Finite Group Databasebeta

← #25062796

Subgroups — #25062796

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583582C211yesmaximal, characteristic
2#19143248C212yesmaximal, complemented
3#19132957C212yesmaximal, complemented
4#19132950C212yesmaximal, complemented
5#19132949C212yesmaximal, complemented
6#19132930C211yesmaximal, characteristic
7#19132929C211yesmaximal, characteristic, complemented
8#19132926C211yesmaximal, characteristic, complemented
9#19132910C211yesmaximal, characteristic
10#19132906C211yesmaximal, characteristic, complemented
11C43×#1458C211yesmaximal, characteristic, complemented
12#14583582—22no—
13#14583582—22no—
14#14583582—22no—
15#14583582—22no—
16C2×#13063320C411yescharacteristic
17C2×#13063319C411yescharacteristic
18C2×#13063317C2211yescharacteristic
19C2×#13063315C411yescharacteristic
20C2×#13063315C2211yescharacteristic
21C2×#13063309C411yescharacteristic
22C2×#13063308C411yescharacteristic
23C2×#13063303C2211yescharacteristic
24C2×#13063302C411yescharacteristic
25C2×C4×Dic86C411yescharacteristic
26C2×(C22⋊D43)⋊C4C2211yescharacteristic
27C2×#13063282C2211yescharacteristic
28C2×#13063281C2211yescharacteristic
29C22×Dic43⋊C4C411yescharacteristic
30#14582959—22no—
31#14582958—22no—
32#14582956C2212yes—
33#14582953C2212yes—
34#14582949C2212yes—
35#14582924—22no—
36#14582861C2212yes—
37C22⋊C8×D43C2212yes—
38#14582853—22no—
39#14582625C2212yes—
40#14582624C2212yes—
41#14582624C2212yes—
42#14582624C2212yes—
43#14582624C2212yes—
44#14582623C2211yescharacteristic
45#14582623C2211yescharacteristic
46C2×#117×C43C2211yescharacteristic
47C43×#431C2212yes—
48C43×#324C2212yes—
49C43×#323C2211yescharacteristic
50C43×#323C2211yescharacteristic
51C22×Dic86C2×C411yescharacteristic
52C22×C22⋊D43C2×C411yescharacteristic
53C23×Dic43C2×C411yescharacteristic
54C23×Dic43C2×C411yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C2×#10621872—22no—
57C2×C8×D43—22no—
58#13063320—22no—
59#13063320—22no—
60#13063319—22no—
61#13063319—22no—
62#13063317—22no—
63#13063317—22no—
64#13063315—22no—
65#13063315—22no—
66#13063315—22no—
67#13063315—22no—
68#13063309—22no—
69#13063309—22no—
70#13063308—22no—
71#13063308—22no—
72#13063303—22no—
73#13063303—22no—
74#13063302—22no—
75#13063302—22no—
76C4×Dic86—21no—
77C4×Dic86—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80(C22⋊D43)⋊C4—22no—
81(C22⋊D43)⋊C4—22no—
82#13063282D412yes—
83#13063282D412yes—
84#13063282D412yes—
85#13063282D412yes—
86#13063281—22no—
87#13063281—22no—
88C2×C4⋊Dic43C2×C411yescharacteristic
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×C4⋊Dic43C2×C411yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2311yescharacteristic
105C2×Dic43⋊C4C2311yescharacteristic
106C2×C22⋊Dic43C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C4⋊(C43⋊C8)—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)C2312yes—
119C22⋊(C43⋊C8)C2312yes—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063236—22no—
123#13063235—22no—
124C8×Dic43—22no—
125C23×C4×C43C2×C411yescharacteristic
126#117×C43—22no—
127#117×C43—22no—
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43C2×C411yescharacteristic
131C2×C22⋊C4×C43C2311yescharacteristic
132C2×C42×C43C2×C411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—22no—
135C22⋊C8×C43C2312yes—
136C22⋊C8×C43C2312yes—
137C4×C8×C43—22no—
138C24×C43C22×C411yescharacteristic
139C23×D43C22×C411yescharacteristic
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—41no—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43—41no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158C22×Dic43—41no—
