Finite Group Databasebeta

← #25102207

Subgroups — #25102207

Order 11008.

1564 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621900C211yesmaximal, characteristic, complemented
2C2×#14583045C211yesmaximal, characteristic
3C2×#14582986C211yesmaximal, characteristic, complemented
4C2×#14582979C211yesmaximal, characteristic, complemented
5#19137103C211yesmaximal, characteristic, complemented
6#19134949C211yesmaximal, characteristic, complemented
7#19134943C211yesmaximal, characteristic, complemented
8#19134916C211yesmaximal, characteristic, complemented
9#19134848C211yesmaximal, characteristic, complemented
10#19134793C211yesmaximal, characteristic, complemented
11#19134532C211yesmaximal, characteristic, complemented
12#19134414C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1864C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C4×#10621900—24no—
21C4×#10621900—24no—
22C2×C4×Dic86C2211yescharacteristic
23C2×#13063290C2211yescharacteristic
24C2×D4×Dic43C2211yescharacteristic
25C2×#13063287—21no—
26C2×#13063287C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×(C22⋊D43)⋊C4—21no—
29C2×#13063283C2211yescharacteristic
30C2×#13063281—21no—
31C22×C4×Dic43—21no—
32C2×C42×D43C2211yescharacteristic
33#14583045C418yescomplemented
34#14582986—24no—
35#14582979—24no—
36C2×#13063258C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46C2×C8×Dic43C2211yescharacteristic
47#14582801C2211yescharacteristic
48#14582789—21no—
49#14582777—21no—
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52#14582746—21no—
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582654C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×#106×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#389C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×D172—21no—
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C23×Dic43—21no—
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C22×C4×D43D411yescharacteristic
78C22×C4×D43D411yescharacteristic
79C22×C4×D43C2311yescharacteristic
80C2×#10621873—22no—
81C2×#10621873—22no—
82C2×#10621873C2×C414yescomplemented
83C2×#10621882—22no—
84C2×#10621882—22no—
85C2×#10621882C2×C414yescomplemented
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063300—22no—
89#13063300C2×C414yescomplemented
90C4×Dic86—22no—
91C4×Dic86—22no—
92#13063290—22no—
93#13063290D414yescomplemented
94D4×Dic43—22no—
95D4×Dic43D414yescomplemented
96#13063287—22no—
97#13063287—22no—
98#13063287—44no—
99C4×C22⋊D43—28no—
100(C22⋊D43)⋊C4—28no—
101#13063283—22no—
102#13063283—22no—
103#13063281—28no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×C22⋊Dic43—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×C4×Dic43—28no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43D411yescharacteristic
121C2×C4×Dic43D411yescharacteristic
122C2×C4×Dic43C2311yescharacteristic
123C42×D43—22no—
124C42×D43—22no—
125#13063258—22no—
126#13063250—22no—
127#13063248—22no—
128#13063248C2×C414yescomplemented
129#13063247—22no—
130#13063246—22no—
131#13063245—22no—
132(C2×D43)⋊C8—22no—
133(C2×D43)⋊C8C2×C414yescomplemented
134C8×Dic43—22no—
135C8×Dic43—22no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C22×D4×C43C2311yescharacteristic
139C23×C4×C43—21no—
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C4×D4×C43—22no—
143C4×D4×C43—22no—
144C2×C4⋊C4×C43—21no—
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C42×C43C2311yescharacteristic
150#106×C43—22no—
151#102×C43—22no—
152#102×C43C2×C414yescomplemented
153#95×C43—21no—
154C24×C43—21no—
155C23×D43—21no—
156C23×D43C2×D411yescharacteristic
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43C22×C412yes—
161C2×D4×C43C2×D412yes—
162C2×D4×C43#4112yes—
163C22×C4×C43—24no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—42no—
168C22×C4×C43—42no—
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2411yescharacteristic
