Finite Group Databasebeta

← #25977182

Subgroups — #25977182

Order 11008.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148173C211yesmaximal, characteristic, complemented
2C2×#14583605C211yesmaximal, characteristic, complemented
3#19147556C212yesmaximal, complemented
4#19147550C212yesmaximal, complemented
5#19147546C212yesmaximal, complemented
6#19147535C212yesmaximal, complemented
7#19147502C212yesmaximal, complemented
8#19147491C212yesmaximal, complemented
9#19147467C212yesmaximal, complemented
10#19147459C212yesmaximal, complemented
11#19145145C211yesmaximal, characteristic, complemented
12#19145139C211yesmaximal, characteristic, complemented
13#19144416C211yesmaximal, characteristic, complemented
14#19144413C211yesmaximal, characteristic, complemented
15#19144408C211yesmaximal, characteristic, complemented
16#19144391C211yesmaximal, characteristic, complemented
17#19144391C211yesmaximal, characteristic, complemented
18#19144388C211yesmaximal, characteristic, complemented
19M16×Dic86C211yesmaximal, characteristic, complemented
20C4×#13063353C211yesmaximal, characteristic
21#19143402C211yesmaximal, characteristic
22#19143402C211yesmaximal, characteristic
23C43×#3166C211yesmaximal, characteristic, complemented
24C2×#13063353C2211yescharacteristic
25#14583629C2211yescharacteristic, complemented
26#14583626C2211yescharacteristic, complemented
27#14583626C2211yescharacteristic, complemented
28#14583624C2211yescharacteristic, complemented
29#14583610C2211yescharacteristic, complemented
30#14583607—21no—
31#14583605—21no—
32#14583605—21no—
33#14583605—21no—
34#14583605—21no—
35#14583605C2212yes—
36#14583605C2212yes—
37#14583605C2212yes—
38#14583605C2212yes—
39#14583605C2211yescharacteristic, complemented
40#14583605C2211yescharacteristic, complemented
41#14583603—21no—
42#14583603—21no—
43#14583564C2211yescharacteristic, complemented
44#14583562—21no—
45#14583453—21no—
46#14583453—21no—
47#14583453—21no—
48#14583452C2211yescharacteristic
49#14583452C2211yescharacteristic
50C2×#13063324C2211yescharacteristic
51C2×#13063316C2211yescharacteristic
52C2×#13063305—21no—
53C2×#13063303—21no—
54C2×#13063303—21no—
55C4×#10621898C2211yescharacteristic
56#14583367C2211yescharacteristic
57#14583367C2211yescharacteristic
58C2×C4×Dic86C2211yescharacteristic
59C4×Q8×D43—21no—
60C2×C4×D172C2211yescharacteristic
61C2×#13063287C2211yescharacteristic
62C2×#13063287C2211yescharacteristic
63C2×C4⋊C4×D43—21no—
64#14583307C2212yescomplemented
65#14583307C2212yescomplemented
66#14583306C2212yescomplemented
67#14583306C2212yescomplemented
68#14583303C2212yescomplemented
69#14583300C2212yescomplemented
70#14583299C2212yescomplemented
71#14583296C2212yescomplemented
72#14583209C2212yescomplemented
73#14583205C2212yescomplemented
74#14583203C2212yescomplemented
75#14583203C2212yescomplemented
76#14583202C2212yes—
77#14583202C2212yes—
78#14583202C2212yescomplemented
79#14583198C2212yes—
80#14583198C2212yes—
81#14583198C2212yescomplemented
82#14583196C2212yes—
83#14583196C2212yes—
84#14583196C2212yescomplemented
85#14583196C2212yescomplemented
86#14583193C2212yescomplemented
87#14583188C2212yes—
88#14583188C2212yes—
89#14583188C2212yescomplemented
90#14583186C2212yes—
91#14583183C2212yescomplemented
92#14583178C2212yes—
93#14583178C2212yes—
94#14583178C2212yescomplemented
95#14583176C2212yes—
96#14583029C2212yescomplemented
97#14583027C2212yescomplemented
98#14583027C2212yescomplemented
99C8×Dic86C2212yescomplemented
100#14583012C2212yes—
101#14583010C2212yes—
102#14583010C2212yes—
103#14583001C2212yes—
104#14582998C2212yes—
105#14582998C2212yes—
