Finite Group Databasebeta

← #25063055

Subgroups — #25063055

Order 11008.

1292 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D43C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3#423×D43C211yesmaximal, characteristic, complemented
4#19133035C211yesmaximal, characteristic, complemented
5#19133034C211yesmaximal, characteristic, complemented
6#19133032C211yesmaximal, characteristic, complemented
7#19133022C212yesmaximal, complemented
8#19133018C212yesmaximal, complemented
9#19132981C212yesmaximal, complemented
10#19132979C212yesmaximal, complemented
11C43×#1489C211yesmaximal, characteristic, complemented
12C2×#41×D43C411yescharacteristic
13C2×M16×D43—21no—
14#41×Dic43C411yescharacteristic
15C4×#10621902C411yescharacteristic
16C4×#10621902C2211yescharacteristic
17C4×#10621898—21no—
18C4×#10621898C2211yescharacteristic
19#14583367—21no—
20#14583367C411yescharacteristic
21C4×#10621900—21no—
22C4×#10621900—21no—
23C4×#10621900C411yescharacteristic
24C4×#10621900C2211yescharacteristic
25C4×Q8×D43C411yescharacteristic
26C4×Q8×D43C2211yescharacteristic
27C4×D4×D43—21no—
28C4×D4×D43—21no—
29C4×D4×D43C411yescharacteristic
30C4×D4×D43C2211yescharacteristic
31#117×D43—21no—
32#117×D43C411yescharacteristic
33C2×C42×D43—21no—
34C2×C42×D43C2211yescharacteristic
35#14582954—21no—
36#14582954—21no—
37#14582950C2212yes—
38#14582950C2212yescomplemented
39#14582923C2211yescharacteristic, complemented
40#14582922—21no—
41#14582922—21no—
42#14582921—21no—
43#14582921C2212yes—
44C4⋊C8×D43—21no—
45C4⋊C8×D43C2212yescomplemented
46#14582862—21no—
47C4×#10621877C2211yescharacteristic, complemented
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C4×#41×C43C2211yescharacteristic
55C43×#423C2211yescharacteristic, complemented
56C4×M16×C43C2211yescharacteristic, complemented
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621898C2×C411yescharacteristic
62C2×#10621900—21no—
63C2×#10621900C2×C411yescharacteristic
64#41×D43—24no—
65#41×D43—24no—
66C2×Q8×D43C2×C411yescharacteristic
67C2×D4×D43—21no—
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2×C411yescharacteristic
73C22×C4×D43D411yescharacteristic
74C22×C4×D43D411yescharacteristic
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621872—22no—
78M16×D43—44no—
79C2×C8×D43—22no—
80Q8×Dic43C2×C411yescharacteristic
81Q8×Dic43C2×C411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86C2311yescharacteristic
86#13063290—21no—
87#13063290—21no—
88#13063290C2×C411yescharacteristic
89#13063290C2×C411yescharacteristic
90C4×D172—21no—
91C4×D172—21no—
92C4×D172C2×C411yescharacteristic
93C4×D172C2311yescharacteristic
94D4×Dic43—21no—
95D4×Dic43—21no—
96D4×Dic43C2×C411yescharacteristic
97D4×Dic43C2×C411yescharacteristic
98#13063287—21no—
99#13063287—21no—
100#13063287C2×C411yescharacteristic
101#13063287C2×C411yescharacteristic
102C4×C22⋊D43—21no—
103C4×C22⋊D43—21no—
104C4×C22⋊D43—21no—
105C4×C22⋊D43—21no—
106C4×C22⋊D43—21no—
107C4×C22⋊D43—21no—
108(C22⋊D43)⋊C4—21no—
109(C22⋊D43)⋊C4—21no—
110(C22⋊D43)⋊C4—21no—
111(C22⋊D43)⋊C4—21no—
112(C22⋊D43)⋊C4—21no—
113(C22⋊D43)⋊C4—21no—
114#13063284—21no—
