Finite Group Databasebeta

← #25155641

Subgroups — #25155641

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139831C211yesmaximal, characteristic, complemented
2#19137567C211yesmaximal, characteristic
3#19136123C211yesmaximal, characteristic
4#19136118C211yesmaximal, characteristic
5#19135967C211yesmaximal, characteristic
6#19135364C211yesmaximal, characteristic, complemented
7#19135362C211yesmaximal, characteristic, complemented
8#19135359C211yesmaximal, characteristic, complemented
9#19135310C211yesmaximal, characteristic, complemented
10#19135184C211yesmaximal, characteristic, complemented
11#19135164C211yesmaximal, characteristic, complemented
12#19134756C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic
14#102×Dic43C211yesmaximal, characteristic
15C43×#2065C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×#13063258C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582839—21no—
28#14582832—21no—
29#14582802C2211yescharacteristic
30#14582795C2211yescharacteristic
31#14582793—21no—
32#14582787—21no—
33#14582785—21no—
34#14582784—21no—
35#14582769C2211yescharacteristic
36#14582764C2211yescharacteristic
37#14582764C2211yescharacteristic
38#14582764C2211yescharacteristic
39#14582760—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62D4×Dic43—22no—
63D4×Dic43Q814yes—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4D411yescharacteristic
72C2×Dic43⋊C4D411yescharacteristic
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43C2311yescharacteristic
80C2×C4×Dic43C2311yescharacteristic
81#13063258—22no—
82#13063258—22no—
83#13063258—41no—
84#13063257—41no—
85#13063257—41no—
86Dic43⋊C8—22no—
87Dic43⋊C8—22no—
88#13063246—22no—
89#13063246—41no—
90C8×Dic43—22no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C22×D4×C43C2311yescharacteristic
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C42×C43C2311yescharacteristic
113#106×C43—41no—
114C4⋊C8×C43—22no—
115#102×C43—22no—
116#102×C43—41no—
117#95×C43—21no—
118C24×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43C2×Q812yes—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—24no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—81no—
137C22×Dic43—81no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43#4112yes—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—42no—
155C22⋊C4×C43—42no—
156C22⋊C4×C43—81no—
157C42×C43—21no—
158C42×C43—21no—
159C22⋊Dic43—24no—
160C22⋊Dic43—42no—
161C22⋊Dic43—81no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—42no—
170C4⋊Dic43—81no—
171C4⋊Dic43C2×Q812yes—
172Dic43⋊C4—22no—
173Dic43⋊C4—41no—
174Dic43⋊C4—81no—
175C4×Dic43—21no—
176C4×Dic43—21no—
177C4×Dic43—81no—
178C4×Dic43—81no—
179C4×Dic43—81no—
180C4×Dic43C2×Q812yes—
181C4×Dic43#4112yes—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8#4112yes—
188C23×C43—22no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43C22×D411yescharacteristic
196D4×C43—22no—
197D4×C43—22no—
198D4×C43—41no—
199D4×C43—41no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43#13512yes—
215C2×C4×C43C22×Q811yescharacteristic
216C2×C4×C43C2×#4111yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43H(5,𝔽2)11yescharacteristic
220C2×C4×C432−1+411yescharacteristic
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—22no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—84no—
244C2×Dic43C22⋊Q812yes—
245C2×Dic43C22⋊Q812yes—
246C8×C43—22no—
247C8×C43—41no—
248C43⋊C8—22no—
249C43⋊C8—41no—
250#26094—431nomaximal, Sylow
251C22×C43—42no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43C2×C22⋊Q811yescharacteristic
259C22×C43#54711yescharacteristic
260C22×C43#55011yescharacteristic
261C22×C43C2×#13511yescharacteristic
262C22×C43#57511yescharacteristic
263C22×C43#57611yescharacteristic
264C22×C43#57711yescharacteristic
265C4×C43—22no—
266C4×C43—41no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43#53311yescharacteristic
271C4×C43#54411yescharacteristic
272C4×C43#55211yescharacteristic
273C4×C43#55311yescharacteristic
274Dic43—22no—
275Dic43—22no—
276Dic43—42no—
277Dic43—41no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281Dic43—81no—
282#2570—431no—
283#2357—431no—
284#2093—431no—
285#2092—431no—
286#2065—431no—
287#2065D4311yescharacteristic
288#1949—431no—
289#1949—431no—
290#1948—431no—
291#1939—431no—
292#1921—431no—
293#1918—431no—
294#1846—431no—
295#1804—431no—
296C4×#102—431no—
297C2×C43—82no—
298C2×C43#244111yescharacteristic
299C2×C43#307611yescharacteristic
300C2×C43#308111yescharacteristic
301C2×C43#333711yescharacteristic
302C2×C43#335511yescharacteristic
303C2×C43#339611yescharacteristic
304C2×C43#340111yescharacteristic
305C2×C4×D4—431no—
306C2×#107—431no—
307C2×#107—431no—
308C2×#107—431no—
309C2×#106—431no—
