Finite Group Databasebeta

← #25992346

Subgroups — #25992346

Order 11008.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148411C211yesmaximal, characteristic, complemented
2#19148157C211yesmaximal, characteristic
3#19147500C212yesmaximal, complemented
4#19147338C212yesmaximal, complemented
5#19147217C212yesmaximal, complemented
6#19147051C212yesmaximal, complemented
7#19147047C212yesmaximal, complemented
8#19146907C212yesmaximal, complemented
9#19146677C212yesmaximal, complemented
10#19146673C212yesmaximal, complemented
11#19145971C211yesmaximal, characteristic, complemented
12#19145969C211yesmaximal, characteristic, complemented
13#19145939C211yesmaximal, characteristic, complemented
14#19145820C211yesmaximal, characteristic, complemented
15#19145816C211yesmaximal, characteristic, complemented
16#19145745C211yesmaximal, characteristic, complemented
17#19144759C211yesmaximal, characteristic, complemented
18#19144757C211yesmaximal, characteristic, complemented
19#19144605C211yesmaximal, characteristic, complemented
20#19144407C211yesmaximal, characteristic, complemented
21#476×D43C211yesmaximal, characteristic, complemented
22#19143709C211yesmaximal, characteristic, complemented
23C43×#3079C211yesmaximal, characteristic, complemented
24#14583629C2212yescomplemented
25#14583624—21no—
26#14583621C2211yescharacteristic
27#14583612C2211yescharacteristic
28#14583610C2212yes—
29#14583608C2211yescharacteristic
30#14583604C2212yes—
31#14583604C2212yescomplemented
32#14583598—21no—
33#14583590C2211yescharacteristic
34#14583588C2211yescharacteristic
35#14583582—21no—
36#14583578—21no—
37#14583573—21no—
38#14583564—21no—
39Q8×C22⋊D43—21no—
40Q8×C22⋊D43—21no—
41#14583548C2211yescharacteristic
42#14583544C2211yescharacteristic
43#14583537C2211yescharacteristic
44#14583530—21no—
45#14583526—21no—
46#14583526—21no—
47#14583456C2211yescharacteristic, complemented
48#14583454C2211yescharacteristic
49#14583454C2211yescharacteristic, complemented
50#14583453C2211yescharacteristic
51C4⋊Q8×D43C2211yescharacteristic
52C4⋊Q8×D43C2211yescharacteristic, complemented
53#14583436C2211yescharacteristic
54#14583433—21no—
55#14583433C2211yescharacteristic
56#14583429—21no—
57#14583408—21no—
58#14583380—21no—
59C4×#10621898C2211yescharacteristic
60C4×#10621900C2211yescharacteristic
61C4×D4×D43C2211yescharacteristic
62C2×#13063282—21no—
63#14583307C2212yescomplemented
64#14583305C2212yescomplemented
65#14583303C2212yescomplemented
66#14583261C2212yes—
67#14583260C2212yes—
68#14583248C2212yescomplemented
69#14583243C2212yescomplemented
70#14583240C2212yescomplemented
71#14583236C2212yes—
72#14583233C2212yes—
73#14583231C2212yes—
74#14583229C2212yescomplemented
75#14583228C2212yescomplemented
76#14583214C2212yes—
77#14583212C2212yes—
78#14583207C2212yescomplemented
79#14583205C2212yescomplemented
80#14583195C2211yescharacteristic, complemented
81#14583194C2211yescharacteristic, complemented
82#14583193C2212yescomplemented
83#14583191C2211yescharacteristic, complemented
84#14583191C2211yescharacteristic, complemented
85#14583190C2211yescharacteristic
86#14583189C2211yescharacteristic
87#14583188C2212yes—
88#14583187C2212yes—
89#14583186C2211yescharacteristic
90#14583186C2211yescharacteristic
91#14583183C2212yescomplemented
92#14583177C2212yes—
93#14583157C2212yescomplemented
94#14583156C2212yescomplemented
95#14583146C2212yes—
96#14583145C2212yes—
97#14583141C2212yes—
98#14583139C2212yes—
99#14583124C2212yes—
100#14583122C2212yes—
101#14583110C2211yescharacteristic, complemented
102#14583109C2211yescharacteristic, complemented
103#14583108C2212yescomplemented
104#14583105C2211yescharacteristic
