Finite Group Databasebeta

← #25159758

Subgroups — #25159758

Order 11008.

932 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583199C211yesmaximal, characteristic, complemented
2C2×C4×#10621882C211yesmaximal, characteristic
3#19138467C211yesmaximal, characteristic, complemented
4#19136129C211yesmaximal, characteristic, complemented
5#19136067C211yesmaximal, characteristic, complemented
6#19135966C211yesmaximal, characteristic, complemented
7#19135933C211yesmaximal, characteristic, complemented
8#19135320C211yesmaximal, characteristic, complemented
9#19135154C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic
11#19134943C211yesmaximal, characteristic
12#19134856C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic, complemented
14#19134841C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583199—24no—
20C4×#10621882—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582834—21no—
35#14582823—21no—
36#14582801C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582770—21no—
41#14582758—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C22×C4⋊C4×C43—21no—
54C43×#389C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#385—21no—
57C43×#385—21no—
58C43×#384C2211yescharacteristic
59C43×#380—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621882—22no—
64C2×#10621882—22no—
65C2×#10621882Q814yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063317—22no—
71#13063317—41no—
72C4×D172—22no—
73C4×D172—41no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86#13063258—22no—
87#13063258—22no—
88#13063256—22no—
89#13063256—22no—
90#13063256—41no—
91C4⋊(C43⋊C8)—22no—
92#13063246—22no—
93#13063246—22no—
94#13063246D414yes—
95#13063245—22no—
96#13063245—22no—
97#13063245—41no—
98C4×C43⋊C8—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C22×D4×C43C2311yescharacteristic
102C23×C4×C43—21no—
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43—41no—
110C4×D4×C43—41no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—44no—
116C2×C4⋊C4×C43D411yescharacteristic
117C2×C4⋊C4×C43D411yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127#95×C43—21no—
128#95×C43—21no—
129#95×C43D411yescharacteristic
130#95×C43D411yescharacteristic
131C24×C43—21no—
132C23×D43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43C2×D412yes—
137C2×D4×C43C2×Q812yes—
138C2×D4×C43#4112yes—
139C22×C4×C43—24no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—81no—
150C22×C4×C43—81no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172C2×Q812yes—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—81no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—81no—
181C4⋊C4×C43#4112yes—
182C22⋊C4×C43—24no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—42no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191#10621882—28no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4—81no—
196(C2×D43)⋊C4—81no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43C2×D412yes—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—81no—
206Dic43⋊C4—81no—
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—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C2×D412yes—
218C2×C43⋊C8C2×Q812yes—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C22×D411yescharacteristic
227C22×D43—22no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234D4×C43—22no—
235D4×C43—22no—
236D4×C43—22no—
237D4×C43C22⋊Q814yes—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—48no—
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—84no—
265C2×C4×C43—84no—
266C2×C4×C43#13512yes—
267C2×C4×C43AGL(1,ℤ/8)12yes—
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C22×Q811yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43H(5,𝔽2)11yescharacteristic
273C2×C4×C432−1+411yescharacteristic
274C2×Dic43—22no—
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—22no—
284D172—22no—
285D172—41no—
286D172—41no—
287C4×D43—84no—
288C43⋊C8—22no—
289C43⋊C8—22no—
290C43⋊C8—41no—
291C43⋊C8—41no—
292#26382—431nomaximal, Sylow
293C22×C43—24no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43#52511yescharacteristic
301C22×C43D4211yescharacteristic
302C22×C43D4×Q811yescharacteristic
303C22×C43C2×#13511yescharacteristic
304C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57711yescharacteristic
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43C2×C22⋊Q811yescharacteristic
324C4×C43#53911yescharacteristic
325C4×C43#54711yescharacteristic
326C4×C43#55411yescharacteristic
327Dic43—42no—
328Dic43—81no—
329Dic43—81no—
330C2×#478—431no—
331C2×C4×D8—431no—
332#2454—431no—
333D4×C4⋊C4D4311yescharacteristic, complemented
334#2094—431no—
335#2083—431no—
336#2065—431no—
337#2059—431no—
338#1941—431no—
339#1916—431no—
340#1879—431no—
341#1879—431no—
342#1864—431no—
343#1864—431no—
344#1862—431no—
345C2×C43—44no—
346C2×C43#244911yescharacteristic
347C2×C43#310511yescharacteristic
348C2×C43#311911yescharacteristic
349C2×C43#326411yescharacteristic
350C2×C43#328411yescharacteristic
351C2×C43#338011yescharacteristic
352C2×C43#338411yescharacteristic
353D43—82no—
354C22×D8—431no—
355C2×#125—431no—
356C2×C4×D4—431no—
357C2×C4×D4C2×D4311yescharacteristic
358C2×C4×D4C2×D4311yescharacteristic
359C2×C4×D4C2×D4311yescharacteristic
