Finite Group Databasebeta

← #25976515

Subgroups — #25976515

Order 11008.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic86C211yesmaximal, characteristic, complemented
2C2×#14583621C211yesmaximal, characteristic, complemented
3#19147442C212yesmaximal, complemented
4#19147433C212yesmaximal, complemented
5#19147427C212yesmaximal, complemented
6#19147418C212yesmaximal, complemented
7#19147336C212yesmaximal, complemented
8#19147314C212yesmaximal, complemented
9#19147281C212yesmaximal, complemented
10#19147245C212yesmaximal, complemented
11#19144983C211yesmaximal, characteristic, complemented
12#19144982C211yesmaximal, characteristic, complemented
13#19144973C211yesmaximal, characteristic, complemented
14#19144400C211yesmaximal, characteristic, complemented
15#19144399C211yesmaximal, characteristic, complemented
16#19144391C211yesmaximal, characteristic, complemented
17#19144091C211yesmaximal, characteristic
18#19144089C211yesmaximal, characteristic
19#19144080C211yesmaximal, characteristic, complemented
20M16×Dic86C211yesmaximal, characteristic, complemented
21#19143419C211yesmaximal, characteristic, complemented
22#19143408C211yesmaximal, characteristic
23C4×#137×C43C211yesmaximal, characteristic, complemented
24C2×#13063355C2211yescharacteristic
25C2×#13063350C2211yescharacteristic
26Q8×Dic86C2211yescharacteristic, complemented
27#14583628C2211yescharacteristic, complemented
28#14583625C2211yescharacteristic, complemented
29#14583625C2211yescharacteristic, complemented
30#14583621—21no—
31#14583621—21no—
32#14583621—21no—
33#14583621—21no—
34#14583621C2212yes—
35#14583621C2212yes—
36#14583621C2212yes—
37#14583621C2212yes—
38#14583608—21no—
39#14583608—21no—
40#14583608C2211yescharacteristic, complemented
41#14583608C2211yescharacteristic, complemented
42#14583606—21no—
43#14583606C2211yescharacteristic, complemented
44D4×Dic86—21no—
45D4×Dic86C2211yescharacteristic, complemented
46#14583456—21no—
47#14583456C2211yescharacteristic
48#14583452—21no—
49#14583452—21no—
50#14583452C2211yescharacteristic
51#14583452C2211yescharacteristic
52C2×#13063323C2211yescharacteristic
53C2×#13063320—21no—
54C2×#13063319—21no—
55C2×#13063314C2211yescharacteristic
56C2×#13063313C2211yescharacteristic
57C2×#13063303—21no—
58#41×Dic43C2211yescharacteristic
59#41×Dic43C2211yescharacteristic
60C2×C4×Dic86—21no—
61C2×C4×Dic86C2211yescharacteristic
62C2×#13063290C2211yescharacteristic
63C2×#13063287C2211yescharacteristic
64C2×#13063282—21no—
65#14583266C2212yescomplemented
66#14583266C2212yescomplemented
67#14583260C2212yes—
68#14583260C2212yes—
69#14583259C2212yes—
70#14583259C2212yes—
71#14583255C2212yes—
72#14583255C2212yes—
73#14583254C2212yes—
74#14583254C2212yes—
75#14583248C2212yescomplemented
76#14583248C2212yescomplemented
77#14583209C2212yescomplemented
78#14583206C2212yescomplemented
79#14583206C2212yescomplemented
80#14583205C2212yescomplemented
81#14583202C2212yes—
82#14583198C2212yes—
83#14583194C2212yescomplemented
84#14583193C2212yescomplemented
85#14583188C2212yes—
86#14583184C2212yescomplemented
87#14583183C2212yescomplemented
88#14583178C2212yes—
89#14583123C2212yes—
90#14583123C2212yes—
91#14583121C2212yes—
92#14583121C2212yes—
93#14583116C2212yes—
94#14583116C2212yes—
95#14583114C2212yes—
96#14583114C2212yes—
97#14583107C2212yescomplemented
98#14583107C2212yescomplemented
99#14583102C2212yescomplemented
100#14583102C2212yescomplemented
101#14583029C2212yescomplemented
102#14583027C2212yescomplemented
103#14583027C2212yescomplemented
104C8×Dic86C2212yescomplemented
105#14583008C2212yes—
106#14583003C2212yescomplemented
107#14583002C2212yes—