172C2×C22⋊D43—24no—
173C2×C22⋊D43—24no—
174C2×C22⋊D43—24no—
175C22×Dic43—24no—
176C22×Dic43—24no—
177C22×Dic43—24no—
178C22×Dic43—24no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—42no—
183C22×Dic43—42no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187#10621900—28no—
188#10621900—28no—
189#10621900—28no—
190#10621900—28no—
191C2×D172—21no—
192C2×D172—24no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—42no—
198C2×D172—42no—
199C2×D172C22×C412yes—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—22no—
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—41no—
210C2×C4×D43—42no—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×C4×D43C22×C412yes—
214C2×C4×D43#4112yes—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86C22×C412yes—
219C2×Dic86C2×D412yes—
220C2×Dic86#4112yes—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43C22×C412yes—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—42no—
232C4⋊C4×C43C22×C412yes—
233C4⋊C4×C43C2×D412yes—
234C22⋊C4×C43—24no—
235C42×C43—21no—
236C42×C43—21no—
237C22⋊Dic43—24no—
238#10621882—28no—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—42no—
242(C2×D43)⋊C4—42no—
243(C2×D43)⋊C4—42no—
244(C2×D43)⋊C4—42no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43C2×D412yes—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251C4×Dic43—24no—
252C4×Dic43—24no—
253C4×Dic43—22no—
254C4×Dic43—22no—
255C4×Dic43—24no—
256C4×Dic43—42no—
257C4×Dic43C2×D412yes—
258C4×Dic43C2×D412yes—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8C22×C412yes—
265#10621873—28no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43C22×D411yescharacteristic
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—22no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43C4×D412yes—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43C4×D414yescomplemented
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—48no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43#13512yes—
308C2×C4×C43C23×C411yescharacteristic
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C22⋊D43—216no—
315C2×Dic43—216no—
316C2×Dic43—22no—
317C2×Dic43—21no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—22no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—48no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43C4×D412yes—
331C2×Dic43#12012yes—
332C2×Dic43#12012yes—
333C2×Dic43#13512yes—
334C2×Dic43AGL(1,ℤ/8)12yes—
335D172—22no—
336D172—22no—
337D172—48no—
338D172—41no—
339D172—41no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—44no—
345C4×D43—44no—
346C4×D43—84no—
347Dic86—22no—
348Dic86—22no—
349Dic86—22no—
350Dic86C4×D414yescomplemented
351C8×C43—22no—
352C8×C43—41no—
353C43⋊C8—22no—
354C43⋊C8—41no—
355C4×#449—431nomaximal, Sylow
356C22×C43—24no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43C2×C4×D411yescharacteristic
364C22×C43C2×#12011yescharacteristic
365C22×C43#52511yescharacteristic
366C22×C43C2×#13511yescharacteristic
367C22×C43C2×#13511yescharacteristic
368C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C43#57511yescharacteristic
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—81no—
381C2×D43—81no—
382C2×D43—81no—
383C2×D43—81no—
384C4×C43—22no—
385C4×C43—42no—
386C4×C43—41no—
387C4×C43—42no—
388C4×C43—81no—
389C4×C43C2×C4×D411yescharacteristic
390C4×C43C2×C4×D411yescharacteristic
391C4×C43#52511yescharacteristic
392C4×C43#52511yescharacteristic
393Dic43—22no—
394Dic43—24no—
395Dic43—22no—
396Dic43—42no—
397Dic43—81no—
398Dic43#44914yescomplemented
399C2×C4×#41—431no—
400C2×#449—431no—
401C2×C4×SD16—431no—
402C2×C4×D8—431no—
403C4×#121—431no—
404#1880—431no—
405#1879—431no—
406#1875—431no—
407#1864D4311yescharacteristic, complemented
408#1863—431no—
409#1854—431no—
410#1788—431no—
411C4×#103—431no—
412C4×#102—431no—
413C4×C22⋊C8—431no—
