Finite Group Databasebeta

← #24987962

Subgroups — #24987962

Order 11008.

1520 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2#19134572C211yesmaximal, characteristic, complemented
3C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
4C2×#14582628C211yesmaximal, characteristic, complemented
5C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6C2×#14582626C211yesmaximal, characteristic, complemented
7C2×C43×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×D4×D43C411yescharacteristic
9C23×C4×D43—21no—
10C2×C4×D172C2211yescharacteristic
11C2×D4×Dic43C411yescharacteristic
12C2×#13063287C411yescharacteristic
13C2×C4×C22⋊D43—21no—
14C2×(C22⋊D43)⋊C4—21no—
15C4×D4×D43—22no—
16C4×D4×D43—22no—
17C4×D4×D43—22no—
18C4×D4×D43—22no—
19C2×C4⋊C4×D43C411yescharacteristic
20C2×C22⋊C4×D43—21no—
21C2×C42×D43C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
23C2×(C2×D43)⋊C8—21no—
24C2×(C2×D43)⋊C8—21no—
25C2×C4×C43⋊C8C2211yescharacteristic, complemented
26#14582653—21no—
27#14582653—21no—
28#14582628—22no—
29D4⋊(C43⋊C8)—22no—
30#14582626—22no—
31C2×C4×D4×C43C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic, complemented
33C2×C4×C8×C43C2211yescharacteristic, complemented
34C43×D4⋊C8—22no—
35C24×D43—21no—
36C22×D172C2×C411yescharacteristic
37C22×C22⋊D43—21no—
38C2×D4×D43—22no—
39C2×D4×D43—22no—
40C2×D4×D43—22no—
41C2×D4×D43—22no—
42C2×D4×D43—22no—
43C2×D4×D43C814yescomplemented
44C23×Dic43—21no—
45C22×C4×D43—24no—
46C22×C4×D43—24no—
47C22×C4×D43—21no—
48C22×C4×D43—21no—
49C22×C4×D43—21no—
50C22×C4×D43—42no—
51C22×C4×D43—42no—
52C22×C4×D43—42no—
53C22×C4×D43—42no—
54C22×C4×D43C2×C411yescharacteristic
55C22×C4×D43D411yescharacteristic
56C22×C4×D43D411yescharacteristic
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59C4×D172—21no—
60C4×D172—21no—
61C4×D172D412yes—
62C4×D172D412yes—
63D4×Dic43—22no—
64D4×Dic43—22no—
65#13063287—22no—
66#13063287—22no—
67C4×C22⋊D43—24no—
68C4×C22⋊D43—24no—
69(C22⋊D43)⋊C4—24no—
70(C22⋊D43)⋊C4—24no—
71C2×C4⋊Dic43C2×C411yescharacteristic
72C2×Dic43⋊C4—21no—
73C4⋊C4×D43—22no—
74C4⋊C4×D43—22no—
75C2×C22⋊Dic43—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C22⋊C4×D43—24no—
79C22⋊C4×D43—24no—
80C2×C4×Dic43C2×C411yescharacteristic
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43D411yescharacteristic
83C42×D43—21no—
84C42×D43—21no—
85C42×D43—21no—
86C42×D43—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89(C2×D43)⋊C8—24no—
90(C2×D43)⋊C8—42no—
91C4×C43⋊C8—21no—
92C4×C43⋊C8—21no—
93C22×D4×C43C2×C411yescharacteristic
94C23×C4×C43—21no—
95C22×C8×C43—21no—
96C22×C8×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43D412yes—
100C4×D4×C43D412yes—
101C2×C4⋊C4×C43C2×C411yescharacteristic
102C2×C22⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43—21no—
105C4⋊C8×C43—21no—
106C4×C8×C43—21no—
107C4×C8×C43—21no—
108C24×C43—21no—
109C23×D43—24no—
110C23×D43—24no—
111C23×D43—21no—
112C23×D43—24no—
113C23×D43—42no—
114C23×D43—42no—
115C23×D43—42no—
116C23×D43—42no—
117C23×D43C22⋊C411yescharacteristic
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43C22⋊C412yes—
