Finite Group Databasebeta

← #25169190

Subgroups — #25169190

Order 11008.

726 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137689C211yesmaximal, characteristic, complemented
2#19135969C211yesmaximal, characteristic
3#19135933C211yesmaximal, characteristic, complemented
4#19135925C211yesmaximal, characteristic, complemented
5#19135741C211yesmaximal, characteristic
6#19135548C211yesmaximal, characteristic, complemented
7#19135330C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic
9#19135212C211yesmaximal, characteristic
10#19135177C211yesmaximal, characteristic, complemented
11#19135177C211yesmaximal, characteristic, complemented
12#19135161C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic
14#19134420C211yesmaximal, characteristic
15C43×#2452C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17C2×#13063258C2211yescharacteristic
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063236C2211yescharacteristic
27#14582797C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582794—21no—
30#14582781—21no—
31#14582780—21no—
32C4×C4⋊Dic43C2211yescharacteristic
33C4×C4⋊Dic43C2211yescharacteristic
34C4×C4⋊Dic43C2211yescharacteristic
35#14582750—21no—
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4⋊Q8×C43C2211yescharacteristic
49C2×C22⋊Q8×C43—21no—
50C2×C4×D4×C43C2211yescharacteristic
51C43×#396—21no—
52C43×#393—21no—
53C43×#390C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#385—21no—
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063317—22no—
64#13063317—22no—
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43—21no—
76#13063258—22no—
77#13063256—22no—
78#13063256—22no—
79#13063256—41no—
80C4⋊(C43⋊C8)—41no—
81#13063246—22no—
82#13063246—22no—
83#13063246—41no—
84#13063246Q814yescomplemented
85#13063236—41no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×Q8×C43—21no—
92C22×D4×C43C2311yescharacteristic
93C23×C4×C43—21no—
94C4⋊Q8×C43—22no—
95C4⋊Q8×C43—41no—
96C22⋊Q8×C43—44no—
97C4×D4×C43—22no—
98C4×D4×C43—41no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#95×C43—21no—
116#95×C43—21no—
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119C24×C43—21no—
120C2×Q8×C43—42no—
121C2×Q8×C43—42no—
122C2×Q8×C43—81no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43C2×Q812yes—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—81no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—41no—
153C4⋊C4×C43—42no—
154C4⋊C4×C43—42no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43#4112yes—
157C22⋊C4×C43—42no—
158C22⋊C4×C43—42no—
159C22⋊C4×C43—42no—
160C22⋊C4×C43—42no—
161C22⋊C4×C43—81no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43C2×Q812yes—
174C4⋊Dic43#4112yes—
175C4⋊Dic43#4112yes—
176Dic43⋊C4—24no—
177Dic43⋊C4—24no—
178Dic43⋊C4—42no—
179Dic43⋊C4—81no—
180C4×Dic43—42no—
181C4×Dic43—81no—
182C4×Dic43—81no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
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⋊C8C2×Q812yes—
195C23×C43—22no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203Q8×C43—84no—
204D4×C43—22no—
205D4×C43—22no—
206D4×C43—41no—
207D4×C43—41no—
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—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
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×C43—41no—
234C2×C4×C43—84no—
235C2×C4×C43AGL(1,ℤ/8)12yes—
236C2×C4×C43C22×Q811yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C43⋊C8—22no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#27026—431nomaximal, Sylow
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43#52511yescharacteristic
267C22×C43#54611yescharacteristic
268C22×C43D4×Q811yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43#57511yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57711yescharacteristic
273C4×C43—22no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—42no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#53311yescharacteristic
283C4×C43#54211yescharacteristic
284C4×C43#55411yescharacteristic
285C4×C43#55611yescharacteristic
286Dic43—42no—
287Dic43—42no—
288Dic43—42no—
289Dic43—81no—
290#2452D4311yescharacteristic
291#2370—431no—
292#2065—431no—
293#2059—431no—
294#2058—431no—
295#2025—431no—
296#1988—431no—
297#1943—431no—
298#1926—431no—
299#1925—431no—
300#1920—431no—
301#1920—431no—
302#1917—431no—
303#1864—431no—
304#1762—431no—
305C2×C43—82no—
306C2×C43#246511yescharacteristic
307C2×C43#311511yescharacteristic
308C2×C43#312511yescharacteristic
309C2×C43#331011yescharacteristic
