Finite Group Databasebeta

← #25117358

Subgroups — #25117358

Order 11008.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143809C211yesmaximal, characteristic
2#19143317C211yesmaximal, characteristic, complemented
3C2×#104×D43C211yesmaximal, characteristic, complemented
4#19143042C211yesmaximal, characteristic, complemented
5#19135480C211yesmaximal, characteristic, complemented
6#19135299C211yesmaximal, characteristic, complemented
7#19135242C211yesmaximal, characteristic, complemented
8#19135035C211yesmaximal, characteristic, complemented
9#19134924C211yesmaximal, characteristic, complemented
10#19134922C211yesmaximal, characteristic, complemented
11#19134870C211yesmaximal, characteristic, complemented
12#19134798C211yesmaximal, characteristic, complemented
13#19134433C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C2×C43×#443C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20#14583406C2211yescharacteristic
21C2×C42×D43C2211yescharacteristic
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
36C2×#13063253C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38C2×#13063252C2211yescharacteristic, complemented
39C2×#13063251C2211yescharacteristic
40#104×D43—24no—
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×#443—24no—
65C2×#108×C43C2211yescharacteristic, complemented
66C2×#104×C43C2211yescharacteristic
67C2×#104×C43C2211yescharacteristic, 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×D43—21no—
83C22×C4×D43C2311yescharacteristic
84#13063345—41no—
85#13063345—41no—
86C2×#10621885C2×C411yescharacteristic, complemented
87C2×#10621883C2×C411yescharacteristic, complemented
88C2×#10621884C2×C411yescharacteristic, complemented
89C2×#10621882C2×C411yescharacteristic, complemented
90#13063332—22no—
91#13063332—41no—
92C2×#10621877—21no—
93C2×#10621877C2311yescharacteristic
94C2×#10621877C2311yescharacteristic
95C2×#10621872—21no—
96M16×D43—22no—
97M16×D43—41no—
98C22×C43⋊C8—21no—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C2×C8×D43—21no—
102#13063306—21no—
103#13063301C2×C411yescharacteristic
104#13063301C2×C411yescharacteristic
105#13063296C2×C411yescharacteristic
106#13063296C2×C411yescharacteristic
107#13063293—21no—
108C4×C22⋊D43—21no—
109C4×C22⋊D43—21no—
110#13063284C2311yescharacteristic
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113C42×D43—22no—
114C42×D43—41no—
115#13063260—41no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118#13063253—22no—
119#13063252—22no—
120#13063252—41no—
121#13063251—22no—
122#13063250C2×C411yescharacteristic, complemented
123#13063250C2×C411yescharacteristic, complemented
124#13063249C2×C411yescharacteristic, complemented
125#13063249C2×C411yescharacteristic, complemented
126#13063247C2×C411yescharacteristic, complemented
127#13063247C2×C411yescharacteristic, complemented
128#13063246C2×C411yescharacteristic, complemented
129#13063246C2×C411yescharacteristic, complemented
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, complemented
154C2×SD16×C43C2×C411yescharacteristic, complemented
155C2×SD16×C43C2×C411yescharacteristic, complemented
156C2×D8×C43C2×C411yescharacteristic, complemented
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
173C4×C8×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—24no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43C22×C411yescharacteristic
235C2×C4×D43C22×C411yescharacteristic
236C2×C4×D43C2×D411yescharacteristic
237C2×C4×D43C2×D411yescharacteristic
238C2×Dic86—21no—
239C2×Dic86C22×C411yescharacteristic
240Q16×C43—22no—
241SD16×C43—22no—
242SD16×C43—22no—
243D8×C43—22no—
244M16×C43—21no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43—42no—
248M16×C43—42no—
249M16×C43C2×D412yes—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—42no—
257C2×C8×C43—42no—
258C2×C8×C43C22×C411yescharacteristic
259C2×C8×C43C22×C411yescharacteristic
260C2×C8×C43C2×D411yescharacteristic
261C2×C8×C43C2×D411yescharacteristic
262C42×C43—21no—
263C42×C43C2×D412yes—
