Finite Group Databasebeta

← #25117349

Subgroups — #25117349

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#19143813C211yesmaximal, characteristic
2C2×#14583018C211yesmaximal, characteristic, complemented
3#19143320C211yesmaximal, characteristic, complemented
4#19143044C211yesmaximal, characteristic, complemented
5#19135480C211yesmaximal, characteristic, complemented
6#19135303C211yesmaximal, characteristic, complemented
7#19135246C211yesmaximal, characteristic, complemented
8#19135043C211yesmaximal, characteristic, complemented
9#19134920C211yesmaximal, characteristic, complemented
10#19134919C211yesmaximal, characteristic, complemented
11#19134868C211yesmaximal, characteristic, complemented
12#19134800C211yesmaximal, characteristic, complemented
13#19134433C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C2×C43×#421C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063333C2211yescharacteristic, complemented
19C2×#13063332C2211yescharacteristic
20C2×#13063332C2211yescharacteristic
21#14583410C2211yescharacteristic
22#14583061C411yescharacteristic, complemented
23#14583061C411yescharacteristic, complemented
24#14583055C411yescharacteristic, complemented
25#14583050C411yescharacteristic, complemented
26#14583044C411yescharacteristic, complemented
27#14583044C411yescharacteristic, complemented
28#14583038C411yescharacteristic, complemented
29#14583033C411yescharacteristic, complemented
30#14583018—24no—
31#14582975—21no—
32#14582970—21no—
33#14582968—21no—
34C8×C22⋊D43—21no—
35C2×#13063260C2211yescharacteristic, complemented
36C2×#13063260C2211yescharacteristic, complemented
37#14582927C2211yescharacteristic, complemented
38C2×#13063253C2211yescharacteristic, complemented
39C2×#13063253C2211yescharacteristic, complemented
40#14582895C2211yescharacteristic
41#14582895C2211yescharacteristic
42#14582867C2211yescharacteristic, complemented
43#14582866—21no—
44#14582866—21no—
45#14582866C2211yescharacteristic
46#14582866C2211yescharacteristic
47#14582863—21no—
48#14582863C2211yescharacteristic
49C2×C22⋊(C43⋊C8)—21no—
50C2×C22⋊(C43⋊C8)C2211yescharacteristic
51C2×C22⋊(C43⋊C8)C2211yescharacteristic
52#14582857C2211yescharacteristic, complemented
53C2×#13063236C2211yescharacteristic, complemented
54C2×C4×C43⋊C8C2211yescharacteristic, complemented
55#14582663C2211yescharacteristic, complemented
56#14582663C2211yescharacteristic, complemented
57#14582659C2211yescharacteristic, complemented
58#14582659C2211yescharacteristic, complemented
59#14582654C2211yescharacteristic, complemented
60#14582654C2211yescharacteristic, complemented
61C22×#41×C43C2211yescharacteristic
62C22×M16×C43C2211yescharacteristic
63C2×#117×C43C2211yescharacteristic
64C43×#421—24no—
65C2×#104×C43C2211yescharacteristic
66C2×#104×C43C2211yescharacteristic
67C2×#104×C43C2211yescharacteristic
68C2×#104×C43C2211yescharacteristic
69C2×#10621898C2311yescharacteristic
70#13063345—22no—
71#13063345—22no—
72#13063345—41no—
73#13063345—41no—
74C2×#10621885C2×C411yescharacteristic
75C2×#10621885C2×C411yescharacteristic
76C2×#10621883C2×C411yescharacteristic
77C2×#10621883C2×C411yescharacteristic
78C2×#10621884C2×C411yescharacteristic
79C2×#10621884C2×C411yescharacteristic
80C2×#10621882C2×C411yescharacteristic
81C2×#10621882C2×C411yescharacteristic
82#13063333—22no—
83#13063333—41no—
84#13063332—22no—
85#13063332—22no—
86#13063332—41no—
87#13063332—41no—
88C2×#10621877—21no—
89C2×#10621877—21no—
90C2×#10621877C2311yescharacteristic
91C2×#10621877C2311yescharacteristic
92C2×#10621872—21no—
93C22×C43⋊C8—21no—
94C22×C43⋊C8—21no—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C2×C8×D43—21no—
100#13063308—21no—
101#13063304C2×C411yescharacteristic
102#13063304C2×C411yescharacteristic
103#13063299C2×C411yescharacteristic
104#13063299C2×C411yescharacteristic
105#13063294—21no—
106C4×C22⋊D43—21no—
107C4×C22⋊D43—21no—
108#13063284C2311yescharacteristic
109#13063260—22no—
110#13063260—41no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063253—22no—