360C22×C4⋊C4—21no—
361#478—864no—
362C4×D8—864no—
363C2×#107—431no—
364C2×#107—431no—
365C2×#106—431no—
366C2×#106—431no—
367C2×#106—431no—
368C2×C4⋊C8—431no—
369C2×#102—431no—
370C2×#102—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×C4×C8—431no—
376#399—861no—
377#396—861no—
378#390—431no—
379#390—431no—
380#389—431no—
381#389—431no—
382#389C2×D4311yescharacteristic
383#389C2×D4311yescharacteristic
384#385—21no—
385#385—21no—
386#385—861no—
387#384C2×D4311yescharacteristic
388#380—21no—
389#380—861no—
390C4×C4⋊C4C2×D4311yescharacteristic
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#336—431no—
396#336—431no—
397#336—431no—
398#336—431no—
399C43#2638211yescharacteristic, complemented, Sylow
400C22×D4—431no—
401C22×D4C22×D4311yescharacteristic
402C23×C4—21no—
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—861no—
406C2×D8—434no—
407C2×D8—862no—
408C2×D8—862no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8—431no—
412C22×C8—431no—
413#125—862no—
414#125—1721no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—41no—
420C4×D4—41no—
421C4×D4—862no—
422C4×D4—1721no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—44no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4C22⋊D4311yescharacteristic
436C2×C4⋊C4C22⋊D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C42C22×D4311yescharacteristic
449C2×C42C22×D4311yescharacteristic
450C2×C42C22×D4311yescharacteristic
451#107—862no—
452#107—862no—
453#106—862no—
454#106—862no—
455#106—1721no—
456C4⋊C8—862no—
457#102—434no—
458#102—862no—
459#102—862no—
460#102—862no—
461#102—862no—
462#102—1721no—
463C4×C8—862no—
464#95—21no—
465#95—21no—
466#95—861no—
467#95—861no—
468#95C22⋊D4311yescharacteristic
469#95C22⋊D4311yescharacteristic
470C24—21no—
471C24—861no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—432no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4#1062189812yes—
482C2×D4D4×D4312yes—
483C2×D4Q8×D4312yes—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—3441no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4C2×C22⋊D4311yescharacteristic
503C22×C4C2×C22⋊D4311yescharacteristic
504C22×C4C2×C22⋊D4311yescharacteristic
505C22×C4C2×C22⋊D4311yescharacteristic
506C22×C4C2×C22⋊D4311yescharacteristic
507C22×C4C2×C22⋊D4311yescharacteristic
508C22×C4C23×D4311yescharacteristic
509D8—868no—
510C2×C8—432no—
511C2×C8—432no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—81no—
533C4⋊C4—432no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—3441no—
540C4⋊C4—3441no—
541C4⋊C4—1722no—
542C4⋊C4—1722no—
543C4⋊C4#1062189812yes—
544C22⋊C4—24no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—3441no—
548C22⋊C4—3441no—
549C22⋊C4—3441no—
550C22⋊C4—1722no—
551C22⋊C4—1722no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—862no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23C22×C22⋊D4311yescharacteristic
573D4—22no—
574D4—22no—
575D4—22no—
576D4—862no—
577D4—862no—
578D4—1721no—
579D4—1721no—
580D4#1306330314yes—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—48no—
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—84no—
608C2×C4—84no—
609C2×C4—862no—
610C2×C4—3444no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4#1306334512yes—
620C2×C4#1306335112yes—
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4C2×Q8×D4311yescharacteristic
623C2×C4C2×#1062189811yescharacteristic
624C2×C4C2×#1062189811yescharacteristic
625C2×C4#1306337011yescharacteristic
626C2×C4#1306337311yescharacteristic
627C8—862no—
628C8—862no—
629C8—1721no—
630C8—1721no—
631C22—24no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—3441no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22#1458341011yescharacteristic
646C22D4×C22⋊D4311yescharacteristic
647C22Q8×C22⋊D4311yescharacteristic
648C22C2×#1306334511yescharacteristic
649C22C2×#1306335111yescharacteristic
650C22#1458370211yescharacteristic
651C22#1458370711yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—3441no—
662C4—3441no—
663C4—1722no—
664C4C2×#1306330311yescharacteristic
665C4#1458349611yescharacteristic
666C4#1458355011yescharacteristic
667C4#1458360411yescharacteristic
668C2—44no—
669C2—3442no—
670C2#1913840411yescharacteristic
671C2#1914464211yescharacteristic
672C2#1914479411yescharacteristic
673C2#1914607111yescharacteristic
674C2#1914632111yescharacteristic
675C2#1914745811yescharacteristic
676C2#1914749011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C4⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterD4×C4⋊C4D43
hypocenterC43#26382
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14583199C2semidirect
3. #19138467C2semidirect
4. #19136129C2semidirect
5. #19136067C2semidirect
6. #19135966C2semidirect
7. #19135933C2semidirect
8. #19135320C2semidirect
9. #19135154C2semidirect
12. #19134856C2semidirect
13. #19134856C2semidirect
14. #19134841C2semidirect
15. D4×C4⋊C4×C43C2semidirect
333. D4×C4⋊C4D43semidirect
399. C43#26382semidirect

Maximal subgroups

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

subgroupindex
C2×#145831992
C2×C4×#106218822
#191384672
#191361292
#191360672
#191359662
#191359332
#191353202
#191351542
#191349432
#191348562
#191348412
D4×C4⋊C4×C432
#2638243