106C4×#10621873C2212yes—
107#14582986C2212yes—
108#14582986C2212yes—
109C4×D344C2212yes—
110#14582981C2212yes—
111#14582981C2212yes—
112#14582942C2211yescharacteristic
113#14582942C2211yescharacteristic
114#14582941C2211yescharacteristic
115#14582939C2211yescharacteristic
116#14582939C2211yescharacteristic
117#14582923C2211yescharacteristic
118#14582922C2211yescharacteristic
119#14582922C2211yescharacteristic
120#14582905C2211yescharacteristic
121#14582903C2211yescharacteristic
122#14582903C2211yescharacteristic
123#14582901C2211yescharacteristic
124#14582898C2211yescharacteristic
125#14582898C2211yescharacteristic
126M16×Dic43C2211yescharacteristic
127M16×Dic43C2211yescharacteristic
128C43×#533C2211yescharacteristic
129C2×#125×C43C2211yescharacteristic
130C43×#501C2212yescomplemented
131C43×#501C2212yescomplemented
132C43×#499C2212yescomplemented
133C43×#499C2212yescomplemented
134C43×#428C2211yescharacteristic
135C43×#428C2211yescharacteristic
136C43×#428C2211yescharacteristic
137C43×#428C2211yescharacteristic
138C4×M16×C43C2211yescharacteristic
139C2×#10621898C2311yescharacteristic
140C22×Dic86—21no—
141C22×Dic86D411yescharacteristic
142C2×Q8×D43—21no—
143C22×D172C2311yescharacteristic
144C22×C4×D43—21no—
145C22×C4×D43—21no—
146C22×C4×D43—21no—
147#13063353Q818yescomplemented
148C2×#10621873C2312yes—
149C2×D344C2312yes—
150C2×#10621877C2311yescharacteristic
151C2×#10621877C2311yescharacteristic
152#13063324—21no—
153#13063324—21no—
154#13063324—21no—
155#13063324—21no—
156#13063324—21no—
157#13063324C2311yescharacteristic
158#13063324C2312yes—
159#13063324C2311yescharacteristic
160#13063324C2311yescharacteristic
161#13063324C2312yes—
162#13063324C2311yescharacteristic
163#13063323—21no—
164#13063323—21no—
165#13063323—21no—
166#13063316—21no—
167#13063316—21no—
168#13063316C2311yescharacteristic
169#13063316C2312yes—
170#13063316C2311yescharacteristic
171#13063316C2311yescharacteristic
172#13063316C2312yes—
173#13063316C2311yescharacteristic
174#13063315—21no—
175#13063315—21no—
176#13063315—21no—
177#13063315—21no—
178#13063315—21no—
179#13063315—21no—
180#13063305—21no—
181#13063305—22no—
182#13063305—22no—
183#13063305—22no—
184#13063305—22no—
185#13063305—21no—
186#13063305—21no—
187#13063303—21no—
188#13063303—21no—
189#13063303—22no—
190#13063303—22no—
191#13063303—22no—
192#13063303—22no—
193#13063303—21no—
194#13063303—21no—
195#13063303—21no—
196#13063303—21no—
197#13063303—22no—
198#13063303—22no—
199#13063303—22no—
200#13063303—22no—
201#13063302—21no—
202#13063302—21no—
203#13063302—21no—
204#13063302—21no—
205#13063301—21no—
206#13063301—21no—
207#13063301—21no—
208Q8×Dic43—21no—
209C4×Dic86—21no—
210C4×Dic86—21no—
211C4×Dic86—21no—
212C4×Dic86—21no—
213C4×Dic86D411yescharacteristic
214C4×Dic86D411yescharacteristic
215C4×Dic86D411yescharacteristic
216C4×Dic86D411yescharacteristic
217C4×Dic86C2311yescharacteristic
218C4×Dic86C2311yescharacteristic
219C4×Dic86C2311yescharacteristic
220C4×Dic86C2311yescharacteristic
221C4×Dic86C2311yescharacteristic
222C4×Dic86C2311yescharacteristic
223#13063290—21no—
224#13063290—21no—
225#13063290—21no—
226#13063290C2311yescharacteristic
227#13063290C2311yescharacteristic
228#13063290C2311yescharacteristic
229#13063290C2311yescharacteristic
230C4×D172—21no—
231C4×D172—21no—
232C4×D172C2311yescharacteristic
233C4×D172C2312yes—
234C4×D172C2312yes—
235C4×D172C2311yescharacteristic
236#13063287—21no—
237#13063287—21no—
238#13063287—21no—
239#13063287—21no—
240#13063287C2311yescharacteristic
241#13063287C2311yescharacteristic
242#13063287C2312yes—
243#13063287C2312yes—
244#13063287C2312yes—