115#13063284C2×C411yescharacteristic
116#13063283—21no—
117#13063283—21no—
118#13063283C2×C411yescharacteristic
119#13063283C2×C411yescharacteristic
120#13063282—21no—
121#13063282—21no—
122#13063282—21no—
123#13063281—21no—
124#13063281—21no—
125#13063281—21no—
126C4⋊C4×D43—21no—
127C4⋊C4×D43—21no—
128C4⋊C4×D43C2×C411yescharacteristic
129C4⋊C4×D43C2×C411yescharacteristic
130C22⋊C4×D43—21no—
131C22⋊C4×D43—21no—
132C22⋊C4×D43—21no—
133C2×C4×Dic43—21no—
134C2×C4×Dic43—21no—
135C2×C4×Dic43—21no—
136C2×C4×Dic43C2×C411yescharacteristic
137C2×C4×Dic43D411yescharacteristic
138C2×C4×Dic43D411yescharacteristic
139C42×D43—21no—
140C42×D43—21no—
141C42×D43—21no—
142C42×D43—21no—
143C42×D43—21no—
144C42×D43—21no—
145C42×D43—21no—
146C42×D43C2×C411yescharacteristic
147C42×D43C2×C411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43D411yescharacteristic
151C42×D43D411yescharacteristic
152C42×D43C2311yescharacteristic
153C42×D43C2311yescharacteristic
154C4⋊(C43⋊C8)—21no—
155C4⋊(C43⋊C8)C2312yes—
156Dic43⋊C8—22no—
157Dic43⋊C8—22no—
158Dic43⋊C8—22no—
159Dic43⋊C8—22no—
160(C2×D43)⋊C8—22no—
161(C2×D43)⋊C8—22no—
162#13063236—21no—
163C4×C43⋊C8C2312yes—
164C2×#41×C43C2×C411yescharacteristic
165C2×M16×C43—21no—
166C2×M16×C43—21no—
167C4×Q8×C43C2×C411yescharacteristic
168C4×Q8×C43C2311yescharacteristic
169C4×D4×C43—21no—
170C4×D4×C43—21no—
171C4×D4×C43C2×C411yescharacteristic
172C4×D4×C43C2311yescharacteristic
173#117×C43—21no—
174#117×C43C2×C411yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177C4⋊C8×C43—21no—
178C4⋊C8×C43C2312yes—
179#97×C43—21no—
180C4×C8×C43C2312yes—
181C23×D43—21no—
182C23×D43C22⋊C411yescharacteristic
183#41×C43—22no—
184#41×C43—22no—
185C2×Q8×C43C22×C411yescharacteristic
186C2×D4×C43—21no—
187C2×D4×C43C22×C411yescharacteristic
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43C22×C411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C2×C22⋊D43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43C22⋊C411yescharacteristic
201C22×Dic43C22⋊C411yescharacteristic
202C22×Dic43C22⋊C411yescharacteristic
203#10621902—22no—
204#10621902M1614yescomplemented
205Q8×D43—22no—
206Q8×D43—22no—
207#10621900—28no—
208#10621900—22no—
209#10621900M1614yescomplemented
210D4×D43—28no—
211D4×D43—22no—
212D4×D43—22no—
213#10621898—28no—
214#10621898—22no—
215#10621898—22no—
216C2×D172—21no—
217C2×D172C22×C411yescharacteristic
218C2×C4×D43—28no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—42no—
233C2×C4×D43—44no—
234C2×C4×D43—42no—
235C2×C4×D43—42no—
236C2×C4×D43C22⋊C411yescharacteristic
237C2×C4×D43C22⋊C411yescharacteristic
238C2×C4×D43C22⋊C411yescharacteristic
239C2×C4×D43C22⋊C411yescharacteristic
240C2×C4×D43C22⋊C411yescharacteristic
241C2×C4×D43C22⋊C411yescharacteristic
242C2×C4×D43C22×C411yescharacteristic
243C2×C4×D43C22×C411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×C4×D43C2×D411yescharacteristic
246C2×C4×D43C2×D411yescharacteristic
247C2×C4×D43C2×D411yescharacteristic
248C2×Dic86—21no—
249C2×Dic86C22×C411yescharacteristic
250M16×C43—42no—
251M16×C43—42no—
252C2×C8×C43—22no—
253C2×C8×C43—22no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C22×C411yescharacteristic
