Finite Group Databasebeta

← #25117381

Subgroups — #25117381

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×#14583013C211yesmaximal, characteristic, complemented
3#19143323C211yesmaximal, characteristic, complemented
4C2×#14582914C211yesmaximal, characteristic, complemented
5#19143042C211yesmaximal, characteristic, complemented
6#19135488C211yesmaximal, characteristic, complemented
7#19135300C211yesmaximal, characteristic, complemented
8#19135243C211yesmaximal, characteristic, complemented
9#19135042C211yesmaximal, characteristic, complemented
10#19134923C211yesmaximal, characteristic, complemented
11#19134922C211yesmaximal, characteristic, complemented
12#19134872C211yesmaximal, characteristic, complemented
13#19134801C211yesmaximal, characteristic, complemented
14#19134364C211yesmaximal, characteristic, complemented
15C43×#1765C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063333C2211yescharacteristic, complemented
20C2×#13063332C2211yescharacteristic
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#14583013—24no—
33#14582978—21no—
34#14582972—21no—
35#14582972—21no—
36C8×D172—21no—
37C2×#13063261C2211yescharacteristic, complemented
38C2×#13063260C2211yescharacteristic, complemented
39#14582926C2211yescharacteristic, complemented
40#14582914—24no—
41C2×#13063253C2211yescharacteristic
42C2×#13063253C2211yescharacteristic, complemented
43C2×#13063252C2211yescharacteristic
44C2×#13063251C2211yescharacteristic
45C2×#13063251C2211yescharacteristic, complemented
46#14582893C2211yescharacteristic
47#14582867—21no—
48#14582867C2211yescharacteristic
49#14582865—21no—
50#14582865C2211yescharacteristic
51#14582865C2211yescharacteristic, complemented
52#14582862—21no—
53#14582862C2211yescharacteristic
54C2×(C2×D43)⋊C8—21no—
55C2×(C2×D43)⋊C8C2211yescharacteristic
56C2×(C2×D43)⋊C8C2211yescharacteristic
57C2×C4×C43⋊C8C2211yescharacteristic, complemented
58#14582663C2211yescharacteristic, complemented
59#14582658C2211yescharacteristic, complemented
60#14582653C2211yescharacteristic, complemented
61#14582653C2211yescharacteristic, complemented
62C2×#131×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C43×#405C2211yescharacteristic, complemented
66C2×#97×C43C2211yescharacteristic, complemented
67C43×#341C2211yescharacteristic, complemented
68C43×#339C2211yescharacteristic, 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#13063333—22no—
97#13063333—41no—
98#13063332—22no—
99#13063332—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#13063261—41no—
126#13063260—22no—
127C4⋊(C43⋊C8)—21no—
128C4⋊(C43⋊C8)—21no—
129#13063253—22no—
130#13063253—22no—
131#13063252—22no—
132#13063251—22no—
133#13063251—41no—
134#13063248C2×C411yescharacteristic
135#13063248C2×C411yescharacteristic
136#13063245C2×C411yescharacteristic
137#13063245C2×C411yescharacteristic
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)⋊C8—21no—
144(C2×D43)⋊C8—21no—
145(C2×D43)⋊C8—21no—
146(C2×D43)⋊C8C2×C411yescharacteristic
147(C2×D43)⋊C8C2×C411yescharacteristic
148(C2×D43)⋊C8C2×C411yescharacteristic
149(C2×D43)⋊C8C2×C411yescharacteristic
150(C2×D43)⋊C8D411yescharacteristic
151(C2×D43)⋊C8D411yescharacteristic
152(C2×D43)⋊C8D411yescharacteristic
153(C2×D43)⋊C8D411yescharacteristic
154C4×C43⋊C8—22no—
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#104×C43D414yescomplemented
167#103×C43C2×C411yescharacteristic
168#103×C43C2×C411yescharacteristic
169#102×C43C2×C411yescharacteristic
170#102×C43C2×C411yescharacteristic
171#97×C43—21no—
172#97×C43—41no—
173C4×C8×C43—21no—
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—42no—
241M16×C43C2×D412yes—
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×C43C2×D412yes—
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×Dic43—21no—
273#10621877—21no—
274#10621877—21no—
275#10621877—21no—
276#10621877—21no—
277#10621877—42no—
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—22no—
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—42no—
341C2×Dic43—41no—
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—22no—
375C8×C43—21no—
376C8×C43—21no—
377C8×C43—41no—
378C43⋊C8—21no—
379C43⋊C8—21no—
380C43⋊C8—21no—
381C43⋊C8—21no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22889—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—42no—
410C4×C43—41no—
411C4×C43—41no—
412C4×C43C2×C4×D411yescharacteristic
413C4×C43#51811yescharacteristic
414C4×C43D4211yescharacteristic
415C4×C43#54611yescharacteristic
416Dic43—21no—