245#13063287C2312yes—
246#13063287C2311yescharacteristic
247#13063287C2311yescharacteristic
248C4×C22⋊D43—21no—
249C4×C22⋊D43—21no—
250(C22⋊D43)⋊C4—21no—
251(C22⋊D43)⋊C4—21no—
252(C22⋊D43)⋊C4—21no—
253(C22⋊D43)⋊C4—21no—
254#13063284C2311yescharacteristic
255#13063282—21no—
256#13063282—21no—
257#13063282—21no—
258C2×C4⋊Dic43—21no—
259C2×C4⋊Dic43D411yescharacteristic
260C2×C4⋊Dic43C2311yescharacteristic
261C2×Dic43⋊C4—21no—
262C2×Dic43⋊C4—21no—
263C2×Dic43⋊C4D411yescharacteristic
264C2×Dic43⋊C4D411yescharacteristic
265C4⋊C4×D43—21no—
266C4⋊C4×D43—21no—
267C4⋊C4×D43—21no—
268C4⋊C4×D43—22no—
269C4⋊C4×D43—22no—
270C4⋊C4×D43—22no—
271C4⋊C4×D43—22no—
272C2×(C2×D43)⋊C4—21no—
273C2×(C2×D43)⋊C4—21no—
274C2×(C2×D43)⋊C4—21no—
275C2×C4×Dic43C2311yescharacteristic
276C2×C4×Dic43C2311yescharacteristic
277C42×D43—21no—
278C42×D43—21no—
279C42×D43—21no—
280#13063259C2312yes—
281#13063258C2312yes—
282#13063258C2312yes—
283#13063258C2312yes—
284#13063258C2312yes—
285#13063257C2312yes—
286#13063256C2312yes—
287#13063256C2312yes—
288#13063256C2312yes—
289#13063256C2312yes—
290C4⋊(C43⋊C8)C2312yes—
291C4⋊(C43⋊C8)C2312yes—
292Dic43⋊C8C2312yes—
293Dic43⋊C8C2312yes—
294Dic43⋊C8C2312yes—
295Dic43⋊C8C2312yes—
296#13063250C2312yes—
297#13063248C2312yes—
298#13063248C2312yes—
299#13063247C2312yes—
300#13063247C2312yes—
301#13063247C2312yes—
302#13063245C2312yes—
303#13063245C2312yes—
304#13063245C2312yes—
305#13063245C2312yes—
306#13063245C2312yes—
307#13063245C2312yes—
308#13063235C2312yes—
309#13063235C2312yes—
310C8×Dic43C2312yes—
311C8×Dic43C2312yes—
312C2×M16×C43C2311yescharacteristic
313C2×M16×C43C2311yescharacteristic
314C4⋊Q8×C43C2311yescharacteristic
315C4⋊Q8×C43C2311yescharacteristic
316#125×C43—21no—
317#125×C43—21no—
318#125×C43C2312yes—
319#125×C43C2311yescharacteristic
320#125×C43C2311yescharacteristic
321#125×C43C2312yes—
322C22⋊Q8×C43—21no—
323C22⋊Q8×C43—21no—
324C4×Q8×C43—21no—
325C4×Q8×C43—21no—
326#117×C43C2311yescharacteristic
327#117×C43C2311yescharacteristic
328C2×C4⋊C4×C43—21no—
329C2×C4⋊C4×C43—21no—
330C2×C4⋊C4×C43C2311yescharacteristic
331C2×C4⋊C4×C43C2311yescharacteristic
332C2×C42×C43C2311yescharacteristic
333#107×C43C2312yes—
334#107×C43C2312yes—
335#107×C43C2312yes—
336#107×C43C2312yes—
337#106×C43C2312yes—
338#106×C43C2312yes—
339#106×C43C2312yes—
340#106×C43C2312yes—
341#97×C43C2312yes—
342C4×C8×C43C2312yes—
343C23×D43—21no—
344C2×Q8×C43—21no—
345C2×Q8×C43—21no—
346C22×C4×C43—21no—
347C22×C4×C43—21no—
348C22×C4×C43C2×D411yescharacteristic
349C22×C4×C43C2×D411yescharacteristic
350C22×C4×C43C2411yescharacteristic
351C2×C22⋊D43—21no—
352C22×Dic43—21no—
353C22×Dic43C2×D411yescharacteristic
354C22×Dic43C2×D411yescharacteristic
355C22×Dic43C2×D411yescharacteristic
356C22×Dic43C2×D411yescharacteristic
357Q8×D43—44no—
358#10621898—22no—
359#10621898C2×Q814yes—
360C2×D172—21no—
361C2×D172—22no—
362C2×D172C2×Q814yescomplemented
363C2×D172C2411yescharacteristic
364C2×D172C2412yes—
365C2×C4×D43—21no—
366C2×C4×D43—21no—
367C2×C4×D43—21no—
368C2×C4×D43—21no—
369C2×C4×D43—22no—
370C2×C4×D43—22no—
371C2×C4×D43—21no—
372C2×C4×D43—22no—
373C2×C4×D43—22no—
374C2×C4×D43—21no—
375C2×C4×D43—21no—
376C2×C4×D43—22no—
377C2×C4×D43—22no—
378C2×C4×D43—44no—
379C2×C4×D43—82no—
380C2×C4×D43—82no—
381C2×Dic86—21no—
382C2×Dic86—21no—
383C2×Dic86—21no—
384C2×Dic86—21no—
385C2×Dic86—22no—
386C2×Dic86—22no—
387C2×Dic86—42no—
388C2×Dic86—82no—
389C2×Dic86C2×D411yescharacteristic
390C2×Dic86C2×D411yescharacteristic
391C2×Dic86C2×D411yescharacteristic
392C2×Dic86C2×D411yescharacteristic
393C2×Dic86C2411yescharacteristic
394M16×C43—22no—
395M16×C43C2×Q814yescomplemented