105#14583104C2211yescharacteristic
106#14583062C2212yes—
107#14583061C2212yes—
108#14583051C2212yes—
109#14583028C2212yescomplemented
110#14583005C2212yescomplemented
111#14583004C2212yescomplemented
112#14582999C2212yes—
113#14582996C2212yes—
114#14582990C2212yes—
115#14582986C2212yes—
116#14582975C2212yescomplemented
117#14582969C2212yes—
118#14582968C2212yes—
119#14582956C2211yescharacteristic, complemented
120#14582955C2211yescharacteristic, complemented
121#14582951C2211yescharacteristic
122#14582938C2212yescomplemented
123#106×D43C2212yes—
124#14582921C2211yescharacteristic, complemented
125C4⋊C8×D43C2211yescharacteristic
126#14582897C2212yes—
127#102×D43C2212yes—
128C2×C4⋊Q8×C43C2211yescharacteristic, complemented
129C4×#41×C43C2211yescharacteristic
130C43×#477C2211yescharacteristic, complemented
131C43×#477C2211yescharacteristic, complemented
132C43×#476C2211yescharacteristic
133C43×#476C2211yescharacteristic
134C43×#475C2212yescomplemented
135C43×#474C2212yes—
136C43×#428C2212yescomplemented
137C43×#423C2211yescharacteristic, complemented
138C43×#417C2212yes—
139C2×#10621898D411yescharacteristic
140C2×#10621900C2311yescharacteristic
141C2×Q8×D43—21no—
142C2×Q8×D43—21no—
143C2×D4×D43C2311yescharacteristic
144C22×C4×D43—21no—
145C2×Dic172C2312yes—
146C2×#10621885C2312yes—
147C2×#10621873C2312yes—
148C2×#10621883C2312yes—
149C2×#10621872C2312yes—
150C2×C8×D43C2312yes—
151#13063325C2311yescharacteristic
152#13063325C2311yescharacteristic
153#13063324—22no—
154#13063324—21no—
155#13063324—21no—
156#13063324C2311yescharacteristic
157#13063324C2312yes—
158#13063324C2312yes—
159#13063323—22no—
160#13063323—22no—
161#13063323—21no—
162#13063323—21no—
163#13063323C2311yescharacteristic
164#13063320—21no—
165#13063320—21no—
166#13063319—21no—
167#13063319—21no—
168#13063319—21no—
169#13063318—21no—
170#13063317—21no—
171#13063317—21no—
172#13063317C2311yescharacteristic
173#13063316—22no—
174#13063316—21no—
175#13063316—21no—
176#13063316C2311yescharacteristic
177#13063315—21no—
178#13063315—22no—
179#13063315—22no—
180#13063315—21no—
181#13063314C2311yescharacteristic
182#13063313—21no—
183#13063313C2311yescharacteristic
184#13063311—21no—
185#13063310—21no—
186#13063310—21no—
187#13063309—21no—
188#13063308—21no—
189#13063308—21no—
190#13063308—21no—
191#13063307—21no—
192#13063306—21no—
193#13063305C2312yes—
194#13063305C2312yes—
195#13063305C2311yescharacteristic
196#13063304—21no—
197#13063304—22no—
198#13063304—22no—
199#13063304—21no—
200#13063304C2312yes—
201#13063304C2311yescharacteristic
202#13063303—21no—
203#13063303—21no—
204#13063303—22no—
205#13063303—22no—
206#13063302—21no—
207#13063302—21no—
208#13063301—21no—
209#13063301—21no—
210#13063301—22no—
211#13063301—22no—
212#13063301C2311yescharacteristic
213#13063301C2311yescharacteristic
214#13063300C2311yescharacteristic
215#13063299—21no—
216#13063299C2311yescharacteristic
217#13063298—21no—
218#13063297—21no—
219#13063297—21no—
220#13063295—21no—
221#13063293—21no—
222Q8×Dic43—21no—
223Q8×Dic43—21no—
224C4×Dic86—21no—
225C4×Dic86—21no—
226C4×Dic86D411yescharacteristic
227C4×Dic86C2312yes—
228C4×Dic86C2311yescharacteristic
229C4×Dic86C2311yescharacteristic
230#13063290—22no—
231#13063290C2311yescharacteristic
232#13063290C2312yes—
233#13063290C2312yes—
234C4×D172—21no—
235C4×D172D411yescharacteristic
236C4×D172C2311yescharacteristic
237C4×D172C2311yescharacteristic
238D4×Dic43C2311yescharacteristic
239D4×Dic43C2311yescharacteristic
240#13063287—22no—
241#13063287C2311yescharacteristic
242C4×C22⋊D43—21no—
243C4×C22⋊D43—22no—
244C4×C22⋊D43—22no—
245C4×C22⋊D43—21no—
246C4×C22⋊D43—21no—
247C4×C22⋊D43D411yescharacteristic
