Finite Group Databasebeta

← #25114943

Subgroups — #25114943

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582999C211yesmaximal, characteristic
2C2×#14582999C211yesmaximal, characteristic
3C2×C4×#10621883C211yesmaximal, characteristic
4#19137515C211yesmaximal, characteristic, complemented
5#19135330C211yesmaximal, characteristic, complemented
6#19135325C211yesmaximal, characteristic, complemented
7#19134862C211yesmaximal, characteristic, complemented
8#19134856C211yesmaximal, characteristic
9#19134848C211yesmaximal, characteristic, complemented
10#19134842C211yesmaximal, characteristic
11#19134761C211yesmaximal, characteristic, complemented
12#19134605C211yesmaximal, characteristic
13#19134597C211yesmaximal, characteristic, complemented
14#19134470C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C43C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14582999—24no—
21#14582999C418yescomplemented
22C4×#10621883—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582794—21no—
41#14582794—21no—
42#14582765C2211yescharacteristic
43#14582763—21no—
44#14582750—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C22×C4⋊C4×C43—21no—
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#385—21no—
58C43×#385—21no—
59C43×#384C2211yescharacteristic
60C43×#380—21no—
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C2×#10621883C2×C414yes—
64C2×#10621883D414yes—
65C2×#10621883Q814yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×Dic86—22no—
73C4×Dic86—41no—
74C4×Dic86—41no—
75C4×Dic86C2×C414yescomplemented
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87#13063258—22no—
88#13063258—41no—
89#13063258C2×C414yescomplemented
90#13063256—22no—
91#13063256—41no—
92C4⋊(C43⋊C8)—22no—
93#13063248—22no—
94#13063248—22no—
95#13063248C2×C414yescomplemented
96#13063246—22no—
97#13063246—22no—
98#13063246C2×C414yes—
99#13063236—22no—
100#13063236C2×C414yescomplemented
101C4×C43⋊C8—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×D4×C43C2311yescharacteristic
107C23×C4×C43—21no—
108C23×C4×C43—21no—
109C23×C4×C43—21no—
110C4×D4×C43—22no—
111C4×D4×C43—22no—
112C4×D4×C43—22no—
113C4×D4×C43—41no—
114C4×D4×C43—41no—
115C4×D4×C43C2×C414yes—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—44no—
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#95×C43—21no—
133#95×C43—21no—
134#95×C43D411yescharacteristic
135#95×C43D411yescharacteristic
136C24×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43C22×C412yes—
141C2×D4×C43C2×D412yes—
142C2×D4×C43C2×Q812yes—
143C22×C4×C43—24no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—81no—
154C22×C4×C43—81no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86C22×C412yes—
170C2×Dic86C2×D412yes—
171C2×Dic86C2×Q812yes—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—81no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—42no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43C22×C412yes—
192C42×C43#4112yes—
193#10621883C4⋊C4116yescomplemented
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—24no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205C4×Dic43—24no—
206C4×Dic43—42no—
207C4×Dic43—42no—
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⋊C8C22×C412yes—
217C2×C43⋊C8C22×C412yes—
218C2×C43⋊C8C2×D412yes—
219C2×C43⋊C8C2×Q812yes—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43C22×D411yescharacteristic
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43C2×C4⋊C414yes—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
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—48no—
249C2×C4×C43—41no—
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—84no—
258C2×C4×C43—84no—
259C2×C4×C43C4×D412yes—
260C2×C4×C43C4×D412yes—
261C2×C4×C43AGL(1,ℤ/8)12yes—
262C2×C4×C43C23×C411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×Q811yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280Dic86—22no—
281Dic86—22no—
282Dic86—22no—
283Dic86C2×C4⋊C414yescomplemented
284C43⋊C8—22no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C43⋊C8C2×C4⋊C414yescomplemented
288#22677—431nomaximal, Sylow
289C22×C43—24no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43C2×C4×D411yescharacteristic
297C22×C43D4211yescharacteristic
298C22×C43D4×Q811yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57811yescharacteristic
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—22no—
306C4×C43—42no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43C22×C4⋊C411yescharacteristic
313C4×C43#52011yescharacteristic
314C4×C43#54711yescharacteristic
315C4×C43#55411yescharacteristic
316Dic43—24no—
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320C2×#440—431no—
321C2×#440—431no—
322C2×C4×SD16—431no—
323#2351—431no—
324D4×C4⋊C4D4311yescharacteristic
325#1943—431no—
326#1942—431no—
327#1865—431no—
328#1864—431no—
329#1863—431no—
330#1862—431no—
331#1847—431no—
332#1804—431no—
333#1803—431no—
334#1771—431no—
335C2×C43—44no—
336C2×C43D4×C4⋊C411yescharacteristic
337C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
338C2×C43#294711yescharacteristic
339C2×C43#326511yescharacteristic
340C2×C43#326911yescharacteristic
341C2×C43#338611yescharacteristic
342C2×C43#338811yescharacteristic