396C2×C8×C43C2412yes—
397C2×C8×C43C2412yes—
398C4⋊C4×C43—22no—
399C4⋊C4×C43—22no—
400C4⋊C4×C43—22no—
401C4⋊C4×C43—22no—
402C4⋊C4×C43—21no—
403C4⋊C4×C43—21no—
404C4⋊C4×C43—21no—
405C4⋊C4×C43—21no—
406C4⋊C4×C43—21no—
407C4⋊C4×C43—21no—
408C4⋊C4×C43—21no—
409C4⋊C4×C43—21no—
410C4⋊C4×C43C2412yes—
411C4⋊C4×C43C2412yes—
412C4⋊C4×C43C2411yescharacteristic
413C4⋊C4×C43C2411yescharacteristic
414C4⋊C4×C43C2411yescharacteristic
415C4⋊C4×C43C2411yescharacteristic
416C22⋊C4×C43—21no—
417C22⋊C4×C43—21no—
418C42×C43—21no—
419C42×C43—21no—
420C42×C43C2×D411yescharacteristic
421C42×C43C2×D411yescharacteristic
422C42×C43C2411yescharacteristic
423C42×C43C2411yescharacteristic
424C22⋊Dic43—21no—
425(C2×D43)⋊C4—22no—
426(C2×D43)⋊C4—22no—
427(C2×D43)⋊C4—21no—
428(C2×D43)⋊C4—21no—
429(C2×D43)⋊C4—22no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—22no—
433(C2×D43)⋊C4—21no—
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—21no—
436(C2×D43)⋊C4—21no—
437C4⋊Dic43—21no—
438C4⋊Dic43—22no—
439C4⋊Dic43—22no—
440C4⋊Dic43—21no—
441C4⋊Dic43—21no—
442C4⋊Dic43—21no—
443C4⋊Dic43—21no—
444C4⋊Dic43C2×D411yescharacteristic
445C4⋊Dic43C2×D411yescharacteristic
446C4⋊Dic43C2×D411yescharacteristic
447C4⋊Dic43C2×D411yescharacteristic
448C4⋊Dic43C2411yescharacteristic
449C4⋊Dic43C2411yescharacteristic
450C4⋊Dic43C2412yes—
451Dic43⋊C4—21no—
452Dic43⋊C4—21no—
453Dic43⋊C4—22no—
454Dic43⋊C4—22no—
455Dic43⋊C4—21no—
456Dic43⋊C4—21no—
457Dic43⋊C4—21no—
458Dic43⋊C4—21no—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—21no—
462Dic43⋊C4—21no—
463Dic43⋊C4—21no—
464Dic43⋊C4—21no—
465Dic43⋊C4—21no—
466Dic43⋊C4—21no—
467Dic43⋊C4—21no—
468Dic43⋊C4—21no—
469Dic43⋊C4C2×D411yescharacteristic
470Dic43⋊C4C2×D411yescharacteristic
471Dic43⋊C4C2×D411yescharacteristic
472Dic43⋊C4C2×D411yescharacteristic
473Dic43⋊C4C2×D411yescharacteristic
474Dic43⋊C4C2×D411yescharacteristic
475Dic43⋊C4C2×D411yescharacteristic
476Dic43⋊C4C2×D411yescharacteristic
477C4×Dic43—21no—
478C4×Dic43—21no—
479C4×Dic43—21no—
480C4×Dic43—21no—
481C4×Dic43—21no—
482C4×Dic43—21no—
483C4×Dic43—21no—
484C4×Dic43C2×D411yescharacteristic
485C4×Dic43C2×D411yescharacteristic
486C4×Dic43C2×D411yescharacteristic
487C4×Dic43C2×D411yescharacteristic
488C4×Dic43C2411yescharacteristic
489C4×Dic43C2411yescharacteristic
490C4×Dic43C2411yescharacteristic
491C4×Dic43C2411yescharacteristic
492#10621877—22no—
493#10621877—22no—
494C2×C43⋊C8C2412yes—
495C2×C43⋊C8C2412yes—
496D344C2×Q818yescomplemented
497#10621873C2×Q818yescomplemented
498C23×C43C22×D411yescharacteristic
499C22×D43—24no—
500C22×D43—21no—
501C22×D43—22no—
502C22×D43—42no—
503C22×D43—42no—
504Q8×C43—42no—
505Q8×C43—81no—
506C2×C4×C43—21no—
507C2×C4×C43—21no—
508C2×C4×C43—21no—
509C2×C4×C43—21no—
510C2×C4×C43—22no—
511C2×C4×C43—22no—
512C2×C4×C43—41no—
513C2×C4×C43—41no—
514C2×C4×C43—42no—
515C2×C4×C43—42no—
516C2×C4×C43C22×D411yescharacteristic
517C2×C4×C43C22×D411yescharacteristic
518C2×C4×C43C22×D411yescharacteristic
519C2×C4×C43C22×D411yescharacteristic
520C2×C4×C43C22×D411yescharacteristic
521C2×C4×C43C22×Q812yes—
522C2×C4×C432−1+412yes—
523C2×C4×C43C2511yescharacteristic
524C22⋊D43—24no—
525C2×Dic43—21no—
526C2×Dic43—22no—
527C2×Dic43—21no—
528C2×Dic43—21no—
529C2×Dic43—22no—
530C2×Dic43—41no—
531C2×Dic43—41no—
532C2×Dic43—41no—
533C2×Dic43—42no—
534C2×Dic43C22×D411yescharacteristic
535C2×Dic43C22×D411yescharacteristic
536C2×Dic43C22×D411yescharacteristic
537C2×Dic43C22×D411yescharacteristic
538C2×Dic43C22×D411yescharacteristic
539C2×Dic43C22×D411yescharacteristic
540C2×Dic43C22×D411yescharacteristic
541C2×Dic43C22×D411yescharacteristic
542D172—24no—
543D172—22no—