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266C22⋊Dic43—21no—
267#10621885—41no—
268#10621884—41no—
269#10621883—41no—
270#10621882—41no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273C4⋊Dic43C22×C411yescharacteristic
274C4⋊Dic43C22×C411yescharacteristic
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C4×Dic43—42no—
281#10621877—21no—
282#10621877—21no—
283#10621877—21no—
284#10621877—21no—
285#10621877—42no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—42no—
293C2×C43⋊C8C22×C411yescharacteristic
294C2×C43⋊C8C22×C411yescharacteristic
295C2×C43⋊C8C2×D411yescharacteristic
296C2×C43⋊C8C2×D411yescharacteristic
297#10621872—42no—
298C8×D43—42no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43C2×#4111yescharacteristic
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—22no—
305C22×D43—21no—
306C22×D43—41no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—81no—
310C22×D43C4×D411yescharacteristic
311C22×D43C4×D411yescharacteristic
312Q8×C43—21no—
313Q8×C43—21no—
314Q8×C43—21no—
315Q8×C43C4×D412yes—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—21no—
319D4×C43—21no—
320D4×C43—21no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43C4×D412yes—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43C23×C411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43H(5,𝔽2)11yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C22⋊D43—42no—
340C22⋊D43—42no—
341C22⋊D43—41no—
342C22⋊D43—41no—
343C22⋊D43—42no—
344C22⋊D43—81no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—22no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—42no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43C4×D411yescharacteristic
355C2×Dic43C4×D411yescharacteristic
356D172—21no—
357D172—21no—
358D172—42no—
359C4×D43—21no—
360C4×D43—21no—
361C4×D43—21no—
362C4×D43—21no—
363C4×D43—21no—
364C4×D43—21no—
365C4×D43—21no—
366C4×D43—21no—
367C4×D43—42no—
368C4×D43—42no—
369C4×D43—48no—
370C4×D43—41no—
371C4×D43—41no—
372Dic86—21no—
373Dic86—21no—
374Dic86—42no—
375C8×C43—21no—
376C8×C43—21no—
377C8×C43—22no—
378C8×C43—21no—
379C8×C43—21no—
380C8×C43—41no—
381C43⋊C8—21no—
382C43⋊C8—21no—
383C43⋊C8—21no—
384C43⋊C8—21no—
385C43⋊C8—41no—
386C43⋊C8—41no—
387#22888—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—22no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43C2×C4×D411yescharacteristic
397C22×C43#54611yescharacteristic
398C22×C43#55111yescharacteristic
399C2×D43—21no—
400C2×D43—21no—
401C2×D43—21no—
402C2×D43—21no—
403C2×D43—21no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—84no—
410C2×D43#44312yescomplemented
411C4×C43—24no—
412C4×C43—22no—
413C4×C43—41no—
414C4×C43C2×C4×D411yescharacteristic
415C4×C43#51811yescharacteristic
416C4×C43D4211yescharacteristic
417C4×C43#54611yescharacteristic
418Dic43—21no—
419Dic43—21no—
420Dic43—42no—
421Dic43—41no—
422Dic43—41no—
423Dic43—41no—
424#3002—431no—
425C2×#443D4311yescharacteristic, complemented
426#2933—431no—
427C22×#104—431no—
428#2880—431no—
429#1974—431no—
430#1937—431no—
431#1929—431no—
432#1896—431no—
433#1876—431no—
434#1876—431no—
435#1866—431no—
436#1855—431no—
437#1764—431no—
438C4×C22⋊C8—431no—
439C2×C43—21no—
440C2×C43—21no—
441C2×C43—42no—
442C2×C43—81no—
443C2×C43#235811yescharacteristic
444C2×C43C2×#44311yescharacteristic
445C2×C43#295611yescharacteristic
446D43—22no—
447D43—41no—
448D43—81no—
449C22×#41—431no—
450C2×#135—431no—
451C2×#135C2×D4311yescharacteristic
452C2×#131—431no—
453C2×#131C2×D4311yescharacteristic
454C2×#131C2×D4311yescharacteristic, complemented
455C22×M16—431no—
456#525—431no—
457C22×C42—431no—
458#452—431no—
459#452—431no—
460#451—431no—
461#450—431no—
462#449—431no—
463#449—431no—
464#448—431no—
465#447—431no—
466#443—24no—
467#436—861no—
468#435—861no—
469#435—861no—
470C8×D4—861no—
471C2×#108—431no—
472C2×#108C2×D4311yescharacteristic, complemented
473#424—431no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104—431no—
478C2×#104—864no—
479C2×#104C2×D4311yescharacteristic
480C2×#104C2×D4311yescharacteristic, complemented
