—22no—
347C2×C22⋊D43—22no—
348C2×C22⋊D43—22no—
349C2×C22⋊D43—22no—
350C2×C22⋊D43—44no—
351C2×C22⋊D43C2×D412yes—
352C2×C22⋊D43C2×D412yes—
353C2×C22⋊D43C2×D412yes—
354C22×Dic43—22no—
355C22×Dic43—22no—
356C22×Dic43—21no—
357C22×Dic43—44no—
358C22×Dic43C2×D411yescharacteristic
359C22×Dic43C2×D412yes—
360#10621902—42no—
361#10621902—44no—
362Q8×D43—42no—
363#10621900—42no—
364#10621900—42no—
365#10621900—42no—
366#10621900—42no—
367#10621900—42no—
368#10621900—44no—
369#10621900—44no—
370#10621900—44no—
371D4×D43—44no—
372D4×D43—42no—
373D4×D43—44no—
374D4×D43—48no—
375#10621898—22no—
376#10621898—22no—
377#10621898—22no—
378#10621898—22no—
379#10621898—42no—
380#10621898—42no—
381#10621898—42no—
382#10621898—42no—
383C2×D172—22no—
384C2×D172—21no—
385C2×D172—21no—
386C2×D172—22no—
387C2×D172—22no—
388C2×D172—21no—
389C2×D172—22no—
390C2×D172—22no—
391C2×D172—22no—
392C2×D172—22no—
393C2×D172—22no—
394C2×D172—42no—
395C2×D172—42no—
396C2×D172—82no—
397C2×D172—84no—
398C2×D172C2×D411yescharacteristic
399C2×D172C2×D412yes—
400C2×D172C2412yes—
401C2×D172C2411yescharacteristic
402C2×C4×D43—22no—
403C2×C4×D43—22no—
404C2×C4×D43—22no—
405C2×C4×D43—21no—
406C2×C4×D43—21no—
407C2×C4×D43—21no—
408C2×C4×D43—42no—
409C2×C4×D43—42no—
410C2×C4×D43C2×D411yescharacteristic
411C2×C4×D43C2×D411yescharacteristic
412C2×C4×D43C2×D412yes—
413C2×C4×D43C2×D412yes—
414C2×C4×D43C2411yescharacteristic
415C2×C4×D43C2411yescharacteristic
416C2×C4×D43C2412yes—
417C2×Dic86—22no—
418C2×Dic86—22no—
419C2×Dic86—21no—
420C2×Dic86C2×D411yescharacteristic
421C2×Dic86C2×D412yes—
422C2×Dic86C2412yes—
423C2×Dic86C2411yescharacteristic
424M16×C43—22no—
425C2×C8×C43—22no—
426C2×C8×C43C2411yescharacteristic
427C2×C8×C43C2412yes—
428C2×C8×C43C2411yescharacteristic
429C4⋊C4×C43—22no—
430C4⋊C4×C43—21no—
431C4⋊C4×C43C2412yes—
432C4⋊C4×C43C2411yescharacteristic
433C4⋊C4×C43C2411yescharacteristic
434C4⋊C4×C43C2411yescharacteristic
435C4⋊C4×C43C2411yescharacteristic
436C22⋊C4×C43—22no—
437C22⋊C4×C43—22no—
438C22⋊C4×C43—22no—
439C22⋊C4×C43—21no—
440C22⋊C4×C43—21no—
441C42×C43—22no—
442C42×C43—21no—
443C42×C43—21no—
444C22⋊Dic43—22no—
445C22⋊Dic43—22no—
446C22⋊Dic43—21no—
447C22⋊Dic43—22no—
448C22⋊Dic43—22no—
449#10621883—42no—
450#10621882—42no—
451#10621882—42no—
452#10621882—42no—
453(C2×D43)⋊C4—22no—
454(C2×D43)⋊C4—21no—
455(C2×D43)⋊C4—22no—
456(C2×D43)⋊C4—22no—
457(C2×D43)⋊C4—22no—
458(C2×D43)⋊C4—21no—
459(C2×D43)⋊C4—22no—
460(C2×D43)⋊C4—21no—
461(C2×D43)⋊C4—21no—
462(C2×D43)⋊C4—22no—
463(C2×D43)⋊C4—22no—
464(C2×D43)⋊C4—21no—
465(C2×D43)⋊C4—22no—
466(C2×D43)⋊C4—21no—
467C4⋊Dic43—22no—
468C4⋊Dic43—22no—
469C4⋊Dic43—21no—
470C4⋊Dic43—21no—
471C4⋊Dic43—22no—
472C4⋊Dic43C2411yescharacteristic
