Finite Group Databasebeta

← #25063155

Subgroups — #25063155

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
4#19133007C212yesmaximal, complemented
5#19133005C212yesmaximal, complemented
6#19132996C212yesmaximal, complemented
7#19132992C212yesmaximal, complemented
8#19132983C211yesmaximal, characteristic, complemented
9#19132982C211yesmaximal, characteristic, complemented
10#19132980C211yesmaximal, characteristic, complemented
11C43×#1477C211yesmaximal, characteristic, complemented
12C22×C8×D43—21no—
13#14583453C411yescharacteristic
14#14583453C2211yescharacteristic
15#14583452C411yescharacteristic
16#14583446C411yescharacteristic
17#14583446C2211yescharacteristic
18#14583445C411yescharacteristic
19#14583436C411yescharacteristic
20#14583436C2211yescharacteristic
21#14583431C411yescharacteristic
22#14583431C2211yescharacteristic
23#14583429—21no—
24#14583429—21no—
25#14583427—21no—
26#14583427—21no—
27#14583411C411yescharacteristic
28#14583408—21no—
29#14583408—21no—
30#14583406C411yescharacteristic
31C4×#10621898—21no—
32C4×#10621898—21no—
33C4×#10621898C2211yescharacteristic
34C2×C42×D43C2211yescharacteristic
35#14582955—21no—
36#14582953—21no—
37#14582952C2211yescharacteristic
38#14582950C2212yes—
39#14582921—21no—
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41C2×Dic43⋊C8—21no—
42C4⋊C8×D43—21no—
43C4⋊C8×D43—21no—
44C4⋊C8×D43C2212yes—
45C4⋊C8×D43C2212yes—
46#14582861—21no—
47C4×#10621872C2212yes—
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C4×#41×C43C2211yescharacteristic
55C43×#431C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2×C411yescharacteristic
62C22×C4×D43C2×C411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C2×#10621872—22no—
66C22×C43⋊C8—21no—
67C2×C8×D43—22no—
68C2×C8×D43—22no—
69C2×C8×D43—44no—
70#13063324C2×C411yescharacteristic
71#13063324C2×C411yescharacteristic
72#13063323C2×C411yescharacteristic
73#13063321C2×C411yescharacteristic
74#13063320—21no—
75#13063320—21no—
76#13063318—21no—
77#13063318—21no—
78#13063316C2×C411yescharacteristic
79#13063316C2×C411yescharacteristic
80#13063315—21no—
81#13063315—21no—
82#13063314C2×C411yescharacteristic
83#13063312C2×C411yescharacteristic
84#13063311—21no—
85#13063311—21no—
86#13063310—21no—
87#13063310—21no—
88#13063309—21no—
89#13063307—21no—
90#13063307—21no—
91#13063306—21no—
92#13063305C2×C411yescharacteristic
93#13063305C2×C411yescharacteristic
94#13063303—21no—
95#13063303—21no—
96#13063302—21no—
97#13063302—21no—
98#13063301C2×C411yescharacteristic
99#13063301C2×C411yescharacteristic
100#13063300C2×C411yescharacteristic
101#13063300C2×C411yescharacteristic
102#13063298—21no—
103#13063298—21no—
104#13063297—21no—
105#13063297—21no—
106#13063296C2×C411yescharacteristic
107#13063296C2×C411yescharacteristic
108#13063295—21no—
109#13063293—21no—
110C4×Dic86—21no—
111C4×Dic86—21no—
112C4×Dic86—21no—
113C4×Dic86—21no—
114C4×Dic86C2×C411yescharacteristic
115C4×Dic86C2311yescharacteristic
116C4×D172—21no—
117C4×D172—21no—
118C4×D172—21no—
119C4×D172—21no—
120C4×D172C2×C411yescharacteristic
121C4×D172C2311yescharacteristic
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129C4×C22⋊D43—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132#13063284—21no—
133#13063284—21no—
134#13063284C2×C411yescharacteristic