481#416—431no—
482#416—431no—
483#408—431no—
484#408—431no—
485#408—431no—
486#408—861no—
487#408—861no—
488#407—431no—
489#407—861no—
490C2×C22⋊C8—431no—
491C2×C22⋊C8—431no—
492C2×C22⋊C8—861no—
493#405—431no—
494C2×C4×C8—431no—
495C2×C4×C8C2×D4311yescharacteristic, complemented
496#341—431no—
497#341—431no—
498#339—431no—
499#339—431no—
500#336—431no—
501#336—431no—
502C43#2288811yescharacteristic, complemented, Sylow
503C2×#41—431no—
504C2×#41—431no—
505C2×#41—431no—
506C2×#41—861no—
507C2×#41—861no—
508C2×#41—862no—
509C2×#41—862no—
510C2×#41—1721no—
511C2×#41—1721no—
512C2×#41C22×D4311yescharacteristic
513C2×#41C22×D4311yescharacteristic
514C22×Q8—431no—
515C22×D4—431no—
516C22×D4—861no—
517C23×C4—431no—
518C23×C4—861no—
519C23×C4—861no—
520#135—22no—
521#135—22no—
522#135—1721no—
523#135—1721no—
524C2×Q16—431no—
525C2×Q16C4×D4311yescharacteristic, complemented
526C2×SD16—431no—
527C2×SD16—431no—
528C2×SD16C4×D4311yescharacteristic, complemented
529C2×SD16C4×D4311yescharacteristic, complemented
530C2×D8—431no—
531C2×D8C4×D4311yescharacteristic, complemented
532#131—22no—
533#131—22no—
534#131—41no—
535#131—41no—
536#131—862no—
537#131—1721no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—431no—
541C2×M16—431no—
542C2×M16—861no—
543C2×M16—861no—
544C2×M16—862no—
545C2×M16—1721no—
546C2×M16C22×D4311yescharacteristic
547C2×M16C22×D4311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8—861no—
553C22×C8—861no—
554C22×C8C22×D4311yescharacteristic
555C22×C8C22×D4311yescharacteristic
556#123—861no—
557C22⋊Q8—431no—
558C22⋊Q8—431no—
559#121—431no—
560#121—431no—
561#120—861no—
562C4×D4—861no—
563C4×D4—861no—
564#117—431no—
565C2×C42—431no—
566C2×C42—862no—
567C2×C42—861no—
568C2×C42—1721no—
569C2×C42C22×D4311yescharacteristic
570#108—22no—
571#108—1721no—
572C4⋊C8—861no—
573C4⋊C8—861no—
574#104—22no—
575#104—862no—
576#104—862no—
577#104—862no—
578#104—1721no—
579#104C22⋊D4314yescomplemented
580#103—431no—
581#103—431no—
582#103—431no—
583#103—431no—
584#102—431no—
585#102—431no—
586#102—431no—
587#102—431no—
588C22⋊C8—431no—
589C22⋊C8—431no—
590C22⋊C8—431no—
591C22⋊C8—431no—
592C22⋊C8—431no—
593C22⋊C8—431no—
594C22⋊C8—431no—
595C22⋊C8—431no—
596C22⋊C8—861no—
597C22⋊C8—861no—
598C22⋊C8—861no—
599C22⋊C8—861no—
600C22⋊C8—861no—
601C22⋊C8—861no—
602C22⋊C8—861no—
603C22⋊C8—861no—
604#97—861no—
605C4×C8—22no—
606C4×C8—861no—
607C4×C8—1721no—
608C24—431no—
609C24—861no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—862no—
617#41—862no—
618#41—861no—
619#41—861no—
620#41—861no—
621#41—861no—
622#41—1722no—
623#41—1722no—
624#41—1721no—
625#41—1722no—
626#41—1722no—
627#41—1721no—
628#41#1062189812yes—
629#41C2×C22⋊D4312yes—
630C2×Q8—431no—
631C2×Q8—861no—
632C2×Q8—862no—
633C2×Q8—1721no—
634C2×Q8C2×C4×D4311yescharacteristic
635C2×Q8C2×C4×D4311yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—431no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—862no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—1721no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4C2×C4×D4311yescharacteristic
650C2×D4C2×C4×D4311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—864no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—1722no—
670C22×C4—1722no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4C23×D4311yescharacteristic
674Q16—22no—
675Q16—1721no—
676SD16—22no—
677SD16—22no—
678SD16—1721no—
679SD16—1721no—
680D8—22no—
681D8—1721no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—861no—
688M16—861no—
689M16—861no—
690M16—861no—
691M16—1722no—
692M16—1722no—
693M16C2×C22⋊D4312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—431no—
703C2×C8—431no—
704C2×C8—431no—
705C2×C8—431no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—1722no—
713C2×C8—1722no—
714C2×C8C2×C4×D4311yescharacteristic
715C2×C8C2×C4×D4311yescharacteristic
716C2×C8D4×D4311yescharacteristic
717C2×C8D4×D4311yescharacteristic
718C4⋊C4—431no—
719C4⋊C4—431no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C42—21no—