108#14582996C2212yescomplemented
109#14582991C2212yescomplemented
110#14582990C2212yescomplemented
111#14582984C2212yes—
112#14582979C2212yes—
113#14582939C2211yescharacteristic
114#14582939C2211yescharacteristic
115#14582923C2211yescharacteristic
116#14582922C2211yescharacteristic
117#14582922C2211yescharacteristic
118#14582909C2211yescharacteristic
119#14582909C2211yescharacteristic
120#14582908C2211yescharacteristic
121#14582908C2211yescharacteristic
122#14582907C2211yescharacteristic
123#14582905C2211yescharacteristic
124#14582905C2211yescharacteristic
125#14582903C2211yescharacteristic
126M16×Dic43C2211yescharacteristic
127M16×Dic43C2211yescharacteristic
128C2×#137×C43C2211yescharacteristic
129C4×#41×C43C2211yescharacteristic
130C2×C4×Q8×C43C2211yescharacteristic
131C43×#441C2212yescomplemented
132C43×#440C2212yescomplemented
133C4×Q16×C43C2212yescomplemented
134C4×SD16×C43C2212yescomplemented
135C43×#428C2211yescharacteristic
136C43×#419C2211yescharacteristic
137C43×#417C2211yescharacteristic
138C4×M16×C43C2211yescharacteristic
139C22×Dic86—21no—
140C22×Dic86D411yescharacteristic
141C22×Dic86C2311yescharacteristic
142C22×D172C2311yescharacteristic
143C22×C4×D43—21no—
144#13063355—24no—
145#13063350—24no—
146C2×#10621885C2312yes—
147C2×#10621883C2312yes—
148C2×#10621884C2312yes—
149C2×#10621882C2312yes—
150C2×#10621877C2311yescharacteristic
151C2×#10621877C2311yescharacteristic
152#13063325—21no—
153#13063325—21no—
154#13063325C2311yescharacteristic
155#13063325C2311yescharacteristic
156#13063324—21no—
157#13063324—21no—
158#13063324—21no—
159#13063324—21no—
160#13063324C2311yescharacteristic
161#13063324C2311yescharacteristic
162#13063324C2311yescharacteristic
163#13063324C2311yescharacteristic
164#13063323—21no—
165#13063323—21no—
166#13063323C2312yes—
167#13063323C2312yes—
168#13063320—22no—
169#13063320—22no—
170#13063320—22no—
171#13063320—22no—
172#13063319—22no—
173#13063319—22no—
174#13063319—22no—
175#13063319—22no—
176#13063317—21no—
177#13063317—21no—
178#13063317C2311yescharacteristic
179#13063317C2311yescharacteristic
180#13063316—21no—
181#13063316—21no—
182#13063316—21no—
183#13063316—21no—
184#13063316C2311yescharacteristic
185#13063316C2311yescharacteristic
186#13063316C2311yescharacteristic
187#13063316C2311yescharacteristic
188#13063314—21no—
189#13063314—21no—
190#13063314C2312yes—
191#13063314C2312yes—
192#13063313—21no—
193#13063313—21no—
194#13063313C2312yes—
195#13063313C2312yes—
196#13063304—21no—
197#13063304—21no—
198#13063304—21no—
199#13063304—21no—
200#13063304—21no—
201#13063304—21no—
202#13063303—22no—
203#13063303—22no—
204#13063303—22no—
205#13063303—22no—
206#13063302—21no—
207#13063302—21no—
208#13063302—21no—
209#13063302—21no—
210#13063302—21no—
211#13063302—21no—
212#13063302—21no—
213#13063302—21no—
214#13063302—21no—
215#13063302—21no—
216#13063302—21no—
217#13063302—21no—
218Q8×Dic43C2311yescharacteristic
219Q8×Dic43C2311yescharacteristic
220Q8×Dic43C2311yescharacteristic
221Q8×Dic43C2311yescharacteristic
222C4×Dic86—21no—
223C4×Dic86—21no—
224C4×Dic86—21no—
225C4×Dic86—21no—
226C4×Dic86—21no—
227C4×Dic86—21no—
228C4×Dic86—21no—
229C4×Dic86—21no—
230C4×Dic86—21no—
231C4×Dic86—21no—
232C4×Dic86D411yescharacteristic
233C4×Dic86D411yescharacteristic
234C4×Dic86D411yescharacteristic
235C4×Dic86D411yescharacteristic
236C4×Dic86C2311yescharacteristic
237C4×Dic86C2311yescharacteristic
238C4×Dic86C2311yescharacteristic
239C4×Dic86C2311yescharacteristic
240#13063290—21no—
241#13063290—21no—
242#13063290C2312yes—
243#13063290C2312yes—
244D4×Dic43—21no—
245D4×Dic43—21no—
246D4×Dic43—21no—
