Finite Group Databasebeta

← #25117348

Subgroups — #25117348

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#19143809C211yesmaximal, characteristic
2C2×#14583018C211yesmaximal, characteristic, complemented
3#19143325C211yesmaximal, characteristic, complemented
4C2×#14582914C211yesmaximal, characteristic, complemented
5#19143043C211yesmaximal, characteristic, complemented
6#19135303C211yesmaximal, characteristic, complemented
7#19135240C211yesmaximal, characteristic, complemented
8#19135040C211yesmaximal, characteristic, complemented
9#19134925C211yesmaximal, characteristic, complemented
10#19134924C211yesmaximal, characteristic, complemented
11#19134867C211yesmaximal, characteristic, complemented
12#19134798C211yesmaximal, characteristic, complemented
13#19134432C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic, complemented
15C43×#1974C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063333C2211yescharacteristic
19C2×#13063332C2211yescharacteristic, complemented
20C2×#13063331C2211yescharacteristic
21C2×M16×D43C2211yescharacteristic
22#14583406C2211yescharacteristic
23C2×#13063282C2211yescharacteristic
24#14583060C411yescharacteristic, complemented
25#14583058C411yescharacteristic, complemented
26#14583053C411yescharacteristic, complemented
27#14583048C411yescharacteristic, complemented
28#14583043C411yescharacteristic, complemented
29#14583041C411yescharacteristic, complemented
30#14583036C411yescharacteristic, complemented
31#14583031C411yescharacteristic, complemented
32#14583018—24no—
33#14582974—21no—
34#14582973—21no—
35#14582967—21no—
36(C22⋊D43)⋊C8—21no—
37C2×#13063260C2211yescharacteristic, complemented
38#14582927C2211yescharacteristic, complemented
39#14582914—24no—
40C2×#13063253C2211yescharacteristic
41C2×#13063252C2211yescharacteristic
42C2×#13063252C2211yescharacteristic, complemented
43C2×#13063251C2211yescharacteristic
44#14582896C2211yescharacteristic
45#14582895C2211yescharacteristic
46#14582866C2211yescharacteristic
47#14582864—21no—
48#14582864—21no—
49#14582862C2211yescharacteristic
50#14582861—21no—
51C2×(C2×D43)⋊C8C2211yescharacteristic
52C2×(C2×D43)⋊C8C2211yescharacteristic
53C22⋊C8×D43—21no—
54#14582854C2211yescharacteristic, complemented
55C2×#13063236C2211yescharacteristic, complemented
56#14582664C2211yescharacteristic, complemented
57#14582663C2211yescharacteristic, complemented
58#14582660C2211yescharacteristic, complemented
59#14582659C2211yescharacteristic, complemented
60#14582653C2211yescharacteristic, complemented
61#14582653C2211yescharacteristic, complemented
62C2×#135×C43C2211yescharacteristic
63C2×#108×C43C2211yescharacteristic, complemented
64C2×#104×C43C2211yescharacteristic
65C2×#104×C43C2211yescharacteristic, complemented
66C43×#408C2211yescharacteristic
67C43×#408C2211yescharacteristic, complemented
68C2×C4×C8×C43C2211yescharacteristic, complemented
69C2×#10621902C2×C411yescharacteristic
70C2×#10621898—21no—
71C2×#10621898C2311yescharacteristic
72C2×#10621900—21no—
73C2×#10621900C2×C411yescharacteristic
74#41×D43—22no—
75#41×D43—22no—
76#41×D43—41no—
77#41×D43—41no—
78C2×Q8×D43C2×C411yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43C2×C411yescharacteristic
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83#13063345—22no—
84#13063345—22no—
85C2×#10621885C2×C411yescharacteristic
86C2×#10621883C2×C411yescharacteristic
87C2×#10621884C2×C411yescharacteristic
88C2×#10621882C2×C411yescharacteristic
89#13063333—22no—
90#13063333—41no—
91#13063332—22no—
92#13063332—41no—
93#13063331—22no—
94#13063331—41no—
95C2×#10621877—21no—