135#13063282—21no—
136#13063282—21no—
137#13063282—21no—
138#13063282—21no—
139#13063282—21no—
140C2×C4×Dic43C2×C411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C42×D43—21no—
144C42×D43C2×C411yescharacteristic
145C42×D43C2×C411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43C2311yescharacteristic
151C42×D43C2311yescharacteristic
152C4⋊(C43⋊C8)—21no—
153C4⋊(C43⋊C8)—21no—
154C4⋊(C43⋊C8)C2312yes—
155Dic43⋊C8—22no—
156Dic43⋊C8—22no—
157Dic43⋊C8—22no—
158C22⋊(C43⋊C8)—21no—
159(C2×D43)⋊C8—22no—
160#13063235—22no—
161C4×C43⋊C8C2312yes—
162C2×#41×C43C2×C411yescharacteristic
163C22×C8×C43—21no—
164C4×Q8×C43C2×C411yescharacteristic
165C4×Q8×C43C2311yescharacteristic
166C4×D4×C43—21no—
167C4×D4×C43—21no—
168C4×D4×C43C2×C411yescharacteristic
169C4×D4×C43C2311yescharacteristic
170#117×C43—21no—
171#117×C43C2×C411yescharacteristic
172C2×C42×C43—21no—
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43—21no—
175C4⋊C8×C43—21no—
176C4⋊C8×C43C2312yes—
177C22⋊C8×C43—21no—
178C4×C8×C43C2312yes—
179C23×D43C22⋊C411yescharacteristic
180#41×C43—22no—
181#41×C43—22no—
182C2×Q8×C43C22×C411yescharacteristic
183C2×D4×C43—21no—
184C2×D4×C43C22×C411yescharacteristic
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—21no—
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C22×Dic43C22⋊C411yescharacteristic
197C22×Dic43C22⋊C411yescharacteristic
198C22×Dic43C22⋊C411yescharacteristic
199#10621898—22no—
200#10621898—22no—
201#10621898—44no—
202#10621898—42no—
203#10621898—42no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172C22×C411yescharacteristic
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—21no—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—42no—
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22⋊C411yescharacteristic
217C2×C4×D43C22⋊C411yescharacteristic
218C2×C4×D43C22⋊C411yescharacteristic
219C2×C4×D43C22⋊C411yescharacteristic
220C2×C4×D43C22⋊C411yescharacteristic
221C2×C4×D43C22×C411yescharacteristic
222C2×C4×D43C22×C411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×C4×D43C2×D411yescharacteristic
225C2×C4×D43C2×D411yescharacteristic
226C2×C4×D43C2×D411yescharacteristic
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86C22×C411yescharacteristic
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43—42no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C22×C411yescharacteristic
236C4⋊C4×C43C22×C411yescharacteristic
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—21no—
243C42×C43C22×C411yescharacteristic
244C42×C43C2×D411yescharacteristic
245C42×C43C2×D411yescharacteristic
246C42×C43C2411yescharacteristic
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—21no—
251C22⋊Dic43—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—21no—
261(C2×D43)⋊C4—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43C22×C411yescharacteristic
267C4⋊Dic43C22×C411yescharacteristic
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277Dic43⋊C4—21no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C4×Dic43—21no—
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22⋊C411yescharacteristic
287C4×Dic43C22×C411yescharacteristic
288C4×Dic43C22×C411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290C4×Dic43C2×D411yescharacteristic