248C4×C22⋊D43D411yescharacteristic
249C4×C22⋊D43C2311yescharacteristic
250C4×C22⋊D43C2311yescharacteristic
251(C22⋊D43)⋊C4—21no—
252(C22⋊D43)⋊C4—21no—
253#13063284—21no—
254#13063284D411yescharacteristic
255#13063283—21no—
256#13063283—21no—
257#13063283C2311yescharacteristic
258#13063282—21no—
259#13063282—21no—
260#13063282—21no—
261#13063282—21no—
262#13063282—21no—
263#13063282—21no—
264#13063282—21no—
265#13063282D411yescharacteristic
266#13063282D411yescharacteristic
267#13063281—21no—
268C2×Dic43⋊C4—21no—
269C2×Dic43⋊C4—21no—
270C4⋊C4×D43—21no—
271C4⋊C4×D43—21no—
272C4⋊C4×D43C2311yescharacteristic
273C4⋊C4×D43C2312yes—
274C4⋊C4×D43C2312yes—
275C2×(C2×D43)⋊C4—21no—
276C2×(C2×D43)⋊C4—21no—
277C22⋊C4×D43—21no—
278C2×C4×Dic43—21no—
279C42×D43C2311yescharacteristic
280C42×D43C2311yescharacteristic
281#13063259C2312yes—
282#13063258C2312yes—
283#13063258C2312yes—
284#13063258C2312yes—
285#13063257C2312yes—
286#13063256C2312yes—
287#13063256C2312yes—
288#13063256C2312yes—
289C4⋊(C43⋊C8)C2311yescharacteristic
290C4⋊(C43⋊C8)C2311yescharacteristic
291Dic43⋊C8C2312yes—
292Dic43⋊C8C2312yes—
293#13063250C2312yes—
294#13063250C2312yes—
295#13063250C2312yes—
296#13063249C2312yes—
297#13063248C2312yes—
298#13063248C2312yes—
299#13063248C2312yes—
300#13063248C2312yes—
301#13063247C2312yes—
302#13063246C2312yes—
303#13063245C2312yes—
304#13063245C2312yes—
305C22⋊(C43⋊C8)C2312yes—
306(C2×D43)⋊C8C2312yes—
307(C2×D43)⋊C8C2312yes—
308#13063236C2312yes—
309#13063235C2312yes—
310C8×Dic43C2312yes—
311C2×#41×C43C2311yescharacteristic
312C22×Q8×C43—21no—
313C2×M16×C43C2312yes—
314C4⋊Q8×C43—21no—
315C4⋊Q8×C43—21no—
316C4⋊Q8×C43C2312yes—
317C4⋊Q8×C43C2311yescharacteristic
318C4⋊Q8×C43C2311yescharacteristic
319C4×Q8×C43C2311yescharacteristic
320C4×Q8×C43C2311yescharacteristic
321C4×D4×C43—21no—
322C4×D4×C43—21no—
323C4×D4×C43C2311yescharacteristic
324C4×D4×C43C2311yescharacteristic
325#117×C43—21no—
326#117×C43C2311yescharacteristic
327C2×C4⋊C4×C43—21no—
328C2×C4⋊C4×C43C2312yes—
329C2×C42×C43—21no—
330C2×C42×C43C2311yescharacteristic
331#107×C43C2312yes—
332#107×C43C2312yes—
333#106×C43C2312yes—
334#106×C43C2312yes—
335C4⋊C8×C43C2311yescharacteristic
336C4⋊C8×C43C2311yescharacteristic
337C4⋊C8×C43C2312yes—
338#103×C43C2312yes—
339#103×C43C2312yes—
340#102×C43C2312yes—
341#102×C43C2312yes—
342C23×D43—21no—
343#41×C43—22no—
344#41×C43—41no—
345C2×Q8×C43—21no—
346C2×Q8×C43—21no—
347C2×Q8×C43—22no—
348C2×Q8×C43—82no—
349C2×Q8×C43C2411yescharacteristic
350C2×D4×C43—21no—
351C2×D4×C43C2411yescharacteristic
352C22×C4×C43—21no—
353C22×C4×C43—21no—
354C22×C4×C43—21no—
355C22×C4×C43—22no—
356C22×C4×C43C2×D411yescharacteristic
357C22×C4×C43C2×D411yescharacteristic
358C22×C4×C43C2411yescharacteristic
359C2×C22⋊D43—21no—
360C2×C22⋊D43—21no—
361C2×C22⋊D43—21no—
362C2×C22⋊D43C2×D411yescharacteristic
363C2×C22⋊D43C2×D411yescharacteristic
364C22×Dic43—21no—
365C22×Dic43—21no—
366C22×Dic43—21no—
367Q8×D43—82no—
368Q8×D43—82no—
369#10621900—22no—
370#10621900—41no—
371D4×D43—22no—
372D4×D43—41no—
373#10621898—24no—
374C2×D172—21no—
375C2×D172C2×D411yescharacteristic
376C2×D172C2411yescharacteristic
377C2×C4×D43—21no—
378C2×C4×D43—21no—
379C2×C4×D43—21no—
380C2×C4×D43—22no—
381C2×C4×D43—22no—
382C2×C4×D43—44no—
383C2×C4×D43C2×D411yescharacteristic
384C2×C4×D43C2×D411yescharacteristic
385C2×C4×D43C2×D411yescharacteristic
386C2×C4×D43C2×D411yescharacteristic
387C2×C4×D43C2411yescharacteristic
388C2×C4×D43C2411yescharacteristic
389C2×Dic86—21no—
390C2×Dic86—21no—
391C2×Dic86—22no—
392C2×Dic86—22no—
393C2×Dic86C2×D411yescharacteristic
394C2×Dic86C2411yescharacteristic
395C2×Dic86C2412yes—
396M16×C43—42no—
