Finite Group Databasebeta

← #25117343

Subgroups — #25117343

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
2#19143317C211yesmaximal, characteristic, complemented
3C2×#14582914C211yesmaximal, characteristic, complemented
4#19143042C211yesmaximal, characteristic, complemented
5#19135480C211yesmaximal, characteristic, complemented
6#19135306C211yesmaximal, characteristic, complemented
7#19135242C211yesmaximal, characteristic, complemented
8#19135040C211yesmaximal, characteristic, complemented
9#19134924C211yesmaximal, characteristic, complemented
10#19134922C211yesmaximal, characteristic, complemented
11#19134870C211yesmaximal, characteristic, complemented
12#19134798C211yesmaximal, characteristic, complemented
13#19134433C211yesmaximal, characteristic, complemented
14#19134364C211yesmaximal, characteristic, complemented
15C2×C43×#444C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20#14583406C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22#14583060C411yescharacteristic, complemented
23#14583058C411yescharacteristic, complemented
24#14583053C411yescharacteristic, complemented
25#14583048C411yescharacteristic, complemented
26#14583043C411yescharacteristic, complemented
27#14583041C411yescharacteristic, complemented
28#14583036C411yescharacteristic, complemented
29#14583031C411yescharacteristic, complemented
30#14582975—21no—
31#14582970—21no—
32#14582968—21no—
33C8×C22⋊D43—21no—
34C2×#13063260C2211yescharacteristic, complemented
35#14582925C2211yescharacteristic, complemented
36#14582914—24no—
37C2×#13063253C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39C2×#13063252C2211yescharacteristic, complemented
40C2×#13063251C2211yescharacteristic
41#14582896C2211yescharacteristic
42#14582895C2211yescharacteristic
43#14582867—21no—
44#14582867C2211yescharacteristic
45#14582866C2211yescharacteristic, complemented
46#14582865—21no—
47#14582865C2211yescharacteristic
48#14582862—21no—
49#14582862C2211yescharacteristic
50C2×(C2×D43)⋊C8—21no—
51C2×(C2×D43)⋊C8C2211yescharacteristic
52C2×(C2×D43)⋊C8C2211yescharacteristic
53#14582857C2211yescharacteristic, complemented
54C2×C4×C43⋊C8C2211yescharacteristic, complemented
55#14582664C2211yescharacteristic, complemented
56#14582663C2211yescharacteristic, complemented
57#14582660C2211yescharacteristic, complemented
58#14582659C2211yescharacteristic, complemented
59#14582653C2211yescharacteristic, complemented
60#14582653C2211yescharacteristic, complemented
61C2×#135×C43C2211yescharacteristic
62C2×#131×C43C2211yescharacteristic
63C2×#131×C43C2211yescharacteristic, complemented
64C43×#444—24no—
65C2×#108×C43C2211yescharacteristic, complemented
66C2×#104×C43C2211yescharacteristic
67C2×#104×C43C2211yescharacteristic, complemented
68C2×#97×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—41no—
84#13063345—41no—
85C2×#10621885C2×C411yescharacteristic
86C2×#10621883C2×C411yescharacteristic
87C2×#10621884C2×C411yescharacteristic
88C2×#10621882C2×C411yescharacteristic
89#13063332—22no—
90#13063332—41no—
91C2×#10621877—21no—
92C2×#10621877C2311yescharacteristic
93C2×#10621877C2311yescharacteristic
94C2×#10621872—21no—
95M16×D43—22no—
96M16×D43—41no—
97C22×C43⋊C8—21no—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C2×C8×D43—21no—
101#13063306—21no—
102#13063301C2×C411yescharacteristic
103#13063301C2×C411yescharacteristic
104#13063296C2×C411yescharacteristic
105#13063296C2×C411yescharacteristic
106#13063293—21no—
107C4×C22⋊D43—21no—
108C4×C22⋊D43—21no—
109#13063284C2311yescharacteristic
110#13063282—22no—
111#13063282—41no—
112C2×Dic43⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×C4×Dic43C2311yescharacteristic
115#13063260—41no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118#13063253—22no—
119#13063252—22no—
120#13063252—41no—
121#13063251—22no—
122#13063250C2×C411yescharacteristic
123#13063250C2×C411yescharacteristic
124#13063249C2×C411yescharacteristic
125#13063249C2×C411yescharacteristic
126#13063247C2×C411yescharacteristic
127#13063247C2×C411yescharacteristic
128#13063246C2×C411yescharacteristic
129#13063246C2×C411yescharacteristic
130C22⋊(C43⋊C8)—21no—
131C22⋊(C43⋊C8)—21no—
132(C2×D43)⋊C8—21no—
133(C2×D43)⋊C8—21no—
134(C2×D43)⋊C8—21no—
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137(C2×D43)⋊C8—21no—
138(C2×D43)⋊C8C2×C411yescharacteristic
139(C2×D43)⋊C8C2×C411yescharacteristic
140(C2×D43)⋊C8C2×C411yescharacteristic
141(C2×D43)⋊C8C2×C411yescharacteristic
142(C2×D43)⋊C8D411yescharacteristic
143(C2×D43)⋊C8D411yescharacteristic
144(C2×D43)⋊C8D411yescharacteristic