291C4×Dic43C2×D411yescharacteristic
292C4×Dic43C2×D411yescharacteristic
293C2×C43⋊C8—22no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8—42no—
296#10621872—44no—
297C8×D43—44no—
298C8×D43—44no—
299C23×C43—21no—
300C23×C43C2×C22⋊C411yescharacteristic
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—21no—
305C22×D43C2×C22⋊C411yescharacteristic
306C22×D43C2×C22⋊C411yescharacteristic
307Q8×C43—21no—
308Q8×C43—21no—
309D4×C43—21no—
310D4×C43—21no—
311D4×C43—42no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—41no—
318C2×C4×C43—42no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—42no—
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C2×C4×C43C2×C22⋊C411yescharacteristic
325C2×C4×C43#13112yes—
326C2×C4×C43#13112yes—
327C2×C4×C43C23×C411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C22⋊D43—42no—
331C22⋊D43—42no—
332C22⋊D43—42no—
333C22⋊D43—42no—
334C22⋊D43—42no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—41no—
341C2×Dic43C2×C22⋊C411yescharacteristic
342C2×Dic43C2×C22⋊C411yescharacteristic
343C2×Dic43C2×C22⋊C411yescharacteristic
344C2×Dic43C2×C22⋊C411yescharacteristic
345C2×Dic43C2×C22⋊C411yescharacteristic
346C2×Dic43C2×C22⋊C411yescharacteristic
347D172—21no—
348D172—21no—
349D172—42no—
350D172—42no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—21no—
355C4×D43—21no—
356C4×D43—21no—
357C4×D43—21no—
358C4×D43—21no—
359C4×D43—21no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—41no—
364C4×D43—41no—
365C4×D43—42no—
366C4×D43—41no—
367C4×D43—41no—
368C4×D43—42no—
369C4×D43AGL(1,ℤ/8)12yes—
370C4×D43#13712yes—
371Dic86—21no—
372Dic86—21no—
373Dic86—42no—
374Dic86—42no—
375C8×C43—42no—
376C8×C43—42no—
377C43⋊C8—42no—
378C43⋊C8—42no—
379#17466—431nomaximal, Sylow
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43#40812yes—
386C22×C43C22×C22⋊C411yescharacteristic
387C2×D43—28no—
388C2×D43—21no—
389C2×D43—21no—
390C2×D43—21no—
391C2×D43—21no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43#41712yes—
396C2×D43#42112yes—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—41no—
403C4×C43#40812yes—
404C4×C43C2×#13111yescharacteristic
405C4×C43C2×#13111yescharacteristic
406C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
407C4×C43C2×#13711yescharacteristic
408Dic43—21no—
409Dic43—21no—
410Dic43—21no—
411Dic43—21no—
412Dic43—21no—
413Dic43—41no—
414Dic43—41no—
415Dic43—41no—
416Dic43#41712yes—
417#3444—431no—
418#2920—431no—
419C22×C4⋊C8—431no—
420#1483—432no—
421#1483—432no—
422#1481—432no—
423#1480—432no—
424#1477—431no—
425#1477—431no—
426#1477—431no—
427#1477D4311yescharacteristic, complemented
428C2×C43—22no—
429C2×C43—81no—
430C2×C43C2×#40811yescharacteristic
431C2×C43C2×#41711yescharacteristic
432C2×C43C2×#42111yescharacteristic
433D43—22no—
434D43—22no—
435D43—81no—
436C23×C8—861no—
437#533—431no—
438#533—431no—
439#533—431no—
440#532—431no—
441#532—431no—
442#532—431no—
443#529—431no—
444#529—431no—
445#529—431no—
446#529—431no—
447#529—861no—
448#529—861no—
449#529—861no—
450#529—861no—
451#525—431no—
452#525—431no—
453#525—861no—
454#525—861no—
455C4×#41—431no—
456C4×#41—861no—
457C4×#41—861no—
458C4×#41C2×D4311yescharacteristic
459C22×C42—431no—
460#432—861no—
461#432—861no—
462#431—431no—
463#431—432no—
464#431C2×D4311yescharacteristic