310C2×C43#332611yescharacteristic
311C2×C43#338411yescharacteristic
312C2×C43#338811yescharacteristic
313C2×C4⋊Q8C2×D4311yescharacteristic
314C2×#125—431no—
315C2×C22⋊Q8—21no—
316C2×C4×D4C2×D4311yescharacteristic
317C2×#107—431no—
318C2×#106—431no—
319C2×#106—431no—
320C2×#106—431no—
321C2×C4⋊C8—431no—
322C2×#102—431no—
323C2×#102—431no—
324C2×#102—431no—
325C2×#102—431no—
326C2×#97—431no—
327#396—21no—
328#393—21no—
329#390C2×D4311yescharacteristic
330#390C2×D4311yescharacteristic
331#389—431no—
332#389—431no—
333#389—861no—
334#389C2×D4311yescharacteristic
335#389C2×D4311yescharacteristic
336#387—861no—
337#387—861no—
338#385—21no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—861no—
343C4×C4⋊C4C2×D4311yescharacteristic
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#336—431no—
353#336—431no—
354#336—431no—
355#336—431no—
356C43#2702611yescharacteristic, complemented, Sylow
357C22×Q8—21no—
358C22×D4C22×D4311yescharacteristic
359C23×C4—21no—
360C22×C8—431no—
361C22×C8—431no—
362C22×C8—431no—
363C22×C8—431no—
364C4⋊Q8—22no—
365C4⋊Q8—41no—
366#125—862no—
367#125—862no—
368C22⋊Q8—44no—
369C4×D4—22no—
370C4×D4—41no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4C22⋊D4311yescharacteristic
383C2×C4⋊C4C22⋊D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42C22×D4311yescharacteristic
396C2×C42C22×D4311yescharacteristic
397C2×C42C22×D4311yescharacteristic
398#107—862no—
399#106—862no—
400#106—862no—
401#106—1721no—
402C4⋊C8—1721no—
403#102—434no—
404#102—862no—
405#102—862no—
406#102—1721no—
407#97—1721no—
408#95—21no—
409#95—21no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95C22⋊D4311yescharacteristic
416#95C22⋊D4311yescharacteristic
417C24—21no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—81no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4Q8×D4312yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—81no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439C22×C4C2×C22⋊D4311yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—432no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—432no—
467C4⋊C4—432no—
468C4⋊C4—432no—
469C4⋊C4—864no—
470C4⋊C4—864no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—3441no—
477C4⋊C4—1722no—
478C4⋊C4#1062190012yes—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—81no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—3441no—
491C42—3441no—
492C42—1722no—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C22×C22⋊D4311yescharacteristic
501Q8—84no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
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—21no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—84no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4#1306335112yes—
546C2×C4C2×Q8×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C2×C4#41×D4311yescharacteristic
549C2×C4C2×#1062190011yescharacteristic
550C2×C4#1306337011yescharacteristic
551C2×C4#1306337311yescharacteristic
552C8—862no—
553C8—1721no—
554C8—1721no—
555C8—1721no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22#1458340611yescharacteristic
564C22#1458354311yescharacteristic
565C22Q8×C22⋊D4311yescharacteristic
566C22C2×#1306335111yescharacteristic
567C22#1458369711yescharacteristic
568C22#1458370711yescharacteristic
569C22#1458371011yescharacteristic
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—3441no—
580C4—1722no—
581C4—1722no—
582C4—1722no—
583C4#1458345111yescharacteristic
584C4#1458351911yescharacteristic
585C4#1458360311yescharacteristic
586C4#1458362011yescharacteristic
587C2—82no—
588C2#1913861211yescharacteristic
589C2#1914474011yescharacteristic
590C2#1914486611yescharacteristic
591C2#1914661611yescharacteristic
592C2#1914684811yescharacteristic
593C2#1914749011yescharacteristic
594C2#1914754011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2452C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2452D43
hypocenterC43#27026
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. #19137689C2semidirect
3. #19135933C2semidirect
4. #19135925C2semidirect
6. #19135548C2semidirect
7. #19135330C2semidirect
10. #19135177C2semidirect
11. #19135177C2semidirect
12. #19135161C2semidirect
84. #13063246Q8semidirect
356. C43#27026semidirect

Maximal subgroups

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

subgroupindex
#191376892
#191359692
#191359332
#191359252
#191357412
#191355482
#191353302
#191352192
#191352122
#191351772
#191351612
#191348562
#191344202
C43×#24522
#2702643