414C2×C43—44no—
415C2×C43C4×#12011yescharacteristic
416C2×C43C4×#13511yescharacteristic
417C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
418C2×C43C2×#44911yescharacteristic
419C2×C43#300211yescharacteristic
420C2×C43#310211yescharacteristic
421C2×C43#310611yescharacteristic
422D43—42no—
423D43—82no—
424C22×#41—431no—
425C22×SD16—431no—
426C22×D8—431no—
427C2×#121—431no—
428C4×#41—864no—
429C4×#41—864no—
430C2×C4×Q8—431no—
431C2×C4×Q8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—861no—
435C2×C4×D4—861no—
436C2×C4×D4—861no—
437C2×C4×D4C2×D4311yescharacteristic
438C2×#117—431no—
439C2×#117—861no—
440C22×C42—431no—
441C22×C42—861no—
442#449—438no—
443C4×SD16—864no—
444C4×D8—864no—
445C2×#107—431no—
446C2×#106C2×D4311yescharacteristic
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102C2×D4311yescharacteristic
454C2×#102C2×D4311yescharacteristic
455C2×C22⋊C8—431no—
456C2×C22⋊C8—431no—
457C2×C4×C8—431no—
458C2×C4×C8—431no—
459#390—431no—
460#389C2×D4311yescharacteristic
461#388—861no—
462#386—861no—
463#380—431no—
464C4×C4⋊C4—431no—
465C4×C22⋊C4—861no—
466#340—431no—
467#340—431no—
468#340—431no—
469#340C2×D4311yescharacteristic
470#336—431no—
471#336C2×D4311yescharacteristic
472C43C4×#44911yescharacteristic, complemented, Sylow
473C2×#41—434no—
474C2×#41—862no—
475C2×#41—862no—
476C2×#41—862no—
477C2×#41—862no—
478C2×#41—862no—
479C22×Q8—431no—
480C22×D4—431no—
481C22×D4—861no—
482C22×D4—861no—
483C22×D4C22×D4311yescharacteristic
484C23×C4—21no—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—431no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491C2×SD16—434no—
492C2×SD16—862no—
493C2×SD16—862no—
494C2×D8—434no—
495C2×D8—862no—
496C2×D8—862no—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8C22×D4311yescharacteristic
500C22×C8C22×D4311yescharacteristic
501#121—434no—
502#121—862no—
503C4×Q8—434no—
504C4×Q8—862no—
505C4×Q8—862no—
506C4×Q8—862no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—434no—
510C4×D4—862no—
511C4×D4—862no—
512C4×D4—862no—
513C4×D4—868no—
514C4×D4—868no—
515C4×D4—1724no—
516#117—868no—
517#117—862no—
518#117—862no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C42—431no—
536C2×C42—431no—
537C2×C42—431no—
538C2×C42—862no—
539C2×C42—862no—
540C2×C42—861no—
541C2×C42—861no—
542C2×C42—868no—
543C2×C42—861no—
544C2×C42—861no—
545C2×C42C22×D4311yescharacteristic
546#107—862no—
547#106—22no—
548#103—434no—
549#103—862no—
550#103—862no—
551#102—22no—
552#102—862no—
553#102—862no—
554#102—862no—
555#102C4×D4314yescomplemented
556C22⋊C8—434no—
557C22⋊C8—862no—
558C4×C8—862no—
559C4×C8—862no—
560#95—21no—
561#95—861no—
562#95—861no—
563C24—21no—
564C24—431no—
565C24—861no—
566#41—868no—
567#41—868no—
568#41—868no—
569#41—868no—
570C2×Q8—432no—
571C2×Q8—432no—
572C2×Q8—432no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8—861no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—432no—
580C2×D4—864no—
581C2×D4—864no—
582C2×D4—864no—
583C2×D4—864no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—1722no—
590C2×D4—1722no—
591C2×D4C2×C4×D4312yes—
592C2×D4D4×D4312yes—
593C2×D4#1062190212yes—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—864no—
610C22×C4—864no—
611C22×C4—864no—
612C22×C4—864no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—862no—
620C22×C4—861no—
621C22×C4—1721no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4D4×D4311yescharacteristic
628C22×C4D4×D4311yescharacteristic
629C22×C4C23×D4311yescharacteristic
630SD16—868no—
631D8—868no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—432no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8C2×C4×D4312yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—432no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4C2×C4×D4312yes—
656C4⋊C4D4×D4312yes—
657C22⋊C4—24no—