247D4×Dic43—21no—
248D4×Dic43C2311yescharacteristic
249D4×Dic43C2311yescharacteristic
250D4×Dic43C2311yescharacteristic
251D4×Dic43C2311yescharacteristic
252#13063287—21no—
253#13063287—21no—
254#13063287C2312yes—
255#13063287C2312yes—
256#13063284—21no—
257#13063284—21no—
258#13063284C2311yescharacteristic
259#13063284C2311yescharacteristic
260#13063282—22no—
261#13063282—22no—
262#13063282—22no—
263#13063282—22no—
264C2×C4⋊Dic43—21no—
265C2×C4⋊Dic43D411yescharacteristic
266C2×Dic43⋊C4—21no—
267C2×Dic43⋊C4—21no—
268C2×Dic43⋊C4—21no—
269C2×Dic43⋊C4—21no—
270C2×Dic43⋊C4—21no—
271C2×Dic43⋊C4D411yescharacteristic
272C2×Dic43⋊C4D411yescharacteristic
273C2×(C2×D43)⋊C4—21no—
274C2×(C2×D43)⋊C4—21no—
275C2×(C2×D43)⋊C4—21no—
276C2×(C2×D43)⋊C4—21no—
277C2×(C2×D43)⋊C4—21no—
278C2×C4×Dic43—21no—
279C2×C4×Dic43—21no—
280C2×C4×Dic43—21no—
281C2×C4×Dic43C2311yescharacteristic
282C2×C4×Dic43C2311yescharacteristic
283#13063258C2312yes—
284#13063258C2312yes—
285#13063256C2312yes—
286#13063256C2312yes—
287C4⋊(C43⋊C8)C2312yes—
288C4⋊(C43⋊C8)C2312yes—
289Dic43⋊C8C2312yes—
290Dic43⋊C8C2312yes—
291Dic43⋊C8C2312yes—
292Dic43⋊C8C2312yes—
293#13063250C2312yes—
294#13063250C2312yes—
295#13063250C2312yes—
296#13063250C2312yes—
297#13063249C2312yes—
298#13063249C2312yes—
299#13063249C2312yes—
300#13063249C2312yes—
301#13063248C2312yes—
302#13063248C2312yes—
303#13063247C2312yes—
304#13063247C2312yes—
305#13063247C2312yes—
306#13063247C2312yes—
307#13063245C2312yes—
308#13063245C2312yes—
309#13063235C2312yes—
310#13063235C2312yes—
311C8×Dic43C2312yes—
312C8×Dic43C2312yes—
313C2×#41×C43C2311yescharacteristic
314C22×Q8×C43C2311yescharacteristic
315#137×C43—24no—
316C2×Q16×C43C2312yes—
317C2×SD16×C43C2312yes—
318C2×M16×C43C2311yescharacteristic
319C2×M16×C43C2311yescharacteristic
320C4×Q8×C43—21no—
321C4×Q8×C43—21no—
322C4×Q8×C43C2312yes—
323C4×Q8×C43C2312yes—
324C4×Q8×C43C2311yescharacteristic
325C4×Q8×C43C2311yescharacteristic
326C4×D4×C43—21no—
327C4×D4×C43—21no—
328C4×D4×C43C2311yescharacteristic
329C4×D4×C43C2311yescharacteristic
330#117×C43—21no—
331#117×C43C2311yescharacteristic
332C2×C4⋊C4×C43—21no—
333C2×C4⋊C4×C43C2311yescharacteristic
334C2×C42×C43—21no—
335C2×C42×C43—21no—
336C2×C42×C43C2311yescharacteristic
337#107×C43C2312yes—
338#106×C43C2312yes—
339#103×C43C2312yes—
340#103×C43C2312yes—
341#103×C43C2312yes—
342#102×C43C2312yes—
343#97×C43C2312yes—
344C4×C8×C43C2312yes—
345C23×D43—21no—
346#41×C43—22no—
347#41×C43#4114yes—
348C2×Q8×C43—21no—
349C2×Q8×C43—22no—
350C2×Q8×C43—22no—
351C2×Q8×C43C2412yes—
352C2×Q8×C43C2411yescharacteristic
353C2×D4×C43—21no—
354C2×D4×C43C2411yescharacteristic
355C22×C4×C43—21no—
356C22×C4×C43—21no—
357C22×C4×C43—21no—
358C22×C4×C43—21no—
359C22×C4×C43—21no—
360C22×C4×C43C2×D411yescharacteristic
361C22×C4×C43C2×D411yescharacteristic
362C22×C4×C43C2411yescharacteristic
363C22×Dic43—21no—
364C22×Dic43—21no—
365C22×Dic43—21no—
366C22×Dic43—21no—
367C22×Dic43—21no—
368C22×Dic43C2×D411yescharacteristic
369C22×Dic43C2×D411yescharacteristic
370C22×Dic43C2×D411yescharacteristic
371C22×Dic43C2×D411yescharacteristic
372C2×D172—21no—
373C2×D172—22no—
374C2×D172—22no—
375C2×D172C2412yes—
376C2×C4×D43—22no—
377C2×C4×D43—22no—
378C2×C4×D43—44no—
379C2×Dic86—22no—
380C2×Dic86—22no—
381C2×Dic86—21no—
382C2×Dic86—21no—
383C2×Dic86—21no—
384C2×Dic86—21no—
385C2×Dic86—21no—
386C2×Dic86—21no—
387C2×Dic86—21no—
388C2×Dic86—42no—
389C2×Dic86—44no—
390C2×Dic86C2×D411yescharacteristic
391C2×Dic86C2×D411yescharacteristic
392C2×Dic86C2×D411yescharacteristic
393C2×Dic86C2×D411yescharacteristic
394C2×Dic86C2412yes—
395Q16×C43—24no—
396SD16×C43—24no—