257C4⋊C4×C43C22×C411yescharacteristic
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C42×C43—21no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43C22×C411yescharacteristic
265C42×C43C2×D411yescharacteristic
266C42×C43C2×D411yescharacteristic
267C42×C43C2411yescharacteristic
268C22⋊Dic43—21no—
269C22⋊Dic43—21no—
270C22⋊Dic43—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43C22×C411yescharacteristic
280C4⋊Dic43C22×C411yescharacteristic
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285Dic43⋊C4—21no—
286Dic43⋊C4—21no—
287C4×Dic43—21no—
288C4×Dic43—21no—
289C4×Dic43—21no—
290C4×Dic43—21no—
291C4×Dic43—21no—
292C4×Dic43—21no—
293C4×Dic43—21no—
294C4×Dic43—21no—
295C4×Dic43—21no—
296C4×Dic43C22⋊C411yescharacteristic
297C4×Dic43C22⋊C411yescharacteristic
298C4×Dic43C22⋊C411yescharacteristic
299C4×Dic43C22⋊C411yescharacteristic
300C4×Dic43C22⋊C411yescharacteristic
301C4×Dic43C22⋊C411yescharacteristic
302C4×Dic43C22×C411yescharacteristic
303C4×Dic43C22×C411yescharacteristic
304C4×Dic43C2×D411yescharacteristic
305C4×Dic43C2×D411yescharacteristic
306C4×Dic43C2×D411yescharacteristic
307C4×Dic43C2×D411yescharacteristic
308#10621877—42no—
309#10621877—42no—
310C2×C43⋊C8—22no—
311C2×C43⋊C8—22no—
312#10621872—44no—
313C8×D43—44no—
314C23×C43—21no—
315C23×C43C2×C22⋊C411yescharacteristic
316C22×D43—24no—
317C22×D43—21no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—41no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43C2×C22⋊C411yescharacteristic
324C22×D43C2×C22⋊C411yescharacteristic
325Q8×C43—21no—
326Q8×C43C2×M1612yescomplemented
327D4×C43—24no—
328D4×C43—21no—
329D4×C43C2×M1612yescomplemented
330C2×C4×C43—24no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—22no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—42no—
342C2×C4×C43C2×C22⋊C411yescharacteristic
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C23×C411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C22⋊D43—24no—
349C22⋊D43—24no—
350C22⋊D43—24no—
351C2×Dic43—21no—
352C2×Dic43—22no—
353C2×Dic43—24no—
354C2×Dic43—22no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—41no—
358C2×Dic43—42no—
359C2×Dic43—42no—
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362C2×Dic43C2×C22⋊C411yescharacteristic
363C2×Dic43C2×C22⋊C411yescharacteristic
364C2×Dic43C2×C22⋊C411yescharacteristic
365C2×Dic43C2×C22⋊C411yescharacteristic
366D172—24no—
367D172—21no—
368D172C2×M1612yescomplemented
369C4×D43—24no—
370C4×D43—24no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—21no—
374C4×D43—21no—
375C4×D43—21no—
376C4×D43—21no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—24no—
381C4×D43—22no—
382C4×D43—41no—
383C4×D43—41no—
384C4×D43—42no—
385C4×D43—42no—
386C4×D43—42no—
387C4×D43—41no—
388C4×D43—41no—
389C4×D43—42no—
390C4×D43—42no—
391C4×D43C2×M1612yes—
392C4×D43C2×M1612yes—
393C4×D43AGL(1,ℤ/8)12yes—
394C4×D43#13712yes—
395Dic86—24no—
396Dic86—21no—
397Dic86C2×M1612yescomplemented
398C8×C43—42no—
399C8×C43—42no—
400C43⋊C8—42no—
401C43⋊C8—42no—
402#17451—431nomaximal, Sylow
