Finite Group Databasebeta

← #25118436

Subgroups — #25118436

Order 11008.

846 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583196C211yesmaximal, characteristic
2#19137506C211yesmaximal, characteristic
3#19135561C211yesmaximal, characteristic, complemented
4#19135363C211yesmaximal, characteristic, complemented
5#19135325C211yesmaximal, characteristic, complemented
6#19135320C211yesmaximal, characteristic, complemented
7#19135187C211yesmaximal, characteristic, complemented
8#19135180C211yesmaximal, characteristic, complemented
9#19134855C211yesmaximal, characteristic
10#19134841C211yesmaximal, characteristic
11C4⋊C4×C43⋊C8C211yesmaximal, characteristic, complemented
12C4×#13063245C211yesmaximal, characteristic
13C4×#13063245C211yesmaximal, characteristic
14C4×#13063245C211yesmaximal, characteristic
15C43×#2370C211yesmaximal, characteristic, complemented
16C2×C4×D172C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583196C418yescomplemented
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582770—21no—
35#14582770—21no—
36#14582765C2211yescharacteristic
37#14582758—21no—
38#95×D43—21no—
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×#125×C43C2211yescharacteristic
50C43×#389—21no—
51C43×#389C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#387—21no—
54C43×#387—21no—
55C4×C4⋊C4×C43—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C4×D172—22no—
69C4×D172—22no—
70C4×D172—22no—
71C4×D172—41no—
72C4×D172—41no—
73C4×D172C2×C414yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82#13063258—41no—
83#13063258C2×C414yescomplemented
84#13063256—41no—
85#13063256C2×C414yescomplemented
86C4⋊(C43⋊C8)C2×C414yescomplemented
87#13063245—22no—
88#13063245C2×C414yes—
89#13063245C2×C414yes—
90#13063245Q814yes—
91C4×C43⋊C8—22no—
92C4×C43⋊C8—41no—
93C4×C43⋊C8—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98#125×C43—22no—
99#125×C43C2×C414yescomplemented
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123C23×D43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172C22×C412yes—
142C2×D172C2×Q812yes—
143C2×D172#4112yes—
144C2×C4×D43—24no—
145C2×C4×D43—42no—
146C2×C4×D43—42no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—81no—
150C2×C4×D43—81no—
151C2×C4×D43—81no—
152C2×C4×D43—81no—
153C4⋊C4×C43—24no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43—81no—
164C4⋊C4×C43C22×C412yes—
165C4⋊C4×C43C22×C412yes—
166C4⋊C4×C43C2×Q812yes—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—42no—
172C42×C43—81no—
173C42×C43—81no—
174C42×C43C22×C412yes—
175C42×C43#4112yes—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C412yes—
185Dic43⋊C4—81no—
186Dic43⋊C4—81no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8C22×C412yes—
197C2×C43⋊C8C22×C412yes—
198C2×C43⋊C8C2×Q812yes—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C4×D412yes—
234C2×C4×C43C4×D412yes—
235C2×C4×C43#13512yes—
236C2×C4×C43#13512yes—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×Q811yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C2×Dic43—22no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252D172—22no—
253D172—22no—
254D172—22no—
255D172C4×Q814yes—
256C4×D43—84no—
257C4×D43—84no—
258C4×D43—84no—
259C43⋊C8—22no—
260C43⋊C8—22no—
261C43⋊C8—22no—
262C43⋊C8—41no—
263#22966—431nomaximal, Sylow
264C22×C43C2×C4×D411yescharacteristic
265C22×C43#54611yescharacteristic
266C22×C43D4×Q811yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43#57611yescharacteristic
270C22×C43#57711yescharacteristic
271C2×D43—24no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—42no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43C2×C4×Q811yescharacteristic
289C4×C43#52011yescharacteristic
290C4×C43#55211yescharacteristic
291C4×C43#55411yescharacteristic
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295C2×#478—431no—
296#2370D4311yescharacteristic, complemented
297#2349—431no—
298#1991—431no—
299#1949—431no—
300#1942—431no—
301#1941—431no—
302#1921—431no—
303#1920—431no—
304#1864—431no—
305#1862—431no—
306C8×C4⋊C4—431no—
307C4×#102—431no—
308C4×#102—431no—
309C4×#102—431no—
310C2×C43#236011yescharacteristic
311C2×C43C4×#13511yescharacteristic
312C2×C43#294611yescharacteristic
313C2×C43#329611yescharacteristic
314C2×C43#329711yescharacteristic
315C2×C43#338011yescharacteristic
316C2×C43#338111yescharacteristic
317D43—44no—
318C2×#125C2×D4311yescharacteristic
319C2×C4×D4—431no—
320C2×C4×D4—431no—
321C2×C4×D4—431no—
322#478—438no—
323C2×#107—431no—
324C2×#107—431no—
325C2×#106—431no—
326C2×#106—431no—
327C2×C4⋊C8—431no—
328C2×#102—431no—
329C2×#102—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×C4×C8—431no—