114#13063253—41no—
115#13063249C2×C411yescharacteristic
116#13063249C2×C411yescharacteristic
117#13063249C2×C411yescharacteristic
118#13063249C2×C411yescharacteristic
119#13063246C2×C411yescharacteristic
120#13063246C2×C411yescharacteristic
121#13063246C2×C411yescharacteristic
122#13063246C2×C411yescharacteristic
123C22⋊(C43⋊C8)—21no—
124C22⋊(C43⋊C8)—21no—
125C22⋊(C43⋊C8)—21no—
126C22⋊(C43⋊C8)—21no—
127C22⋊(C43⋊C8)—21no—
128C22⋊(C43⋊C8)—21no—
129C22⋊(C43⋊C8)C2×C411yescharacteristic
130C22⋊(C43⋊C8)C2×C411yescharacteristic
131C22⋊(C43⋊C8)C2×C411yescharacteristic
132C22⋊(C43⋊C8)C2×C411yescharacteristic
133C22⋊(C43⋊C8)D411yescharacteristic
134C22⋊(C43⋊C8)D411yescharacteristic
135C22⋊(C43⋊C8)D411yescharacteristic
136C22⋊(C43⋊C8)D411yescharacteristic
137(C2×D43)⋊C8—21no—
138(C2×D43)⋊C8—21no—
139#13063236—22no—
140#13063235—21no—
141C4×C43⋊C8—41no—
142C8×Dic43—21no—
143C2×#41×C43—21no—
144C2×#41×C43—21no—
145C2×#41×C43—22no—
146C2×#41×C43—22no—
147C2×#41×C43—41no—
148C2×#41×C43—41no—
149C2×#41×C43C2×C411yescharacteristic
150C2×#41×C43C2×C411yescharacteristic
151C2×#41×C43C2311yescharacteristic
152C2×#41×C43C2311yescharacteristic
153C22×Q8×C43C2×C411yescharacteristic
154C22×D4×C43—21no—
155C22×D4×C43C2×C411yescharacteristic
156C23×C4×C43—21no—
157C23×C4×C43C2311yescharacteristic
158C2×M16×C43—21no—
159C2×M16×C43—22no—
160C2×M16×C43—41no—
161C2×M16×C43C2311yescharacteristic
162C2×M16×C43C2311yescharacteristic
163C22×C8×C43—21no—
164#117×C43—22no—
165#117×C43—41no—
166C2×C4⋊C4×C43—21no—
167C2×C22⋊C4×C43—21no—
168C2×C42×C43C2311yescharacteristic
169C2×C42×C43C2311yescharacteristic
170#104×C43—22no—
171#104×C43—22no—
172#104×C43—22no—
173#104×C43D414yescomplemented
174C24×C43—21no—
175C24×C43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—22no—
179#41×C43—22no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184#41×C43—42no—
185#41×C43—42no—
186#41×C43—41no—
187#41×C43—41no—
188#41×C43—42no—
189#41×C43—42no—
190#41×C43C2×D412yes—
191#41×C43#4112yes—
192C2×Q8×C43—21no—
193C2×Q8×C43—22no—
194C2×Q8×C43—41no—
195C2×Q8×C43C22×C411yescharacteristic
196C2×Q8×C43C22×C411yescharacteristic
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—22no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—41no—
206C2×D4×C43C22×C411yescharacteristic
207C2×D4×C43C22×C411yescharacteristic
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—42no—
220C22×C4×C43—42no—
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43#4111yescharacteristic
226C22×C4×C43C2411yescharacteristic
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230#10621898—21no—
231#10621898—21no—
232#10621898—21no—
233#10621898—21no—
234C2×D172C22×C411yescharacteristic
235C2×C4×D43—21no—
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—42no—
245C4⋊C4×C43—42no—
246C22⋊C4×C43—42no—
247C42×C43—21no—
248C42×C43—21no—
249C42×C43—21no—
250C42×C43C2×D412yes—
251C22⋊Dic43—21no—
252C22⋊Dic43—21no—
253C22⋊Dic43—21no—
254#10621885—22no—
255#10621885—41no—
256#10621884—22no—
257#10621884—41no—
258#10621883—22no—
259#10621883—41no—
260#10621882—22no—
261#10621882—41no—
262(C2×D43)⋊C4—21no—
263(C2×D43)⋊C4—21no—
264C4⋊Dic43C22×C411yescharacteristic
265C4⋊Dic43C22×C411yescharacteristic
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268C4×Dic43—21no—
269#10621877—21no—
270#10621877—21no—
271#10621877—21no—
272#10621877—21no—
273#10621877—42no—
274#10621877—42no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
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—21no—
285C2×C43⋊C8—42no—
286C2×C43⋊C8—42no—
287C2×C43⋊C8C22×C411yescharacteristic
288C2×C43⋊C8C22×C411yescharacteristic
289C2×C43⋊C8C22×C411yescharacteristic
290C2×C43⋊C8C22×C411yescharacteristic
291C2×C43⋊C8C2×D411yescharacteristic
292C2×C43⋊C8C2×D411yescharacteristic
293C2×C43⋊C8C2×D411yescharacteristic
294C2×C43⋊C8C2×D411yescharacteristic
295#10621872—42no—
296C8×D43—42no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43—81no—
306C23×C43C4×D411yescharacteristic