473C4⋊Dic43C2411yescharacteristic
474Dic43⋊C4—22no—
475Dic43⋊C4—22no—
476Dic43⋊C4—21no—
477Dic43⋊C4—21no—
478C4×Dic43—21no—
479C4×Dic43—21no—
480C4×Dic43—21no—
481#10621877—22no—
482C2×C43⋊C8—22no—
483C2×C43⋊C8C2412yes—
484C2×C43⋊C8C2411yescharacteristic
485C2×C43⋊C8C2411yescharacteristic
486Dic172—42no—
487#10621873—42no—
488#10621873—42no—
489#10621873—42no—
490#10621872—42no—
491#10621872—42no—
492C8×D43—42no—
493C8×D43—42no—
494C23×C43—22no—
495C23×C43—42no—
496C23×C43—81no—
497C23×C43—81no—
498C23×C43C22×D412yes—
499C23×C43C22×D411yescharacteristic
500C22×D43—22no—
501C22×D43—21no—
502C22×D43—22no—
503C22×D43—42no—
504C22×D43—41no—
505C22×D43—42no—
506C22×D43—41no—
507C22×D43—42no—
508C22×D43—44no—
509C22×D43—42no—
510C22×D43—81no—
511C22×D43—82no—
512C22×D43—81no—
513C22×D43—82no—
514C22×D43C22×D411yescharacteristic
515C22×D43C22×D412yes—
516C22×D43C22×D411yescharacteristic
517Q8×C43—22no—
518D4×C43—24no—
519D4×C43—22no—
520D4×C43—22no—
521D4×C43—22no—
522D4×C43—42no—
523D4×C43—82no—
524D4×C43—82no—
525C2×C4×C43—22no—
526C2×C4×C43—22no—
527C2×C4×C43—21no—
528C2×C4×C43—21no—
529C2×C4×C43—21no—
530C2×C4×C43—21no—
531C2×C4×C43—22no—
532C2×C4×C43—81no—
533C2×C4×C43—82no—
534C2×C4×C43C22×D412yes—
535C2×C4×C43C22×D411yescharacteristic
536C2×C4×C43H(5,𝔽2)12yes—
537C2×C4×C43H(5,𝔽2)12yes—
538C2×C4×C43C2511yescharacteristic
539C22⋊D43—24no—
540C22⋊D43—42no—
541C22⋊D43—42no—
542C22⋊D43—44no—
543C22⋊D43—44no—
544C22⋊D43—44no—
545C22⋊D43—42no—
546C22⋊D43—82no—
547C22⋊D43—82no—
548C2×Dic43—22no—
549C2×Dic43—21no—
550C2×Dic43—21no—
551C2×Dic43—22no—
552C2×Dic43—21no—
553C2×Dic43—42no—
554C2×Dic43—44no—
555C2×Dic43—44no—
556C2×Dic43—42no—
557C2×Dic43C22×D411yescharacteristic
558C2×Dic43C22×D411yescharacteristic
559C2×Dic43C22×D412yes—
560D172—22no—
561D172—22no—
562D172—21no—
563D172—22no—
564D172—21no—
565D172—42no—
566D172—44no—
567D172—42no—
568D172—44no—
569D172—42no—
570D172—81no—
571D172—82no—
572D172—82no—
573D172—82no—
574D172—82no—
575C4×D43—22no—
576C4×D43—22no—
577C4×D43—22no—
578C4×D43—22no—
579C4×D43—21no—
580C4×D43—21no—
581C4×D43—21no—
582C4×D43—21no—
583C4×D43—42no—
584C4×D43—42no—
585C4×D43—44no—
586C4×D43—42no—
587C4×D43—81no—
588C4×D43—81no—
589Dic86—22no—
590Dic86—22no—
591Dic86—22no—
592Dic86—21no—
593Dic86—21no—
594Dic86—42no—
595Dic86—42no—
596C8×C43—21no—
597C8×C43—22no—
598C8×C43—21no—
599C43⋊C8—21no—
600C43⋊C8—22no—
601C43⋊C8—21no—
602#60760—431nomaximal, Sylow
603C22×C43—21no—
604C22×C43—21no—
605C22×C43—22no—
606C22×C43—22no—
607C22×C43—22no—
608C22×C43—42no—
609C22×C43—42no—
610C22×C43—42no—
611C22×C43—84no—
612C22×C43#53412yes—
613C22×C43C23×D411yescharacteristic
614C2×D43—21no—
615C2×D43—21no—
616C2×D43—22no—