145(C2×D43)⋊C8D411yescharacteristic
146#13063235—21no—
147C4×C43⋊C8—41no—
148C8×Dic43—21no—
149C2×#41×C43C2311yescharacteristic
150C2×#41×C43C2311yescharacteristic
151#135×C43—22no—
152#135×C43—22no—
153C2×Q16×C43C2×C411yescharacteristic
154C2×SD16×C43C2×C411yescharacteristic
155C2×SD16×C43C2×C411yescharacteristic
156C2×D8×C43C2×C411yescharacteristic
157#131×C43—22no—
158#131×C43—22no—
159#131×C43—41no—
160#131×C43—41no—
161C2×M16×C43—21no—
162C2×M16×C43—21no—
163C2×M16×C43C2311yescharacteristic
164C2×M16×C43C2311yescharacteristic
165C22×C8×C43—21no—
166C22×C8×C43—21no—
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C2×C42×C43C2311yescharacteristic
170#108×C43—22no—
171#104×C43—22no—
172#104×C43D414yescomplemented
173#97×C43—22no—
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×C43C2×D412yes—
183#41×C43#4112yes—
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—21no—
217#10621898—21no—
218#10621898—42no—
219#10621898—42no—
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—22no—
238SD16×C43—22no—
239SD16×C43—22no—
240D8×C43—22no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244M16×C43—42no—
245M16×C43—42no—
246M16×C43C2×D412yes—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—42no—
254C2×C8×C43—42no—
255C2×C8×C43C22×C411yescharacteristic
256C2×C8×C43C22×C411yescharacteristic
257C2×C8×C43C2×D411yescharacteristic
258C2×C8×C43C2×D411yescharacteristic
259C42×C43—21no—
260C42×C43C2×D412yes—
261C22⋊Dic43—21no—
262C22⋊Dic43—21no—
263C22⋊Dic43—21no—
264#10621885—41no—
265#10621884—41no—
266#10621883—41no—
267#10621882—41no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—42no—
271C4⋊Dic43C22×C411yescharacteristic
272C4⋊Dic43C22×C411yescharacteristic
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—42no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279#10621877—21no—
280#10621877—21no—
281#10621877—21no—
282#10621877—21no—
283#10621877—42no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—42no—
291C2×C43⋊C8C22×C411yescharacteristic
292C2×C43⋊C8C22×C411yescharacteristic
293C2×C43⋊C8C2×D411yescharacteristic
294C2×C43⋊C8C2×D411yescharacteristic
295#10621872—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×C43C4×D412yes—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—21no—
317D4×C43—21no—
318D4×C43—21no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43C4×D412yes—
322C2×C4×C43—21no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
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—42no—
338C22⋊D43—42no—
339C22⋊D43—42no—
340C22⋊D43—41no—
341C22⋊D43—41no—
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—21no—
356D172—42no—
357C4×D43—21no—
358C4×D43—21no—
359C4×D43—21no—
360C4×D43—21no—
361C4×D43—21no—
362C4×D43—21no—
363C4×D43—21no—
364C4×D43—21no—
365C4×D43—42no—
366C4×D43—42no—
367C4×D43—41no—
368C4×D43—41no—
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#22887—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—22no—
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—21no—
399C2×D43—21no—
400C2×D43—21no—
401C2×D43—21no—
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×C43C2×C4×D411yescharacteristic
412C4×C43#51811yescharacteristic
413C4×C43D4211yescharacteristic
414C4×C43#54611yescharacteristic
415Dic43—21no—
416Dic43—21no—
417Dic43—41no—
418Dic43—41no—
419Dic43—41no—
420Dic43—81no—
421#3002—431no—
422C2×#444D4311yescharacteristic, complemented
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#1866—431no—
433#1855—431no—
434#1764—431no—
435#1750—431no—
436C2×C43—21no—
437C2×C43—21no—
438C2×C43—42no—
439C2×C43—81no—
440C2×C43#235811yescharacteristic
441C2×C43#295511yescharacteristic
442C2×C43#295711yescharacteristic
443D43—41no—
444D43—41no—
445D43—81no—
446C22×#41—431no—
447C2×#135—431no—
448C2×#135C2×D4311yescharacteristic
449C2×#131—431no—
450C2×#131C2×D4311yescharacteristic
451C2×#131C2×D4311yescharacteristic, complemented
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—24no—
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—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×#97C2×D4311yescharacteristic, complemented
492C2×C4×C8—431no—
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—22no—
517#135—22no—
518#135—1721no—
519#135—1721no—
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—22no—
529#131—22no—
530#131—41no—
531#131—41no—
532#131—862no—
533#131—1721no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—431no—
537C2×M16—431no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—862no—