310C2×#106—431no—
311C2×#106C2×D4311yescharacteristic
312C2×C4⋊C8—431no—
313C2×C4⋊C8—431no—
314C2×C4⋊C8C2×D4311yescharacteristic
315C2×#102—431no—
316C2×#102—431no—
317C2×#102C2×D4311yescharacteristic
318C2×#102C2×D4311yescharacteristic
319C2×C4×C8—431no—
320#400—861no—
321#398—861no—
322#390—431no—
323#390C2×D4311yescharacteristic
324#389—431no—
325#389C2×D4311yescharacteristic
326#388—861no—
327#388—861no—
328#387—861no—
329#387—861no—
330#384—431no—
331#382—431no—
332#382—431no—
333#382—431no—
334#381—861no—
335C4×C4⋊C4—431no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4—431no—
338C4×C4⋊C4—431no—
339C4×C22⋊C4—861no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340C2×D4311yescharacteristic
346#336—431no—
347#336—431no—
348C43#2609411yescharacteristic, complemented, Sylow
349C22×D4C22×D4311yescharacteristic
350C23×C4—861no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8C22×D4311yescharacteristic
354C22×C8C22×D4311yescharacteristic
355C4×D4—434no—
356C4×D4—862no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—431no—
359C2×C4⋊C4—431no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4C22×D4311yescharacteristic
368C2×C4⋊C4C22×D4311yescharacteristic
369C2×C4⋊C4C22×D4311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C42—431no—
376C2×C42—431no—
377C2×C42—861no—
378C2×C42—861no—
379C2×C42—861no—
380C2×C42C22×D4311yescharacteristic
381#107—862no—
382#107—862no—
383#107—1721no—
384#106—41no—
385#106—1721no—
386#106—1721no—
387C4⋊C8—22no—
388C4⋊C8—862no—
389C4⋊C8—862no—
390#102—22no—
391#102—41no—
392#102—862no—
393#102—1721no—
394C4×C8—862no—
395#95—21no—
396#95—431no—
397#95—431no—
398#95—861no—
399#95—861no—
400#95—861no—
401#95—861no—
402#95—861no—
403#95—861no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408C24—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4Q8×D4312yes—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—431no—
419C22×C4—431no—
420C22×C4—431no—
421C22×C4—431no—
422C22×C4—864no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—3441no—
428C22×C4—3441no—
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4311yescharacteristic
431C22×C4C23×D4311yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—432no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8#1062190012yes—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—42no—
451C4⋊C4—432no—
452C4⋊C4—862no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—3441no—
461C4⋊C4—3441no—
462C4⋊C4—1721no—
463C4⋊C4—1722no—
464C22⋊C4—42no—
465C22⋊C4—81no—
466C22⋊C4—864no—
467C22⋊C4—3441no—
468C22⋊C4—1722no—
469C42—21no—
470C42—21no—
471C42—432no—
472C42—432no—
473C42—861no—
474C42—861no—
475C42—3441no—
476C42—3441no—
477C42—3441no—
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C2×D4×D4311yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—432no—
505C2×C4—432no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—862no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—3444no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306334612yes—
530C2×C4C2×Q8×D4311yescharacteristic
531C2×C4#41×D4311yescharacteristic
532C2×C4#41×D4311yescharacteristic
533C2×C4C2×#1062190011yescharacteristic
534C2×C4#1306337011yescharacteristic
535C2×C4#1306337211yescharacteristic
536C8—22no—
537C8—41no—
538C8—862no—
539C8—1721no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C22⋊Q8×D4311yescharacteristic
548C22#1458354911yescharacteristic
549C22#1458356711yescharacteristic
550C22C2×#1306334611yescharacteristic
551C22#1458369511yescharacteristic
552C22#1458370311yescharacteristic
553C22#1458370611yescharacteristic
554C4—22no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—862no—
560C4—862no—
561C4—3441no—
562C4—3441no—
563C4—3441no—
564C4—1721no—
565C4—1721no—
566C4—1722no—
567C4#1458345111yescharacteristic
568C4#1458352811yescharacteristic
569C4#1458358511yescharacteristic
570C4#1458359211yescharacteristic
571C2—82no—
572C2#1913830311yescharacteristic
573C2#1914438411yescharacteristic
574C2#1914442511yescharacteristic
575C2#1914698011yescharacteristic
576C2#1914719611yescharacteristic
577C2#1914760611yescharacteristic
578C2#1914765811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2065C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2065D43
hypocenterC43#26094
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. #19139831C2semidirect
6. #19135364C2semidirect
7. #19135362C2semidirect
8. #19135359C2semidirect
9. #19135310C2semidirect
10. #19135184C2semidirect
11. #19135164C2semidirect
12. #19134756C2semidirect
348. C43#26094semidirect

Maximal subgroups

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

subgroupindex
#191398312
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