96C2×#10621877C2311yescharacteristic
97C2×#10621877C2311yescharacteristic
98C2×#10621872—21no—
99C2×#10621872—21no—
100C2×#10621872—21no—
101M16×D43—22no—
102M16×D43—41no—
103C22×C43⋊C8—21no—
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C2×C8×D43—21no—
107C2×C8×D43—21no—
108C2×C8×D43—21no—
109#13063306—21no—
110#13063301C2×C411yescharacteristic
111#13063301C2×C411yescharacteristic
112#13063296C2×C411yescharacteristic
113#13063296C2×C411yescharacteristic
114#13063293—21no—
115C4×C22⋊D43—21no—
116C4×C22⋊D43—21no—
117#13063284C2311yescharacteristic
118#13063282—22no—
119#13063282—41no—
120C2×Dic43⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×C4×Dic43C2311yescharacteristic
123#13063260—22no—
124Dic43⋊C8—21no—
125Dic43⋊C8—21no—
126#13063253D414yescomplemented
127#13063252—22no—
128#13063252—41no—
129#13063251—22no—
130#13063250C2×C411yescharacteristic
131#13063250C2×C411yescharacteristic
132#13063249C2×C411yescharacteristic
133#13063249C2×C411yescharacteristic
134#13063247C2×C411yescharacteristic
135#13063247C2×C411yescharacteristic
136#13063246C2×C411yescharacteristic
137#13063246C2×C411yescharacteristic
138C22⋊(C43⋊C8)—21no—
139C22⋊(C43⋊C8)—21no—
140(C2×D43)⋊C8—21no—
141(C2×D43)⋊C8—21no—
142(C2×D43)⋊C8C2×C411yescharacteristic
143(C2×D43)⋊C8C2×C411yescharacteristic
144(C2×D43)⋊C8C2×C411yescharacteristic
145(C2×D43)⋊C8C2×C411yescharacteristic
146(C2×D43)⋊C8D411yescharacteristic
147(C2×D43)⋊C8D411yescharacteristic
148(C2×D43)⋊C8D411yescharacteristic
149(C2×D43)⋊C8D411yescharacteristic
150#13063236—22no—
151#13063235—21no—
152C8×Dic43—21no—
153C2×#41×C43C2311yescharacteristic
154C2×#41×C43C2311yescharacteristic
155#135×C43—41no—
156#135×C43—41no—
157C2×Q16×C43C2×C411yescharacteristic
158C2×SD16×C43C2×C411yescharacteristic
159C2×SD16×C43C2×C411yescharacteristic
160C2×D8×C43C2×C411yescharacteristic
161C2×M16×C43C2311yescharacteristic
162C2×M16×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C2×C42×C43C2311yescharacteristic
166#108×C43—41no—
167#104×C43—22no—
168#104×C43—22no—
169C22⋊C8×C43—21no—
170C22⋊C8×C43—21no—
171C22⋊C8×C43—21no—
172C22⋊C8×C43—21no—
173C4×C8×C43—41no—
174C23×D43—21no—
175C23×D43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184C2×Q8×C43C22×C411yescharacteristic
185C2×Q8×C43C22×C411yescharacteristic
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43C22×C411yescharacteristic
189C2×D4×C43C22×C411yescharacteristic
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C2×C22⋊D43—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43#4111yescharacteristic
202#10621902—22no—
203#10621902—41no—
204Q8×D43—22no—
205Q8×D43—41no—
206#10621900—22no—
207#10621900—41no—
208#10621900—42no—
209#10621900—42no—
210D4×D43—22no—
211D4×D43—42no—
212D4×D43—42no—
213D4×D43—41no—
214#10621898—21no—
215#10621898—21no—
216#10621898—42no—
217#10621898—42no—
218#10621898C2×D412yes—
219#10621898#4112yes—
220C2×D172—21no—
221C2×D172C22×C411yescharacteristic
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—21no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×C4×D43C22×C411yescharacteristic
232C2×C4×D43C22×C411yescharacteristic
233C2×C4×D43C2×D411yescharacteristic
234C2×C4×D43C2×D411yescharacteristic
235C2×Dic86—21no—
236C2×Dic86C22×C411yescharacteristic
237Q16×C43—41no—
238SD16×C43—41no—
239SD16×C43—41no—
240D8×C43—41no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244M16×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43C22×C411yescharacteristic
252C2×C8×C43C22×C411yescharacteristic
253C2×C8×C43C2×D411yescharacteristic
254C2×C8×C43C2×D411yescharacteristic