617C2×D43—21no—
618C2×D43—21no—
619C2×D43—22no—
620C2×D43—21no—
621C2×D43—21no—
622C2×D43—22no—
623C2×D43—42no—
624C2×D43—41no—
625C2×D43—42no—
626C2×D43—41no—
627C2×D43—41no—
628C2×D43—42no—
629C2×D43—82no—
630C2×D43—84no—
631C2×D43—162no—
632C2×D43—164no—
633C4×C43—22no—
634C4×C43—41no—
635C4×C43—41no—
636C4×C43—41no—
637C4×C43—42no—
638C4×C43—41no—
639C4×C43#53412yes—
640C4×C43C2×H(5,𝔽2)11yescharacteristic
641C4×C43C2×H(5,𝔽2)11yescharacteristic
642Dic43—22no—
643Dic43—21no—
644Dic43—21no—
645Dic43—41no—
646Dic43—41no—
647Dic43—42no—
648Dic43—41no—
649#3488—431no—
650#3449—431no—
651#3204—432no—
652#3203—432no—
653#3198—432no—
654#3198—432no—
655#3197—432no—
656#3194—432no—
657#3191—432no—
658#3188—432no—
659#3097—431no—
660#3096D4311yescharacteristic, complemented
661#3094—431no—
662#3091—431no—
663#3063—431no—
664#3062—431no—
665#3058—431no—
666#3057—431no—
667#3009—431no—
668#3008—431no—
669#3005—431no—
670C2×#449—431no—
671#2880—431no—
672C2×C43—22no—
673C2×C43—42no—
674C2×C43—82no—
675C2×C43C2×#53411yescharacteristic
676C2×C43#358411yescharacteristic
677C2×C43#358511yescharacteristic
678D43—41no—
679D43—42no—
680D43—41no—
681D43—82no—
682D43—81no—
683C2×H(5,𝔽2)—431no—
684C22×#41—431no—
685C22×#41—431no—
686C2×#137—431no—
687C2×AGL(1,ℤ/8)—431no—
688C22×SD16—431no—
689C22×D8—431no—
690C2×#131—431no—
691C2×#131—431no—
692#550—861no—
693#548—861no—
694#546—862no—
695#546—861no—
696D42—862no—
697D42—861no—
698#537—432no—
699#537—432no—
700#537—432no—
701#537—431no—
702#536—431no—
703#536—431no—
704#536—861no—
705#535—431no—
706#535—432no—
707#535—431no—
708#535—861no—
709#535C2×D4311yescharacteristic
710#534—862no—
711#532—861no—
712#532—861no—
713#525—432no—
714#525—432no—
715#525—431no—
716#525—432no—
717#525—862no—
718C2×#121—431no—
719C2×#121—432no—
720#520C2×D4311yescharacteristic
721C2×#117—431no—
722#485—432no—
723#485—432no—
724#485—431no—
725#485—431no—
726#484—432no—
727#484—431no—
728#483—432no—
729#483—431no—
730#482—431no—
731#482—432no—
732#482—431no—
733#482—432no—
734#482C2×D4312yescomplemented
735#482C2×D4312yescomplemented
736#481—431no—
737#481—432no—
738#481C2×D4312yescomplemented
739#480—431no—
740#480—432no—
741#480C2×D4312yescomplemented
742#470—432no—
743#469—432no—
744#469—432no—
745#469—432no—
746#468—432no—
747#468—432no—
748#468—432no—
749#468—432no—
750#467—432no—
751#466—432no—
752#466—432no—
753#466—432no—
754#465—432no—
755#465—432no—
756#465—432no—
757#465—432no—
758#452—432no—
759#452—432no—
760#452—432no—
761#452—432no—
762#450—432no—
763#450—432no—
764#449—432no—
765#449—432no—
766#449—432no—
767#449—432no—
768#449—432no—
769#449—432no—
770#449—432no—
771#449—432no—
772#447—432no—
773#447—432no—