544D172—21no—
545D172C22×Q814yes—
546D172C22×Q812yes—
547C4×D43—24no—
548C4×D43—44no—
549C4×D43—42no—
550C4×D43—42no—
551C4×D43—44no—
552C4×D43—42no—
553C4×D43—81no—
554C4×D43—81no—
555C4×D43—82no—
556C4×D43—82no—
557C4×D43—81no—
558C4×D43—82no—
559C4×D43—82no—
560Dic86—21no—
561Dic86—22no—
562Dic86—22no—
563Dic86—41no—
564Dic86—41no—
565Dic86—42no—
566Dic86—42no—
567Dic86—81no—
568Dic86—81no—
569Dic86—82no—
570Dic86—82no—
571Dic86C22×Q812yes—
572C8×C43—22no—
573C8×C43C22×Q814yes—
574C43⋊C8—22no—
575C43⋊C8—22no—
576#61367—431nomaximal, Sylow
577C22×C43—21no—
578C22×C43—21no—
579C22×C43D4×Q812yes—
580C22×C43C23×D411yescharacteristic
581C2×D43—24no—
582C2×D43—22no—
583C2×D43—48no—
584C2×D43—42no—
585C2×D43—41no—
586C2×D43—42no—
587C2×D43—41no—
588C4×C43—21no—
589C4×C43—21no—
590C4×C43—21no—
591C4×C43—21no—
592C4×C43—42no—
593C4×C43—41no—
594C4×C43—41no—
595C4×C43—41no—
596C4×C43—41no—
597C4×C43—42no—
598C4×C43D4×Q812yes—
599C4×C43C23×Q811yescharacteristic
600C4×C43C2×2−1+411yescharacteristic
601Dic43—21no—
602Dic43—21no—
603Dic43—21no—
604Dic43—21no—
605Dic43—22no—
606Dic43—21no—
607Dic43—21no—
608Dic43—21no—
609Dic43—42no—
610Dic43—41no—
611Dic43—41no—
612Dic43#57512yes—
613Q8×#41—431no—
614C2×#554—431no—
615#3389—432no—
616#3389—432no—
617#3388—432no—
618#3388—432no—
619#3385—432no—
620#3384—432no—
621#3381—432no—
622#3380—432no—
623#3166—431no—
624#3166D4311yescharacteristic, complemented
625#3165—431no—
626#3080—431no—
627#3080—431no—
628#3079—431no—
629#3077—431no—
630#3077—431no—
631#3077—431no—
632Q8×M16—431no—
633C4×AGL(1,ℤ/8)—431no—
634C4×AGL(1,ℤ/8)—431no—
635C4×AGL(1,ℤ/8)—431no—
636C2×C43—22no—
637C2×C43C2×D4×Q811yescharacteristic
638C2×C43C2×#57511yescharacteristic
639C2×C43#358511yescharacteristic
640D43—42no—
641D43—44no—
642C2×AGL(1,ℤ/8)—431no—
643Q82—431no—
644#557—431no—
645#557—431no—
646#557—431no—
647#554—431no—
648#554—431no—
649#554—432no—
650#554—432no—
651#554—432no—
652#554—432no—
653#554—431no—
654#554—861no—
655#554—861no—
656#554—861no—
657#554—861no—
658#554—861no—
659#554—861no—
660#554—861no—
661D4×Q8—431no—
662D4×Q8—861no—
663#533—431no—
664#533—431no—
665#533—861no—
666#533—861no—
667#533—861no—
668#533C2×D4311yescharacteristic
669C2×C4⋊Q8—431no—
670C2×#125—431no—
671C2×#125C2×D4311yescharacteristic
672C2×C22⋊Q8—861no—
673C2×C22⋊Q8—861no—
674C2×C22⋊Q8—861no—
675C4×#41—431no—
676C4×#41—431no—
677C4×#41—431no—
678C2×C4×Q8—431no—
679C2×C4×Q8—861no—
680C2×C4×D4—431no—
681C2×C4×D4—431no—
682C2×C4×D4—431no—
683C22×C4⋊C4—861no—
684#501—432no—
685#501—432no—
686#501—432no—
687#501—432no—
688#501C2×D4312yescomplemented
689#501C2×D4312yescomplemented
690#500—432no—
691#499—432no—
692#499—432no—
693#499C2×D4312yescomplemented
694#499C2×D4312yescomplemented
695#498—432no—
696#479—432no—
697#479—432no—
698#479—432no—
699#479—432no—
700#478—432no—
701#478—432no—
702#478—432no—
703#478—432no—
704#478—432no—
705#478—432no—
706#478—432no—
707#478—432no—
708#478—432no—
709#478—432no—
710#477—432no—
711#476—432no—
712#476—432no—
713#476—432no—
714#476—432no—
715#475—432no—
716#474—432no—
717#474—432no—
718#474—432no—
719#474—432no—
720#446—432no—
721#446—432no—
722#446—432no—
723C8×Q8—432no—
724#442—432no—
725#442—432no—
726#442—432no—
727#440—432no—
728#440—432no—
729#440—432no—
730C4×SD16—432no—
731C4×SD16—432no—
732C4×SD16—432no—
733C4×D8—432no—
734C4×D8—432no—
735C4×D8—432no—
736#428—431no—
737#428—431no—
738#428—431no—
739#428—431no—
740#428—431no—
741#428C2×D4311yescharacteristic
742#428C2×D4311yescharacteristic
743#428C2×D4311yescharacteristic
744#428C2×D4311yescharacteristic
745#423—431no—
746#423—431no—
