Finite Group Databasebeta

← #25199310

Subgroups — #25199310

Order 11008.

664 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137335C211yesmaximal, characteristic, complemented
2#19137233C211yesmaximal, characteristic
3#19136070C211yesmaximal, characteristic, complemented
4#19136002C211yesmaximal, characteristic
5#19135935C211yesmaximal, characteristic, complemented
6#19135740C211yesmaximal, characteristic
7#19135221C211yesmaximal, characteristic
8#19135213C211yesmaximal, characteristic
9#19135187C211yesmaximal, characteristic, complemented
10#19135185C211yesmaximal, characteristic, complemented
11#19135165C211yesmaximal, characteristic, complemented
12#19134845C211yesmaximal, characteristic
13#19134841C211yesmaximal, characteristic
14#19134739C211yesmaximal, characteristic, complemented
15C43×#1920C211yesmaximal, characteristic, complemented
16C2×#13063316C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063247C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063245C2211yescharacteristic
24C2×#13063245C2211yescharacteristic
25#14582800C2211yescharacteristic
26#14582800C2211yescharacteristic
27#14582797C2211yescharacteristic
28#14582795—21no—
29#14582795C2211yescharacteristic
30#14582795C2211yescharacteristic
31#14582794—21no—
32#14582790—21no—
33#14582790—21no—
34#14582784—21no—
35#14582781—21no—
36#14582768C2211yescharacteristic
37#14582761—21no—
38#14582758—21no—
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41#14582745C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C4×D43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063316—22no—
64#13063316—22no—
65C4×D172—22no—
66C4×D172—22no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063259—22no—
87#13063258—22no—
88#13063258—22no—
89#13063247—22no—
90#13063247—22no—
91#13063245—22no—
92#13063245—22no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95D411yescharacteristic
99C43⋊#95D411yescharacteristic
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C22×C8×C43C2311yescharacteristic
103C22×C8×C43C2311yescharacteristic
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C42×C43—21no—
110C2×C42×C43C2311yescharacteristic
111#106×C43—22no—
112#95×C43—21no—
113#95×C43—21no—
114C23×D43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43C2×D411yescharacteristic
126C22×Dic43C2×D411yescharacteristic
127C22×Dic43C2×D411yescharacteristic
128C22×Dic43C2×D411yescharacteristic
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172#4112yes—
135C2×C4×D43—24no—
136C2×C4×D43—81no—
137C2×C4×D43—81no—
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—81no—
152C4⋊C4×C43#4112yes—
153C42×C43—21no—
154C42×C43—21no—
155C42×C43—81no—
156(C2×D43)⋊C4—24no—
157(C2×D43)⋊C4—81no—
158(C2×D43)⋊C4—81no—
159(C2×D43)⋊C4—81no—
160(C2×D43)⋊C4—81no—
161C4⋊Dic43—24no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43#4112yes—
167C4⋊Dic43#4112yes—
168Dic43⋊C4—24no—
169Dic43⋊C4—81no—
170Dic43⋊C4—81no—
171Dic43⋊C4—81no—
172Dic43⋊C4—81no—
173Dic43⋊C4—81no—
174C4×Dic43—21no—
175C4×Dic43—21no—
176C4×Dic43—21no—
177C4×Dic43—21no—
178C4×Dic43—81no—
179C4×Dic43—81no—
180C2×C43⋊C8—21no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C23×C43C22×D411yescharacteristic
187C22×D43—22no—
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C2×C4×C43—22no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
213C2×C4×C43C2×#4111yescharacteristic
214C2×C4×C43C2×#4111yescharacteristic
215C2×C4×C43C2×#4111yescharacteristic