397C2×C8×C43C2412yes—
398C2×C8×C43C2412yes—
399C4⋊C4×C43—21no—
400C4⋊C4×C43—21no—
401C4⋊C4×C43—22no—
402C4⋊C4×C43—22no—
403C4⋊C4×C43—21no—
404C4⋊C4×C43—21no—
405C4⋊C4×C43C2412yes—
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×C43C2×D411yescharacteristic
416C42×C43C2×D411yescharacteristic
417C42×C43C2411yescharacteristic
418C42×C43C2411yescharacteristic
419C22⋊Dic43—21no—
420C22⋊Dic43—21no—
421C22⋊Dic43—22no—
422C22⋊Dic43—21no—
423C22⋊Dic43C2×D411yescharacteristic
424C22⋊Dic43C2×D411yescharacteristic
425#10621885—42no—
426#10621883—24no—
427(C2×D43)⋊C4—21no—
428(C2×D43)⋊C4—21no—
429(C2×D43)⋊C4—21no—
430(C2×D43)⋊C4—21no—
431(C2×D43)⋊C4—21no—
432(C2×D43)⋊C4—21no—
433(C2×D43)⋊C4—21no—
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—21no—
436(C2×D43)⋊C4—21no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—22no—
439(C2×D43)⋊C4—21no—
440(C2×D43)⋊C4—21no—
441(C2×D43)⋊C4C2×D411yescharacteristic
442(C2×D43)⋊C4C2×D411yescharacteristic
443(C2×D43)⋊C4C2×D411yescharacteristic
444(C2×D43)⋊C4C2×D411yescharacteristic
445C4⋊Dic43—21no—
446C4⋊Dic43—21no—
447C4⋊Dic43—21no—
448C4⋊Dic43—21no—
449C4⋊Dic43—21no—
450C4⋊Dic43—22no—
451C4⋊Dic43—22no—
452C4⋊Dic43C2×D411yescharacteristic
453C4⋊Dic43C2×D411yescharacteristic
454C4⋊Dic43C2412yes—
455C4⋊Dic43C2411yescharacteristic
456C4⋊Dic43C2411yescharacteristic
457Dic43⋊C4—21no—
458Dic43⋊C4—21no—
459Dic43⋊C4—21no—
460Dic43⋊C4—21no—
461Dic43⋊C4—22no—
462Dic43⋊C4—22no—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—21no—
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4—21no—
469Dic43⋊C4—21no—
470Dic43⋊C4—21no—
471Dic43⋊C4—21no—
472Dic43⋊C4—21no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—21no—
476Dic43⋊C4—21no—
477Dic43⋊C4C2×D411yescharacteristic
478Dic43⋊C4C2×D411yescharacteristic
479Dic43⋊C4C2×D411yescharacteristic
480Dic43⋊C4C2×D411yescharacteristic
481C4×Dic43—21no—
482C4×Dic43—22no—
483C4×Dic43—21no—
484C4×Dic43—21no—
485C4×Dic43—22no—
486C4×Dic43—22no—
487C4×Dic43C2×D411yescharacteristic
488C4×Dic43C2×D411yescharacteristic
489C4×Dic43C2×D411yescharacteristic
490C4×Dic43C2×D411yescharacteristic
491C4×Dic43C2411yescharacteristic
492C4×Dic43C2411yescharacteristic
493C2×C43⋊C8C2412yes—
494C2×C43⋊C8C2412yes—
495Dic172—42no—
496#10621873—42no—
497#10621872—42no—
498C8×D43—42no—
499C23×C43—21no—
500C23×C43C22×D411yescharacteristic
501C22×D43—21no—
502C22×D43—42no—
503C22×D43—42no—
504C22×D43—81no—
505C22×D43C22×D411yescharacteristic
506C22×D43C22×D411yescharacteristic
507Q8×C43—21no—
508Q8×C43—21no—
509Q8×C43—42no—
510Q8×C43—42no—
511Q8×C43—82no—
512D4×C43—21no—
513D4×C43—42no—
514D4×C432−1+412yes—
515C2×C4×C43—22no—
516C2×C4×C43—21no—
517C2×C4×C43—21no—
518C2×C4×C43—21no—
519C2×C4×C43—22no—
520C2×C4×C43—22no—
521C2×C4×C43—21no—
522C2×C4×C43—21no—
523C2×C4×C43—41no—
524C2×C4×C43—42no—
525C2×C4×C43—42no—
526C2×C4×C43—81no—
527C2×C4×C43—82no—
528C2×C4×C43C22×D411yescharacteristic
529C2×C4×C43C22×D411yescharacteristic
530C2×C4×C43C22×D411yescharacteristic
531C2×C4×C43C22×D411yescharacteristic
532C2×C4×C43C22×D411yescharacteristic
533C2×C4×C43C2511yescharacteristic
534C22⋊D43—22no—
535C22⋊D43—22no—
536C22⋊D43—42no—
537C22⋊D43—42no—
538C22⋊D43—81no—
539C2×Dic43—22no—
540C2×Dic43—21no—
541C2×Dic43—21no—
542C2×Dic43—22no—
543C2×Dic43—21no—
544C2×Dic43—42no—
545C2×Dic43—42no—
546C2×Dic43—81no—
547C2×Dic43C22×D411yescharacteristic
548C2×Dic43C22×D411yescharacteristic
549C2×Dic43C22×D411yescharacteristic
550C2×Dic43C22×D411yescharacteristic
551C2×Dic43C22×D411yescharacteristic
552C2×Dic43C22×D411yescharacteristic
553D172—22no—
554D172—21no—
555D172—21no—
556D172—81no—
557C4×D43—22no—
558C4×D43—21no—
559C4×D43—21no—
560C4×D43—21no—