397M16×C43—22no—
398M16×C43—22no—
399C2×C8×C43C2412yes—
400C2×C8×C43C2412yes—
401C4⋊C4×C43—22no—
402C4⋊C4×C43—22no—
403C4⋊C4×C43—21no—
404C4⋊C4×C43—21no—
405C4⋊C4×C43—21no—
406C4⋊C4×C43C2412yes—
407C4⋊C4×C43C2411yescharacteristic
408C4⋊C4×C43C2411yescharacteristic
409C22⋊C4×C43—21no—
410C22⋊C4×C43—21no—
411C22⋊C4×C43—21no—
412C42×C43—21no—
413C42×C43—21no—
414C42×C43—21no—
415C42×C43—22no—
416C42×C43—22no—
417C42×C43C2×D411yescharacteristic
418C42×C43C2×D411yescharacteristic
419C42×C43C2411yescharacteristic
420C42×C43C2411yescharacteristic
421C22⋊Dic43—21no—
422C22⋊Dic43—21no—
423C22⋊Dic43—21no—
424C22⋊Dic43—21no—
425C22⋊Dic43—21no—
426C22⋊Dic43—21no—
427#10621885—24no—
428#10621884—24no—
429#10621883—24no—
430#10621882—24no—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—22no—
433(C2×D43)⋊C4—22no—
434(C2×D43)⋊C4—22no—
435(C2×D43)⋊C4—22no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—22no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441C4⋊Dic43—21no—
442C4⋊Dic43—21no—
443C4⋊Dic43—21no—
444C4⋊Dic43—21no—
445C4⋊Dic43—21no—
446C4⋊Dic43—21no—
447C4⋊Dic43—21no—
448C4⋊Dic43—21no—
449C4⋊Dic43—21no—
450C4⋊Dic43—21no—
451C4⋊Dic43C2×D411yescharacteristic
452C4⋊Dic43C2×D411yescharacteristic
453C4⋊Dic43C2×D411yescharacteristic
454C4⋊Dic43C2×D411yescharacteristic
455C4⋊Dic43C2411yescharacteristic
456C4⋊Dic43C2411yescharacteristic
457C4⋊Dic43C2411yescharacteristic
458C4⋊Dic43C2411yescharacteristic
459Dic43⋊C4—21no—
460Dic43⋊C4—21no—
461Dic43⋊C4—21no—
462Dic43⋊C4—21no—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467Dic43⋊C4—21no—
468Dic43⋊C4—21no—
469Dic43⋊C4—21no—
470Dic43⋊C4—21no—
471Dic43⋊C4—22no—
472Dic43⋊C4—22no—
473Dic43⋊C4—21no—
474Dic43⋊C4—21no—
475Dic43⋊C4—21no—
476Dic43⋊C4—21no—
477Dic43⋊C4C2×D411yescharacteristic
478Dic43⋊C4C2×D411yescharacteristic
479Dic43⋊C4C2×D411yescharacteristic
480Dic43⋊C4C2×D411yescharacteristic
481Dic43⋊C4C2×D411yescharacteristic
482Dic43⋊C4C2×D411yescharacteristic
483Dic43⋊C4C2×D411yescharacteristic
484Dic43⋊C4C2×D411yescharacteristic
485C4×Dic43—21no—
486C4×Dic43—21no—
487C4×Dic43—22no—
488C4×Dic43—22no—
489C4×Dic43—21no—
490C4×Dic43—21no—
491C4×Dic43—21no—
492C4×Dic43—21no—
493C4×Dic43C2×D411yescharacteristic
494C4×Dic43C2×D411yescharacteristic
495C4×Dic43C2×D411yescharacteristic
496C4×Dic43C2×D411yescharacteristic
497C4×Dic43C2411yescharacteristic
498C4×Dic43C2411yescharacteristic
499C4×Dic43C2411yescharacteristic
500C4×Dic43C2411yescharacteristic
501#10621877—22no—
502#10621877—22no—
503C2×C43⋊C8C2412yes—
504C2×C43⋊C8C2412yes—
505C23×C43—21no—
506C23×C43C22×D411yescharacteristic
507C22×D43—22no—
508C22×D43—42no—
509C22×D43—42no—
510C22×D43—42no—
511Q8×C43—21no—
512Q8×C43—22no—
513Q8×C43—22no—
514Q8×C43—42no—
515Q8×C43C2×#4112yes—
516D4×C43—24no—
517D4×C43—21no—
518D4×C43C2×#4112yes—
519C2×C4×C43—21no—
520C2×C4×C43—24no—
521C2×C4×C43—22no—
522C2×C4×C43—21no—
523C2×C4×C43—21no—
524C2×C4×C43—22no—
525C2×C4×C43—41no—
526C2×C4×C43—41no—
527C2×C4×C43—42no—
528C2×C4×C43—42no—
529C2×C4×C43—42no—
530C2×C4×C43—81no—
531C2×C4×C43C22×D411yescharacteristic
532C2×C4×C43C22×D411yescharacteristic
533C2×C4×C43C22×D411yescharacteristic
534C2×C4×C43C22×D411yescharacteristic
535C2×C4×C43C22×D411yescharacteristic
536C2×C4×C43C2×#4112yes—
537C2×C4×C432−1+412yes—
538C2×C4×C43C2511yescharacteristic
539C2×Dic43—22no—
540C2×Dic43—22no—
541C2×Dic43—21no—
542C2×Dic43—21no—
543C2×Dic43—21no—
544C2×Dic43—21no—
545C2×Dic43—41no—
546C2×Dic43—41no—
547C2×Dic43—41no—
548C2×Dic43—42no—
549C2×Dic43—42no—
550C2×Dic43—42no—
551C2×Dic43—81no—
552C2×Dic43—81no—
553C2×Dic43C22×D411yescharacteristic
554C2×Dic43C22×D411yescharacteristic
