Finite Group Databasebeta

← #25199246

Subgroups — #25199246

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137343C211yesmaximal, characteristic, complemented
2#19137239C211yesmaximal, characteristic
3#19136078C211yesmaximal, characteristic, complemented
4#19136010C211yesmaximal, characteristic
5#19135929C211yesmaximal, characteristic, complemented
6#19135732C211yesmaximal, characteristic
7#19135223C211yesmaximal, characteristic
8#19135223C211yesmaximal, characteristic
9#19135181C211yesmaximal, characteristic, complemented
10#19135181C211yesmaximal, characteristic, complemented
11#19135174C211yesmaximal, characteristic, complemented
12#19135167C211yesmaximal, characteristic, complemented
13#19134859C211yesmaximal, characteristic
14#19134845C211yesmaximal, characteristic
15C43×#1840C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26#14582803—21no—
27#14582803—21no—
28#14582801C2211yescharacteristic
29#14582801C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582788—21no—
35#14582788—21no—
36#14582782—21no—
37#14582782—21no—
38#14582765C2211yescharacteristic
39#14582761—21no—
40#14582758—21no—
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C43×#376C2211yescharacteristic
53C43×#336C2211yescharacteristic
54C43×#336C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62#13063325—22no—
63#13063325—22no—
64C4×D172—22no—
65C4×D172—22no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063259—22no—
87#13063257—22no—
88#13063257—22no—
89#13063257—22no—
90#13063247—22no—
91#13063247—22no—
92#13063247—22no—
93#13063247—22no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×C8×C43C2311yescharacteristic
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C2×C42×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110#95×C43D411yescharacteristic
111#95×C43D411yescharacteristic
112#95×C43D411yescharacteristic
113#95×C43D411yescharacteristic
114C23×D43—21no—
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
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×Dic86—24no—
139C2×Dic86—81no—
140C2×Dic86—81no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C42×C43—21no—
154C42×C43—21no—
155C42×C43—21no—
156C42×C43—21no—
157C42×C43—21no—
158C42×C43—21no—
159(C2×D43)⋊C4—24no—
160(C2×D43)⋊C4—81no—
161(C2×D43)⋊C4—81no—
162(C2×D43)⋊C4—81no—
163(C2×D43)⋊C4—81no—
164C4⋊Dic43—24no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43#4112yes—
177C4⋊Dic43#4112yes—
178C4⋊Dic43#4112yes—
179Dic43⋊C4—81no—
180Dic43⋊C4—81no—
181Dic43⋊C4—81no—
182Dic43⋊C4—81no—
183C4×Dic43—81no—
184C4×Dic43—81no—
185C4×Dic43—81no—
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—21no—
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—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
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—22no—
219C2×Dic43—22no—
220C2×Dic43—22no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
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—
244Dic86—84no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249#29400—431nomaximal, Sylow
250C22×C43#52511yescharacteristic
251C22×C43#52511yescharacteristic
252C22×C43#53611yescharacteristic
253C22×C43#57611yescharacteristic
254C22×C43#57711yescharacteristic
255C22×C43#57711yescharacteristic
256C22×C43#57711yescharacteristic
257C2×D43—42no—
258C2×D43—42no—
259C2×D43—42no—
260C2×D43—81no—
261C2×D43—81no—
262C2×D43—81no—
263C2×D43—81no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43#55211yescharacteristic
271C4×C43#55211yescharacteristic
272C4×C43#55611yescharacteristic
273C4×C43#55611yescharacteristic