465#423—861no—
466C2×C4⋊C8—431no—
467C2×C4⋊C8—432no—
468C2×C4⋊C8—432no—
469C2×C4⋊C8—861no—
470C2×C4⋊C8—861no—
471C2×C4⋊C8—861no—
472C2×C4⋊C8C2×D4311yescharacteristic
473#407—861no—
474C4×M16—432no—
475Q8⋊C8—432no—
476Q8⋊C8—432no—
477Q8⋊C8—432no—
478Q8⋊C8C2×D4312yescomplemented
479D4⋊C8—432no—
480D4⋊C8—432no—
481D4⋊C8—432no—
482D4⋊C8C2×D4312yescomplemented
483C43#1746611yescharacteristic, complemented, Sylow
484C2×#41—431no—
485C2×#41—861no—
486C2×#41—861no—
487C2×#41C4×D4311yescharacteristic
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—431no—
491C2×M16—862no—
492C22×C8—21no—
493C22×C8—862no—
494C22×C8—862no—
495C22×C8—861no—
496C22×C8—1724no—
497C4⋊Q8—431no—
498C4⋊Q8—431no—
499C4⋊Q8—431no—
500#127—431no—
501#126—861no—
502#126—861no—
503#126—861no—
504#126—861no—
505#125—431no—
506#125—431no—
507#125—861no—
508#125—861no—
509#124—431no—
510#124—431no—
511#124—861no—
512#124—861no—
513#123—861no—
514#123—861no—
515#123—861no—
516#123—861no—
517#123—861no—
518#123—861no—
519C22⋊Q8—431no—
520C22⋊Q8—431no—
521C22⋊Q8—431no—
522C22⋊Q8—431no—
523C22⋊Q8—861no—
524C22⋊Q8—861no—
525C22⋊Q8—861no—
526C22⋊Q8—861no—
527#121—431no—
528#121—431no—
529#121—431no—
530#121—431no—
531#121—861no—
532#121—861no—
533#121—861no—
534#121—861no—
535#120—861no—
536#120—861no—
537C4×Q8—431no—
538C4×Q8—431no—
539C4×Q8—861no—
540C4×Q8—861no—
541C4×Q8—861no—
542C4×Q8—861no—
543C4×Q8C4×D4311yescharacteristic
544C4×Q8C22×D4311yescharacteristic
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—431no—
548C4×D4—431no—
549C4×D4—861no—
550C4×D4—861no—
551C4×D4—861no—
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×D4C4×D4311yescharacteristic
564C4×D4C22×D4311yescharacteristic
565#117—21no—
566#117—431no—
567#117—861no—
568#117—861no—
569#117—861no—
570#117—861no—
571#117—861no—
572#117—861no—
573#117—861no—
574#117C4×D4311yescharacteristic
575C2×C42—21no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—431no—
581C2×C42—431no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—431no—
587C2×C42—861no—
588C2×C42C22×D4311yescharacteristic
589C4⋊C8—21no—
590C4⋊C8—21no—
591C4⋊C8—432no—
592C4⋊C8—862no—
593C4⋊C8—862no—
594C4⋊C8—862no—
595C4⋊C8—861no—
596C4⋊C8—861no—
597C4⋊C8C22×D4312yes—
598C22⋊C8—21no—
599C22⋊C8—862no—
600C22⋊C8—861no—
601#97—862no—
602C4×C8—432no—
603C4×C8C22×D4312yes—
604C24—431no—
605#41—22no—
606#41—22no—
607#41—862no—
608#41—862no—
609#41—1722no—
610#41—1722no—
611#41—1724no—
612C2×Q8—431no—
613C2×Q8—861no—
614C2×Q8—861no—
615C2×Q8C2×C4×D4311yescharacteristic
616C2×D4—21no—
617C2×D4—431no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4—861no—
622C2×D4—861no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4C2×C4×D4311yescharacteristic
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—1722no—
652C22×C4C2×C4×D4311yescharacteristic
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655M16—1724no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—42no—
659C2×C8—862no—
660C2×C8—862no—
661C2×C8—1724no—
662C2×C8—1724no—
663C2×C8—1722no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—431no—
667C4⋊C4—431no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4C2×C4×D4311yescharacteristic
683C4⋊C4C2×C4×D4311yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—861no—
688C22⋊C4—861no—