774#428—431no—
775#428C2×D4311yescharacteristic, complemented
776#427—431no—
777#427C2×D4311yescharacteristic, complemented
778#419—431no—
779#418—431no—
780#418—431no—
781#418C2×D4311yescharacteristic, complemented
782#416—431no—
783#416—431no—
784C2×#103—431no—
785C2×#102C2×D4311yescharacteristic, complemented
786#408—431no—
787#408—432no—
788#408—432no—
789#408C2×D4311yescharacteristic
790#407—431no—
791#407—432no—
792C2×C22⋊C8—431no—
793C2×C22⋊C8—432no—
794C43#6076011yescharacteristic, complemented, Sylow
795H(5,𝔽2)—1722no—
796H(5,𝔽2)—1722no—
797C2×#41—431no—
798C2×#41—432no—
799C2×#41—431no—
800C2×#41—431no—
801C2×#41—432no—
802C2×#41—432no—
803C2×#41—432no—
804C2×#41—431no—
805C2×#41—432no—
806C2×#41—861no—
807C2×#41—861no—
808C2×#41—861no—
809C2×#41—1722no—
810C2×#41—1722no—
811C2×#41—1722no—
812C2×#41—1722no—
813C2×#41C22×D4311yescharacteristic
814C22×Q8—431no—
815C22×Q8—431no—
816C22×D4—432no—
817C22×D4—431no—
818C22×D4—431no—
819C22×D4—432no—
820C22×D4—861no—
821C22×D4—862no—
822C22×D4—861no—
823C22×D4—862no—
824C22×D4—861no—
825C22×D4C22×D4311yescharacteristic
826C23×C4—431no—
827C23×C4—432no—
828C23×C4—861no—
829#137—1722no—
830AGL(1,ℤ/8)—1722no—
831C2×Q16—432no—
832C2×SD16—432no—
833C2×SD16—432no—
834C2×SD16—432no—
835C2×SD16—432no—
836C2×SD16—1722no—
837C2×D8—432no—
838C2×D8—432no—
839C2×D8—432no—
840C2×D8—1722no—
841#131—1722no—
842#131—1722no—
843C2×M16—431no—
844C2×M16—432no—
845C2×M16—432no—
846C2×M16C22×D4311yescharacteristic
847C22×C8—431no—
848C22×C8—432no—
849C22×C8—432no—
850C22×C8C22×D4311yescharacteristic
851C4⋊Q8—861no—
852C4⋊Q8—861no—
853#127—21no—
854#127—861no—
855#127—862no—
856#127—861no—
857#124—21no—
858#124—861no—
859#124—861no—
860#124—862no—
861#124—861no—
862#124—861no—
863#123—862no—
864#123—862no—
865#123—861no—
866#123—862no—
867#123—862no—
868#123—862no—
869C22⋊Q8—432no—
870C22⋊Q8—432no—
871C22⋊Q8—431no—
872C22⋊Q8—432no—
873C22⋊Q8—432no—
874C22⋊Q8—431no—
875C22⋊Q8—432no—
876C22⋊Q8—862no—
877C22⋊Q8—862no—
878C22⋊Q8—861no—
879C22⋊Q8—862no—
880#121—432no—
881#121—432no—
882#121—432no—
883#121—431no—
884#121—432no—
885#121—432no—
886#121—432no—
887#121—431no—
888#121—432no—
889#121—862no—
890#121—862no—
891#121—861no—
892#121—862no—
893#121—861no—
894#121—862no—
895#121—861no—
896#121—862no—
897#121—862no—
898#121—862no—
899#121—862no—
900#121—862no—
901#121—862no—
902#121—862no—
903#121—862no—
904#121C22×D4312yes—
905#121C22×D4312yes—
906#120—22no—
907#120—862no—
908#120—862no—
909#120—862no—
910#120—861no—
911#120—862no—
912#120—862no—
913#120—862no—
914#120—862no—
915C4×Q8—21no—
916C4×D4—22no—
917C4×D4—21no—
918C4×D4—861no—
919C4×D4—862no—
920C4×D4—861no—
921C4×D4—862no—
922C4×D4—862no—