343C22×SD16—431no—
344C2×C4×Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8—431no—
347C2×C4×D4C2×D4311yescharacteristic
348C2×C4×D4C2×D4311yescharacteristic
349C2×C4×D4C2×D4311yescharacteristic
350C22×C4⋊C4—21no—
351#440—438no—
352#440—864no—
353C4×SD16—864no—
354C2×#107—431no—
355C2×#107—431no—
356C2×#107—431no—
357C2×#106—431no—
358C2×#106—431no—
359C2×C4⋊C8—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×#97—431no—
367C2×#97—431no—
368C2×C4×C8—431no—
369#389—431no—
370#389—431no—
371#389—861no—
372#389—861no—
373#389C2×D4311yescharacteristic
374#389C2×D4311yescharacteristic
375#385—21no—
376#385—21no—
377#384C2×D4311yescharacteristic
378#382—431no—
379#382—861no—
380#380—21no—
381C4×C4⋊C4—861no—
382C4×C4⋊C4C2×D4311yescharacteristic
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#336—431no—
388#336—431no—
389C43#2267711yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×D4C22×D4311yescharacteristic
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—21no—
395C2×SD16—434no—
396C2×SD16—434no—
397C2×SD16—434no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8—431no—
402C4×Q8—434no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—862no—
406C4×Q8—1721no—
407C4×Q8—1721no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—41no—
412C4×D4—41no—
413C4×D4C4×D4314yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—44no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4C22⋊D4311yescharacteristic
428C2×C4⋊C4C22⋊D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42C22×D4311yescharacteristic
439C2×C42C22×D4311yescharacteristic
440C2×C42C22×D4311yescharacteristic
441#107—434no—
442#107—862no—
443#107—1721no—
444#106—862no—
445#106—1721no—
446C4⋊C8—862no—
447#103—434no—
448#103—862no—
449#103—862no—
450#102—434no—
451#102—862no—
452#102—862no—
453#97—434no—
454#97—862no—
455C4×C8—862no—
456#95—21no—
457#95—21no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95C22⋊D4311yescharacteristic
463#95C22⋊D4311yescharacteristic
464C24—21no—
465C2×Q8—432no—
466C2×Q8—432no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4C2×C4×D4312yes—
475C2×D4D4×D4312yes—
476C2×D4Q8×D4312yes—
477C22×C4—21no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4C2×C22⋊D4311yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C2×C22⋊D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500SD16—4316no—
501C2×C8—432no—
502C2×C8—432no—
503C2×C8—432no—
504C2×C8—432no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—41no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—81no—
524C4⋊C4—432no—
525C4⋊C4—864no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4C2×C4×D4312yes—
536C22⋊C4—24no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—864no—
544C42—1722no—
545C42—1722no—
546C42C2×C4×D4312yes—
547C42#1062189812yes—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C22×C22⋊D4311yescharacteristic
556Q8—434no—
557Q8—862no—
558Q8—862no—
559Q8—862no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4C4⋊C4×D4314yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—48no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4C4×C22⋊D4312yes—
604C2×C4C4×C22⋊D4312yes—
605C2×C4#1306335112yes—
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4C2×D4×D4311yescharacteristic
608C2×C4C2×Q8×D4311yescharacteristic
609C2×C4C2×#1062189811yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337311yescharacteristic
612C8—434no—
613C8—862no—
614C8—1721no—
615C8—1721no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C2×C4×C22⋊D4311yescharacteristic
624C22D4×C22⋊D4311yescharacteristic
625C22Q8×C22⋊D4311yescharacteristic
626C22C2×#1306335111yescharacteristic
627C22#1458369711yescharacteristic
628C22#1458371011yescharacteristic
629C22#1458371411yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—42no—
637C4—81no—
638C4—81no—
639C4—864no—
640C4—3441no—
641C4—3441no—
642C4—1722no—
643C4C2×C4⋊C4×D4311yescharacteristic
644C4#1458338011yescharacteristic
645C4#1458355011yescharacteristic
646C4#1458360411yescharacteristic
647C2—44no—
648C2C4⋊C4×C22⋊D4311yescharacteristic
649C2C4×#1306335111yescharacteristic
650C2#1914343411yescharacteristic
651C2#1914608611yescharacteristic
652C2#1914614611yescharacteristic
653C2#1914751611yescharacteristic
654C2#1914754011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×C4⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterD4×C4⋊C4D43
hypocenterC43#22677
LCSG ▷ C2×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
4. #19137515C2semidirect
5. #19135330C2semidirect
6. #19135325C2semidirect
7. #19134862C2semidirect
9. #19134848C2semidirect
11. #19134761C2semidirect
13. #19134597C2semidirect
14. #19134470C2semidirect
21. #14582999C4semidirect
75. C4×Dic86C2×C4semidirect
89. #13063258C2×C4semidirect
95. #13063248C2×C4semidirect
100. #13063236C2×C4semidirect
193. #10621883C4⋊C4semidirect
283. Dic86C2×C4⋊C4semidirect
287. C43⋊C8C2×C4⋊C4semidirect
389. C43#22677semidirect

Maximal subgroups

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

subgroupindex
C2×#145829992
C2×C4×#106218832
#191375152
#191353302
#191353252
#191348622
#191348562
#191348482
#191348422
#191347612
#191346052
#191345972
#191344702
D4×C4⋊C4×C432
#2267743