403C22×C43—22no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43C22×C22⋊C411yescharacteristic
410C2×D43—21no—
411C2×D43—21no—
412C2×D43—21no—
413C2×D43—21no—
414C2×D43—22no—
415C2×D43—44no—
416C2×D43—48no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43#40712yes—
420C2×D43#41712yes—
421C4×C43—22no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—41no—
426C4×C43—41no—
427C4×C43#42112yes—
428C4×C43C22×M1611yescharacteristic
429C4×C43C22×M1611yescharacteristic
430C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
431C4×C43C2×#13711yescharacteristic
432Dic43—21no—
433Dic43—22no—
434Dic43—21no—
435Dic43—21no—
436Dic43—21no—
437Dic43—41no—
438Dic43—41no—
439Dic43#40712yes—
440Dic43#41712yes—
441C2×C4×#41—431no—
442#2920—431no—
443C2×#423—431no—
444#1489—431no—
445#1489—431no—
446#1489—431no—
447#1489D4311yescharacteristic, complemented
448#1487—432no—
449#1486—432no—
450#1477—432no—
451#1477—432no—
452C2×C43—41no—
453C2×C43—42no—
454C2×C43C2×#40711yescharacteristic
455C2×C43C2×#41711yescharacteristic
456C2×C43C2×#42111yescharacteristic
457D43—22no—
458D43—22no—
459D43—42no—
460C22×#41—431no—
461C22×M16—861no—
462C4×#41—431no—
463C4×#41—431no—
464C4×#41—431no—
465C4×#41—431no—
466C4×#41—431no—
467C4×#41—431no—
468C4×#41—431no—
469C4×#41—861no—
470C4×#41—861no—
471C4×#41—861no—
472C4×#41—861no—
473C4×#41C2×D4311yescharacteristic
474C2×C4×Q8—431no—
475C2×C4×Q8—431no—
476C2×C4×D4—431no—
477C2×C4×D4—431no—
478C2×C4×D4—861no—
479C2×C4×D4—861no—
480C2×#117—431no—
481C2×#117—861no—
482C22×C42—431no—
483C22×C42—861no—
484#432—861no—
485#432—861no—
486#431—432no—
487#431—432no—
488#423—431no—
489#423—432no—
490#423—861no—
491#423—861no—
492#423—861no—
493#423C2×D4311yescharacteristic, complemented
494C2×C4⋊C8—432no—
495C2×C4⋊C8—861no—
496#407—861no—
497C4×M16—431no—
498C4×M16C2×D4311yescharacteristic, complemented
499Q8⋊C8—432no—
500Q8⋊C8—432no—
501Q8⋊C8—432no—
502Q8⋊C8C2×D4312yescomplemented
503D4⋊C8—432no—
504D4⋊C8—432no—
505D4⋊C8—432no—
506D4⋊C8C2×D4312yescomplemented
507C43#1745111yescharacteristic, complemented, Sylow
508C2×#41—431no—
509C2×#41—431no—
510C2×#41—431no—
511C2×#41—861no—
512C2×#41—861no—
513C2×#41—864no—
514C2×#41—864no—
515C2×#41C4×D4311yescharacteristic
516C22×Q8—431no—
517C22×D4—431no—
518C22×D4—861no—
519C23×C4—431no—
520C23×C4—431no—
521C23×C4—431no—
522C23×C4—861no—
523C23×C4—861no—
524C23×C4—861no—
525C2×M16—21no—
526C2×M16—21no—
527C2×M16—862no—
528C2×M16—861no—
529C2×M16—861no—
530C2×M16—1724no—
531C22×C8—862no—
532C4×Q8—431no—
533C4×Q8—431no—
534C4×Q8—431no—
535C4×Q8—431no—
536C4×Q8—431no—
537C4×Q8—431no—
538C4×Q8—861no—
539C4×Q8—861no—
540C4×Q8—861no—
541C4×Q8—861no—
542C4×Q8C4×D4311yescharacteristic
543C4×Q8C22×D4311yescharacteristic
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—431no—
547C4×D4—431no—
548C4×D4—431no—
549C4×D4—431no—
550C4×D4—431no—
551C4×D4—431no—
552C4×D4—861no—
553C4×D4—861no—
554C4×D4—861no—
555C4×D4—861no—
556C4×D4—861no—
557C4×D4—861no—
558C4×D4—861no—
559C4×D4—861no—
560C4×D4—861no—
561C4×D4—861no—
562C4×D4—861no—
563C4×D4—861no—
564C4×D4—861no—
565C4×D4—861no—
566C4×D4—861no—
567C4×D4—861no—