923C4×D4—862no—
924C4×D4—862no—
925C4×D4—862no—
926#117—431no—
927#117—431no—
928#117—431no—
929#117—861no—
930#117—861no—
931#117C22×D4311yescharacteristic
932#117C22×D4311yescharacteristic
933#117C22×D4312yes—
934C2×C4⋊C4—431no—
935C2×C4⋊C4—431no—
936C2×C4⋊C4C22×D4311yescharacteristic
937C2×C4⋊C4C22×D4312yes—
938C2×C22⋊C4—861no—
939C2×C22⋊C4—861no—
940C2×C22⋊C4—862no—
941C2×C42—861no—
942#107—431no—
943#107—431no—
944#107—432no—
945#107C22×D4311yescharacteristic
946#107C22×D4311yescharacteristic
947#107C22×D4312yes—
948#106—431no—
949#106—431no—
950#106—432no—
951#106C22×D4311yescharacteristic
952#106C22×D4311yescharacteristic
953#106C22×D4312yes—
954#103—431no—
955#103—431no—
956#103—432no—
957#103—432no—
958#103—431no—
959#103—431no—
960#103—432no—
961#103—432no—
962#102—431no—
963#102—431no—
964#102—432no—
965#102—432no—
966#102—431no—
967#102—431no—
968#102—432no—
969#102—432no—
970#102C22×D4312yes—
971#102C22×D4312yes—
972#102C22×D4312yes—
973#102C22×D4312yes—
974C22⋊C8—432no—
975C22⋊C8—432no—
976C22⋊C8—431no—
977C22⋊C8—431no—
978C22⋊C8—432no—
979C22⋊C8—431no—
980C22⋊C8—431no—
981C22⋊C8—432no—
982C22⋊C8C22×D4312yes—
983C22⋊C8C22×D4312yes—
984C24—21no—
985C24—431no—
986C24—432no—
987C24—862no—
988C24—861no—
989#41—22no—
990#41—22no—
991#41—862no—
992#41—862no—
993#41—862no—
994#41—862no—
995#41—1722no—
996#41—1722no—
997#41—1722no—
998#41—1722no—
999#41—1724no—
1000#41—1722no—
1001#41—1722no—
1002#41—1722no—
1003#41—1722no—
1004#41—1722no—
1005#41—1724no—
1006#41—1724no—
1007#41—1722no—
1008#41—1724no—
1009C2×Q8—431no—
1010C2×Q8—432no—
1011C2×Q8—432no—
1012C2×Q8—431no—
1013C2×Q8—861no—
1014C2×Q8—862no—
1015C2×Q8—862no—
1016C2×Q8—1722no—
1017C2×Q8D4×D4311yescharacteristic
1018C2×D4—22no—
1019C2×D4—22no—
1020C2×D4—21no—
1021C2×D4—22no—
1022C2×D4—22no—
1023C2×D4—432no—
1024C2×D4—432no—
1025C2×D4—432no—
1026C2×D4—431no—
1027C2×D4—432no—
1028C2×D4—432no—
1029C2×D4—431no—
1030C2×D4—862no—
1031C2×D4—861no—
1032C2×D4—862no—
1033C2×D4—862no—
1034C2×D4—862no—
1035C2×D4—861no—
1036C2×D4—862no—
1037C2×D4—862no—
1038C2×D4—862no—
1039C2×D4—862no—
1040C2×D4—862no—
1041C2×D4—862no—
1042C2×D4—861no—
1043C2×D4—862no—
1044C2×D4—861no—
1045C2×D4—862no—
1046C2×D4—862no—
1047C2×D4—3442no—
1048C2×D4—3444no—
1049C2×D4—1722no—
1050C2×D4—1722no—
1051C2×D4—1722no—
1052C2×D4—1724no—
1053C2×D4—1728no—
1054C2×D4—1724no—
1055C2×D4—1724no—
1056C2×D4D4×D4312yes—
1057C2×D4D4×D4311yescharacteristic
1058C2×D4C23×D4312yes—
1059C22×C4—22no—
1060C22×C4—21no—
1061C22×C4—431no—
1062C22×C4—432no—
1063C22×C4—431no—
1064C22×C4—431no—
1065C22×C4—431no—
1066C22×C4—431no—
1067C22×C4—432no—
1068C22×C4—432no—
1069C22×C4—432no—
1070C22×C4—861no—
1071C22×C4—861no—
1072C22×C4—862no—