216C2×C4×C432−1+411yescharacteristic
217C2×C4×C432−1+411yescharacteristic
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—22no—
221C2×Dic43—22no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
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—
239D172—22no—
240D172—22no—
241D172—41no—
242D172—41no—
243C4×D43—84no—
244C8×C43—41no—
245C8×C43—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248#29404—431nomaximal, Sylow
249C22×C43#52511yescharacteristic
250C22×C43#52511yescharacteristic
251C22×C43#53611yescharacteristic
252C22×C43#57611yescharacteristic
253C22×C43#57611yescharacteristic
254C22×C43#57711yescharacteristic
255C22×C43#57811yescharacteristic
256C2×D43—42no—
257C2×D43—42no—
258C2×D43—42no—
259C2×D43—81no—
260C2×D43—81no—
261C2×D43—81no—
262C2×D43—81no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—42no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43#55211yescharacteristic
270C4×C43#55211yescharacteristic
271C4×C43#55611yescharacteristic
272C4×C43#55611yescharacteristic
273Dic43—41no—
274Dic43—42no—
275Dic43—42no—
276Dic43—41no—
277Dic43—41no—
278Dic43—41no—
279Dic43—81no—
280#2330—431no—
281#2319—431no—
282#2083—431no—
283#2071—431no—
284#2059—431no—
285#2025—431no—
286#1926—431no—
287#1925—431no—
288#1921—431no—
289#1921—431no—
290#1920D4311yescharacteristic, complemented
291#1918—431no—
292#1862—431no—
293#1862—431no—
294#1840—431no—
295C2×C43#259911yescharacteristic
296C2×C43#311911yescharacteristic
297C2×C43#312011yescharacteristic
298C2×C43#312211yescharacteristic
299C2×C43#312411yescharacteristic
300C2×C43#324111yescharacteristic
301C2×C43#324311yescharacteristic
302D43—82no—
303C2×#125—431no—
304C2×C4×D4—431no—
305C2×#107—431no—
306C2×#107—431no—
307C2×#107—431no—
308C2×#106C2×D4311yescharacteristic
309C2×#102—431no—
310C2×#102—431no—
311C2×#102—431no—
312C2×#102—431no—
313#390—431no—
314#390—431no—
315#389—431no—
316#389—431no—
317#389—431no—
318#389—861no—
319#389—861no—
320#389C2×D4311yescharacteristic
321#388—861no—
322#388—861no—
323#387—861no—
324#387—861no—
325#384—431no—
326#381—861no—
327#380—861no—
328C4×C4⋊C4—431no—
329C4×C4⋊C4—431no—
330C4×C4⋊C4C2×D4311yescharacteristic
331#376—431no—
332#340—431no—
333#340—431no—
334#340—431no—
335#340—431no—
336#340—431no—
337#340C2×D4311yescharacteristic
338#340C2×D4311yescharacteristic
339#340C2×D4311yescharacteristic
340#336—431no—
341#336—431no—
342#336—431no—
343#336—431no—
344#336—431no—
345#336C2×D4311yescharacteristic
346C43#2940411yescharacteristic, complemented, Sylow
347C22×D4—431no—
348C23×C4—861no—
349C22×C8—431no—
350C22×C8—431no—
351C22×C8C22×D4311yescharacteristic
352C22×C8C22×D4311yescharacteristic
353#125—862no—
354#125—862no—
355C4×D4—862no—
356C4×D4—862no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—431no—
359C2×C4⋊C4—431no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4C22×D4311yescharacteristic
369C2×C4⋊C4C22×D4311yescharacteristic
370C2×C4⋊C4C22×D4311yescharacteristic
371C2×C4⋊C4C22×D4311yescharacteristic
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C22⋊C4—861no—
377C2×C42—21no—
378C2×C42—431no—
379C2×C42—431no—
380C2×C42—861no—
381C2×C42—861no—
382C2×C42C22×D4311yescharacteristic
383#107—862no—
384#107—862no—
385#107—862no—
386#106—22no—
387#102—862no—
388#102—862no—
389#102—862no—
390#102—862no—
391#95—21no—
392#95—21no—
393#95—431no—
394#95—431no—
395#95—431no—
396#95—431no—
397#95—861no—
398#95—861no—
399#95—861no—