561C4×D43—21no—
562C4×D43—41no—
563C4×D43—41no—
564C4×D43—42no—
565C4×D43—42no—
566C4×D43—42no—
567C4×D43—82no—
568C4×D43—82no—
569C4×D43#13714yes—
570Dic86—22no—
571Dic86—22no—
572Dic86—21no—
573Dic86—22no—
574Dic86—21no—
575Dic86—42no—
576Dic86—81no—
577Dic86—82no—
578Dic86—82no—
579C8×C43—22no—
580C8×C43—22no—
581C43⋊C8—22no—
582C43⋊C8—22no—
583#62108—431nomaximal, Sylow
584C22×C43—21no—
585C22×C43—22no—
586C22×C43—21no—
587C22×C43—21no—
588C22×C43—41no—
589C22×C43—41no—
590C22×C43C23×D411yescharacteristic
591C2×D43—21no—
592C2×D43—21no—
593C2×D43—21no—
594C2×D43—21no—
595C2×D43—21no—
596C2×D43—41no—
597C2×D43—41no—
598C2×D43—41no—
599C2×D43—84no—
600C2×D43C2×#13712yes—
601C4×C43—21no—
602C4×C43—21no—
603C4×C43—21no—
604C4×C43—21no—
605C4×C43—42no—
606C4×C43—42no—
607C4×C43—41no—
608C4×C43—41no—
609C4×C43—41no—
610C4×C43C2×#13712yes—
611C4×C43C2×2−1+411yescharacteristic
612C4×C43#58511yescharacteristic
613Dic43—21no—
614Dic43—21no—
615Dic43—21no—
616Dic43—21no—
617Dic43—21no—
618Dic43—42no—
619Dic43—41no—
620Dic43—42no—
621Dic43—41no—
622Dic43—41no—
623Dic43C2×#13712yes—
624#3503—431no—
625#3475—431no—
626#3385—432no—
627#3369—432no—
628#3357—432no—
629#3344—432no—
630#3344—432no—
631#3331—432no—
632#3314—432no—
633#3314—432no—
634#3252—431no—
635#3252—431no—
636#3249—431no—
637#3238—431no—
638#3238—431no—
639#3230—431no—
640#3116—431no—
641#3116—431no—
642#3101—431no—
643#3079—431no—
644#3079D4311yescharacteristic, complemented
645C2×#476—431no—
646#2989—431no—
647C2×C43—42no—
648C2×C43—41no—
649C2×C43#348911yescharacteristic
650C2×C43C22×#13711yescharacteristic
651C2×C43#358511yescharacteristic
652D43—22no—
653D43—41no—
654D43—81no—
655Q82—432no—
656#557—861no—
657#556—431no—
658#555—431no—
659#554—432no—
660#554—432no—
661#554—432no—
662#554—431no—
663#553—861no—
664#552—431no—
665#552—431no—
666#552—861no—
667#551—861no—
668#551—861no—
669D4×Q8—861no—
670D4×Q8—861no—
671D4×Q8—861no—
672#547—431no—
673#546—431no—
674#546—431no—
675#544—861no—
676#544—861no—
677#544—861no—
678#533—431no—
679#533—431no—
680#533—431no—
681#533—431no—
682C2×C4⋊Q8—431no—
683C2×C4⋊Q8—431no—
684C2×C4⋊Q8C2×D4311yescharacteristic, complemented
685#529—431no—
686#529—431no—
687#529—861no—
688#529—861no—
689#525—861no—
690#520—861no—
691C4×#41—431no—
692C4×#41—431no—
693C4×#41C2×D4311yescharacteristic
694C2×C4×D4—431no—
695C2×#117—861no—
696#501—432no—
697#501—432no—
698#500—432no—
699#489—432no—
700#489—432no—
701#487—432no—
702#485—432no—
703#485—432no—
704#484—432no—
705#484—432no—
706#483—432no—
707#483—432no—
708#483—432no—
709#480—432no—
710#480—432no—
711#479—432no—
712#479—432no—
713#477—431no—
714#477—431no—
715#477—431no—
716#477—432no—
717#477—431no—
718#477C2×D4311yescharacteristic, complemented
719#477C2×D4311yescharacteristic, complemented
720#476—431no—
721#476—431no—
722#476—431no—
723#476—432no—
724#476—431no—
725#476—432no—
726#476C2×D4311yescharacteristic
727#476C2×D4311yescharacteristic
728#475—432no—
729#475C2×D4312yescomplemented
730#474—432no—
731#474C2×D4312yes—
732#470—432no—
733#470—432no—
734#468—432no—
735#468—432no—
736#467—432no—
737#467—432no—
738#464—432no—
739#464—432no—
740#462—431no—
741#462—431no—
742#462—432no—
743#461—431no—
744#461—431no—
745#452—432no—
746#452—432no—
747#450—432no—
748#446—432no—
749#441—432no—
750#441—432no—
751#440—432no—
752#440—432no—
753C4×SD16—432no—
754C4×SD16—432no—
755#436—432no—
756#435—432no—
757#435—432no—
758#432—431no—
759#432—431no—
760#431—431no—
761#428—432no—
762#428C2×D4312yescomplemented
763C2×#106—432no—
764#423—431no—
765#423C2×D4311yescharacteristic, complemented
766C2×C4⋊C8—431no—
767#417—432no—
768#417C2×D4312yes—