417Dic43—21no—
418Dic43—41no—
419Dic43—41no—
420Dic43—81no—
421#3002—431no—
422C2×#443—431no—
423#2933—431no—
424C2×#421—431no—
425#2880—431no—
426#1975—431no—
427#1937—431no—
428#1929—431no—
429#1897—431no—
430#1876—431no—
431#1876—431no—
432#1866—431no—
433#1855—431no—
434#1765D4311yescharacteristic, complemented
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#443—864no—
464#436—861no—
465#435—861no—
466#435—861no—
467C8×D4—861no—
468C2×#108—431no—
469C2×#108—431no—
470#424—431no—
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#405C2×D4311yescharacteristic, complemented
491C2×#97C2×D4311yescharacteristic, complemented
492C2×C4×C8—431no—
493#341—431no—
494#341C2×D4311yescharacteristic, complemented
495#339—431no—
496#339C2×D4311yescharacteristic, complemented
497#336—431no—
498#336—431no—
499C43#2288911yescharacteristic, 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—862no—
568#108—1721no—
569C4⋊C8—861no—
570C4⋊C8—861no—
571#104—862no—
572#104—862no—
573#104—862no—
574#104—862no—
575#104—1721no—
576#104D17214yescomplemented
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—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—862no—
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#41C2×D17212yes—
626#41#1062189812yes—
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—42no—
680M16—861no—
681M16—861no—
682M16—861no—
683M16—861no—
684M16—1722no—
685M16—1722no—
686M16—1722no—
687M16C2×D17212yes—
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—861no—
726C42—861no—
727C42C2×D17212yes—
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—
747Q8C4×D17212yes—
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—
764D4C4×D17212yes—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
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—1722no—
788C2×C4—1722no—
789C2×C4—1722no—
790C2×C4—1721no—
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×C4C22×D17211yescharacteristic
800C2×C4C2×#1062189811yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337111yescharacteristic
803C8—21no—
804C8—21no—
805C8—22no—
806C8—21no—
807C8—21no—
808C8—41no—
809C8—861no—
810C8—861no—
811C8—861no—
812C8—861no—
813C8—1721no—
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#1458354411yescharacteristic
837C22#1458357311yescharacteristic
838C4—22no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—861no—
843C4—861no—
844C4—3441no—
845C4—1721no—
846C4—1721no—
847C4C2×C4×D17211yescharacteristic
848C4#1458337111yescharacteristic
849C4D4×D17211yescharacteristic
850C4#1458353911yescharacteristic
851C2—21no—
852C2—21no—
853C2—42no—
854C2—3441no—
855C2—3441no—
856C2—1721no—
857C2—1721no—
858C2#1913757711yescharacteristic
859C2#1914349511yescharacteristic
860C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1765C2
socleC22×C43C2×C4×D4
prime radical#19143815C2
cosocleC22×C4×C43C24
hypercenter#1765D43
hypocenterC43#22889
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. C2×#14583013C2semidirect
3. #19143323C2semidirect
4. C2×#14582914C2semidirect
5. #19143042C2semidirect
6. #19135488C2semidirect
7. #19135300C2semidirect
8. #19135243C2semidirect
9. #19135042C2semidirect
10. #19134923C2semidirect
11. #19134922C2semidirect
12. #19134872C2semidirect
13. #19134801C2semidirect
14. #19134364C2semidirect
15. C43×#1765C2semidirect
19. C2×#13063333C22semidirect
24. #14583064C4semidirect
25. #14583062C4semidirect
26. #14583056C4semidirect
27. #14583051C4semidirect
28. #14583047C4semidirect
29. #14583045C4semidirect
30. #14583039C4semidirect
31. #14583034C4semidirect
37. C2×#13063261C22semidirect
38. C2×#13063260C22semidirect
39. #14582926C22semidirect
42. C2×#13063253C22semidirect
45. C2×#13063251C22semidirect
51. #14582865C22semidirect
57. C2×C4×C43⋊C8C22semidirect
58. #14582663C22semidirect
59. #14582658C22semidirect
60. #14582653C22semidirect
61. #14582653C22semidirect
65. C43×#405C22semidirect
66. C2×#97×C43C22semidirect
67. C43×#341C22semidirect
68. C43×#339C22semidirect
166. #104×C43D4semidirect
434. #1765D43semidirect
490. #405C2×D43semidirect
491. C2×#97C2×D43semidirect
494. #341C2×D43semidirect
496. #339C2×D43semidirect
499. C43#22889semidirect
576. #104D172semidirect

Maximal subgroups

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

subgroupindex
#191438152
C2×#145830132
#191433232
C2×#145829142
#191430422
#191354882
#191353002
#191352432
#191350422
#191349232
#191349222
#191348722
#191348012
#191343642
C43×#17652
#2288943