307C23×C43C4×D411yescharacteristic
308C23×C43C2×#4111yescharacteristic
309C22×D43—21no—
310Q8×C43—21no—
311Q8×C43—21no—
312Q8×C43—21no—
313Q8×C43—42no—
314Q8×C43C4×D412yes—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—21no—
318D4×C43—21no—
319D4×C43—21no—
320D4×C43—42no—
321D4×C43—42no—
322D4×C43—42no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43C4×D412yes—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—22no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43—42no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43C4×D411yescharacteristic
352C2×C4×C43C4×D411yescharacteristic
353C2×C4×C43C23×C411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
358C2×C4×C43H(5,𝔽2)11yescharacteristic
359C22⋊D43—42no—
360C22⋊D43—41no—
361C22⋊D43—41no—
362C22⋊D43—81no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366D172—21no—
367D172—21no—
368C4×D43—41no—
369C4×D43—41no—
370Dic86—21no—
371Dic86—21no—
372C8×C43—22no—
373C8×C43—41no—
374C43⋊C8—21no—
375C43⋊C8—21no—
376C43⋊C8—21no—
377C43⋊C8—21no—
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—21no—
388C22×C43—21no—
389C22×C43—22no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43—84no—
402C22×C43C2×C4×D411yescharacteristic
403C22×C43#54611yescharacteristic
404C22×C43#55111yescharacteristic
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—22no—
411C4×C43—42no—
412C4×C43—41no—
413C4×C43—81no—
414C4×C43C2×C4×D411yescharacteristic
415C4×C43#51811yescharacteristic
416C4×C43D4211yescharacteristic
417C4×C43#54611yescharacteristic
418Dic43—41no—
419Dic43—41no—
420Dic43—41no—
421#3002—431no—
422C2×#444—431no—
423#2933—431no—
424C2×#421D4311yescharacteristic, complemented
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—41no—
439C2×C43—41no—
440C2×C43—42no—
441C2×C43—81no—
442C2×C43#235811yescharacteristic
443C2×C43#295511yescharacteristic
444C2×C43#295711yescharacteristic
445D43—81no—
446C22×#41C2×D4311yescharacteristic
447C2×#135—431no—
448C2×#135—431no—
449C2×#131—431no—
450C2×#131—431no—
451C2×#131—431no—
452C22×M16C2×D4311yescharacteristic
453#525—431no—
454C2×#117C2×D4311yescharacteristic
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×#108—431no—
470#424—431no—
471#421—24no—
472C2×#104—431no—
473C2×#104—431no—
474C2×#104C2×D4311yescharacteristic
475C2×#104C2×D4311yescharacteristic
476C2×#104C2×D4311yescharacteristic
477C2×#104C2×D4311yescharacteristic
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×#97—431no—
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—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—431no—
507C2×#41C4×D4311yescharacteristic
508C2×#41C4×D4311yescharacteristic
509C2×#41C22×D4311yescharacteristic
510C2×#41C22×D4311yescharacteristic
511C22×Q8C4×D4311yescharacteristic
512C22×D4—21no—
513C22×D4C4×D4311yescharacteristic
514C23×C4—21no—
515C23×C4C22×D4311yescharacteristic
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—862no—
529#131—862no—
530#131—862no—
531#131—1721no—
532#131—1721no—
533#131—1721no—
534C2×M16—21no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—431no—
538C2×M16—431no—
539C2×M16—861no—
540C2×M16—861no—
541C2×M16—861no—
542C2×M16C22×D4311yescharacteristic
543C2×M16C22×D4311yescharacteristic
544C22×C8—21no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—431no—
548C22×C8—431no—
549C22×C8—861no—
550C22×C8—861no—
551C22×C8—861no—
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—22no—
561#117—41no—
562#117—431no—
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C22×D4311yescharacteristic
566C2×C42C22×D4311yescharacteristic
567#108—862no—
568#108—1721no—
569C4⋊C8—861no—
570C4⋊C8—861no—
571#104—22no—
572#104—22no—
573#104—22no—
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—861no—
602#97—862no—
603C4×C8—861no—
604C4×C8—1721no—
605C24—21no—
606C24#1062190011yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—861no—
622#41—861no—
623#41—861no—
624#41—861no—
625#41#1062189812yes—