769C2×#102—432no—
770C43#6210811yescharacteristic, complemented, Sylow
771C2×#41—431no—
772C2×#41—431no—
773C2×#41C22×D4311yescharacteristic
774C22×Q8—21no—
775C22×Q8—861no—
776C22×Q8—861no—
777C22×D4—431no—
778C23×C4—861no—
779C2×Q16—432no—
780C2×Q16—432no—
781C2×SD16—432no—
782C2×SD16—432no—
783C2×M16—432no—
784C2×M16C22×D4312yes—
785C22×C8—432no—
786C4⋊Q8—21no—
787C4⋊Q8—21no—
788C4⋊Q8—432no—
789C4⋊Q8—432no—
790C4⋊Q8—431no—
791C4⋊Q8—431no—
792C4⋊Q8—431no—
793C4⋊Q8—431no—
794C4⋊Q8—861no—
795C4⋊Q8—861no—
796C4⋊Q8—861no—
797C4⋊Q8—861no—
798C4⋊Q8—862no—
799C4⋊Q8—862no—
800C4⋊Q8—862no—
801C4⋊Q8C22×D4311yescharacteristic
802C4⋊Q8C22×D4311yescharacteristic
803C4⋊Q8C22×D4312yes—
804#126—861no—
805#126—861no—
806#126—861no—
807#126—861no—
808#126—861no—
809#126—861no—
810#125—431no—
811#125—431no—
812#125—861no—
813#125—861no—
814#125—861no—
815#125—861no—
816#125—861no—
817#125—862no—
818#125—862no—
819#125—862no—
820#125—861no—
821#124—431no—
822#124—431no—
823#124—861no—
824#124—861no—
825#123—861no—
826#123—861no—
827#123—861no—
828#123—861no—
829#123—861no—
830#123—861no—
831#123—861no—
832#123—861no—
833C22⋊Q8—431no—
834C22⋊Q8—431no—
835C22⋊Q8—431no—
836C22⋊Q8—432no—
837C22⋊Q8—431no—
838C22⋊Q8—432no—
839C22⋊Q8—432no—
840C22⋊Q8—861no—
841C22⋊Q8—861no—
842C22⋊Q8—862no—
843C22⋊Q8—862no—
844C22⋊Q8—862no—
845C22⋊Q8—862no—
846C22⋊Q8—862no—
847C22⋊Q8—862no—
848C22⋊Q8—861no—
849C22⋊Q8—861no—
850C22⋊Q8—861no—
851C22⋊Q8—861no—
852C22⋊Q8—861no—
853C22⋊Q8—861no—
854#121—431no—
855#121—431no—
856#121—861no—
857#121—861no—
858#121—861no—
859#121—861no—
860#120—861no—
861#120—861no—
862C4×Q8—431no—
863C4×Q8—431no—
864C4×Q8—431no—
865C4×Q8—432no—
866C4×Q8—432no—
867C4×Q8—431no—
868C4×Q8—432no—
869C4×Q8—861no—
870C4×Q8—861no—
871C4×Q8—861no—
872C4×Q8—862no—
873C4×Q8—861no—
874C4×Q8C22×D4311yescharacteristic
875C4×Q8C22×D4311yescharacteristic
876C4×D4—21no—
877C4×D4—21no—
878C4×D4—431no—
879C4×D4—431no—
880C4×D4—431no—
881C4×D4—431no—
882C4×D4—431no—
883C4×D4—431no—
884C4×D4—431no—
885C4×D4—431no—
886C4×D4—431no—
887C4×D4—431no—
888C4×D4—861no—
889C4×D4—861no—
890C4×D4—861no—
891C4×D4—861no—
892C4×D4—862no—
893C4×D4—861no—
894C4×D4—862no—
895C4×D4—862no—
896C4×D4—861no—
897C4×D4C22×D4311yescharacteristic
898C4×D4C22×D4311yescharacteristic
899#117—21no—
900#117—431no—
901#117—431no—
902#117—431no—
903#117—431no—
904#117—861no—
905#117—861no—
906#117—861no—
907#117—861no—
908#117—861no—
909#117—861no—
910#117—861no—
911#117—861no—
912#117—861no—
913#117—861no—
914#117—861no—
915#117C22×D4311yescharacteristic
916C2×C4⋊C4—21no—
917C2×C4⋊C4—431no—
918C2×C4⋊C4—432no—
919C2×C4⋊C4—432no—
920C2×C4⋊C4—861no—
921C2×C4⋊C4—861no—
922C2×C4⋊C4—861no—
923C2×C4⋊C4—861no—
924C2×C4⋊C4C22×D4312yes—
925C2×C22⋊C4—861no—
926C2×C22⋊C4—861no—
927C2×C22⋊C4—861no—
928C2×C42—21no—
929C2×C42—431no—
930C2×C42—431no—
931C2×C42—861no—
932C2×C42C22×D4311yescharacteristic
933#107—432no—
934#107—432no—
935#107—432no—
936#107—432no—
937#107C22×D4312yes—
938#107C22×D4312yes—
939#106—432no—
940#106—432no—
941#106—432no—
942#106—432no—
943#106C22×D4312yes—
944#106C22×D4312yes—
945C4⋊C8—432no—
946C4⋊C8—432no—
947C4⋊C8—431no—
948C4⋊C8—431no—
949C4⋊C8C22×D4311yescharacteristic
950C4⋊C8C22×D4311yescharacteristic
951C4⋊C8C22×D4312yes—
952#103—432no—
953#103—432no—
954#103—432no—
955#103—432no—
956#103—432no—
957#103—432no—
958#103—432no—
959#103—432no—
960#103C22×D4312yes—
961#103C22×D4312yes—
962#102—432no—
963#102—432no—
964#102—432no—
965#102—432no—
966#102C22×D4312yes—
967#102C22×D4312yes—
968C22⋊C8—432no—
969C22⋊C8—432no—
970C22⋊C8—432no—
971#97—432no—
972#97—432no—
973C4×C8—432no—
974C24—861no—
975#41—22no—
976#41—41no—
977#41—864no—