122C2×D4×C43C2×C812yes—
123C2×D4×C43M1612yes—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—41no—
128C22×C4×C43—41no—
129C22×C4×C43—41no—
130C22×C4×C43—41no—
131C22×C4×C43C22×C411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C2×C22⋊D43—24no—
135C2×C22⋊D43—24no—
136C2×C22⋊D43—24no—
137C22×Dic43—24no—
138C22×Dic43—21no—
139C22×Dic43—42no—
140C22×Dic43—42no—
141C22×Dic43C22⋊C411yescharacteristic
142C22×Dic43C22⋊C411yescharacteristic
143C22×Dic43C22⋊C411yescharacteristic
144D4×D43—28no—
145D4×D43—28no—
146D4×D43—28no—
147D4×D43—28no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C22⋊C412yes—
152C2×D172C2×C812yes—
153C2×D172M1612yes—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—24no—
163C2×C4×D43—24no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—41no—
170C2×C4×D43—42no—
171C2×C4×D43—48no—
172C2×C4×D43—48no—
173C2×C4×D43—48no—
174C2×C4×D43—48no—
175C2×C4×D43—42no—
176C2×C4×D43—41no—
177C2×C4×D43—41no—
178C2×C4×D43—41no—
179C2×C4×D43—41no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43C2×C812yes—
183C2×C4×D43M1612yes—
184C2×C4×D43D812yes—
185C2×C4×D43SD1612yes—
186C2×C8×C43—22no—
187C2×C8×C43—41no—
188C2×C8×C43—41no—
189C2×C8×C43—41no—
190C2×C8×C43—41no—
191C2×C8×C43—41no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C22⋊C412yes—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—22no—
196C42×C43C2×D411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C22⋊Dic43—24no—
201(C2×D43)⋊C4—24no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204C4⋊Dic43—21no—
205C4⋊Dic43C22⋊C412yes—
206Dic43⋊C4—24no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C2×C43⋊C8—22no—
214C2×C43⋊C8—41no—
215C2×C43⋊C8—41no—
216C2×C43⋊C8—41no—
217C2×C43⋊C8—41no—
218C2×C43⋊C8—41no—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C2×C22⋊C411yescharacteristic
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—216no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—22no—
235C22×D43—48no—
236C22×D43—48no—
237C22×D43—48no—
238C22×D43—48no—
239C22×D43—48no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—48no—
245C22×D43C22⋊C812yes—
246C22×D43#10212yes—
247C22×D43#10412yes—
248D4×C43—22no—
249D4×C43—22no—
250D4×C43—22no—
251D4×C43C22⋊C814yescomplemented
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—22no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43C2×C22⋊C411yescharacteristic
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43#12011yescharacteristic
264C2×C4×C43#12011yescharacteristic
265C2×C4×C43#12011yescharacteristic
266C2×C4×C43#12011yescharacteristic
267C2×C4×C43C22×C811yescharacteristic
268C2×C4×C43C2×M1611yescharacteristic
269C2×C4×C43C2×M1611yescharacteristic
270C2×C4×C43C2×M1611yescharacteristic
271C2×C4×C43C2×D811yescharacteristic
272C2×C4×C43C2×SD1611yescharacteristic
273C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
274C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
275C22⋊D43—216no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—22no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—48no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43C22⋊C812yes—
