Finite Group Databasebeta

← #25117347

Subgroups — #25117347

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143815C211yesmaximal, characteristic
2C2×#14583019C211yesmaximal, characteristic, complemented
3#19143319C211yesmaximal, characteristic, complemented
4C2×#14582914C211yesmaximal, characteristic, complemented
5#19143042C211yesmaximal, characteristic, complemented
6#19135481C211yesmaximal, characteristic, complemented
7#19135305C211yesmaximal, characteristic, complemented
8#19135241C211yesmaximal, characteristic, complemented
9#19135042C211yesmaximal, characteristic, complemented
10#19134921C211yesmaximal, characteristic, complemented
11#19134920C211yesmaximal, characteristic, complemented
12#19134798C211yesmaximal, characteristic, complemented
13#19134435C211yesmaximal, characteristic, complemented
14#19134360C211yesmaximal, characteristic, complemented
15C43×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20C2×#13063331C2211yescharacteristic, complemented
21C2×M16×D43C2211yescharacteristic
22#14583411C2211yescharacteristic
23C2×#13063282C2211yescharacteristic
24#14583064C411yescharacteristic, complemented
25#14583062C411yescharacteristic, complemented
26#14583056C411yescharacteristic, complemented
27#14583051C411yescharacteristic, complemented
28#14583047C411yescharacteristic, complemented
29#14583045C411yescharacteristic, complemented
30#14583039C411yescharacteristic, complemented
31#14583034C411yescharacteristic, complemented
32#14583019—24no—
33#14582976—21no—
34#14582969—21no—
35#14582969—21no—
36#14582964—21no—
37C2×#13063260C2211yescharacteristic, complemented
38#14582914—24no—
39C2×#13063253C2211yescharacteristic
40C2×#13063253C2211yescharacteristic, complemented
41C2×#13063252C2211yescharacteristic
42C2×#13063251C2211yescharacteristic
43C2×#13063251C2211yescharacteristic, complemented
44#14582893C2211yescharacteristic
45#14582867—21no—
46#14582867C2211yescharacteristic
47#14582867C2211yescharacteristic, complemented
48#14582865—21no—
49#14582865C2211yescharacteristic
50#14582862—21no—
51#14582862C2211yescharacteristic
52C2×(C2×D43)⋊C8—21no—
53C2×(C2×D43)⋊C8C2211yescharacteristic
54C2×(C2×D43)⋊C8C2211yescharacteristic
55#14582855C2211yescharacteristic, complemented
56C2×#13063235C2211yescharacteristic, complemented
57C2×C8×Dic43C2211yescharacteristic, complemented
58#14582664C2211yescharacteristic, complemented
59#14582663C2211yescharacteristic, complemented
60#14582658C2211yescharacteristic, complemented
61#14582654C2211yescharacteristic, complemented
62C2×#131×C43C2211yescharacteristic
63C2×#108×C43C2211yescharacteristic, complemented
64C43×#424C2211yescharacteristic, complemented
65C2×#104×C43C2211yescharacteristic
66C43×#416C2211yescharacteristic
67C43×#339C2211yescharacteristic, complemented
68C43×#336C2211yescharacteristic, complemented
69C2×#10621902C2×C411yescharacteristic
70C2×#10621898—21no—
71C2×#10621898C2311yescharacteristic
72C2×#10621898C2311yescharacteristic
73C2×#10621900—21no—
74C2×#10621900C2×C411yescharacteristic
75#41×D43—22no—
76#41×D43—22no—
77#41×D43—41no—
78#41×D43—41no—
79C2×Q8×D43C2×C411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43C2×C411yescharacteristic
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84#13063347—41no—
85#13063347—41no—
86#13063345—22no—
87#13063345—22no—
88C2×Dic172C2×C411yescharacteristic
89C2×#10621885C2×C411yescharacteristic
90C2×#10621873C2×C411yescharacteristic
91C2×#10621873C2×C411yescharacteristic
92C2×#10621883C2×C411yescharacteristic
93C2×#10621884C2×C411yescharacteristic
94C2×D344C2×C411yescharacteristic
95C2×#10621882C2×C411yescharacteristic
96#13063332—22no—
97#13063332—41no—
98#13063331—22no—
99#13063331—41no—
100C2×#10621877—21no—
101C2×#10621877C2311yescharacteristic