1073C22×C4—862no—
1074C22×C4—862no—
1075C22×C4—862no—
1076C22×C4—861no—
1077C22×C4—862no—
1078C22×C4—861no—
1079C22×C4—1722no—
1080C22×C4—1722no—
1081C22×C4—1724no—
1082C22×C4C23×D4312yes—
1083C22×C4C23×D4311yescharacteristic
1084Q16—1722no—
1085SD16—1722no—
1086SD16—1722no—
1087SD16—1722no—
1088SD16—1722no—
1089D8—1722no—
1090D8—1722no—
1091D8—1722no—
1092M16—22no—
1093M16—862no—
1094M16—1722no—
1095M16—1722no—
1096C2×C8—22no—
1097C2×C8—432no—
1098C2×C8—431no—
1099C2×C8—431no—
1100C2×C8—862no—
1101C2×C8—1722no—
1102C2×C8—1722no—
1103C2×C8C23×D4312yes—
1104C2×C8C23×D4311yescharacteristic
1105C2×C8C23×D4311yescharacteristic
1106C4⋊C4—22no—
1107C4⋊C4—21no—
1108C4⋊C4—431no—
1109C4⋊C4—431no—
1110C4⋊C4—861no—
1111C4⋊C4—861no—
1112C4⋊C4—861no—
1113C4⋊C4—862no—
1114C4⋊C4—861no—
1115C4⋊C4—862no—
1116C4⋊C4—862no—
1117C4⋊C4—862no—
1118C4⋊C4—862no—
1119C4⋊C4C23×D4311yescharacteristic
1120C4⋊C4C23×D4311yescharacteristic
1121C4⋊C4C23×D4312yes—
1122C4⋊C4C23×D4311yescharacteristic
1123C4⋊C4C23×D4311yescharacteristic
1124C22⋊C4—21no—
1125C22⋊C4—22no—
1126C22⋊C4—21no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—862no—
1130C22⋊C4—861no—
1131C22⋊C4—862no—
1132C22⋊C4—862no—
1133C22⋊C4—862no—
1134C22⋊C4—862no—
1135C22⋊C4—861no—
1136C22⋊C4—861no—
1137C22⋊C4—861no—
1138C22⋊C4—861no—
1139C22⋊C4—862no—
1140C22⋊C4—861no—
1141C22⋊C4—862no—
1142C22⋊C4—862no—
1143C22⋊C4—862no—
1144C22⋊C4—862no—
1145C22⋊C4—861no—
1146C22⋊C4—862no—
1147C22⋊C4—862no—
1148C42—21no—
1149C42—22no—
1150C42—21no—
1151C42—861no—
1152C42—861no—
1153C42—861no—
1154C23—22no—
1155C23—42no—
1156C23—81no—
1157C23—81no—
1158C23—431no—
1159C23—432no—
1160C23—431no—
1161C23—862no—
1162C23—862no—
1163C23—861no—
1164C23—3441no—
1165C23—3442no—
1166C23—3441no—
1167C23—3442no—
1168C23—1722no—
1169C23—1721no—
1170C23—1722no—
1171C23—1721no—
1172C23—1722no—
1173C23—1724no—
1174C23—1722no—
1175C23C2×D4×D4312yes—
1176C23C2×D4×D4311yescharacteristic
1177Q8—22no—
1178Q8—862no—
1179Q8—862no—
1180Q8—861no—
1181Q8—862no—
1182Q8—861no—
1183Q8—1722no—
1184Q8—1722no—
1185D4—24no—
1186D4—22no—
1187D4—22no—
1188D4—22no—
1189D4—42no—
1190D4—82no—
1191D4—82no—
1192D4—864no—
1193D4—862no—
1194D4—862no—
1195D4—861no—
1196D4—862no—
1197D4—861no—
1198D4—3442no—
1199D4—3442no—
1200D4—3442no—
1201D4—3441no—
1202D4—3442no—
1203D4—3442no—
1204D4—3442no—
1205D4—1722no—
1206D4—1724no—
1207D4—1724no—
1208D4—1722no—
1209D4—1722no—
1210D4—1722no—
1211D4—1724no—
1212D4—1724no—
1213D4—1724no—
1214D4—1722no—
1215D4—1722no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—81no—
1224C2×C4—82no—
1225C2×C4—431no—
1226C2×C4—432no—
1227C2×C4—431no—
1228C2×C4—862no—
1229C2×C4—862no—
1230C2×C4—862no—
1231C2×C4—862no—