255C42×C43—21no—
256C42×C43C2×D412yes—
257C22⋊Dic43—21no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260#10621885—22no—
261#10621884—22no—
262#10621883—22no—
263#10621882—22no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—42no—
267C4⋊Dic43C22×C411yescharacteristic
268C4⋊Dic43C22×C411yescharacteristic
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—42no—
272C4×Dic43—21no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275#10621877—21no—
276#10621877—21no—
277#10621877—21no—
278#10621877—42no—
279#10621877C2×D412yes—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—42no—
287C2×C43⋊C8C22×C411yescharacteristic
288C2×C43⋊C8C22×C411yescharacteristic
289C2×C43⋊C8C2×D411yescharacteristic
290C2×C43⋊C8C2×D411yescharacteristic
291#10621872—42no—
292#10621872—42no—
293#10621872—42no—
294C8×D43—42no—
295C8×D43—42no—
296C8×D43—42no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43C2×#4111yescharacteristic
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×C43—21no—
312Q8×C43—21no—
313Q8×C43—21no—
314D4×C43—21no—
315D4×C43—21no—
316D4×C43—21no—
317D4×C43—21no—
318D4×C43—41no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—41no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43C23×C411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C2×#4111yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C2×C4×C43H(5,𝔽2)11yescharacteristic
337C22⋊D43—22no—
338C22⋊D43—22no—
339C22⋊D43—42no—
340C22⋊D43—42no—
341C22⋊D43—42no—
342C22⋊D43—81no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—42no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43C4×D411yescharacteristic
353C2×Dic43C4×D411yescharacteristic
354D172—21no—
355D172—42no—
356D172C4×D412yes—
357C4×D43—21no—
358C4×D43—21no—
359C4×D43—21no—
360C4×D43—21no—
361C4×D43—21no—
362C4×D43—22no—
363C4×D43—21no—
364C4×D43—22no—
365C4×D43—21no—
366C4×D43—21no—
367C4×D43—42no—
368C4×D43—42no—
369Dic86—21no—
370Dic86—42no—
371Dic86C4×D412yes—
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—21no—
381C43⋊C8—22no—
382C43⋊C8—21no—
383C43⋊C8—41no—
384#22887—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43C2×C4×D411yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43#55111yescharacteristic
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—22no—
399C2×D43—21no—
400C2×D43—21no—
401C2×D43—21no—
402C2×D43—21no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43—81no—
406C2×D43—81no—
407C2×D43—84no—
408C4×C43—42no—
409C4×C43—41no—
410C4×C43—41no—
411C4×C43C2×C4×D411yescharacteristic
412C4×C43#51811yescharacteristic
413C4×C43D4211yescharacteristic
414C4×C43#54611yescharacteristic
415Dic43—22no—
416Dic43—21no—
417Dic43—21no—
418Dic43—41no—
419Dic43—41no—
420Dic43—81no—
421#3002—431no—
422C2×#444—431no—
423#2933—431no—
424C2×#421—431no—
425#2880—431no—
426#1974D4311yescharacteristic, complemented
427#1938—431no—
428#1929—431no—
429#1897—431no—
430#1876—431no—
431#1876—431no—
432#1866—431no—
433#1855—431no—
434#1764—431no—
435#1750—431no—
436C2×C43—21no—
437C2×C43—21no—
438C2×C43—81no—
439C2×C43—81no—
440C2×C43#235811yescharacteristic
441C2×C43#295511yescharacteristic
442C2×C43#295711yescharacteristic
443D43—41no—
444D43—41no—
445D43—42no—
446C22×#41—431no—
447C2×#135—431no—
448C2×#135C2×D4311yescharacteristic
449C2×#131—431no—
450C2×#131—431no—
451C2×#131—431no—
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#424—431no—
471#421—864no—
472C2×#104—431no—
473C2×#104—431no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104C2×D4311yescharacteristic
477C2×#104C2×D4311yescharacteristic, complemented
478#416—431no—