555C2×Dic43C22×D411yescharacteristic
556C2×Dic43C22×D411yescharacteristic
557C2×Dic43C22×D411yescharacteristic
558C2×Dic43C22×D411yescharacteristic
559C2×Dic43C22×D411yescharacteristic
560C2×Dic43C22×D411yescharacteristic
561D172—22no—
562D172—22no—
563D172—42no—
564C4×D43—44no—
565C4×D43—44no—
566Dic86—22no—
567Dic86—22no—
568Dic86—22no—
569Dic86—22no—
570Dic86—41no—
571Dic86—41no—
572Dic86—42no—
573Dic86—42no—
574Dic86—42no—
575Dic86—42no—
576Dic86—81no—
577Dic86—81no—
578Dic86—81no—
579C8×C43—22no—
580C8×C43—22no—
581C43⋊C8—22no—
582C43⋊C8—22no—
583#61323—431nomaximal, Sylow
584C22×C43—21no—
585C22×C43—21no—
586C22×C43—22no—
587C22×C43—41no—
588C22×C43—41no—
589C22×C43#54812yes—
590C22×C43C23×D411yescharacteristic
591C2×D43—42no—
592C2×D43—42no—
593C2×D43—42no—
594C2×D43—84no—
595C4×C43—21no—
596C4×C43—21no—
597C4×C43—22no—
598C4×C43—21no—
599C4×C43—21no—
600C4×C43—41no—
601C4×C43—42no—
602C4×C43—41no—
603C4×C43—42no—
604C4×C43#54812yes—
605C4×C43C22×#4111yescharacteristic
606C4×C43C2×2−1+411yescharacteristic
607Dic43—21no—
608Dic43—21no—
609Dic43—21no—
610Dic43—21no—
611Dic43—21no—
612Dic43—21no—
613Dic43—21no—
614Dic43—41no—
615Dic43—41no—
616Dic43—42no—
617Dic43—41no—
618Dic43—41no—
619Dic43#57512yes—
620Q8×#41—431no—
621C2×#556—431no—
622#3377—432no—
623#3377—432no—
624#3376—432no—
625#3376—432no—
626#3369—432no—
627#3367—432no—
628#3364—432no—
629#3360—432no—
630#3140—431no—
631#3140—431no—
632#3139—431no—
633#3078—431no—
634#3078—431no—
635#3077—431no—
636#3040—431no—
637#3040—431no—
638#3039—431no—
639Q8×M16—431no—
640C4×#137—431no—
641C4×#137D4311yescharacteristic, complemented
642C4×AGL(1,ℤ/8)—431no—
643C2×C43—22no—
644C2×C43—42no—
645C2×C43C2×#54811yescharacteristic
646C2×C43C2×#57511yescharacteristic
647C2×C43#358611yescharacteristic
648D43—82no—
649C2×#137—431no—
650C2×#137C2×D4311yescharacteristic
651C2×AGL(1,ℤ/8)—431no—
652Q82—431no—
653#557—431no—
654#557—431no—
655#557—431no—
656#556—432no—
657#556—432no—
658#556—432no—
659#556—432no—
660#556—861no—
661#556—861no—
662#556—861no—
663#556—861no—
664#554—431no—
665#554—431no—
666#554—431no—
667#554—861no—
668#554—861no—
669#554—861no—
670D4×Q8—431no—
671D4×Q8—861no—
672#533—431no—
673#533—431no—
674#533—431no—
675#533—861no—
676#533—861no—
677#533—861no—
678C2×C4⋊Q8—431no—
679C2×#126—861no—
680C2×#126—861no—
681C2×#124—431no—
682C2×#124—431no—
683C2×C22⋊Q8—861no—
684C4×#41—431no—
685C4×#41—431no—
686C4×#41C2×D4311yescharacteristic
687C2×C4×Q8—431no—
688C2×C4×Q8—431no—
689C2×C4×Q8—861no—
690C2×C4×Q8C2×D4311yescharacteristic
691C2×C4×D4—431no—
692C2×#117—861no—
693#491—432no—
694#491—432no—
695#489—432no—
696#489—432no—
697#489—432no—
698#489—432no—
699#488—432no—
700#488—432no—
701#488—432no—
702#488—432no—
703#487—432no—
704#487—432no—
705#479—432no—
706#479—432no—
707#479—432no—
708#479—432no—
709#478—432no—
710#478—432no—
711#477—432no—
712#477—432no—
713#476—432no—
714#475—432no—
715#475—432no—
716#474—432no—
717#464—432no—
718#464—432no—
719#464—432no—
720#464—432no—
721#463—432no—
722#463—432no—
723#463—432no—
724#463—432no—
725#462—432no—
726#462—432no—
727#461—432no—
728#461—432no—
729#446—432no—
730#446—432no—
731#446—432no—
732C8×Q8—432no—
733#442—432no—
734#441—432no—
735#441C2×D4312yescomplemented
736#440—432no—
737#440—432no—
738#440C2×D4312yescomplemented
739C4×Q16—432no—
740C4×Q16C2×D4312yescomplemented
741C4×SD16—432no—
742C4×SD16—432no—
743C4×SD16C2×D4312yescomplemented
744C4×D8—432no—
745#428—431no—
746#428—431no—
747#428C2×D4311yescharacteristic
748#423—431no—
749#423—431no—
750#423—431no—
751#419—431no—
752#419—431no—
753#419—431no—