568C4×D4—861no—
569C4×D4—861no—
570C4×D4C4×D4311yescharacteristic
571C4×D4C22×D4311yescharacteristic
572#117—21no—
573#117—431no—
574#117—431no—
575#117—431no—
576#117—861no—
577#117—861no—
578#117—861no—
579#117—861no—
580#117—861no—
581#117—861no—
582#117—861no—
583#117—861no—
584#117—861no—
585#117C4×D4311yescharacteristic
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4—861no—
593C2×C42—21no—
594C2×C42—431no—
595C2×C42—431no—
596C2×C42—431no—
597C2×C42—431no—
598C2×C42—431no—
599C2×C42—431no—
600C2×C42—431no—
601C2×C42—431no—
602C2×C42—431no—
603C2×C42—431no—
604C2×C42—431no—
605C2×C42—861no—
606C2×C42—861no—
607C2×C42—861no—
608C2×C42—861no—
609C2×C42—861no—
610C2×C42—861no—
611C2×C42—861no—
612C2×C42—861no—
613C2×C42—861no—
614C2×C42—861no—
615C2×C42C22×D4311yescharacteristic
616C4⋊C8—21no—
617C4⋊C8—432no—
618C4⋊C8—862no—
619C4⋊C8—862no—
620C4⋊C8—862no—
621C4⋊C8—862no—
622C4⋊C8—861no—
623C4⋊C8C22×D4312yes—
624C22⋊C8—862no—
625C22⋊C8—862no—
626#97—21no—
627#97—861no—
628C4×C8—432no—
629C4×C8C22×D4312yes—
630C24—431no—
631C24—861no—
632#41—22no—
633#41—22no—
634#41—434no—
635#41—434no—
636#41—862no—
637#41—862no—
638#41—868no—
639#41—862no—
640#41—862no—
641#41—868no—
642C2×Q8—431no—
643C2×Q8—861no—
644C2×Q8—862no—
645C2×Q8—862no—
646C2×Q8C2×C4×D4311yescharacteristic
647C2×D4—21no—
648C2×D4—431no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4—862no—
652C2×D4—868no—
653C2×D4—861no—
654C2×D4—861no—
655C2×D4—862no—
656C2×D4C2×C4×D4311yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—431no—
675C22×C4—861no—
676C22×C4—862no—
677C22×C4—862no—
678C22×C4—862no—
679C22×C4—862no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—868no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—1722no—
693C22×C4—1722no—
694C22×C4—1722no—
695C22×C4—1724no—
696C22×C4C2×C4×D4311yescharacteristic
697C22×C4D4×D4311yescharacteristic
698C22×C4D4×D4311yescharacteristic
699M16—42no—
700M16—42no—
701M16—1724no—
702M16—1722no—
703M16—1722no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—862no—
707C2×C8—862no—
708C2×C8—1724no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—431no—
712C4⋊C4—431no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4C2×C4×D4311yescharacteristic
722C4⋊C4C2×C4×D4311yescharacteristic
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C22⋊C4—861no—
732C22⋊C4—861no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—431no—
739C42—431no—
740C42—431no—
741C42—431no—
742C42—431no—
743C42—431no—
744C42—431no—
745C42—431no—
746C42—431no—
747C42—431no—
748C42—431no—
749C42—431no—
750C42—861no—
751C42—861no—
752C42—861no—
753C42—861no—
754C42—861no—
755C42—861no—
756C42—861no—
757C42—861no—
758C42—861no—
759C42C2×C4×D4311yescharacteristic
760C42D4×D4311yescharacteristic
761C42D4×D4311yescharacteristic
762C42C23×D4311yescharacteristic
763C23—21no—
764C23—431no—
765C23—431no—
766C23—862no—
767C23—862no—
768C23—864no—
769C23—861no—
770C23—1721no—
771C23—1722no—
772C23—1722no—
773C23C22⋊C4×D4311yescharacteristic
774Q8—21no—
775Q8—432no—
776Q8—864no—
777Q8—861no—
778Q8M16×D4312yescomplemented
779D4—24no—
780D4—21no—