288C2×Dic43#10212yes—
289D172—22no—
290D172—22no—
291D172—22no—
292D172C22⋊C814yescomplemented
293C4×D43—22no—
294C4×D43—22no—
295C4×D43—22no—
296C4×D43—22no—
297C4×D43—22no—
298C4×D43—22no—
299C4×D43—22no—
300C4×D43—22no—
301C4×D43—48no—
302C4×D43—42no—
303C4×D43—42no—
304C4×D43—48no—
305C4×D43—42no—
306C4×D43—42no—
307C4×D43—42no—
308C4×D43—42no—
309C8×C43—42no—
310C8×C43—81no—
311C43⋊C8—42no—
312C43⋊C8—81no—
313#8310—431nomaximal, Sylow
314C22×C43—24no—
315C22×C43—42no—
316C22×C43—42no—
317C22×C43—42no—
318C22×C43—42no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43#37911yescharacteristic
322C22×C43C2×C22⋊C811yescharacteristic
323C22×C43#40711yescharacteristic
324C22×C43C2×#10211yescharacteristic
325C22×C43#41811yescharacteristic
326C22×C43C2×#10411yescharacteristic
327C22×C43#42111yescharacteristic
328C2×D43—22no—
329C2×D43—22no—
330C2×D43—22no—
331C2×D43—22no—
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—24no—
335C2×D43—432no—
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43D4⋊C814yescomplemented
343C4×C43—21no—
344C4×C43—21no—
345C4×C43—42no—
346C4×C43C2×C22⋊C811yescharacteristic
347C4×C43C2×C22⋊C811yescharacteristic
348C4×C43#40711yescharacteristic
349C4×C43#40711yescharacteristic
350C4×C43#44711yescharacteristic
351C4×C43#44711yescharacteristic
352C4×C43#45011yescharacteristic
353C4×C43#45011yescharacteristic
354Dic43—22no—
355Dic43—22no—
356Dic43—42no—
357Dic43—41no—
358C22×C4×D4—431no—
359#1797—431no—
360C4×C22⋊C8—431no—
361C2×D4⋊C8—431no—
362C2×D4⋊C8—431no—
363C2×D4⋊C8—431no—
364C2×D4⋊C8D4311yescharacteristic, complemented
365C2×C43—44no—
366C2×C43C2×D4⋊C811yescharacteristic
367C2×C43#147811yescharacteristic
368C2×C43#148611yescharacteristic
369C2×C43#149011yescharacteristic
370C2×C43#177911yescharacteristic
371C2×C43#178611yescharacteristic
372C2×C43#178911yescharacteristic
373D43—24no—
374D43—44no—
375C23×D4—431no—
376C24×C4—861no—
377C2×C4×D4—431no—
378C2×C4×D4—431no—
379C2×C4×D4—431no—
380C2×C4×D4—861no—
381C2×C4×D4—861no—
382C2×C4×D4—862no—
383C2×C4×D4—862no—
384C2×C4×D4—862no—
385C2×C4×D4—862no—
386C2×C4×D4C2×D4311yescharacteristic
387C22×C4⋊C4—431no—
388C22×C22⋊C4—861no—
389C22×C42—431no—
390C2×C4⋊C8—431no—
391C2×C4⋊C8C2×D4311yescharacteristic, complemented
392C2×C22⋊C8—861no—
393C2×C22⋊C8—861no—
394C2×C4×C8—431no—
395C2×C4×C8C2×D4311yescharacteristic, complemented
396#336—861no—
397#336—861no—
398D4⋊C8—22no—
399D4⋊C8—862no—
400D4⋊C8—862no—
401D4⋊C8—862no—
402C43#831011yescharacteristic, complemented, Sylow
403C25—861no—
404C22×D4—434no—
405C22×D4—431no—
406C22×D4—862no—
407C22×D4—861no—
408C22×D4—862no—
409C22×D4—862no—
410C22×D4—862no—
411C22×D4—862no—
412C22×D4C4×D4311yescharacteristic
413C23×C4—21no—
414C23×C4—431no—
415C23×C4—431no—
416C23×C4—431no—
417C23×C4—861no—
418C23×C4—861no—
419C23×C4—864no—
420C23×C4—864no—
421C23×C4—861no—
422C23×C4—861no—
423C23×C4—1722no—
424C23×C4—1722no—
425C23×C4—1722no—
426C23×C4—1722no—
427C22×C8—21no—
428C22×C8—21no—
429C22×C8—861no—
430C22×C8—861no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—432no—
434C4×D4—432no—
435C4×D4—864no—