754#419—431no—
755#419—431no—
756#419C2×D4311yescharacteristic
757#418—431no—
758#418—431no—
759#418—431no—
760#417C2×D4311yescharacteristic
761C4×M16—431no—
762C4×M16—431no—
763C4×M16C2×D4311yescharacteristic
764C43#6132311yescharacteristic, complemented, Sylow
765C2×#41C22×D4311yescharacteristic
766C22×Q8—431no—
767C22×Q8—431no—
768C22×Q8—861no—
769C22×Q8C22×D4311yescharacteristic
770C22×D4—431no—
771C23×C4—861no—
772#137—24no—
773#137—864no—
774AGL(1,ℤ/8)—864no—
775C2×Q16—432no—
776C2×Q16C22×D4312yes—
777C2×SD16—432no—
778C2×SD16—432no—
779C2×SD16C22×D4312yes—
780C2×D8—432no—
781C2×M16—431no—
782C2×M16—431no—
783C2×M16C22×D4311yescharacteristic
784C2×M16C22×D4311yescharacteristic
785C4⋊Q8—431no—
786C4⋊Q8—431no—
787C4⋊Q8—431no—
788C4⋊Q8—431no—
789C4⋊Q8—432no—
790C4⋊Q8—432no—
791C4⋊Q8—431no—
792C4⋊Q8—431no—
793C4⋊Q8—861no—
794C4⋊Q8—861no—
795C4⋊Q8—861no—
796C4⋊Q8—861no—
797C4⋊Q8—861no—
798C4⋊Q8—861no—
799C4⋊Q8—861no—
800C4⋊Q8—861no—
801#126—862no—
802#126—862no—
803#126—862no—
804#126—862no—
805#126—862no—
806#126—862no—
807#126—862no—
808#126—862no—
809#125—431no—
810#125—431no—
811#125—431no—
812#125—431no—
813#125—431no—
814#125—431no—
815#125—861no—
816#125—861no—
817#125—861no—
818#125—861no—
819#125—861no—
820#125—861no—
821#124—432no—
822#124—432no—
823#124—432no—
824#124—432no—
825#124—861no—
826#124—861no—
827#124—861no—
828#124—861no—
829C22⋊Q8—861no—
830C22⋊Q8—861no—
831C22⋊Q8—861no—
832C22⋊Q8—861no—
833C22⋊Q8—861no—
834C22⋊Q8—861no—
835C22⋊Q8—861no—
836C22⋊Q8—861no—
837C22⋊Q8—861no—
838C22⋊Q8—861no—
839C22⋊Q8—861no—
840C22⋊Q8—861no—
841C22⋊Q8—862no—
842C22⋊Q8—862no—
843C22⋊Q8—862no—
844C22⋊Q8—862no—
845C22⋊Q8—861no—
846C22⋊Q8—861no—
847C22⋊Q8—861no—
848C22⋊Q8—861no—
849C22⋊Q8—861no—
850C22⋊Q8—861no—
851C4×Q8—21no—
852C4×Q8—21no—
853C4×Q8—431no—
854C4×Q8—431no—
855C4×Q8—431no—
856C4×Q8—431no—
857C4×Q8—431no—
858C4×Q8—431no—
859C4×Q8—431no—
860C4×Q8—431no—
861C4×Q8—431no—
862C4×Q8—431no—
863C4×Q8—431no—
864C4×Q8—431no—
865C4×Q8—432no—
866C4×Q8—432no—
867C4×Q8—861no—
868C4×Q8—861no—
869C4×Q8—861no—
870C4×Q8—861no—
871C4×Q8—861no—
872C4×Q8—861no—
873C4×Q8—861no—
874C4×Q8—861no—
875C4×Q8—861no—
876C4×Q8—861no—
877C4×Q8—861no—
878C4×Q8—861no—
879C4×Q8C22×D4312yes—
880C4×Q8C22×D4312yes—
881C4×Q8C22×D4311yescharacteristic
882C4×Q8C22×D4311yescharacteristic
883C4×D4—21no—
884C4×D4—21no—
885C4×D4—431no—
886C4×D4—431no—
887C4×D4—431no—
888C4×D4—431no—
889C4×D4—432no—
890C4×D4—432no—
891C4×D4—861no—
892C4×D4—861no—
893C4×D4—861no—
894C4×D4—861no—
895C4×D4—861no—
896C4×D4—861no—
897C4×D4C22×D4311yescharacteristic
898C4×D4C22×D4311yescharacteristic
899#117—21no—
900#117—431no—
901#117—431no—
902#117—862no—
903#117—862no—
904#117—862no—
905#117—862no—
906#117—861no—
907#117—861no—
908#117C22×D4311yescharacteristic
909C2×C4⋊C4—21no—
910C2×C4⋊C4—431no—
911C2×C4⋊C4—431no—
912C2×C4⋊C4—431no—
913C2×C4⋊C4—861no—
914C2×C4⋊C4—861no—
915C2×C4⋊C4—861no—
916C2×C4⋊C4—861no—
917C2×C4⋊C4—861no—
918C2×C4⋊C4—861no—
919C2×C4⋊C4C22×D4311yescharacteristic
920C2×C22⋊C4—861no—
921C2×C22⋊C4—861no—
922C2×C22⋊C4—861no—
923C2×C22⋊C4—861no—
924C2×C22⋊C4—861no—
925C2×C42—21no—
926C2×C42—21no—
927C2×C42—431no—
928C2×C42—431no—
929C2×C42—861no—
930C2×C42—861no—
931C2×C42—861no—
932C2×C42C22×D4311yescharacteristic
933#107—432no—
934#107—432no—
935#107C22×D4312yes—
936#106—432no—
937#106—432no—
938#106C22×D4312yes—
939C4⋊C8—432no—
940C4⋊C8—432no—
941C4⋊C8—432no—
942C4⋊C8—432no—
943C4⋊C8—432no—
944C4⋊C8—432no—
945#103—432no—
946#103—432no—
947#103—432no—
948#103—432no—
949#103—432no—
950#103—432no—
951#103—432no—
952#103—432no—
953#103—432no—
954#103—432no—