333C2×C4×C8—431no—
334C2×C4×C8—431no—
335#389—21no—
336#389—431no—
337#389—431no—
338#389C2×D4311yescharacteristic
339#389C2×D4311yescharacteristic
340#387—21no—
341#387—21no—
342#385—861no—
343#385—861no—
344#382—431no—
345#380—861no—
346C4×C4⋊C4—21no—
347C4×C4⋊C4C2×D4311yescharacteristic
348C4×C4⋊C4C2×D4311yescharacteristic
349C4×C4⋊C4C2×D4311yescharacteristic
350C4×C4⋊C4C2×D4311yescharacteristic
351C2×#95—861no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#336—431no—
361#336—431no—
362C43#2296611yescharacteristic, complemented, Sylow
363C22×D4—431no—
364C23×C4—861no—
365C23×C4—861no—
366C23×C4—861no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8—431no—
370C22×C8—431no—
371#125—22no—
372#125C4×D4314yescomplemented
373C4×D4—434no—
374C4×D4—862no—
375C4×D4—862no—
376C4×D4—862no—
377C4×D4—1721no—
378C4×D4—1721no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4C22⋊D4311yescharacteristic
389C2×C4⋊C4C22⋊D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42C22×D4311yescharacteristic
401C2×C42C22×D4311yescharacteristic
402C2×C42C22×D4311yescharacteristic
403#107—434no—
404#107—1721no—
405#106—434no—
406#106—1721no—
407C4⋊C8—434no—
408#102—434no—
409#102—434no—
410#102—434no—
411#102—862no—
412C4×C8—862no—
413C4×C8—1721no—
414C4×C8—1721no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95C22⋊D4311yescharacteristic
425#95C22⋊D4311yescharacteristic
426C24—861no—
427C2×D4—432no—
428C2×D4—432no—
429C2×D4—432no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—861no—
438C22×C4—864no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—3441no—
442C22×C4—3441no—
443C22×C4—3441no—
444C22×C4—3441no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4—1722no—
449C22×C4C2×C22⋊D4311yescharacteristic
450C22×C4C2×C22⋊D4311yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C23×D4311yescharacteristic
456C2×C8—432no—
457C2×C8—432no—
458C2×C8—432no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—432no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—3441no—
486C4⋊C4—3441no—
487C4⋊C4C2×C4×D4312yes—
488C4⋊C4C2×C4×D4312yes—
489C4⋊C4Q8×D4312yes—
490C22⋊C4—864no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—81no—
499C42—81no—
500C42C2×C4×D4312yes—
501C42#1062189812yes—
502C23—862no—
503C23—862no—
504C23—862no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23C22×C22⋊D4311yescharacteristic
510D4—434no—
511D4—862no—
512D4—862no—
513D4—862no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—862no—
541C2×C4—3444no—
542C2×C4—3444no—
543C2×C4—3444no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4C4×C22⋊D4312yes—
553C2×C4C4×C22⋊D4312yes—
554C2×C4#1306334512yes—
555C2×C4#1306334512yes—
556C2×C4C22×C4×D4311yescharacteristic
557C2×C4C2×Q8×D4311yescharacteristic
558C2×C4#41×D4311yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337111yescharacteristic
561C2×C4#1306337311yescharacteristic
562C8—862no—
563C8—862no—
564C8—862no—
565C8—1721no—
566C22—864no—
567C22—1722no—
568C22—1722no—
569C22—1722no—
570C22—1722no—
571C22—1722no—
572C22—1722no—
573C22C2×C4×C22⋊D4311yescharacteristic
574C22#1458353711yescharacteristic
575C22Q8×C22⋊D4311yescharacteristic
576C22C2×#1306334511yescharacteristic
577C22C2×#1306334511yescharacteristic
578C22#1458370211yescharacteristic
579C22#1458370711yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—42no—
589C4—81no—
590C4—3441no—
591C4—3441no—
592C4—1722no—
593C4C4×Q8×D4311yescharacteristic
594C4#1458338111yescharacteristic
595C4#1458359011yescharacteristic
596C4#1458360911yescharacteristic
597C2—1724no—
598C2#1913759611yescharacteristic
599C2C4×#1306334511yescharacteristic
600C2#1914342311yescharacteristic
601C2#1914642411yescharacteristic
602C2#1914643911yescharacteristic
603C2#1914745811yescharacteristic
604C2#1914746611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2370C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#2370D43
hypocenterC43#22966
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
3. #19135561C2semidirect
4. #19135363C2semidirect
5. #19135325C2semidirect
6. #19135320C2semidirect
7. #19135187C2semidirect
8. #19135180C2semidirect
11. C4⋊C4×C43⋊C8C2semidirect
15. C43×#2370C2semidirect
19. #14583196C4semidirect
83. #13063258C2×C4semidirect
85. #13063256C2×C4semidirect
86. C4⋊(C43⋊C8)C2×C4semidirect
99. #125×C43C2×C4semidirect
296. #2370D43semidirect
362. C43#22966semidirect
372. #125C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
#191375062
#191355612
#191353632
#191353252
#191353202
#191351872
#191351802
#191348552
#191348412
C4⋊C4×C43⋊C82
C4×#130632452
C43×#23702
#2296643