436C4×D4—864no—
437C4×D4—862no—
438C4×D4—862no—
439C4×D4—864no—
440C4×D4—864no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—861no—
444C4×D4—861no—
445C4×D4D17212yes—
446C4×D4C22⋊D4312yes—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—862no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—862no—
451C2×C4⋊C4C4×D4311yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—864no—
454C2×C22⋊C4—864no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42—861no—
464C2×C42—861no—
465C2×C42C22×D4311yescharacteristic
466C4⋊C8—21no—
467C4⋊C8—21no—
468C4⋊C8—861no—
469C4⋊C8—861no—
470C22⋊C8—864no—
471C22⋊C8—1722no—
472C4×C8—21no—
473C4×C8—21no—
474C4×C8—861no—
475C4×C8—861no—
476C24—21no—
477C24—431no—
478C24—864no—
479C24—864no—
480C24—864no—
481C24—861no—
482C24—1722no—
483C24—1722no—
484C24—1722no—
485C24—1722no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—432no—
490C2×D4—432no—
491C2×D4—432no—
492C2×D4—864no—
493C2×D4—868no—
494C2×D4—868no—
495C2×D4—868no—
496C2×D4—864no—
497C2×D4—864no—
498C2×D4—868no—
499C2×D4—861no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4C8×D4312yes—
503C2×D4#1062187212yes—
504C2×D4(C2×D43)⋊C412yes—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—432no—
515C22×C4—432no—
516C22×C4—432no—
517C22×C4—432no—
518C22×C4—431no—
519C22×C4—862no—
520C22×C4—864no—
521C22×C4—864no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—864no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—862no—
534C22×C4—861no—
535C22×C4—862no—
536C22×C4—1721no—
537C22×C4—1722no—
538C22×C4—1722no—
539C22×C4—1728no—
540C22×C4—1728no—
541C22×C4—1728no—
542C22×C4—1728no—
543C22×C4—1722no—
544C22×C4—1722no—
545C22×C4—1722no—
546C22×C4—1722no—
547C22×C4—1721no—
548C22×C4—1721no—
549C22×C4—1721no—
550C22×C4—1721no—
551C22×C4C2×C4×D4311yescharacteristic
552C22×C4D4×D4311yescharacteristic
553C22×C4D4×D4311yescharacteristic
554C2×C8—22no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—862no—
561C2×C8—1721no—
562C2×C8—1721no—
563C2×C8—1721no—
564C2×C8—1721no—
565C2×C8—1721no—
566C4⋊C4—21no—
567C4⋊C4—432no—
568C4⋊C4—864no—
569C4⋊C4—861no—
570C4⋊C4(C2×D43)⋊C412yes—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—864no—
574C22⋊C4—864no—
575C22⋊C4—862no—
576C22⋊C4—862no—
577C42—861no—
578C42—861no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42C2×D17211yescharacteristic
584C42D4×D4311yescharacteristic
585C42D4×D4311yescharacteristic
586C42C2×C22⋊D4311yescharacteristic
587C23—22no—
588C23—22no—
589C23—22no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—432no—
595C23—432no—
596C23—432no—
597C23—8616no—
598C23—861no—
599C23—861no—
600C23—861no—
601C23—861no—
602C23—862no—
603C23—862no—
604C23—862no—
605C23—1728no—
606C23—1728no—
607C23—1728no—
608C23—1728no—
609C23—1728no—
610C23—1728no—
611C23—1721no—
612C23—1721no—
613C23—1721no—
614C23—1721no—
615C23C22⋊C4×D4311yescharacteristic
616D4—22no—
617D4—22no—
618D4—22no—
619D4—434no—
620D4—8616no—
621D4—862no—
622D4—862no—
623D4—862no—
624D4(C2×D43)⋊C814yescomplemented
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—432no—
635C2×C4—432no—