400#95—861no—
401#95—861no—
402C24—861no—
403C2×D4—432no—
404C2×D4—861no—
405C2×D4—861no—
406C2×D4—861no—
407C2×D4—861no—
408C2×D4—861no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—431no—
414C22×C4—431no—
415C22×C4—431no—
416C22×C4—431no—
417C22×C4—864no—
418C22×C4—861no—
419C22×C4—861no—
420C22×C4—861no—
421C22×C4—3441no—
422C22×C4—3441no—
423C22×C4D4×D4311yescharacteristic
424C22×C4D4×D4311yescharacteristic
425C22×C4C23×D4311yescharacteristic
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—861no—
433C2×C8—861no—
434C2×C8—861no—
435C2×C8—861no—
436C2×C8—861no—
437C2×C8—861no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—81no—
446C4⋊C4—432no—
447C4⋊C4—432no—
448C4⋊C4—864no—
449C4⋊C4—864no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—3441no—
455C4⋊C4—3441no—
456C4⋊C4—3441no—
457C4⋊C4—3441no—
458C4⋊C4—3441no—
459C4⋊C4#1062189812yes—
460C22⋊C4—864no—
461C22⋊C4—3441no—
462C22⋊C4—3441no—
463C22⋊C4—3441no—
464C22⋊C4—3441no—
465C42—21no—
466C42—21no—
467C42—81no—
468C42—861no—
469C42—861no—
470C42—861no—
471C42—861no—
472C42—3441no—
473C42—3441no—
474C23—862no—
475C23—1721no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23C2×D4×D4311yescharacteristic
482D4—862no—
483D4—862no—
484D4—1721no—
485D4—1721no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—41no—
494C2×C4—41no—
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—862no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—862no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—3444no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4#41×D4311yescharacteristic
527C2×C4#41×D4311yescharacteristic
528C2×C4#41×D4311yescharacteristic
529C2×C4C2×#1062189811yescharacteristic
530C2×C4#1306337211yescharacteristic
531C2×C4#1306337311yescharacteristic
532C8—41no—
533C8—41no—
534C8—1721no—
535C8—1721no—
536C22—3441no—
537C22—3441no—
538C22—3441no—
539C22—3441no—
540C22—1722no—
541C22—1722no—
542C22—1722no—
543C22#1458340711yescharacteristic
544C22#1458340811yescharacteristic
545C22#1458347211yescharacteristic
546C22#1458370111yescharacteristic
547C22#1458370311yescharacteristic
548C22#1458370511yescharacteristic
549C22#1458371511yescharacteristic
550C4—41no—
551C4—41no—
552C4—42no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—3441no—
557C4—1721no—
558C4—1722no—
559C4—1721no—
560C4—1722no—
561C4—1721no—
562C4—1721no—
563C4#1458358111yescharacteristic
564C4#1458358811yescharacteristic
565C4#1458361611yescharacteristic
566C4#1458362111yescharacteristic
567C2—3442no—
568C2#1914017011yescharacteristic
569C2#1914480011yescharacteristic
570C2#1914481211yescharacteristic
571C2#1914483411yescharacteristic
572C2#1914486111yescharacteristic
573C2#1914584711yescharacteristic
574C2#1914588511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1920C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1920D43
hypocenterC43#29404
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
1. #19137335C2semidirect
3. #19136070C2semidirect
5. #19135935C2semidirect
9. #19135187C2semidirect
10. #19135185C2semidirect
11. #19135165C2semidirect
14. #19134739C2semidirect
15. C43×#1920C2semidirect
290. #1920D43semidirect
346. C43#29404semidirect

Maximal subgroups

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

subgroupindex
#191373352
#191372332
#191360702
#191360022
#191359352
#191357402
#191352212
#191352132
#191351872
#191351852
#191351652
#191348452
#191348412
#191347392
C43×#19202
#2940443