Finite Group Databasebeta

← #25200201

Subgroups — #25200201

Order 11008.

828 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142926C211yesmaximal, characteristic
2#19136031C211yesmaximal, characteristic, complemented
3#19135795C211yesmaximal, characteristic, complemented
4#19135777C211yesmaximal, characteristic
5#19135596C211yesmaximal, characteristic
6#19135452C211yesmaximal, characteristic, complemented
7#19135325C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic, complemented
9#19135274C211yesmaximal, characteristic, complemented
10#19135215C211yesmaximal, characteristic, complemented
11#19135180C211yesmaximal, characteristic, complemented
12#19134950C211yesmaximal, characteristic, complemented
13#19134849C211yesmaximal, characteristic, complemented
14C4×C22⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063308—21no—
18C2×#13063299C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582790—21no—
37#14582790—21no—
38#14582778—21no—
39#14582759C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#387—21no—
54C43×#385—21no—
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43—21no—
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C2×#10621884—22no—
62C2×#10621884—22no—
63C2×#10621884—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063308—44no—
69#13063299—41no—
70#13063299—41no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82#13063258—22no—
83#13063258—41no—
84#13063256—22no—
85#13063249—22no—
86#13063249—22no—
87#13063249—41no—
88#13063245—22no—
89#13063245—22no—
90#13063245—41no—
91C22⋊(C43⋊C8)—22no—
92C22⋊(C43⋊C8)—22no—
93C4×C43⋊C8—41no—
94C4×C43⋊C8—41no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C22×Q8×C43C2311yescharacteristic
99C23×C4×C43D411yescharacteristic
100C23×C4×C43D411yescharacteristic
101C23×C4×C43C2311yescharacteristic
102C22⋊Q8×C43—22no—
103C22⋊Q8×C43—22no—
104C4×Q8×C43—41no—
105C4×Q8×C43—41no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43—41no—
117C2×C42×C43—41no—
118C2×C42×C43D411yescharacteristic
119C2×C42×C43D411yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43C2×D411yescharacteristic
128C23×D43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43#4112yes—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—42no—
158C2×C22⋊D43—42no—
159C2×C22⋊D43—42no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C4⋊C4×C43—24no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—42no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43#4112yes—
178C22⋊C4×C43—24no—
179C22⋊C4×C43—42no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—41no—
185C42×C43—41no—
186C42×C43—42no—
187C42×C43—42no—
188C22⋊Dic43—42no—
189#10621884—44no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8#4112yes—
214C2×C43⋊C8#4112yes—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43#13512yes—
222C23×C43C22×D411yescharacteristic
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230Q8×C43—22no—
231Q8×C43—22no—
232Q8×C43—41no—
233Q8×C43—41no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—44no—
249C2×C4×C43—44no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43#13512yes—
265C2×C4×C43AGL(1,ℤ/8)12yes—
266C2×C4×C43#13712yes—
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43H(5,𝔽2)11yescharacteristic
272C2×C4×C43H(5,𝔽2)11yescharacteristic
273C22⋊D43—84no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283D172—41no—
284D172—41no—
285D172—41no—
286D172—41no—
287C43⋊C8—22no—
288C43⋊C8—22no—
289C43⋊C8—41no—
290C43⋊C8—41no—
291#29467—431nomaximal, Sylow
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43#52511yescharacteristic
300C22×C43#53211yescharacteristic
301C22×C43#53411yescharacteristic
302C22×C43C2×#13511yescharacteristic
303C22×C43C2×#13511yescharacteristic
304C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C43C2×#13711yescharacteristic
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C4×C43—22no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—42no—
319C4×C43—41no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43#55111yescharacteristic
323C4×C43#55311yescharacteristic
324C4×C43#55311yescharacteristic
325C4×C43#55911yescharacteristic
326Dic43—81no—
327Dic43—81no—
328Dic43—81no—
329#2854—431no—
330C4×C22⋊Q8D4311yescharacteristic, complemented
331#2077—431no—
332#2036—431no—
333#2033—431no—
334#2000—431no—
335#1968—431no—
336#1942—431no—
337#1934—431no—
338#1933—431no—
339#1925—431no—
340#1920—431no—
341#1880—431no—
342#1863—431no—
343C4×C22⋊C8—431no—
344C2×C43—42no—
345C2×C43#260211yescharacteristic
346C2×C43#310611yescharacteristic
347C2×C43#310811yescharacteristic
348C2×C43#316811yescharacteristic
349C2×C43#318211yescharacteristic
350C2×C43#318811yescharacteristic
351C2×C43#319011yescharacteristic
352D43—161no—
353C22×SD16—431no—
354C2×#123—861no—