102C2×#10621877C2311yescharacteristic
103C2×#10621872—21no—
104C2×#10621872—21no—
105M16×D43—22no—
106M16×D43—41no—
107C22×C43⋊C8—21no—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110C2×C8×D43—21no—
111C2×C8×D43—21no—
112#13063309—21no—
113#13063305C2×C411yescharacteristic
114#13063305C2×C411yescharacteristic
115#13063300C2×C411yescharacteristic
116#13063300C2×C411yescharacteristic
117#13063295—21no—
118C4×D172—21no—
119C4×D172—21no—
120#13063282—22no—
121#13063282—41no—
122C2×Dic43⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×C4×Dic43C2311yescharacteristic
125#13063260—22no—
126#13063253—22no—
127#13063253—41no—
128#13063252D414yescomplemented
129#13063251—22no—
130#13063251—22no—
131#13063248C2×C411yescharacteristic
132#13063248C2×C411yescharacteristic
133#13063245C2×C411yescharacteristic
134#13063245C2×C411yescharacteristic
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137(C2×D43)⋊C8—21no—
138(C2×D43)⋊C8—21no—
139(C2×D43)⋊C8—21no—
140(C2×D43)⋊C8—21no—
141(C2×D43)⋊C8—21no—
142(C2×D43)⋊C8—21no—
143(C2×D43)⋊C8C2×C411yescharacteristic
144(C2×D43)⋊C8C2×C411yescharacteristic
145(C2×D43)⋊C8C2×C411yescharacteristic
146(C2×D43)⋊C8C2×C411yescharacteristic
147(C2×D43)⋊C8D411yescharacteristic
148(C2×D43)⋊C8D411yescharacteristic
149(C2×D43)⋊C8D411yescharacteristic
150(C2×D43)⋊C8D411yescharacteristic
151#13063236—21no—
152#13063235—22no—
153C4×C43⋊C8—21no—
154C8×Dic43—41no—
155C2×#41×C43C2311yescharacteristic
156#131×C43—22no—
157#131×C43—41no—
158C2×M16×C43—21no—
159C2×M16×C43C2311yescharacteristic
160C2×M16×C43C2311yescharacteristic
161C22×C8×C43—21no—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164#117×C43C2311yescharacteristic
165C2×C42×C43C2311yescharacteristic
166#108×C43—41no—
167C4⋊C8×C43—21no—
168C4⋊C8×C43—21no—
169#104×C43—22no—
170#103×C43C2×C411yescharacteristic
171#103×C43C2×C411yescharacteristic
172#102×C43C2×C411yescharacteristic
173#102×C43C2×C411yescharacteristic
174C23×D43—21no—
175C23×D43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43C2×D412yes—
179#41×C43#4112yes—
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43#4111yescharacteristic
193#10621902—22no—
194#10621902—41no—
195Q8×D43—22no—
196Q8×D43—41no—
197#10621900—22no—
198#10621900—41no—
199#10621900—42no—
200#10621900—42no—
201D4×D43—22no—
202D4×D43—42no—
203D4×D43—42no—
204D4×D43—41no—
205#10621898—21no—
206#10621898—21no—
207#10621898—21no—
208#10621898—21no—
209#10621898—21no—
210#10621898—21no—
211#10621898—21no—
212#10621898—21no—
213#10621898—42no—
214#10621898—42no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172C22×C411yescharacteristic
219C2×D172C22×C411yescharacteristic
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43C22×C411yescharacteristic
231C2×C4×D43C22×C411yescharacteristic
232C2×C4×D43C2×D411yescharacteristic
233C2×C4×D43C2×D411yescharacteristic
234C2×Dic86—21no—
235C2×Dic86C22×C411yescharacteristic
236C2×Dic86C22×C411yescharacteristic
237M16×C43—21no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—21no—
241M16×C43—42no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—42no—
249C2×C8×C43C22×C411yescharacteristic
250C2×C8×C43C22×C411yescharacteristic
251C2×C8×C43C2×D411yescharacteristic
252C2×C8×C43C2×D411yescharacteristic
253C4⋊C4×C43C22×C411yescharacteristic
254C4⋊C4×C43C22×C411yescharacteristic
255C22⋊C4×C43—21no—
256C42×C43—21no—
257C42×C43—21no—
258C42×C43—21no—
259#10621885—22no—
260#10621884—22no—
261#10621883—22no—
262#10621882—22no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—42no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270Dic43⋊C4—42no—
271C4×Dic43—21no—
272C4×Dic43C2×D412yes—
273#10621877—21no—
274#10621877—21no—
275#10621877—21no—
276#10621877—42no—
277#10621877C2×D412yes—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—42no—