781D4—432no—
782D4—864no—
783D4—864no—
784D4—864no—
785D4—864no—
786D4—861no—
787D4M16×D4312yescomplemented
788C2×C4—24no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—431no—
801C2×C4—431no—
802C2×C4—432no—
803C2×C4—432no—
804C2×C4—432no—
805C2×C4—432no—
806C2×C4—431no—
807C2×C4—431no—
808C2×C4—431no—
809C2×C4—431no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—864no—
813C2×C4—862no—
814C2×C4—862no—
815C2×C4—864no—
816C2×C4—864no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—864no—
820C2×C4—861no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—861no—
828C2×C4—861no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4—1722no—
832C2×C4—1722no—
833C2×C4—1722no—
834C2×C4—1722no—
835C2×C4—1722no—
836C2×C4—1721no—
837C2×C4—1722no—
838C2×C4—1722no—
839C2×C4—1721no—
840C2×C4—1721no—
841C2×C4C22⋊C4×D4311yescharacteristic
842C2×C4C22⋊C4×D4311yescharacteristic
843C2×C4C22⋊C4×D4311yescharacteristic
844C2×C4C22×C4×D4311yescharacteristic
845C2×C4C2×D4×D4311yescharacteristic
846C2×C4C2×D4×D4311yescharacteristic
847C8—42no—
848C8—42no—
849C8—1722no—
850C8—1722no—
851C22—21no—
852C22—22no—
853C22—21no—
854C22—21no—
855C22—41no—
856C22—41no—
857C22—432no—
858C22—432no—
859C22—861no—
860C22—861no—
861C22—861no—
862C22—861no—
863C22—862no—
864C22—1724no—
865C22—1728no—
866C22—1721no—
867C22—1721no—
868C22C2×C22⋊C4×D4311yescharacteristic
869C4—21no—
870C4—22no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—432no—
876C4—432no—
877C4—861no—
878C4—862no—
879C4—861no—
880C4—861no—
881C4—861no—
882C4—1721no—
883C4—1721no—
884C4#1458291412yes—
885C4C2×M16×D4311yescharacteristic
886C4C2×M16×D4311yescharacteristic
887C4AGL(1,ℤ/8)×D4311yescharacteristic
888C4#137×D4311yescharacteristic
889C2—41no—
890C2—42no—
891C2—862no—
892C2—862no—
893C2—1722no—
894C2#407×D4311yescharacteristic
895C2#417×D4311yescharacteristic
896C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1489C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#41×D43C4
cosocleC42×C43C24
hypercenter#1489D43
hypocenterC43#17451
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. #423×D43C2semidirect
4. #19133035C2semidirect
5. #19133034C2semidirect
6. #19133032C2semidirect
7. #19133022C2semidirect
8. #19133018C2semidirect
9. #19132981C2semidirect
10. #19132979C2semidirect
11. C43×#1489C2semidirect
38. #14582950C22semidirect
39. #14582923C22semidirect
45. C4⋊C8×D43C22semidirect
47. C4×#10621877C22semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
55. C43×#423C22semidirect
56. C4×M16×C43C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
204. #10621902M16semidirect
209. #10621900M16semidirect
326. Q8×C43C2×M16semidirect
329. D4×C43C2×M16semidirect
368. D172C2×M16semidirect
397. Dic86C2×M16semidirect
447. #1489D43semidirect
493. #423C2×D43semidirect
498. C4×M16C2×D43semidirect
502. Q8⋊C8C2×D43semidirect
506. D4⋊C8C2×D43semidirect
507. C43#17451semidirect
778. Q8M16×D43semidirect
787. D4M16×D43semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D432
#191432262
#423×D432
#191330352
#191330342
#191330322
#191330222
#191330182
#191329812
#191329792
C43×#14892
#1745143