955#103C22×D4312yes—
956#103C22×D4312yes—
957#103C22×D4312yes—
958#102—432no—
959#102—432no—
960#102—432no—
961#102—432no—
962#102—432no—
963#102—432no—
964#102C22×D4312yes—
965#97—432no—
966#97—432no—
967#97C22×D4312yes—
968C4×C8—432no—
969C4×C8—432no—
970C4×C8C22×D4312yes—
971C24—861no—
972#41—22no—
973#41#1062189814yes—
974C2×Q8—21no—
975C2×Q8—22no—
976C2×Q8—22no—
977C2×Q8—431no—
978C2×Q8—431no—
979C2×Q8—431no—
980C2×Q8—431no—
981C2×Q8—432no—
982C2×Q8—861no—
983C2×Q8—861no—
984C2×Q8—861no—
985C2×Q8—861no—
986C2×Q8—861no—
987C2×Q8—861no—
988C2×Q8—861no—
989C2×Q8—862no—
990C2×Q8—862no—
991C2×Q8—1722no—
992C2×Q8—1724no—
993C2×Q8C23×D4312yes—
994C2×Q8C23×D4311yescharacteristic
995C2×D4—21no—
996C2×D4—432no—
997C2×D4—861no—
998C2×D4—862no—
999C2×D4—862no—
1000C2×D4C23×D4311yescharacteristic
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—431no—
1007C22×C4—431no—
1008C22×C4—431no—
1009C22×C4—431no—
1010C22×C4—862no—
1011C22×C4—862no—
1012C22×C4—861no—
1013C22×C4—861no—
1014C22×C4—861no—
1015C22×C4—861no—
1016C22×C4—861no—
1017C22×C4—1724no—
1018C22×C4D4×D4311yescharacteristic
1019C22×C4D4×D4311yescharacteristic
1020C22×C4C23×D4311yescharacteristic
1021Q16—24no—
1022Q16—864no—
1023SD16—24no—
1024SD16—864no—
1025SD16—864no—
1026D8—864no—
1027M16—22no—
1028M16—22no—
1029M16—862no—
1030M16—862no—
1031C2×C8—432no—
1032C2×C8—432no—
1033C2×C8C23×D4312yes—
1034C2×C8C23×D4312yes—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
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—431no—
1050C4⋊C4—431no—
1051C4⋊C4—431no—
1052C4⋊C4—431no—
1053C4⋊C4—431no—
1054C4⋊C4—431no—
1055C4⋊C4—431no—
1056C4⋊C4—862no—
1057C4⋊C4—862no—
1058C4⋊C4—862no—
1059C4⋊C4—862no—
1060C4⋊C4—861no—
1061C4⋊C4—861no—
1062C4⋊C4—861no—
1063C4⋊C4—861no—
1064C4⋊C4—861no—
1065C4⋊C4—861no—
1066C4⋊C4—862no—
1067C4⋊C4—862no—
1068C4⋊C4—861no—
1069C4⋊C4—861no—
1070C4⋊C4—861no—
1071C4⋊C4—861no—
1072C4⋊C4—861no—
1073C4⋊C4—861no—
1074C4⋊C4—861no—
1075C4⋊C4—861no—
1076C4⋊C4—861no—
1077C4⋊C4—861no—
1078C4⋊C4—861no—
1079C4⋊C4—861no—
1080C4⋊C4—861no—
1081C4⋊C4—861no—
1082C4⋊C4—861no—
1083C4⋊C4—861no—
1084C4⋊C4C23×D4311yescharacteristic
1085C4⋊C4C23×D4311yescharacteristic
1086C4⋊C4C23×D4312yes—
1087C22⋊C4—21no—
1088C22⋊C4—21no—
1089C22⋊C4—21no—
1090C22⋊C4—862no—
1091C22⋊C4—862no—
1092C22⋊C4—862no—
1093C22⋊C4—862no—
1094C22⋊C4—862no—
1095C22⋊C4—862no—
1096C22⋊C4—861no—
1097C22⋊C4—861no—
1098C22⋊C4—861no—
1099C22⋊C4—861no—
1100C22⋊C4—861no—
1101C22⋊C4—861no—
1102C22⋊C4—862no—
1103C22⋊C4—862no—
1104C22⋊C4—862no—
1105C22⋊C4—862no—
1106C42—21no—
1107C42—22no—
1108C42—22no—
1109C42—21no—
1110C42—21no—
1111C42—431no—
1112C42—431no—
1113C42—431no—
1114C42—431no—
1115C42—431no—
1116C42—431no—
1117C42—431no—
1118C42—431no—
1119C42—862no—
1120C42—862no—
1121C42—861no—
1122C42—861no—
1123C42—861no—
1124C42—861no—
1125C42—861no—
1126C42—861no—
1127C42D4×D4311yescharacteristic
1128C42D4×D4311yescharacteristic
1129C42C23×D4311yescharacteristic
1130C42C23×D4311yescharacteristic
1131C23—21no—
1132C23—862no—
1133C23—1722no—
1134C23—1722no—
1135C23—1722no—
1136C23C2×D4×D4311yescharacteristic
1137Q8—21no—
1138Q8—22no—
1139Q8—22no—
1140Q8—42no—
1141Q8—862no—
1142Q8—862no—
1143Q8—862no—
1144Q8—862no—
1145Q8—3441no—
1146Q8—3441no—
1147Q8—3441no—
1148Q8—1721no—
1149Q8—1721no—
1150Q8—1722no—
1151Q8—1722no—
1152Q8—1722no—
1153Q8—1722no—
1154Q8C2×#1062189812yes—
1155D4—24no—
1156D4—21no—
1157D4—862no—
1158D4—862no—
1159D4—1722no—
1160D4C2×#1062189812yes—
1161C2×C4—21no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—81no—
1173C2×C4—431no—
1174C2×C4—431no—
1175C2×C4—431no—
1176C2×C4—431no—
1177C2×C4—431no—