285C2×C43⋊C8C22×C411yescharacteristic
286C2×C43⋊C8C22×C411yescharacteristic
287C2×C43⋊C8C2×D411yescharacteristic
288C2×C43⋊C8C2×D411yescharacteristic
289Dic172—41no—
290D344—41no—
291#10621873—41no—
292#10621873—41no—
293#10621872—42no—
294#10621872—42no—
295C8×D43—42no—
296C8×D43—42no—
297C23×C43—21no—
298C23×C43C2×#4111yescharacteristic
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—81no—
308C22×D43C4×D411yescharacteristic
309C22×D43C4×D411yescharacteristic
310Q8×C43—21no—
311Q8×C43C4×D412yes—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—21no—
315D4×C43C4×D412yes—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43C23×C411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C22⋊D43—42no—
331C22⋊D43—42no—
332C22⋊D43—41no—
333C22⋊D43—41no—
334C22⋊D43—41no—
335C22⋊D43—41no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—22no—
341C2×Dic43—42no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43C4×D411yescharacteristic
345C2×Dic43C4×D411yescharacteristic
346D172—21no—
347D172—21no—
348D172—21no—
349D172—21no—
350D172—42no—
351D172—42no—
352D172—81no—
353C4×D43—21no—
354C4×D43—21no—
355C4×D43—21no—
356C4×D43—21no—
357C4×D43—21no—
358C4×D43—21no—
359C4×D43—21no—
360C4×D43—21no—
361C4×D43—42no—
362C4×D43—42no—
363C4×D43—41no—
364C4×D43—41no—
365C4×D43—41no—
366C4×D43—41no—
367Dic86—21no—
368Dic86—21no—
369Dic86—21no—
370Dic86—21no—
371Dic86—42no—
372C8×C43—21no—
373C8×C43—21no—
374C8×C43—21no—
375C8×C43—21no—
376C8×C43—41no—
377C8×C43—41no—
378C43⋊C8—21no—
379C43⋊C8—21no—
380C43⋊C8—22no—
381C43⋊C8—21no—
382C43⋊C8—21no—
383C43⋊C8—41no—
384#22887—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—22no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43C2×C4×D411yescharacteristic
391C22×C43#54611yescharacteristic
392C22×C43#55111yescharacteristic
393C2×D43—21no—
394C2×D43—21no—
395C2×D43—21no—
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—21no—
399C2×D43—41no—
400C2×D43—41no—
401C2×D43—41no—
402C2×D43—41no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43—81no—
406C2×D43—81no—
407C2×D43—84no—
408C4×C43—22no—
409C4×C43—41no—
410C4×C43—41no—
411C4×C43—81no—
412C4×C43C2×C4×D411yescharacteristic
413C4×C43#51811yescharacteristic
414C4×C43D4211yescharacteristic
415C4×C43#54611yescharacteristic
416Dic43—21no—
417Dic43—21no—
418Dic43—42no—
419Dic43—41no—
420Dic43—41no—
421#3002—431no—
422C2×#444—431no—
423#2933—431no—
424C2×#421—431no—
425#2880—431no—
426#1974—431no—
427#1938—431no—
428#1929—431no—
429#1897—431no—
430#1876—431no—
431#1876—431no—
432#1866D4311yescharacteristic, complemented
433#1855—431no—
434#1764—431no—
435#1750—431no—
436C2×C43—21no—
437C2×C43—21no—
438C2×C43—42no—
439C2×C43#235811yescharacteristic
440C2×C43#295511yescharacteristic
441C2×C43#295711yescharacteristic
442D43—41no—
443D43—41no—
444D43—81no—
445D43—81no—
446C22×#41—431no—
447C2×#135—431no—
448C2×#135—431no—
449C2×#131—431no—
450C2×#131—431no—
451C2×#131C2×D4311yescharacteristic
452C22×M16—431no—
453#525—431no—
454C2×#117—431no—
455#452—431no—
456#452—431no—
457#451—431no—
458#450—431no—
459#449—431no—
460#449—431no—
461#448—431no—
462#447—431no—
463#444—864no—
464#436—861no—
465#435—861no—
466#435—861no—
467C8×D4—861no—
468C2×#108—431no—
469C2×#108C2×D4311yescharacteristic, complemented
470#424C2×D4311yescharacteristic, complemented
471#421—864no—
472C2×#104—431no—
473C2×#104—431no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104C2×D4311yescharacteristic
478#416—431no—
479#416C2×D4311yescharacteristic
480#408—431no—
481#408—431no—
482#408—431no—
483#408—861no—
484#408—861no—
485#407—431no—
486#407—861no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—431no—
489C2×C22⋊C8—861no—
490#405—431no—
491C2×#97—431no—
492C2×C4×C8—431no—
493#341—431no—
494#341—431no—