626#41C2×C22⋊D4312yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—431no—
631C2×Q8C2×C4×D4311yescharacteristic
632C2×Q8C2×C4×D4311yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—431no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4C2×C4×D4311yescharacteristic
647C2×D4C2×C4×D4311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—861no—
662C22×C4C2×C4×D4311yescharacteristic
663C22×C4C2×C4×D4311yescharacteristic
664C22×C4D4×D4311yescharacteristic
665C22×C4D4×D4311yescharacteristic
666C22×C4#1062190011yescharacteristic
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×C22⋊D4312yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—42no—
691C2×C8—431no—
692C2×C8—431no—
693C2×C8—431no—
694C2×C8—431no—
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—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—1722no—
710C2×C8—1722no—
711C2×C8—1722no—
712C4⋊C4—42no—
713C4⋊C4—431no—
714C4⋊C4—431no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C22⋊C4—42no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—861no—
727C42C2×C22⋊D4312yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—861no—
738C23(C22⋊D43)⋊C411yescharacteristic
739C23(C22⋊D43)⋊C411yescharacteristic
740C23C2×#1062190011yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—861no—
746Q8—861no—
747Q8C4×C22⋊D4312yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—861no—
759D4—861no—
760D4—3441no—
761D4—1722no—
762D4—1721no—
763D4—1721no—
764D4C4×C22⋊D4312yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4(C22⋊D43)⋊C411yescharacteristic
796C2×C4(C22⋊D43)⋊C411yescharacteristic
797C2×C4C22×C4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C22×C22⋊D4311yescharacteristic
800C2×C4C2×#1062189811yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337011yescharacteristic
803C8—22no—
804C8—41no—
805C8—861no—
806C8—861no—
807C8—861no—
808C8—861no—
809C8—861no—
810C8—861no—
811C8—861no—
812C8—861no—
813C8—1721no—
814C8—1721no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—1721no—
833C22—1721no—
834C22—1721no—
835C22C2×(C22⋊D43)⋊C411yescharacteristic
836C22#1458354311yescharacteristic
837C22#1458357511yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—81no—
844C4—1721no—
845C4—1721no—
846C4—1721no—
847C4C2×C4×C22⋊D4311yescharacteristic
848C4#1458337211yescharacteristic
849C4D4×C22⋊D4311yescharacteristic
850C4#1458353911yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—3441no—
858C2#1913757411yescharacteristic
859C2#1914349411yescharacteristic
860C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC22×C43C2×C4×D4
prime radical#19143813C2
cosocleC22×C4×C43C24
hypercenterC2×#421D43
hypocenterC43#22887
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#14583018C2semidirect
3. #19143320C2semidirect
4. #19143044C2semidirect
5. #19135480C2semidirect
6. #19135303C2semidirect
7. #19135246C2semidirect
8. #19135043C2semidirect
9. #19134920C2semidirect
10. #19134919C2semidirect
11. #19134868C2semidirect
12. #19134800C2semidirect
13. #19134433C2semidirect
14. #19134361C2semidirect
15. C2×C43×#421C2semidirect
18. C2×#13063333C22semidirect
22. #14583061C4semidirect
23. #14583061C4semidirect
24. #14583055C4semidirect
25. #14583050C4semidirect
26. #14583044C4semidirect
27. #14583044C4semidirect
28. #14583038C4semidirect
29. #14583033C4semidirect
35. C2×#13063260C22semidirect
36. C2×#13063260C22semidirect
37. #14582927C22semidirect
38. C2×#13063253C22semidirect
39. C2×#13063253C22semidirect
42. #14582867C22semidirect
52. #14582857C22semidirect
53. C2×#13063236C22semidirect
54. C2×C4×C43⋊C8C22semidirect
55. #14582663C22semidirect
56. #14582663C22semidirect
57. #14582659C22semidirect
58. #14582659C22semidirect
59. #14582654C22semidirect
60. #14582654C22semidirect
173. #104×C43D4semidirect
424. C2×#421D43semidirect
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
#191438132
C2×#145830182
#191433202
#191430442
#191354802
#191353032
#191352462
#191350432
#191349202
#191349192
#191348682
#191348002
#191344332
#191343612
C2×C43×#4212
#2288743