978#41—862no—
979#41—1721no—
980C2×Q8—21no—
981C2×Q8—21no—
982C2×Q8—22no—
983C2×Q8—82no—
984C2×Q8—431no—
985C2×Q8—431no—
986C2×Q8—432no—
987C2×Q8—861no—
988C2×Q8—862no—
989C2×Q8—862no—
990C2×Q8—861no—
991C2×Q8—3442no—
992C2×Q8—3442no—
993C2×Q8C23×D4311yescharacteristic
994C2×D4—21no—
995C2×D4—431no—
996C2×D4—431no—
997C2×D4—431no—
998C2×D4—431no—
999C2×D4—861no—
1000C2×D4—861no—
1001C2×D4—862no—
1002C2×D4—861no—
1003C2×D4—861no—
1004C2×D4—1721no—
1005C2×D4C23×D4311yescharacteristic
1006C22×C4—22no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—431no—
1011C22×C4—431no—
1012C22×C4—431no—
1013C22×C4—431no—
1014C22×C4—431no—
1015C22×C4—431no—
1016C22×C4—861no—
1017C22×C4—862no—
1018C22×C4—862no—
1019C22×C4—861no—
1020C22×C4—861no—
1021C22×C4—861no—
1022C22×C4—861no—
1023C22×C4—861no—
1024C22×C4—1724no—
1025C22×C4D4×D4311yescharacteristic
1026C22×C4D4×D4311yescharacteristic
1027C22×C4C23×D4311yescharacteristic
1028Q16—1722no—
1029Q16—1722no—
1030SD16—864no—
1031SD16—1722no—
1032M16—42no—
1033M16—1722no—
1034C2×C8—432no—
1035C2×C8—432no—
1036C2×C8—1722no—
1037C2×C8C23×D4312yes—
1038C2×C8C23×D4312yes—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—431no—
1046C4⋊C4—431no—
1047C4⋊C4—431no—
1048C4⋊C4—431no—
1049C4⋊C4—431no—
1050C4⋊C4—431no—
1051C4⋊C4—432no—
1052C4⋊C4—431no—
1053C4⋊C4—431no—
1054C4⋊C4—861no—
1055C4⋊C4—862no—
1056C4⋊C4—862no—
1057C4⋊C4—861no—
1058C4⋊C4—861no—
1059C4⋊C4—861no—
1060C4⋊C4—861no—
1061C4⋊C4—862no—
1062C4⋊C4—862no—
1063C4⋊C4—861no—
1064C4⋊C4—861no—
1065C4⋊C4—862no—
1066C4⋊C4—862no—
1067C4⋊C4—861no—
1068C4⋊C4—861no—
1069C4⋊C4—862no—
1070C4⋊C4—862no—
1071C4⋊C4—861no—
1072C4⋊C4—861no—
1073C4⋊C4—861no—
1074C4⋊C4—861no—
1075C4⋊C4—861no—
1076C4⋊C4—861no—
1077C4⋊C4—861no—
1078C4⋊C4—862no—
1079C4⋊C4—861no—
1080C4⋊C4—862no—
1081C4⋊C4C23×D4312yes—
1082C4⋊C4C23×D4312yes—
1083C4⋊C4C23×D4311yescharacteristic
1084C4⋊C4C23×D4311yescharacteristic
1085C22⋊C4—21no—
1086C22⋊C4—21no—
1087C22⋊C4—21no—
1088C22⋊C4—431no—
1089C22⋊C4—431no—
1090C22⋊C4—431no—
1091C22⋊C4—431no—
1092C22⋊C4—431no—
1093C22⋊C4—431no—
1094C22⋊C4—861no—
1095C22⋊C4—861no—
1096C22⋊C4—861no—
1097C22⋊C4—861no—
1098C22⋊C4—861no—
1099C22⋊C4—861no—
1100C22⋊C4—861no—
1101C22⋊C4—862no—
1102C22⋊C4—862no—
1103C22⋊C4—861no—
1104C22⋊C4—861no—
1105C22⋊C4—861no—
1106C22⋊C4—862no—
1107C22⋊C4—861no—
1108C22⋊C4—861no—
1109C22⋊C4—861no—
1110C22⋊C4—861no—
1111C22⋊C4—861no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—431no—
1116C42—431no—
1117C42—431no—
1118C42—431no—
1119C42—431no—
1120C42—431no—
1121C42—861no—
1122C42—861no—
1123C42—862no—
1124C42—862no—
1125C42—861no—
1126C42—862no—
1127C42D4×D4311yescharacteristic
1128C42D4×D4311yescharacteristic
1129C42C23×D4311yescharacteristic
1130C42C23×D4311yescharacteristic
1131C23—21no—
1132C23—431no—
1133C23—431no—
1134C23—861no—
1135C23—3441no—
1136C23—1722no—
1137C23—1722no—
1138C23C2×D4×D4311yescharacteristic
1139Q8—21no—
1140Q8—21no—
1141Q8—42no—
1142Q8—42no—
1143Q8—82no—
1144Q8—862no—
1145Q8—862no—
1146Q8—861no—
1147Q8—862no—
1148Q8—861no—
1149Q8—3442no—
1150Q8—3442no—
1151Q8—3441no—
1152Q8—1722no—
1153D4—21no—
1154D4—42no—
1155D4—862no—
1156D4—862no—
1157D4—862no—
1158D4—861no—
1159D4—861no—
1160D4—3441no—
1161D4—3441no—
1162D4—1722no—
1163D4—1722no—
1164D4#1306337312yes—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—81no—
1177C2×C4—82no—
1178C2×C4—431no—
1179C2×C4—434no—
1180C2×C4—431no—
1181C2×C4—431no—
1182C2×C4—431no—
1183C2×C4—431no—
1184C2×C4—431no—
1185C2×C4—862no—
1186C2×C4—861no—
1187C2×C4—861no—
1188C2×C4—861no—
1189C2×C4—861no—
1190C2×C4—862no—
1191C2×C4—861no—
1192C2×C4—861no—
1193C2×C4—862no—
1194C2×C4—861no—
1195C2×C4—3442no—