495#339—431no—
496#339C2×D4311yescharacteristic, complemented
497#336—431no—
498#336C2×D4311yescharacteristic, complemented
499C43#2288711yescharacteristic, complemented, Sylow
500C2×#41—431no—
501C2×#41—431no—
502C2×#41—431no—
503C2×#41—431no—
504C2×#41—861no—
505C2×#41—861no—
506C2×#41—862no—
507C2×#41—862no—
508C2×#41—1721no—
509C2×#41—1721no—
510C2×#41C22×D4311yescharacteristic
511C22×Q8—431no—
512C22×D4—431no—
513C22×D4—861no—
514C23×C4—431no—
515C23×C4—861no—
516#135—862no—
517#135—862no—
518#135—1721no—
519#135—1721no—
520C2×Q16—431no—
521C2×Q16—431no—
522C2×SD16—431no—
523C2×SD16—431no—
524C2×SD16—431no—
525C2×SD16—431no—
526C2×D8—431no—
527C2×D8—431no—
528#131—22no—
529#131—41no—
530#131—862no—
531#131—862no—
532#131—1721no—
533#131—1721no—
534C2×M16—21no—
535C2×M16—431no—
536C2×M16—431no—
537C2×M16—861no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—862no—
541C2×M16—1721no—
542C2×M16C22×D4311yescharacteristic
543C2×M16C22×D4311yescharacteristic
544C22×C8—21no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—861no—
548C22×C8—861no—
549C22×C8—861no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#123—861no—
553C22⋊Q8—431no—
554C22⋊Q8—431no—
555#121—431no—
556#121—431no—
557#120—861no—
558C4×D4—861no—
559C4×D4—861no—
560#117—862no—
561#117—1721no—
562#117C22×D4311yescharacteristic
563C2×C4⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C42—431no—
566C2×C42C22×D4311yescharacteristic
567#108—41no—
568#108—862no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—434no—
573#104—862no—
574#104—862no—
575#104—862no—
576#104—1721no—
577#103—431no—
578#103—431no—
579#103C4×D4311yescharacteristic
580#103C4×D4311yescharacteristic
581#102—431no—
582#102—431no—
583#102C4×D4311yescharacteristic
584#102C4×D4311yescharacteristic
585C22⋊C8—431no—
586C22⋊C8—431no—
587C22⋊C8—431no—
588C22⋊C8—431no—
589C22⋊C8—431no—
590C22⋊C8—431no—
591C22⋊C8—431no—
592C22⋊C8—431no—
593C22⋊C8—861no—
594C22⋊C8—861no—
595C22⋊C8—861no—
596C22⋊C8—861no—
597C22⋊C8—861no—
598C22⋊C8—861no—
599C22⋊C8—861no—
600C22⋊C8—861no—
601#97—861no—
602#97—862no—
603C4×C8—861no—
604C4×C8—1721no—
605C24—431no—
606C24—861no—
607#41—21no—
608#41—21no—
609#41—862no—
610#41—862no—
611#41—861no—
612#41—861no—
613#41—861no—
614#41—861no—
615#41—861no—
616#41—861no—
617#41—861no—
618#41—861no—
619#41—1722no—
620#41—1722no—
621#41—1721no—
622#41—1722no—
623#41—1722no—
624#41—1721no—
625#41D4×D4312yes—
626#41#1062190212yes—
627C2×Q8—431no—
628C2×Q8—431no—
629C2×Q8—861no—
630C2×Q8—862no—
631C2×Q8—1721no—
632C2×Q8C2×C4×D4311yescharacteristic
633C2×D4—21no—
634C2×D4—431no—
635C2×D4—431no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—862no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—1721no—
645C2×D4—1722no—
646C2×D4—1722no—
647C2×D4C2×C4×D4311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—431no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—1722no—
666C22×C4—1722no—
667C22×C4C23×D4311yescharacteristic
668Q16—862no—
669Q16—1721no—
670SD16—862no—
671SD16—862no—
672SD16—1721no—
673SD16—1721no—
674D8—862no—
675D8—1721no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—42no—
681M16—432no—
682M16—861no—
683M16—861no—
684M16—861no—
685M16—1722no—
686M16—1722no—
687M16—1722no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—431no—
696C2×C8—431no—
697C2×C8—431no—
698C2×C8—431no—
699C2×C8—861no—
700C2×C8—861no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—1722no—
706C2×C8—1722no—
707C2×C8—1722no—
708C2×C8C2×C4×D4311yescharacteristic
709C2×C8C2×C4×D4311yescharacteristic
710C2×C8D4×D4311yescharacteristic
711C2×C8D4×D4311yescharacteristic
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—1722no—
715C4⋊C4C2×C4×D4311yescharacteristic