541C2×M16—1721no—
542C2×M16C22×D4311yescharacteristic
543C2×M16C22×D4311yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—431no—
547C22×C8—431no—
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—22no—
568#108—1721no—
569C4⋊C8—861no—
570C4⋊C8—861no—
571#104—22no—
572#104—862no—
573#104—862no—
574#104—862no—
575#104—1721no—
576#104C22⋊D4314yescomplemented
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—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—22no—
602#97—861no—
603C4×C8—861no—
604C4×C8—1721no—
605C24—431no—
606C24—861no—
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—862no—
614#41—862no—
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#41#1062189812yes—
626#41C2×C22⋊D4312yes—
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—22no—
669Q16—1721no—
670SD16—22no—
671SD16—22no—
672SD16—1721no—
673SD16—1721no—
674D8—22no—
675D8—1721no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—42no—
680M16—42no—
681M16—861no—
682M16—861no—
683M16—861no—
684M16—861no—
685M16—1722no—
686M16—1722no—
687M16C2×C22⋊D4312yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—431no—
697C2×C8—431no—
698C2×C8—431no—
699C2×C8—431no—
700C2×C8—861no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
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—
727C42C2×C22⋊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—861no—
745Q8—861no—
746Q8—1722no—
747Q8C4×C22⋊D4312yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—41no—
754D4—41no—
755D4—861no—
756D4—861no—
757D4—3441no—
758D4—1722no—
759D4—1722no—
760D4—1722no—
761D4—1722no—
762D4—1721no—
763D4—1721no—
764D4C4×C22⋊D4312yes—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
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—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—1722no—
790C2×C4—1722no—
791C2×C4—1722no—
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×C22⋊D4311yescharacteristic
800C2×C4C2×#1062189811yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337111yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—22no—
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—41no—
821C22—41no—
822C22—41no—
823C22—861no—
824C22—861no—
825C22—861no—
826C22—861no—
827C22—861no—
828C22—861no—
829C22—3441no—
830C22—3441no—
831C22—3444no—
832C22—1721no—
833C22—1721no—
834C22—1721no—
835C22C4×D4×D4311yescharacteristic
836C22#1458353711yescharacteristic
837C22#1458357811yescharacteristic
838C4—22no—
839C4—42no—
840C4—41no—
841C4—861no—
842C4—861no—
843C4—3441no—
844C4—1721no—
845C4—1721no—
846C4—1721no—
847C4C2×C4×C22⋊D4311yescharacteristic
848C4#1458337111yescharacteristic
849C4D4×C22⋊D4311yescharacteristic
850C4#1458354511yescharacteristic
851C2—21no—
852C2—21no—
853C2—42no—
854C2—81no—
855C2—3441no—
856C2—1721no—
857C2—1721no—
858C2#1913757211yescharacteristic
859C2#1914349511yescharacteristic
860C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#444C2
socleC22×C43C2×C4×D4
prime radical#19143809C2
cosocleC22×C4×C43C24
hypercenterC2×#444D43
hypocenterC43#22887
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
2. #19143317C2semidirect
3. C2×#14582914C2semidirect
4. #19143042C2semidirect
5. #19135480C2semidirect
6. #19135306C2semidirect
7. #19135242C2semidirect
8. #19135040C2semidirect
9. #19134924C2semidirect
10. #19134922C2semidirect
11. #19134870C2semidirect
12. #19134798C2semidirect
13. #19134433C2semidirect
14. #19134364C2semidirect
15. C2×C43×#444C2semidirect
22. #14583060C4semidirect
23. #14583058C4semidirect
24. #14583053C4semidirect
25. #14583048C4semidirect
26. #14583043C4semidirect
27. #14583041C4semidirect
28. #14583036C4semidirect
29. #14583031C4semidirect
34. C2×#13063260C22semidirect
35. #14582925C22semidirect
39. C2×#13063252C22semidirect
45. #14582866C22semidirect
53. #14582857C22semidirect
54. C2×C4×C43⋊C8C22semidirect
55. #14582664C22semidirect
56. #14582663C22semidirect
57. #14582660C22semidirect
58. #14582659C22semidirect
59. #14582653C22semidirect
60. #14582653C22semidirect
63. C2×#131×C43C22semidirect
65. C2×#108×C43C22semidirect
67. C2×#104×C43C22semidirect
68. C2×#97×C43C22semidirect
172. #104×C43D4semidirect
422. C2×#444D43semidirect
451. C2×#131C2×D43semidirect
469. C2×#108C2×D43semidirect
477. C2×#104C2×D43semidirect
491. C2×#97C2×D43semidirect
499. C43#22887semidirect
576. #104C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191438092
#191433172
C2×#145829142
#191430422
#191354802
#191353062
#191352422
#191350402
#191349242
#191349222
#191348702
#191347982
#191344332
#191343642
C2×C43×#4442
#2288743