658C22⋊C4—864no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—1722no—
662C22⋊C4—1722no—
663C22⋊C4—1722no—
664C22⋊C4—1722no—
665C42—21no—
666C42—21no—
667C42—432no—
668C42—432no—
669C42—862no—
670C42—862no—
671C42—864no—
672C42—864no—
673C42—864no—
674C42—1722no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—432no—
683C23—861no—
684C23—861no—
685C23—861no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—862no—
690C23—1721no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23—1721no—
696C23C2×D4×D4311yescharacteristic
697Q8—434no—
698Q8—862no—
699Q8—862no—
700Q8—862no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—8616no—
705D4—862no—
706D4—862no—
707D4—1728no—
708D4—1721no—
709D4—1721no—
710D4#1306328714yescomplemented
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—48no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—432no—
727C2×C4—432no—
728C2×C4—432no—
729C2×C4—432no—
730C2×C4—432no—
731C2×C4—8616no—
732C2×C4—862no—
733C2×C4—861no—
734C2×C4—862no—
735C2×C4—861no—
736C2×C4—862no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—3444no—
745C2×C4—1724no—
746C2×C4—1724no—
747C2×C4—1728no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4#1306334612yes—
754C2×C4C22×C4×D4311yescharacteristic
755C2×C4C2×D4×D4311yescharacteristic
756C2×C4C2×D4×D4311yescharacteristic
757C2×C4#41×D4311yescharacteristic
758C2×C4#41×D4311yescharacteristic
759C2×C4C2×#1062190211yescharacteristic
760C8—22no—
761C8—41no—
762C8—862no—
763C8—1721no—
764C22—24no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—862no—
772C22—862no—
773C22—862no—
774C22—3441no—
775C22—3441no—
776C22—3441no—
777C22—3441no—
778C22—1722no—
779C22—1722no—
780C22—1722no—
781C22—1721no—
782C22—1721no—
783C22—1721no—
784C22—1721no—
785C22C4×D4×D4311yescharacteristic
786C22#120×D4311yescharacteristic
787C22#1458341211yescharacteristic
788C22#135×D4311yescharacteristic
789C22C2×#1306334611yescharacteristic
790C22AGL(1,ℤ/8)×D4311yescharacteristic
791C22#1458369511yescharacteristic
792C4—22no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—81no—
797C4—434no—
798C4—862no—
799C4—864no—
800C4—862no—
801C4—3441no—
802C4—1722no—
803C4C4×D4×D4311yescharacteristic
804C4C2×#1306328711yescharacteristic
805C4#1458340711yescharacteristic
806C4#1458341211yescharacteristic
807C2—44no—
808C2—3442no—
809C2—1722no—
810C2#1913709611yescharacteristic
811C2C4×#1306334611yescharacteristic
812C2#1914340611yescharacteristic
813C2#449×D4311yescharacteristic
814C2#1914381411yescharacteristic
815C2#1914461811yescharacteristic
816C2#1914465711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1864C2
socleC23×C43C22×D4
prime radicalC2×#14583045C2
cosocleC22×C4×C43C24
hypercenter#1864D43
hypocenterC43C4×#449
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
1. C2×C4×#10621900C2semidirect
3. C2×#14582986C2semidirect
4. C2×#14582979C2semidirect
5. #19137103C2semidirect
6. #19134949C2semidirect
7. #19134943C2semidirect
8. #19134916C2semidirect
9. #19134848C2semidirect
10. #19134793C2semidirect
11. #19134532C2semidirect
12. #19134414C2semidirect
13. #102×Dic43C2semidirect
14. #19134352C2semidirect
15. C43×#1864C2semidirect
33. #14583045C4semidirect
69. C2×#10621900C2×C4semidirect
82. C2×#10621873C2×C4semidirect
85. C2×#10621882C2×C4semidirect
89. #13063300C2×C4semidirect
93. #13063290D4semidirect
95. D4×Dic43D4semidirect
128. #13063248C2×C4semidirect
133. (C2×D43)⋊C8C2×C4semidirect
152. #102×C43C2×C4semidirect
291. D4×C43C4×D4semidirect
350. Dic86C4×D4semidirect
398. Dic43#449semidirect
407. #1864D43semidirect
472. C43C4×#449semidirect
555. #102C4×D43semidirect
710. D4#13063287semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
C2×#145830452
C2×#145829862
C2×#145829792
#191371032
#191349492
#191349432
#191349162
#191348482
#191347932
#191345322
#191344142
#102×Dic432
#191343522
C43×#18642
C4×#44943