636C2×C4—861no—
637C2×C4—861no—
638C2×C4—861no—
639C2×C4—861no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—862no—
643C2×C4—862no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—862no—
648C2×C4—861no—
649C2×C4—861no—
650C2×C4—861no—
651C2×C4—862no—
652C2×C4—1722no—
653C2×C4—1722no—
654C2×C4—1728no—
655C2×C4—1728no—
656C2×C4—1728no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1722no—
660C2×C4—1722no—
661C2×C4—1722no—
662C2×C4—1722no—
663C2×C4C22⋊C4×D4311yescharacteristic
664C2×C4C2×(C2×D43)⋊C411yescharacteristic
665C2×C4#1306329311yescharacteristic
666C2×C4#1306329311yescharacteristic
667C2×C4#1306329511yescharacteristic
668C2×C4#1306329511yescharacteristic
669C2×C4C2×C8×D4311yescharacteristic
670C2×C4M16×D4311yescharacteristic
671C2×C4M16×D4311yescharacteristic
672C2×C4C2×#1062187211yescharacteristic
673C2×C4D8×D4311yescharacteristic
674C2×C4SD16×D4311yescharacteristic
675C2×C4#1306334911yescharacteristic
676C2×C4#1306335211yescharacteristic
677C8—42no—
678C8—81no—
679C8—3441no—
680C8—1722no—
681C22—24no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—434no—
689C22—862no—
690C22—862no—
691C22—862no—
692C22—862no—
693C22—862no—
694C22—862no—
695C22—864no—
696C22—17232no—
697C22—1722no—
698C22—1722no—
699C22—1722no—
700C22—1722no—
701C22—1722no—
702C22—1722no—
703C22#1458275411yescharacteristic
704C22C22⋊C8×D4311yescharacteristic
705C22#1458286111yescharacteristic
706C22#102×D4311yescharacteristic
707C22#1458290211yescharacteristic
708C22#104×D4311yescharacteristic
709C22#1458291411yescharacteristic
710C4—21no—
711C4—21no—
712C4—42no—
713C4—862no—
714C4—862no—
715C4—1722no—
716C4—1721no—
717C4C22⋊C8×D4311yescharacteristic
718C4C2×(C2×D43)⋊C811yescharacteristic
719C4#1458286111yescharacteristic
720C4#1458286211yescharacteristic
721C4#1458303111yescharacteristic
722C4#1458303411yescharacteristic
723C4#1458304811yescharacteristic
724C4#1458305111yescharacteristic
725C2—44no—
726C2—864no—
727C2—1724no—
728C2D4⋊C8×D4311yescharacteristic
729C2#1913298411yescharacteristic
730C2#1913301811yescharacteristic
731C2#1913303611yescharacteristic
732C2#1913450411yescharacteristic
733C2#1913452411yescharacteristic
734C2#1913453711yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC2×C43×D4⋊C8C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D4×D43C4
cosocleC2×C42×C43C23
hypercenterC2×D4⋊C8D43
hypocenterC43#8310
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #19134572C2semidirect
3. C4×(C2×D43)⋊C8C2semidirect
4. C2×#14582628C2semidirect
5. C2×D4⋊(C43⋊C8)C2semidirect
6. C2×#14582626C2semidirect
7. C2×C43×D4⋊C8C2semidirect
22. C2×C4⋊(C43⋊C8)C22semidirect
25. C2×C4×C43⋊C8C22semidirect
32. C2×C4⋊C8×C43C22semidirect
33. C2×C4×C8×C43C22semidirect
43. C2×D4×D43C8semidirect
251. D4×C43C22⋊C8semidirect
292. D172C22⋊C8semidirect
342. C2×D43D4⋊C8semidirect
364. C2×D4⋊C8D43semidirect
391. C2×C4⋊C8C2×D43semidirect
395. C2×C4×C8C2×D43semidirect
402. C43#8310semidirect
624. D4(C2×D43)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
#191345722
C4×(C2×D43)⋊C82
C2×#145826282
C2×D4⋊(C43⋊C8)2
C2×#145826262
C2×C43×D4⋊C82
#831043