1232C2×C4—862no—
1233C2×C4—861no—
1234C2×C4—861no—
1235C2×C4—861no—
1236C2×C4—861no—
1237C2×C4—861no—
1238C2×C4—861no—
1239C2×C4—861no—
1240C2×C4—862no—
1241C2×C4—3441no—
1242C2×C4—3441no—
1243C2×C4—1722no—
1244C2×C4—1722no—
1245C2×C4—1724no—
1246C2×C4—1722no—
1247C2×C4—1724no—
1248C2×C4—1724no—
1249C2×C4—1722no—
1250C2×C4—1722no—
1251C2×C4C2×D4×D4312yes—
1252C2×C4C2×D4×D4311yescharacteristic
1253C2×C4#1306337112yes—
1254C2×C4#1306337112yes—
1255C2×C4C24×D4311yescharacteristic
1256C8—21no—
1257C8—21no—
1258C8—22no—
1259C8—861no—
1260C8—861no—
1261C8—862no—
1262C22—21no—
1263C22—21no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—84no—
1271C22—861no—
1272C22—862no—
1273C22—861no—
1274C22—861no—
1275C22—862no—
1276C22—861no—
1277C22—861no—
1278C22—861no—
1279C22—862no—
1280C22—3442no—
1281C22—3444no—
1282C22—1722no—
1283C22—1721no—
1284C22—1722no—
1285C22—1721no—
1286C22—1722no—
1287C22—1721no—
1288C22—6882no—
1289C22—6884no—
1290C22#1458346012yes—
1291C22C22×D4×D4311yescharacteristic
1292C4—22no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—41no—
1297C4—41no—
1298C4—861no—
1299C4—861no—
1300C4—862no—
1301C4—1721no—
1302C4—1721no—
1303C4—1721no—
1304C4—1722no—
1305C4#1458346012yes—
1306C4C2×#1306337111yescharacteristic
1307C4C2×#1306337111yescharacteristic
1308C2—22no—
1309C2—42no—
1310C2—82no—
1311C2—3442no—
1312C2—3441no—
1313C2—1721no—
1314C2—1721no—
1315C2—1722no—
1316C2C2×#1458346011yescharacteristic
1317C2#1914936711yescharacteristic
1318C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3096C2
socleC22×C43C23×D4
hypercenter#3096D43
hypocenterC43#60760
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3096

Complements

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

NH ≅ G/Ntype
1. #19148265C2semidirect
2. #19147926C2semidirect
3. #19145508C2semidirect
4. #19145495C2semidirect
5. #19145445C2semidirect
6. #19145445C2semidirect
7. #19145435C2semidirect
8. #19145408C2semidirect
9. #19145386C2semidirect
10. #19145359C2semidirect
11. #19144564C2semidirect
12. #19144537C2semidirect
13. #19144512C2semidirect
14. #19144287C2semidirect
15. #19144273C2semidirect
16. #19144242C2semidirect
17. #19144235C2semidirect
18. #19143874C2semidirect
19. #19143861C2semidirect
20. #19143839C2semidirect
21. C2×#14583045C2semidirect
22. #19143043C2semidirect
23. C43×#3096C2semidirect
25. C22×#10621900C22semidirect
27. C2×#13063358C22semidirect
28. C2×#13063351C22semidirect
29. C22×#10621873C22semidirect
30. C22×#10621882C22semidirect
31. C2×#13063333C22semidirect
32. C2×#13063331C22semidirect
40. #14583480C22semidirect
41. #14583478C22semidirect
42. #14583478C22semidirect
43. #14583475C22semidirect
47. #14583468C22semidirect