479#416—431no—
480#408—431no—
481#408—861no—
482#408—861no—
483#408C2×D4311yescharacteristic
484#408C2×D4311yescharacteristic, complemented
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×C8C2×D4311yescharacteristic, complemented
493#341—431no—
494#341—431no—
495#339—431no—
496#339—431no—
497#336—431no—
498#336—431no—
499C43#2288711yescharacteristic, complemented, Sylow
500C2×#41—431no—
501C2×#41—431no—
502C2×#41—431no—
503C2×#41—861no—
504C2×#41—861no—
505C2×#41—862no—
506C2×#41—862no—
507C2×#41—1721no—
508C2×#41—1721no—
509C2×#41C22×D4311yescharacteristic
510C2×#41C22×D4311yescharacteristic
511C22×Q8—431no—
512C22×D4—431no—
513C22×D4—861no—
514C23×C4—431no—
515C23×C4—861no—
516#135—41no—
517#135—41no—
518#135—862no—
519#135—862no—
520C2×Q16—431no—
521C2×Q16C4×D4311yescharacteristic
522C2×SD16—431no—
523C2×SD16—431no—
524C2×SD16C4×D4311yescharacteristic
525C2×SD16C4×D4311yescharacteristic
526C2×D8—431no—
527C2×D8C4×D4311yescharacteristic
528#131—862no—
529#131—862no—
530#131—862no—
531#131—1721no—
532#131—1721no—
533#131—1721no—
534C2×M16—431no—
535C2×M16—431no—
536C2×M16—861no—
537C2×M16—861no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—862no—
541C2×M16—1721no—
542C2×M16C22×D4311yescharacteristic
543C2×M16C22×D4311yescharacteristic
544C22×C8—431no—
545C22×C8—431no—
546C22×C8—861no—
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—431no—
561#117—862no—
562#117—1721no—
563C2×C4⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C42—431no—
566C2×C42C22×D4311yescharacteristic
567#108—41no—
568#108—862no—
569C4⋊C8—861no—
570C4⋊C8—861no—
571#104—22no—
572#104—22no—
573#104—434no—
574#104—862no—
575#104—862no—
576#104—1721no—
577#103—431no—
578#103—431no—
579#103—431no—
580#103—431no—
581#102—431no—
582#102—431no—
583#102—431no—
584#102—431no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—431no—
590C22⋊C8—431no—
591C22⋊C8—431no—
592C22⋊C8—431no—
593C22⋊C8—431no—
594C22⋊C8—431no—
595C22⋊C8—431no—
596C22⋊C8—431no—
597C22⋊C8—861no—
598C22⋊C8—861no—
599C22⋊C8—861no—
600C22⋊C8—861no—
601#97—861no—
602#97—862no—
603C4×C8—41no—
604C4×C8—861no—
605C24—431no—
606C24—861no—
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—432no—
616#41—432no—
617#41—861no—
618#41—861no—
619#41—862no—
620#41—862no—
621#41—1722no—
622#41—1722no—
623#41—1721no—
624#41—1722no—
625#41—1722no—
626#41—1721no—
627C2×Q8—431no—
628C2×Q8—861no—
629C2×Q8—862no—
630C2×Q8—1721no—
631C2×Q8C2×C4×D4311yescharacteristic
632C2×Q8C2×C4×D4311yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—431no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—862no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—1721no—
644C2×D4—1722no—
645C2×D4—1722no—
646C2×D4C2×C4×D4311yescharacteristic
647C2×D4C2×C4×D4311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
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—41no—
669Q16—862no—
670SD16—41no—
671SD16—41no—
672SD16—862no—
673SD16—862no—
674D8—41no—
675D8—862no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—432no—
681M16—861no—
682M16—861no—
683M16—861no—
684M16—1722no—
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—431no—
695C2×C8—431no—
696C2×C8—431no—
697C2×C8—431no—
698C2×C8—861no—
699C2×C8—861no—
700C2×C8—861no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—1722no—
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—431no—
713C4⋊C4—431no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—1722no—
717C22⋊C4—861no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—1722no—
723C42—21no—
724C42—861no—
725C42—861no—
726C42—861no—
727C42D4×D4312yes—