159C22×Dic43—42no—
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C2×C4×D43—42no—
168C2×C4×D43C2×D412yes—
169C2×C4×D43C2×D412yes—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—42no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43C2×D412yes—
182C42×C43C2×D412yes—
183C22⋊Dic43—22no—
184(C2×D43)⋊C4—22no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4C22⋊C412yes—
188(C2×D43)⋊C4C22⋊C412yes—
189(C2×D43)⋊C4C22⋊C412yes—
190(C2×D43)⋊C4C22⋊C412yes—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4C22⋊C411yescharacteristic
209Dic43⋊C4C22⋊C411yescharacteristic
210Dic43⋊C4C22⋊C411yescharacteristic
211Dic43⋊C4C22⋊C411yescharacteristic
212Dic43⋊C4C22⋊C412yes—
213Dic43⋊C4C22⋊C412yes—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222#10621872—44no—
223C8×D43—44no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43#13112yes—
229C23×C43C23×C411yescharacteristic
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43C2×C22⋊C412yes—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C412yes—
251C2×C4×C43C22×D412yes—
252C22⋊D43—44no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C412yes—
275C2×Dic43C2×C22⋊C411yescharacteristic
276C4×D43—24no—
277C4×D43—42no—
278Dic86—42no—
279Dic86—42no—
280C8×C43—42no—
281C8×C43—42no—
282C43⋊C8—42no—
283C43⋊C8—42no—
284#17413—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—22no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43C22×C22⋊C411yescharacteristic
293C22×C43C2×#13111yescharacteristic
294C22×C43#56811yescharacteristic
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—81no—
299C2×D43—81no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—22no—
303C4×C43—22no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—22no—
311Dic43—41no—
312Dic43—41no—
313Dic43—41no—
314Dic43—41no—
315Dic43#41012yes—
316C2×#552—431no—
317#2924—432no—
318#1472—432no—
319#1470—432no—
320#1470—432no—
321#1465—431no—
322#1464—431no—
323#1464—431no—
324#1459—431no—
325#1458—431no—
326#1458D4311yescharacteristic, complemented
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—42no—
330C2×C43#288011yescharacteristic
331C2×C43C2×#41011yescharacteristic
332C2×C43#288911yescharacteristic
333D43—42no—
334#552—862no—
335#552—862no—
336#552—862no—
337#552—862no—
338C2×#126—431no—
339C2×#126—431no—
340C2×#125—431no—
341C2×#125—431no—
342C2×#125—431no—
343C2×#123—431no—
344C2×#123—431no—
345C2×C22⋊Q8—431no—
346C2×C22⋊Q8—431no—
347C2×C4×Q8—431no—
348C2×C4×D4—431no—
349C2×#117—431no—
350C2×#117—431no—
351C2×#117C2×D4311yescharacteristic
352C22×C4⋊C4—431no—
353#433—862no—
354#433—862no—
355#432—432no—
356#432—432no—
357#431—432no—
358#431C2×D4312yes—
359#424—862no—
360#407—432no—
361C2×C22⋊C8—432no—
362#405—862no—
363#324—432no—
364#324—432no—
365#324—432no—
366#324—432no—
367#324—432no—
368#324C2×D4312yes—
369#323—431no—
370#323—431no—
371#323C2×D4311yescharacteristic
372#323C2×D4311yescharacteristic
373C43#1741311yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C22×D4—431no—
376C23×C4—431no—
377C23×C4—431no—
378C23×C4—431no—
379C23×C4C4×D4311yescharacteristic
380C2×M16—862no—
381C22×C8—862no—
382#126—862no—
383#126—862no—
384#126—862no—
385#126—862no—
386#125—862no—
387#125—862no—
388#125—862no—
389#125—862no—
390#125—862no—
391#125—862no—
392#123—862no—
393#123—862no—
394#123—862no—
395#123—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×D4—862no—
405C4×D4—862no—
406#117—22no—
407#117—22no—
408#117—432no—
409#117—432no—
410#117—432no—
411#117—432no—
412#117—862no—
413#117—862no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C4×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—431no—