1196C2×C4—3442no—
1197C2×C4—3441no—
1198C2×C4—1721no—
1199C2×C4—1721no—
1200C2×C4—1722no—
1201C2×C4—1722no—
1202C2×C4—1722no—
1203C2×C4—1722no—
1204C2×C4—1722no—
1205C2×C4C2×D4×D4311yescharacteristic
1206C2×C4C2×D4×D4311yescharacteristic
1207C2×C4C2×D4×D4311yescharacteristic
1208C2×C4C2×D4×D4311yescharacteristic
1209C2×C4C2×D4×D4311yescharacteristic
1210C2×C4C24×D4311yescharacteristic
1211C8—22no—
1212C8—22no—
1213C8—862no—
1214C8—862no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—22no—
1219C22—41no—
1220C22—41no—
1221C22—432no—
1222C22—861no—
1223C22—861no—
1224C22—861no—
1225C22—861no—
1226C22—861no—
1227C22—3444no—
1228C22—1721no—
1229C22—1721no—
1230C22—1721no—
1231C22C22×D4×D4311yescharacteristic
1232C4—21no—
1233C4—21no—
1234C4—21no—
1235C4—21no—
1236C4—41no—
1237C4—42no—
1238C4—42no—
1239C4—41no—
1240C4—41no—
1241C4—432no—
1242C4—861no—
1243C4—861no—
1244C4—861no—
1245C4—861no—
1246C4—861no—
1247C4—1721no—
1248C4—1722no—
1249C4—1721no—
1250C4—1721no—
1251C4—1722no—
1252C4#137×D4312yes—
1253C4C2×#1306337311yescharacteristic
1254C4#1458373511yescharacteristic
1255C2—41no—
1256C2—42no—
1257C2—862no—
1258C2—3441no—
1259C2—1721no—
1260C2#1914827111yescharacteristic
1261C2C2×#137×D4311yescharacteristic
1262C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3079C2
socleC22×C43C23×D4
prime radical#19148157C2
hypercenter#3079D43
hypocenterC43#62108
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #19148411C2semidirect
3. #19147500C2semidirect
4. #19147338C2semidirect
5. #19147217C2semidirect
6. #19147051C2semidirect
7. #19147047C2semidirect
8. #19146907C2semidirect
9. #19146677C2semidirect
10. #19146673C2semidirect
11. #19145971C2semidirect
12. #19145969C2semidirect
13. #19145939C2semidirect
14. #19145820C2semidirect
15. #19145816C2semidirect
16. #19145745C2semidirect
17. #19144759C2semidirect
18. #19144757C2semidirect
19. #19144605C2semidirect
20. #19144407C2semidirect
21. #476×D43C2semidirect
22. #19143709C2semidirect
23. C43×#3079C2semidirect
24. #14583629C22semidirect
31. #14583604C22semidirect
47. #14583456C22semidirect
49. #14583454C22semidirect
52. C4⋊Q8×D43C22semidirect
63. #14583307C22semidirect
64. #14583305C22semidirect
65. #14583303C22semidirect
68. #14583248C22semidirect
69. #14583243C22semidirect
70. #14583240C22semidirect
74. #14583229C22semidirect
75. #14583228C22semidirect
78. #14583207C22semidirect
79. #14583205C22semidirect
80. #14583195C22semidirect
81. #14583194C22semidirect
82. #14583193C22semidirect
83. #14583191C22semidirect
84. #14583191C22semidirect
91. #14583183C22semidirect
93. #14583157C22semidirect
94. #14583156C22semidirect
101. #14583110C22semidirect
102. #14583109C22semidirect
103. #14583108C22semidirect
109. #14583028C22semidirect
110. #14583005C22semidirect
111. #14583004C22semidirect
116. #14582975C22semidirect
119. #14582956C22semidirect
120. #14582955C22semidirect
122. #14582938C22semidirect
124. #14582921C22semidirect
128. C2×C4⋊Q8×C43C22semidirect
130. C43×#477C22semidirect
131. C43×#477C22semidirect
134. C43×#475C22semidirect
136. C43×#428C22semidirect
137. C43×#423C22semidirect
644. #3079D43semidirect
684. C2×C4⋊Q8C2×D43semidirect
718. #477C2×D43semidirect
719. #477C2×D43semidirect
729. #475C2×D43semidirect
762. #428C2×D43semidirect
765. #423C2×D43semidirect
770. C43#62108semidirect

Maximal subgroups

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

subgroupindex
#191484112
#191481572
#191475002
#191473382
#191472172
#191470512
#191470472
#191469072
#191466772
#191466732
#191459712
#191459692
#191459392
#191458202
#191458162
#191457452
#191447592
#191447572
#191446052
#191444072
#476×D432
#191437092
C43×#30792
#6210843