747#423—431no—
748#418—431no—
749#418—431no—
750#418—431no—
751#417—431no—
752#417—431no—
753#417—431no—
754C4×M16—431no—
755C4×M16—431no—
756C4×M16C2×D4311yescharacteristic
757C43#6136711yescharacteristic, complemented, Sylow
758C2×#41—431no—
759C22×Q8—431no—
760C22×Q8—861no—
761C22×Q8—861no—
762C22×D4—431no—
763C23×C4—861no—
764C23×C4—861no—
765C23×C4—861no—
766AGL(1,ℤ/8)—438no—
767C2×SD16—432no—
768C2×D8—432no—
769C2×M16—431no—
770C2×M16—431no—
771C2×M16C22×D4311yescharacteristic
772C2×M16C22×D4311yescharacteristic
773C4⋊Q8—432no—
774C4⋊Q8—432no—
775C4⋊Q8—431no—
776C4⋊Q8—431no—
777C4⋊Q8—431no—
778C4⋊Q8—431no—
779C4⋊Q8—861no—
780C4⋊Q8—861no—
781C4⋊Q8—861no—
782C4⋊Q8—861no—
783C4⋊Q8—861no—
784C4⋊Q8—861no—
785C4⋊Q8—861no—
786C4⋊Q8—861no—
787C4⋊Q8C22×D4311yescharacteristic
788C4⋊Q8C22×D4311yescharacteristic
789#125—21no—
790#125—21no—
791#125—432no—
792#125—432no—
793#125—431no—
794#125—431no—
795#125—431no—
796#125—431no—
797#125—861no—
798#125—861no—
799#125—861no—
800#125—861no—
801#125—861no—
802#125—861no—
803#125—861no—
804#125—861no—
805#125C22×D4312yes—
806#125C22×D4312yes—
807#125C22×D4311yescharacteristic
808#125C22×D4311yescharacteristic
809C22⋊Q8—21no—
810C22⋊Q8—21no—
811C22⋊Q8—861no—
812C22⋊Q8—861no—
813C22⋊Q8—861no—
814C22⋊Q8—861no—
815C22⋊Q8—862no—
816C22⋊Q8—862no—
817C22⋊Q8—862no—
818C22⋊Q8—862no—
819C22⋊Q8—862no—
820C22⋊Q8—862no—
821C22⋊Q8—862no—
822C22⋊Q8—862no—
823C22⋊Q8—861no—
824C22⋊Q8—861no—
825C22⋊Q8—861no—
826C22⋊Q8—861no—
827C22⋊Q8—861no—
828C22⋊Q8—861no—
829C22⋊Q8—862no—
830C22⋊Q8—862no—
831C22⋊Q8—862no—
832C22⋊Q8—862no—
833C22⋊Q8—861no—
834C22⋊Q8—861no—
835C22⋊Q8—861no—
836C22⋊Q8—861no—
837C22⋊Q8—861no—
838C22⋊Q8—861no—
839C4×Q8—21no—
840C4×Q8—21no—
841C4×Q8—431no—
842C4×Q8—431no—
843C4×Q8—431no—
844C4×Q8—431no—
845C4×Q8—431no—
846C4×Q8—431no—
847C4×Q8—431no—
848C4×Q8—431no—
849C4×Q8—431no—
850C4×Q8—431no—
851C4×Q8—431no—
852C4×Q8—431no—
853C4×Q8—431no—
854C4×Q8—431no—
855C4×Q8—861no—
856C4×Q8—861no—
857C4×Q8—861no—
858C4×Q8—861no—
859C4×Q8—861no—
860C4×Q8—861no—
861C4×Q8—861no—
862C4×Q8—861no—
863C4×D4—432no—
864C4×D4—432no—
865C4×D4—432no—
866C4×D4—432no—
867C4×D4—431no—
868C4×D4—431no—
869C4×D4—431no—
870C4×D4—431no—
871C4×D4—432no—
872C4×D4—432no—
873C4×D4—431no—
874C4×D4—431no—
875C4×D4—861no—
876C4×D4—861no—
877C4×D4—861no—
878C4×D4—861no—
879C4×D4—861no—
880C4×D4—861no—
881C4×D4—861no—
882C4×D4—861no—
883C4×D4—861no—
884C4×D4—861no—
885C4×D4—861no—
886C4×D4—861no—
887#117—431no—
888#117—861no—
889#117—861no—
890#117—861no—
891#117C22×D4311yescharacteristic
892#117C22×D4311yescharacteristic
893C2×C4⋊C4—21no—
894C2×C4⋊C4—21no—
895C2×C4⋊C4—431no—
896C2×C4⋊C4—431no—
897C2×C4⋊C4—431no—
898C2×C4⋊C4—431no—
899C2×C4⋊C4—862no—
900C2×C4⋊C4—862no—
901C2×C4⋊C4—862no—
902C2×C4⋊C4—862no—
903C2×C4⋊C4—861no—
904C2×C4⋊C4—861no—
905C2×C4⋊C4—861no—
906C2×C4⋊C4—861no—
907C2×C4⋊C4—861no—
908C2×C4⋊C4—861no—
909C2×C4⋊C4C22×D4311yescharacteristic
910C2×C4⋊C4C22×D4311yescharacteristic
911C2×C22⋊C4—861no—
912C2×C22⋊C4—861no—
913C2×C22⋊C4—861no—
914C2×C42—431no—
915C2×C42—431no—
916C2×C42—861no—
917C2×C42—861no—
918C2×C42—861no—
919C2×C42C22×D4311yescharacteristic
920#107—432no—
921#107—432no—
922#107—432no—
923#107—432no—
924#107—432no—
925#107C22×D4312yes—
926#107C22×D4312yes—
927#107C22×D4312yes—
928#107C22×D4312yes—
929#106—432no—
930#106—432no—
931#106—432no—
932#106—432no—
933#106—432no—
934#106C22×D4312yes—
935#106C22×D4312yes—
936#106C22×D4312yes—
937#106C22×D4312yes—
938C4⋊C8—432no—
939C4⋊C8—432no—
940C4⋊C8—432no—
941C4⋊C8—432no—
942C4⋊C8—432no—
943C4⋊C8—432no—
944#103—432no—
945#103—432no—
946#103—432no—
947#102—432no—