435C2×C22⋊C4—431no—
436C2×C22⋊C4—431no—
437C2×C22⋊C4—431no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—431no—
440C2×C22⋊C4C4×D4311yescharacteristic
441C2×C22⋊C4C22×D4311yescharacteristic
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42C4×D4311yescharacteristic
446C2×C42C22×D4311yescharacteristic
447C4⋊C8—22no—
448C4⋊C8—862no—
449C4⋊C8—862no—
450C4⋊C8—862no—
451C22⋊C8—432no—
452C22⋊C8—432no—
453C22⋊C8—862no—
454C22⋊C8—862no—
455C22⋊C8C22×D4312yes—
456C22⋊C8C22×D4312yes—
457#97—862no—
458#97—862no—
459C4×C8—22no—
460C4×C8—862no—
461C24—431no—
462C24C2×C4×D4311yescharacteristic
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—1722no—
466C2×D4—862no—
467C2×D4—862no—
468C2×D4—1721no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—862no—
487C22×C4—1722no—
488C22×C4—1721no—
489C22×C4—1722no—
490C22×C4C2×C4×D4311yescharacteristic
491C22×C4C2×C4×D4311yescharacteristic
492C22×C4C2×C4×D4311yescharacteristic
493C22×C4C2×C4×D4311yescharacteristic
494C22×C4C2×C4×D4311yescharacteristic
495C22×C4C23×D4311yescharacteristic
496M16—1724no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—862no—
500C2×C8—862no—
501C2×C8—1724no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—431no—
505C4⋊C4—431no—
506C4⋊C4—431no—
507C4⋊C4—431no—
508C4⋊C4—432no—
509C4⋊C4—432no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—862no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—432no—
530C22⋊C4—432no—
531C22⋊C4—432no—
532C22⋊C4—432no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C42—21no—
538C42—21no—
539C42—432no—
540C42—432no—
541C42—861no—
542C42—861no—
543C42—861no—
544C42—861no—
545C42D4×D4312yes—
546C42D4×D4312yes—
547C23—21no—
548C23—21no—
549C23—41no—
550C23—41no—
551C23—432no—
552C23—861no—
553C23—861no—
554C23—1721no—
555C23—1721no—
556C23#1306333112yes—
557C23C22×C4×D4311yescharacteristic
558Q8—1722no—
559Q8—1722no—
560D4—1724no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—432no—
578C2×C4—431no—
579C2×C4—864no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1721no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4C22⋊C4×D4311yescharacteristic
600C2×C4C22⋊C4×D4311yescharacteristic
601C2×C4C22⋊C4×D4312yes—
602C2×C4C2×D4×D4312yes—
603C8—42no—
604C8—42no—
605C8—1722no—
606C8—1722no—
607C22—21no—
608C22—21no—
609C22—22no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22—41no—
614C22—862no—
615C22—862no—
616C22—862no—
617C22—3441no—
618C22—3441no—
619C22C2×C22⋊C4×D4311yescharacteristic
620C22C2×#1306333111yescharacteristic
621C22#1458366511yescharacteristic
622C4—21no—
623C4—21no—
624C4—22no—
625C4—22no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—432no—
630C4—861no—
631C4—861no—
632C4—861no—
633C4—862no—
634C4—1721no—
635C4—1721no—
636C4—1721no—
637C4—1721no—
638C2—21no—
639C2—21no—
640C2—42no—
641C2—1722no—
642C2#1914304111yescharacteristic
643C2#410×D4311yescharacteristic
644C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1458C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1458D43
hypocenterC43#17413
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #19143248C2semidirect
3. #19132957C2semidirect
4. #19132950C2semidirect
5. #19132949C2semidirect
7. #19132929C2semidirect
8. #19132926C2semidirect
10. #19132906C2semidirect
11. C43×#1458C2semidirect
326. #1458D43semidirect
373. C43#17413semidirect

Maximal subgroups

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

subgroupindex
C2×#145835822
#191432482
#191329572
#191329502
#191329492
#191329302
#191329292
#191329262
#191329102
#191329062
C43×#14582
#1741343