728C23—21no—
729C23—21no—
730C23—431no—
731C23—431no—
732C23—861no—
733C23—861no—
734C23—861no—
735C23—3441no—
736C23—1721no—
737C23—1721no—
738C23—1722no—
739C23—1722no—
740C23#41×D4311yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—432no—
746Q8—861no—
747Q8—1722no—
748D4—21no—
749D4—21no—
750D4—21no—
751D4—21no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—432no—
757D4—862no—
758D4—862no—
759D4—861no—
760D4—3441no—
761D4—1722no—
762D4—1722no—
763D4—1722no—
764D4—1722no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—431no—
775C2×C4—431no—
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—862no—
785C2×C4—861no—
786C2×C4—862no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—1722no—
792C2×C4—1722no—
793C2×C4—1722no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4C22×C4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C2×D4×D4311yescharacteristic
800C2×C4#41×D4311yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337011yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—861no—
810C8—861no—
811C8—861no—
812C8—861no—
813C8—862no—
814C8—1721no—
815C22—21no—
816C22—21no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—861no—
824C22—861no—
825C22—862no—
826C22—861no—
827C22—861no—
828C22—861no—
829C22—861no—
830C22—3441no—
831C22—3441no—
832C22—3444no—
833C22—1721no—
834C22—1721no—
835C22C4×D4×D4311yescharacteristic
836C22#1458353811yescharacteristic
837C22#1458357911yescharacteristic
838C4—42no—
839C4—41no—
840C4—41no—
841C4—861no—
842C4—861no—
843C4—862no—
844C4—3441no—
845C4—1721no—
846C4—1721no—
847C4C4×D4×D4311yescharacteristic
848C4#1458337211yescharacteristic
849C4#1458353411yescharacteristic
850C4#1458353811yescharacteristic
851C2—21no—
852C2—21no—
853C2—81no—
854C2—81no—
855C2—1721no—
856C2—1721no—
857C2—1722no—
858C2#1913757611yescharacteristic
859C2#1914349311yescharacteristic
860C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1974C2
socleC22×C43C2×C4×D4
prime radical#19143809C2
cosocleC22×C4×C43C24
hypercenter#1974D43
hypocenterC43#22887
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C2×#14583018C2semidirect
3. #19143325C2semidirect
4. C2×#14582914C2semidirect
5. #19143043C2semidirect
6. #19135303C2semidirect
7. #19135240C2semidirect
8. #19135040C2semidirect
9. #19134925C2semidirect
10. #19134924C2semidirect
11. #19134867C2semidirect
12. #19134798C2semidirect
13. #19134432C2semidirect
14. #19134362C2semidirect
15. C43×#1974C2semidirect
19. C2×#13063332C22semidirect
24. #14583060C4semidirect
25. #14583058C4semidirect
26. #14583053C4semidirect
27. #14583048C4semidirect
28. #14583043C4semidirect
29. #14583041C4semidirect
30. #14583036C4semidirect
31. #14583031C4semidirect
37. C2×#13063260C22semidirect
38. #14582927C22semidirect
42. C2×#13063252C22semidirect
54. #14582854C22semidirect
55. C2×#13063236C22semidirect
56. #14582664C22semidirect
57. #14582663C22semidirect
58. #14582660C22semidirect
59. #14582659C22semidirect
60. #14582653C22semidirect
61. #14582653C22semidirect
63. C2×#108×C43C22semidirect
65. C2×#104×C43C22semidirect
67. C43×#408C22semidirect
68. C2×C4×C8×C43C22semidirect
126. #13063253D4semidirect
426. #1974D43semidirect
469. C2×#108C2×D43semidirect
477. C2×#104C2×D43semidirect
484. #408C2×D43semidirect
492. C2×C4×C8C2×D43semidirect
499. C43#22887semidirect

Maximal subgroups

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

subgroupindex
#191438092
C2×#145830182
#191433252
C2×#145829142
#191430432
#191353032
#191352402
#191350402
#191349252
#191349242
#191348672
#191347982
#191344322
#191343622
C43×#19742
#2288743