948#102—432no—
949#102—432no—
950#102—432no—
951#102—432no—
952#102—432no—
953#102—432no—
954#102—432no—
955#102—432no—
956#97—432no—
957#97—432no—
958#97C22×D4312yes—
959C4×C8—432no—
960C4×C8—432no—
961C4×C8C22×D4312yes—
962C24—861no—
963#41—434no—
964#41—862no—
965C2×Q8—21no—
966C2×Q8—21no—
967C2×Q8—431no—
968C2×Q8—431no—
969C2×Q8—431no—
970C2×Q8—431no—
971C2×Q8—431no—
972C2×Q8—861no—
973C2×Q8—861no—
974C2×Q8—862no—
975C2×Q8—862no—
976C2×Q8—861no—
977C2×Q8—861no—
978C2×Q8—3442no—
979C2×Q8—1722no—
980C2×Q8—1724no—
981C2×D4—434no—
982C2×D4—431no—
983C2×D4—432no—
984C2×D4—861no—
985C2×D4—861no—
986C2×D4—862no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—431no—
990C22×C4—431no—
991C22×C4—431no—
992C22×C4—431no—
993C22×C4—861no—
994C22×C4—861no—
995C22×C4—862no—
996C22×C4—862no—
997C22×C4—861no—
998C22×C4—861no—
999C22×C4—862no—
1000C22×C4—862no—
1001C22×C4—861no—
1002C22×C4—861no—
1003C22×C4—861no—
1004C22×C4—862no—
1005C22×C4—862no—
1006C22×C4—861no—
1007C22×C4—3442no—
1008C22×C4—3442no—
1009C22×C4—1724no—
1010C22×C4D4×D4311yescharacteristic
1011C22×C4D4×D4311yescharacteristic
1012C22×C4C23×D4311yescharacteristic
1013SD16—438no—
1014D8—438no—
1015M16—22no—
1016M16—862no—
1017M16—862no—
1018M16Q8×D4314yescomplemented
1019C2×C8—432no—
1020C2×C8—432no—
1021C2×C8C23×D4312yes—
1022C2×C8C23×D4312yes—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—431no—
1036C4⋊C4—431no—
1037C4⋊C4—431no—
1038C4⋊C4—431no—
1039C4⋊C4—431no—
1040C4⋊C4—431no—
1041C4⋊C4—431no—
1042C4⋊C4—431no—
1043C4⋊C4—431no—
1044C4⋊C4—431no—
1045C4⋊C4—431no—
1046C4⋊C4—431no—
1047C4⋊C4—431no—
1048C4⋊C4—431no—
1049C4⋊C4—432no—
1050C4⋊C4—862no—
1051C4⋊C4—862no—
1052C4⋊C4—862no—
1053C4⋊C4—862no—
1054C4⋊C4—861no—
1055C4⋊C4—861no—
1056C4⋊C4—861no—
1057C4⋊C4—861no—
1058C4⋊C4—861no—
1059C4⋊C4—861no—
1060C4⋊C4—862no—
1061C4⋊C4—862no—
1062C4⋊C4—861no—
1063C4⋊C4—861no—
1064C4⋊C4—861no—
1065C4⋊C4—861no—
1066C4⋊C4—861no—
1067C4⋊C4—861no—
1068C4⋊C4—861no—
1069C4⋊C4—861no—
1070C4⋊C4—861no—
1071C4⋊C4—861no—
1072C4⋊C4—861no—
1073C4⋊C4—861no—
1074C4⋊C4—861no—
1075C4⋊C4C23×D4311yescharacteristic
1076C4⋊C4C23×D4311yescharacteristic
1077C4⋊C4C23×D4311yescharacteristic
1078C4⋊C4C23×D4311yescharacteristic
1079C4⋊C4C23×D4312yes—
1080C4⋊C4C23×D4312yes—
1081C22⋊C4—21no—
1082C22⋊C4—21no—
1083C22⋊C4—862no—
1084C22⋊C4—862no—
1085C22⋊C4—862no—
1086C22⋊C4—862no—
1087C22⋊C4—861no—
1088C22⋊C4—861no—
1089C22⋊C4—861no—
1090C22⋊C4—861no—
1091C22⋊C4—861no—
1092C22⋊C4—862no—
1093C22⋊C4—862no—
1094C22⋊C4—861no—
1095C22⋊C4—861no—
1096C42—21no—
1097C42—21no—
1098C42—431no—
1099C42—431no—
1100C42—431no—
1101C42—431no—
1102C42—431no—
1103C42—431no—
1104C42—431no—
1105C42—431no—
1106C42—861no—
1107C42—861no—
1108C42—861no—
1109C42—861no—
1110C42—861no—
1111C42—861no—
1112C42—861no—
1113C42D4×D4311yescharacteristic
1114C42D4×D4311yescharacteristic
1115C42C23×D4311yescharacteristic
1116C42C23×D4311yescharacteristic
1117C23—864no—
1118C23—861no—
1119C23—862no—
1120C23—1722no—
1121C23—1722no—
1122C23C2×D4×D4311yescharacteristic
1123Q8—42no—
1124Q8—81no—
1125Q8—432no—
1126Q8—862no—
1127Q8—862no—
1128Q8—861no—
1129Q8—3442no—
1130Q8—3442no—
1131Q8—3441no—
1132Q8—3441no—
1133Q8—1721no—
1134Q8—1721no—
1135Q8—1722no—
1136Q8—1722no—
1137D4—432no—
1138D4—434no—
1139D4—864no—
1140D4—864no—
1141D4—862no—
1142D4—861no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—431no—
1154C2×C4—431no—
1155C2×C4—431no—
1156C2×C4—431no—
1157C2×C4—431no—
1158C2×C4—431no—
1159C2×C4—431no—
1160C2×C4—431no—
1161C2×C4—862no—
1162C2×C4—861no—
1163C2×C4—864no—
1164C2×C4—861no—
1165C2×C4—861no—
1166C2×C4—862no—
1167C2×C4—3442no—
1168C2×C4—3442no—