1178C2×C4—431no—
1179C2×C4—431no—
1180C2×C4—431no—
1181C2×C4—862no—
1182C2×C4—862no—
1183C2×C4—861no—
1184C2×C4—861no—
1185C2×C4—861no—
1186C2×C4—861no—
1187C2×C4—3441no—
1188C2×C4—3441no—
1189C2×C4—1724no—
1190C2×C4—1724no—
1191C2×C4—1722no—
1192C2×C4—1721no—
1193C2×C4—1721no—
1194C2×C4—1721no—
1195C2×C4—1722no—
1196C2×C4—1722no—
1197C2×C4C2×D4×D4311yescharacteristic
1198C2×C4C2×D4×D4311yescharacteristic
1199C2×C4C2×D4×D4311yescharacteristic
1200C2×C4C2×D4×D4311yescharacteristic
1201C2×C4C2×D4×D4311yescharacteristic
1202C2×C4C2×#1062189812yes—
1203C2×C4#1306337212yes—
1204C2×C4C24×D4311yescharacteristic
1205C8—22no—
1206C8—22no—
1207C8—862no—
1208C8—862no—
1209C22—21no—
1210C22—21no—
1211C22—22no—
1212C22—41no—
1213C22—41no—
1214C22—3444no—
1215C22—1722no—
1216C22—1722no—
1217C22—1722no—
1218C22#1458355812yes—
1219C22C22×D4×D4311yescharacteristic
1220C4—21no—
1221C4—21no—
1222C4—22no—
1223C4—21no—
1224C4—21no—
1225C4—42no—
1226C4—41no—
1227C4—42no—
1228C4—41no—
1229C4—432no—
1230C4—861no—
1231C4—861no—
1232C4—861no—
1233C4—861no—
1234C4—861no—
1235C4—861no—
1236C4—861no—
1237C4—1721no—
1238C4—1721no—
1239C4—1722no—
1240C4—1721no—
1241C4—1721no—
1242C4#1458355812yes—
1243C4C22×#1062189811yescharacteristic
1244C4C2×#1306337211yescharacteristic
1245C2—22no—
1246C2—42no—
1247C2—3442no—
1248C2C2×#1458355811yescharacteristic
1249C2#575×D4311yescharacteristic
1250C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC4×#137×C43C2
socleC22×C43C23×D4
prime radicalC2×#13063350C22
hypercenterC4×#137D43
hypocenterC43#61323
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
1. #41×Dic86C2semidirect
2. C2×#14583621C2semidirect
3. #19147442C2semidirect
4. #19147433C2semidirect
5. #19147427C2semidirect
6. #19147418C2semidirect
7. #19147336C2semidirect
8. #19147314C2semidirect
9. #19147281C2semidirect
10. #19147245C2semidirect
11. #19144983C2semidirect
12. #19144982C2semidirect
13. #19144973C2semidirect
14. #19144400C2semidirect
15. #19144399C2semidirect
16. #19144391C2semidirect
19. #19144080C2semidirect
20. M16×Dic86C2semidirect
21. #19143419C2semidirect
23. C4×#137×C43C2semidirect
26. Q8×Dic86C22semidirect
27. #14583628C22semidirect
28. #14583625C22semidirect
29. #14583625C22semidirect
40. #14583608C22semidirect
41. #14583608C22semidirect
43. #14583606C22semidirect
45. D4×Dic86C22semidirect
65. #14583266C22semidirect
66. #14583266C22semidirect
75. #14583248C22semidirect
76. #14583248C22semidirect
77. #14583209C22semidirect
78. #14583206C22semidirect
79. #14583206C22semidirect
80. #14583205C22semidirect
83. #14583194C22semidirect
84. #14583193C22semidirect
86. #14583184C22semidirect
87. #14583183C22semidirect
97. #14583107C22semidirect
98. #14583107C22semidirect
99. #14583102C22semidirect
100. #14583102C22semidirect
101. #14583029C22semidirect
102. #14583027C22semidirect
103. #14583027C22semidirect
104. C8×Dic86C22semidirect
106. #14583003C22semidirect
108. #14582996C22semidirect
109. #14582991C22semidirect
110. #14582990C22semidirect
131. C43×#441C22semidirect
132. C43×#440C22semidirect
133. C4×Q16×C43C22semidirect
134. C4×SD16×C43C22semidirect
641. C4×#137D43semidirect
735. #441C2×D43semidirect
738. #440C2×D43semidirect
740. C4×Q16C2×D43semidirect
743. C4×SD16C2×D43semidirect
764. C43#61323semidirect

Maximal subgroups

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

subgroupindex
#41×Dic862
C2×#145836212
#191474422
#191474332
#191474272
#191474182
#191473362
#191473142
#191472812
#191472452
#191449832
#191449822
#191449732
#191444002
#191443992
#191443912
#191440912
#191440892
#191440802
M16×Dic862
#191434192
#191434082
C4×#137×C432
#6132343