728C42—861no—
729C42—861no—
730C42—861no—
731C42—1722no—
732C42C2×C22⋊D4312yes—
733C23—21no—
734C23—21no—
735C23—431no—
736C23—431no—
737C23—862no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—3441no—
742C23—1721no—
743C23—1722no—
744C23—1722no—
745C23#41×D4311yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—861no—
750Q8—861no—
751Q8—1722no—
752Q8C4×C22⋊D4312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—41no—
759D4—41no—
760D4—861no—
761D4—861no—
762D4—3441no—
763D4—1722no—
764D4—1722no—
765D4—1722no—
766D4—1722no—
767D4—1721no—
768D4—1721no—
769D4C4×C22⋊D4312yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—431no—
780C2×C4—431no—
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—861no—
790C2×C4—861no—
791C2×C4—862no—
792C2×C4—861no—
793C2×C4—861no—
794C2×C4—861no—
795C2×C4—1722no—
796C2×C4—1722no—
797C2×C4—1728no—
798C2×C4—1722no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4C22×C4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C22×C22⋊D4311yescharacteristic
806C2×C4C2×#1062189811yescharacteristic
807C2×C4#1306337011yescharacteristic
808C2×C4#1306337111yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—22no—
814C8—41no—
815C8—861no—
816C8—861no—
817C8—861no—
818C8—861no—
819C8—1721no—
820C8—1721no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—432no—
830C22—861no—
831C22—861no—
832C22—861no—
833C22—861no—
834C22—861no—
835C22—3444no—
836C22—1722no—
837C22—1722no—
838C22—1721no—
839C22—1721no—
840C22—1721no—
841C22C4×D4×D4311yescharacteristic
842C22#1458353711yescharacteristic
843C22#1458357811yescharacteristic
844C4—24no—
845C4—22no—
846C4—41no—
847C4—861no—
848C4—861no—
849C4—1722no—
850C4—1721no—
851C4—1721no—
852C4—1721no—
853C4C2×C4×C22⋊D4311yescharacteristic
854C4#1458337111yescharacteristic
855C4D4×C22⋊D4311yescharacteristic
856C4#1458354511yescharacteristic
857C2—21no—
858C2—21no—
859C2—42no—
860C2—81no—
861C2—862no—
862C2—3441no—
863C2—1721no—
864C2#1913757211yescharacteristic
865C2#443×D4311yescharacteristic
866C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#443C2
socleC22×C43C2×C4×D4
prime radical#19143809C2
cosocleC22×C4×C43C24
hypercenterC2×#443D43
hypocenterC43#22888
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. #19143317C2semidirect
3. C2×#104×D43C2semidirect
4. #19143042C2semidirect
5. #19135480C2semidirect
6. #19135299C2semidirect
7. #19135242C2semidirect
8. #19135035C2semidirect
9. #19134924C2semidirect
10. #19134922C2semidirect
11. #19134870C2semidirect
12. #19134798C2semidirect
13. #19134433C2semidirect
14. C4×(C2×D43)⋊C8C2semidirect
15. C2×C43×#443C2semidirect
22. #14583060C4semidirect
23. #14583058C4semidirect
24. #14583053C4semidirect
25. #14583048C4semidirect
26. #14583043C4semidirect
27. #14583041C4semidirect
28. #14583036C4semidirect
29. #14583031C4semidirect
34. C2×#13063260C22semidirect
35. #14582925C22semidirect
38. 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×C4×C8×C43C22semidirect
86. C2×#10621885C2×C4semidirect
87. C2×#10621883C2×C4semidirect
88. C2×#10621884C2×C4semidirect
89. C2×#10621882C2×C4semidirect
122. #13063250C2×C4semidirect
123. #13063250C2×C4semidirect
124. #13063249C2×C4semidirect
125. #13063249C2×C4semidirect
126. #13063247C2×C4semidirect
127. #13063247C2×C4semidirect
128. #13063246C2×C4semidirect
129. #13063246C2×C4semidirect
153. C2×Q16×C43C2×C4semidirect
154. C2×SD16×C43C2×C4semidirect
155. C2×SD16×C43C2×C4semidirect
156. C2×D8×C43C2×C4semidirect
172. #104×C43D4semidirect
410. C2×D43#443semidirect
425. C2×#443D43semidirect
454. C2×#131C2×D43semidirect
472. C2×#108C2×D43semidirect
480. C2×#104C2×D43semidirect
495. C2×C4×C8C2×D43semidirect
502. C43#22888semidirect
525. C2×Q16C4×D43semidirect
528. C2×SD16C4×D43semidirect
529. C2×SD16C4×D43semidirect
531. C2×D8C4×D43semidirect
579. #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×#104×D432
#191430422
#191354802
#191352992
#191352422
#191350352
#191349242
#191349222
#191348702
#191347982
#191344332
C4×(C2×D43)⋊C82
C2×C43×#4432
#2288843