48. #14583466C22semidirect
54. #14583411C22semidirect
55. #14583409C22semidirect
56. #14583409C22semidirect
59. C2×#13063300C22semidirect
60. #117×D43C22semidirect
61. #14583243C22semidirect
62. #14583242C22semidirect
63. #14583240C22semidirect
64. #14583240C22semidirect
65. #14583236C22semidirect
66. #14583234C22semidirect
67. #14583231C22semidirect
68. #14583229C22semidirect
69. #14583226C22semidirect
70. #14583226C22semidirect
71. #14583225C22semidirect
72. #14583225C22semidirect
73. #14583219C22semidirect
74. #14583219C22semidirect
75. #14583214C22semidirect
76. #14583214C22semidirect
77. #14583158C22semidirect
78. #14583151C22semidirect
79. #14583151C22semidirect
80. #14583151C22semidirect
81. #14583146C22semidirect
82. #14583146C22semidirect
83. #14583146C22semidirect
84. #14583144C22semidirect
85. #14583141C22semidirect
86. #14583134C22semidirect
87. #14583134C22semidirect
88. #14583134C22semidirect
89. #14583129C22semidirect
90. #14583129C22semidirect
91. #14583129C22semidirect
92. #14583127C22semidirect
93. #14583063C22semidirect
94. #14583063C22semidirect
95. #14583062C22semidirect
96. #14583062C22semidirect
97. #14583052C22semidirect
98. #14583052C22semidirect
99. #14583045C22semidirect
100. #14583045C22semidirect
101. #14583045C22semidirect
102. #14583045C22semidirect
103. #14583045C22semidirect
104. #14583045C22semidirect
105. #14583042C22semidirect
106. #14583042C22semidirect
107. #14583032C22semidirect
108. #14583032C22semidirect
109. #14582939C22semidirect
110. #14582935C22semidirect
111. #14582907C22semidirect
112. #14582905C22semidirect
113. #14582903C22semidirect
114. #14582896C22semidirect
115. #14582893C22semidirect
116. C2×#13063248C22semidirect
118. #14582864C22semidirect
119. #14582864C22semidirect
120. #14582862C22semidirect
121. #14582861C22semidirect
122. C2×(C2×D43)⋊C8C22semidirect
123. C22⋊C8×D43C22semidirect
126. C43×#482C22semidirect
127. C43×#482C22semidirect
128. C43×#481C22semidirect
129. C43×#480C22semidirect
130. C43×#428C22semidirect
131. C43×#427C22semidirect
132. C43×#418C22semidirect
133. C2×#102×C43C22semidirect
660. #3096D43semidirect
734. #482C2×D43semidirect
735. #482C2×D43semidirect
738. #481C2×D43semidirect
741. #480C2×D43semidirect
775. #428C2×D43semidirect
777. #427C2×D43semidirect
781. #418C2×D43semidirect
785. C2×#102C2×D43semidirect
794. C43#60760semidirect

Maximal subgroups

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

subgroupindex
#191482652
#191479262
#191455082
#191454952
#191454452
#191454352
#191454082
#191453862
#191453592
#191445642
#191445372
#191445122
#191442872
#191442732
#191442422
#191442352
#191438742
#191438612
#191438392
C2×#145830452
#191430432
C43×#30962
#6076043