689C22⋊C4—861no—
690C22⋊C4—861no—
691C22⋊C4—861no—
692C22⋊C4—861no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C22⋊C4—861no—
697C22⋊C4—861no—
698C22⋊C4—861no—
699C22⋊C4—861no—
700C22⋊C4—861no—
701C22⋊C4—861no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—431no—
706C42—431no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—431no—
712C42—431no—
713C42—431no—
714C42—431no—
715C42—431no—
716C42—431no—
717C42—861no—
718C42—861no—
719C42—861no—
720C42C2×C4×D4311yescharacteristic
721C42D4×D4311yescharacteristic
722C42D4×D4311yescharacteristic
723C42C23×D4311yescharacteristic
724C23—21no—
725C23—431no—
726C23—431no—
727C23—862no—
728C23—862no—
729C23—862no—
730C23—861no—
731C23C22⋊C4×D4311yescharacteristic
732Q8—21no—
733Q8—21no—
734Q8—861no—
735Q8—861no—
736Q8—1722no—
737Q8—1722no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—861no—
742D4—861no—
743D4—1722no—
744D4—1722no—
745D4—1722no—
746D4—1722no—
747D4—1722no—
748D4—1722no—
749D4—1722no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—431no—
761C2×C4—432no—
762C2×C4—432no—
763C2×C4—431no—
764C2×C4—431no—
765C2×C4—431no—
766C2×C4—431no—
767C2×C4—431no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—861no—
777C2×C4—861no—
778C2×C4—861no—
779C2×C4—861no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4—1722no—
788C2×C4—1721no—
789C2×C4—1722no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4C22⋊C4×D4311yescharacteristic
793C2×C4C22⋊C4×D4311yescharacteristic
794C2×C4C22⋊C4×D4311yescharacteristic
795C2×C4#1306333112yes—
796C2×C4#1306333312yes—
797C2×C4C22×C4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C2×D4×D4311yescharacteristic
800C8—42no—
801C8—42no—
802C8—1722no—
803C8—1722no—
804C22—21no—
805C22—21no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—432no—
810C22—432no—
811C22—868no—
812C22—861no—
813C22—861no—
814C22—861no—
815C22—861no—
816C22—1721no—
817C22—1721no—
818C22—1721no—
819C22#1458286412yes—
820C22C2×C22⋊C4×D4311yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—432no—
828C4—861no—
829C4—861no—
830C4—861no—
831C4—861no—
832C4—861no—
833C4—1721no—
834C4—1721no—
835C4—1721no—
836C4#1458286412yes—
837C4C2×#1306333111yescharacteristic
838C4C2×#1306333311yescharacteristic
839C4AGL(1,ℤ/8)×D4311yescharacteristic
840C4#137×D4311yescharacteristic
841C2—22no—
842C2—81no—
843C2—862no—
844C2—862no—
845C2—3441no—
846C2C2×#1458286411yescharacteristic
847C2#417×D4311yescharacteristic
848C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1477C2
socleC22×C43C22×C22⋊C4
prime radical#19147888C2
cosocleC42×C43C24
hypercenter#1477D43
hypocenterC43#17466
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. C2×C4⋊C8×D43C2semidirect
4. #19133007C2semidirect
5. #19133005C2semidirect
6. #19132996C2semidirect
7. #19132992C2semidirect
8. #19132983C2semidirect
9. #19132982C2semidirect
10. #19132980C2semidirect
11. C43×#1477C2semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
427. #1477D43semidirect
478. Q8⋊C8C2×D43semidirect
482. D4⋊C8C2×D43semidirect
483. C43#17466semidirect

Maximal subgroups

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

subgroupindex
#191478882
#191432232
C2×C4⋊C8×D432
#191330072
#191330052
#191329962
#191329922
#191329832
#191329822
#191329802
C43×#14772
#1746643