1169C2×C4—3441no—
1170C2×C4—3442no—
1171C2×C4—3442no—
1172C2×C4—3441no—
1173C2×C4—3441no—
1174C2×C4—1722no—
1175C2×C4—1724no—
1176C2×C4—1722no—
1177C2×C4—1724no—
1178C2×C4—1722no—
1179C2×C4—1721no—
1180C2×C4—1721no—
1181C2×C4—1721no—
1182C2×C4—1722no—
1183C2×C4C2×D4×D4311yescharacteristic
1184C2×C4C2×D4×D4311yescharacteristic
1185C2×C4C2×D4×D4311yescharacteristic
1186C2×C4C2×D4×D4311yescharacteristic
1187C2×C4C2×D4×D4311yescharacteristic
1188C2×C4C2×Q8×D4312yes—
1189C2×C4#1306337312yes—
1190C2×C4C24×D4311yescharacteristic
1191C8—22no—
1192C8—862no—
1193C8—862no—
1194C8C2×Q8×D4314yes—
1195C22—21no—
1196C22—21no—
1197C22—862no—
1198C22—864no—
1199C22—1728no—
1200C22—1721no—
1201C22—1722no—
1202C22—1722no—
1203C22—1721no—
1204C22#1458356412yes—
1205C22C22×D4×D4311yescharacteristic
1206C4—21no—
1207C4—21no—
1208C4—21no—
1209C4—21no—
1210C4—42no—
1211C4—41no—
1212C4—41no—
1213C4—42no—
1214C4—41no—
1215C4—41no—
1216C4—432no—
1217C4—861no—
1218C4—861no—
1219C4—861no—
1220C4—862no—
1221C4—861no—
1222C4—861no—
1223C4—861no—
1224C4—861no—
1225C4—1721no—
1226C4—1722no—
1227C4—1721no—
1228C4#1458356412yes—
1229C4C22×Q8×D4311yescharacteristic
1230C4C2×#1306337311yescharacteristic
1231C2—22no—
1232C2—1724no—
1233C2—1722no—
1234C2C2×#1458356411yescharacteristic
1235C2#575×D4311yescharacteristic
1236C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3166C2
socleC22×C43C23×D4
prime radicalC2×#13063353C22
hypercenter#3166D43
hypocenterC43#61367
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
1. #19148173C2semidirect
2. C2×#14583605C2semidirect
3. #19147556C2semidirect
4. #19147550C2semidirect
5. #19147546C2semidirect
6. #19147535C2semidirect
7. #19147502C2semidirect
8. #19147491C2semidirect
9. #19147467C2semidirect
10. #19147459C2semidirect
11. #19145145C2semidirect
12. #19145139C2semidirect
13. #19144416C2semidirect
14. #19144413C2semidirect
15. #19144408C2semidirect
16. #19144391C2semidirect
17. #19144391C2semidirect
18. #19144388C2semidirect
19. M16×Dic86C2semidirect
23. C43×#3166C2semidirect
25. #14583629C22semidirect
26. #14583626C22semidirect
27. #14583626C22semidirect
28. #14583624C22semidirect
29. #14583610C22semidirect
39. #14583605C22semidirect
40. #14583605C22semidirect
43. #14583564C22semidirect
64. #14583307C22semidirect
65. #14583307C22semidirect
66. #14583306C22semidirect
67. #14583306C22semidirect
68. #14583303C22semidirect
69. #14583300C22semidirect
70. #14583299C22semidirect
71. #14583296C22semidirect
72. #14583209C22semidirect
73. #14583205C22semidirect
74. #14583203C22semidirect
75. #14583203C22semidirect
78. #14583202C22semidirect
81. #14583198C22semidirect
84. #14583196C22semidirect
85. #14583196C22semidirect
86. #14583193C22semidirect
89. #14583188C22semidirect
91. #14583183C22semidirect
94. #14583178C22semidirect
96. #14583029C22semidirect
97. #14583027C22semidirect
98. #14583027C22semidirect
99. C8×Dic86C22semidirect
130. C43×#501C22semidirect
131. C43×#501C22semidirect
132. C43×#499C22semidirect
133. C43×#499C22semidirect
147. #13063353Q8semidirect
362. C2×D172C2×Q8semidirect
395. M16×C43C2×Q8semidirect
496. D344C2×Q8semidirect
497. #10621873C2×Q8semidirect
624. #3166D43semidirect
688. #501C2×D43semidirect
689. #501C2×D43semidirect
693. #499C2×D43semidirect
694. #499C2×D43semidirect
757. C43#61367semidirect
1018. M16Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191481732
C2×#145836052
#191475562
#191475502
#191475462
#191475352
#191475022
#191474912
#191474672
#191474592
#191451452
#191451392
#191444162
#191444132
#191444082
#191443912
#191443882
M16×Dic862
C4×#130633532
#191434022
C43×#31662
#6136743