716C4⋊C4C2×C4×D4311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—1722no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—432no—
727C42—861no—
728C23—21no—
729C23—431no—
730C23—431no—
731C23—861no—
732C23—861no—
733C23—861no—
734C23—861no—
735C23—3441no—
736C23—1721no—
737C23—1721no—
738C23—1722no—
739C23—1722no—
740C23#41×D4311yescharacteristic
741Q8—21no—
742Q8—861no—
743Q8—861no—
744Q8—861no—
745Q8—861no—
746Q8—1722no—
747Q8#1306328712yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—861no—
752D4—861no—
753D4—861no—
754D4—861no—
755D4—3441no—
756D4—1722no—
757D4—1722no—
758D4—1722no—
759D4—1722no—
760D4—1721no—
761D4—1721no—
762D4—1721no—
763D4—1721no—
764D4#1306328712yes—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—431no—
774C2×C4—431no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—861no—
778C2×C4—861no—
779C2×C4—861no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—862no—
788C2×C4—1722no—
789C2×C4—1722no—
790C2×C4—1722no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4C22×C4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C2×D4×D4311yescharacteristic
800C2×C4C2×#1062190211yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337111yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—861no—
810C8—861no—
811C8—862no—
812C8—861no—
813C8—861no—
814C8—1721no—
815C22—21no—
816C22—21no—
817C22—22no—
818C22—41no—
819C22—41no—
820C22—861no—
821C22—861no—
822C22—861no—
823C22—861no—
824C22—861no—
825C22—861no—
826C22—3441no—
827C22—3441no—
828C22—3444no—
829C22—1721no—
830C22—1721no—
831C22—1721no—
832C22—1721no—
833C22—1721no—
834C22—1721no—
835C22C4×D4×D4311yescharacteristic
836C22#1458354111yescharacteristic
837C22#1458357611yescharacteristic
838C4—22no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—861no—
843C4—861no—
844C4—1722no—
845C4—1721no—
846C4—1721no—
847C4C2×#1306328711yescharacteristic
848C4#1458337111yescharacteristic
849C4#1458353111yescharacteristic
850C4#1458354011yescharacteristic
851C2—21no—
852C2—21no—
853C2—42no—
854C2—3441no—
855C2—3441no—
856C2—1721no—
857C2—1721no—
858C2#1913757111yescharacteristic
859C2#1914349511yescharacteristic
860C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1866C2
socleC22×C43C2×C4×D4
prime radical#19143815C2
cosocleC22×C4×C43C24
hypercenter#1866D43
hypocenterC43#22887
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. #19143319C2semidirect
4. C2×#14582914C2semidirect
5. #19143042C2semidirect
6. #19135481C2semidirect
7. #19135305C2semidirect
8. #19135241C2semidirect
9. #19135042C2semidirect
10. #19134921C2semidirect
11. #19134920C2semidirect
12. #19134798C2semidirect
13. #19134435C2semidirect
14. #19134360C2semidirect
15. C43×#1866C2semidirect
20. C2×#13063331C22semidirect
24. #14583064C4semidirect
25. #14583062C4semidirect
26. #14583056C4semidirect
27. #14583051C4semidirect
28. #14583047C4semidirect
29. #14583045C4semidirect
30. #14583039C4semidirect
31. #14583034C4semidirect
37. C2×#13063260C22semidirect
40. C2×#13063253C22semidirect
43. C2×#13063251C22semidirect
47. #14582867C22semidirect
55. #14582855C22semidirect
56. C2×#13063235C22semidirect
57. C2×C8×Dic43C22semidirect
58. #14582664C22semidirect
59. #14582663C22semidirect
60. #14582658C22semidirect
61. #14582654C22semidirect
63. C2×#108×C43C22semidirect
64. C43×#424C22semidirect
67. C43×#339C22semidirect
68. C43×#336C22semidirect
128. #13063252D4semidirect
432. #1866D43semidirect
469. C2×#108C2×D43semidirect
470. #424C2×D43semidirect
496. #339C2×D43semidirect
498. #336C2×D43semidirect
499. C43#22887semidirect

Maximal subgroups

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

subgroupindex
#191438152
C2×#145830192
#191433192
C2×#145829142
#191430422
#191354812
#191353052
#191352412
#191350422
#191349212
#191349202
#191347982
#191344352
#191343602
C43×#18662
#2288743