355C2×C22⋊Q8C2×D4311yescharacteristic
356C2×#121—431no—
357C2×C4×Q8C2×D4311yescharacteristic
358C22×C42C2×D4311yescharacteristic
359C2×#107—431no—
360C2×#107—431no—
361C2×#106—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×C22⋊C8—431no—
369C2×C22⋊C8—431no—
370C2×C4×C8—431no—
371C2×C4×C8—431no—
372#391C2×D4311yescharacteristic
373#390—431no—
374#390—431no—
375#389—431no—
376#389—431no—
377#389C2×D4311yescharacteristic
378#388—861no—
379#388—861no—
380#387—21no—
381#386—861no—
382#385—21no—
383#380—431no—
384#380C2×D4311yescharacteristic
385C4×C4⋊C4—21no—
386C4×C4⋊C4C2×D4311yescharacteristic
387C4×C22⋊C4—21no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#336—431no—
395#336—431no—
396C43#2946711yescharacteristic, complemented, Sylow
397C22×Q8C22×D4311yescharacteristic
398C22×D4—431no—
399C22×D4—861no—
400C23×C4C22⋊D4311yescharacteristic
401C23×C4C22⋊D4311yescharacteristic
402C23×C4C22×D4311yescharacteristic
403C2×SD16—862no—
404C2×SD16—862no—
405C2×SD16—1721no—
406C22×C8—431no—
407C22×C8—431no—
408C22×C8—431no—
409C22×C8—431no—
410#123—1724no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413#121—1721no—
414#121—1721no—
415C4×Q8—41no—
416C4×Q8—41no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—41no—
439C2×C42—41no—
440C2×C42C22⋊D4311yescharacteristic
441C2×C42C22⋊D4311yescharacteristic
442C2×C42C22×D4311yescharacteristic
443C2×C42C22×D4311yescharacteristic
444#107—862no—
445#107—1721no—
446#106—862no—
447#103—862no—
448#103—862no—
449#103—1721no—
450#102—862no—
451#102—862no—
452#102—1721no—
453C22⋊C8—862no—
454C22⋊C8—862no—
455C4×C8—1721no—
456C4×C8—1721no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—861no—
463#95—861no—
464#95—861no—
465C24—861no—
466C24C2×C22⋊D4311yescharacteristic
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8#1062189812yes—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—1722no—
480C2×D4—1722no—
481C2×D4—1722no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4C2×C22⋊D4311yescharacteristic
502C22×C4C2×C22⋊D4311yescharacteristic
503C22×C4C2×C22⋊D4311yescharacteristic
504C22×C4C2×C22⋊D4311yescharacteristic
505C22×C4C2×C22⋊D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507SD16—1724no—
508C2×C8—432no—
509C2×C8—432no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4#1062189812yes—
537C22⋊C4—24no—
538C22⋊C4—42no—
539C22⋊C4—1722no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—41no—
550C42—41no—
551C42—42no—
552C42—42no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23#1306334512yes—
567C23C22×C22⋊D4311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—3444no—
573D4—1721no—
574D4—1721no—
575D4—1721no—
576D4—1721no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4#1306334512yes—
617C2×C4#1306335012yes—
618C2×C4#1306335612yes—
619C2×C4#41×D4311yescharacteristic
620C2×C4#41×D4311yescharacteristic
621C2×C4C2×#1062189811yescharacteristic
622C2×C4C2×#1062189811yescharacteristic
623C2×C4#1306337011yescharacteristic
624C2×C4#1306337011yescharacteristic
625C8—862no—
626C8—862no—
627C8—1721no—
628C8—1721no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—3441no—
637C22—3441no—
638C22—3441no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—3441no—
643C22#1458341011yescharacteristic
644C22#1458344511yescharacteristic
645C22#1458345811yescharacteristic
646C22C2×#1306334511yescharacteristic
647C22C2×#1306334511yescharacteristic
648C22C2×#1306335011yescharacteristic
649C22C2×#1306335611yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—81no—
658C4—81no—
659C4—3441no—
660C4—3441no—
661C4—3441no—
662C4#1458357811yescharacteristic
663C4#1458359811yescharacteristic
664C4#1458359911yescharacteristic
665C4#1458363211yescharacteristic
666C2—42no—
667C2—6881no—
668C2#1914020711yescharacteristic
669C2#1914465511yescharacteristic
670C2#1914467511yescharacteristic
671C2#1914515911yescharacteristic
672C2#1914531411yescharacteristic
673C2#1914535611yescharacteristic
674C2#1914537611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×C22⋊Q8×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC4×C22⋊Q8D43
hypocenterC43#29467
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #19136031C2semidirect
3. #19135795C2semidirect
6. #19135452C2semidirect
7. #19135325C2semidirect
8. #19135277C2semidirect
9. #19135274C2semidirect
10. #19135215C2semidirect
11. #19135180C2semidirect
12. #19134950C2semidirect
13. #19134849C2semidirect
14. C4×C22⋊(C43⋊C8)C2semidirect
15. C4×C22⋊Q8×C43C2semidirect
330. C4×C22⋊Q8D43semidirect
396. C43#29467semidirect

Maximal subgroups

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

subgroupindex
#191429262
#191360312
#191357952
#191357772
#191355962
#191354522
#191353252
#191352772
#191352742
#191352152
#191351802
#191349502
#191348492
C4×C22⋊(C43⋊C8)2
C4×C22⋊Q8×C432
#2946743