274Dic43—42no—
275Dic43—42no—
276Dic43—42no—
277Dic43—81no—
278Dic43—81no—
279Dic43—81no—
280Dic43—81no—
281#2331—431no—
282#2319—431no—
283#2085—431no—
284#2073—431no—
285#2058—431no—
286#2023—431no—
287#1926—431no—
288#1926—431no—
289#1920—431no—
290#1920—431no—
291#1919—431no—
292#1918—431no—
293#1864—431no—
294#1862—431no—
295#1840D4311yescharacteristic, complemented
296C2×C43#259911yescharacteristic
297C2×C43#311811yescharacteristic
298C2×C43#311811yescharacteristic
299C2×C43#312511yescharacteristic
300C2×C43#312611yescharacteristic
301C2×C43#324111yescharacteristic
302C2×C43#324411yescharacteristic
303D43—82no—
304C2×C4⋊Q8—431no—
305C2×C4×D4—431no—
306C2×#107—431no—
307C2×#106—431no—
308C2×#106—431no—
309C2×#106—431no—
310C2×#102—431no—
311C2×#102—431no—
312C2×#102—431no—
313C2×#102—431no—
314#391—861no—
315#391—861no—
316#390—431no—
317#390—431no—
318#389—431no—
319#389—431no—
320#389—431no—
321#389—431no—
322#388—861no—
323#388—861no—
324#387—861no—
325#387—861no—
326#382—431no—
327#381—861no—
328#380—861no—
329C4×C4⋊C4—431no—
330C4×C4⋊C4—431no—
331C4×C4⋊C4—431no—
332#376C2×D4311yescharacteristic
333#340—431no—
334#340—431no—
335#340—431no—
336#340—431no—
337#340—431no—
338#340—431no—
339#340—431no—
340#340—431no—
341#336C2×D4311yescharacteristic
342#336C2×D4311yescharacteristic
343#336C2×D4311yescharacteristic
344#336C2×D4311yescharacteristic
345#336C2×D4311yescharacteristic
346#336C2×D4311yescharacteristic
347C43#2940011yescharacteristic, complemented, Sylow
348C22×Q8—861no—
349C22×D4—431no—
350C23×C4—861no—
351C22×C8C22×D4311yescharacteristic
352C22×C8C22×D4311yescharacteristic
353C22×C8C22×D4311yescharacteristic
354C22×C8C22×D4311yescharacteristic
355C4⋊Q8—862no—
356C4⋊Q8—862no—
357C4×D4—862no—
358C4×D4—862no—
359C2×C4⋊C4—431no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C22⋊C4—861no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C42—861no—
377C2×C42—861no—
378C2×C42—861no—
379C2×C42C22×D4311yescharacteristic
380C2×C42C22×D4311yescharacteristic
381C2×C42C22×D4311yescharacteristic
382#107—862no—
383#106—862no—
384#106—862no—
385#106—862no—
386#102—862no—
387#102—862no—
388#102—862no—
389#102—862no—
390#95—861no—
391#95—861no—
392#95—861no—
393#95—861no—
394#95—861no—
395#95—861no—
396#95—861no—
397#95—861no—
398#95—861no—
399#95D17211yescharacteristic
400#95D17211yescharacteristic
401#95D17211yescharacteristic
402#95D17211yescharacteristic
403C24—861no—
404C2×Q8—864no—
405C2×Q8—3441no—
406C2×Q8—3441no—
407C2×D4—432no—
408C2×D4—861no—
409C2×D4—861no—
410C2×D4—861no—
411C2×D4—861no—
412C2×D4—861no—
413C22×C4—864no—
414C22×C4—861no—
415C22×C4—861no—
416C22×C4—861no—
417C22×C4—861no—
418C22×C4—861no—
419C22×C4—861no—
420C22×C4—861no—
421C22×C4—3441no—
422C22×C4—3441no—
423C22×C4C2×D17211yescharacteristic
424C22×C4C2×D17211yescharacteristic
425C22×C4C2×D17211yescharacteristic
426C22×C4C2×D17211yescharacteristic
427C22×C4C2×D17211yescharacteristic
428C22×C4C2×D17211yescharacteristic
429C22×C4C23×D4311yescharacteristic
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C4⋊C4—432no—
443C4⋊C4—432no—
444C4⋊C4—432no—
445C4⋊C4—864no—
446C4⋊C4—861no—
447C4⋊C4—861no—
448C4⋊C4—861no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—3441no—
458C4⋊C4—3441no—
459C4⋊C4—3441no—
460C4⋊C4—3441no—
461C22⋊C4—864no—
462C22⋊C4—3441no—
463C22⋊C4—3441no—
464C22⋊C4—3441no—
465C22⋊C4—3441no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—3441no—
473C42—3441no—
474C42—3441no—
475C23—862no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23—1721no—
482C23C22×D17211yescharacteristic
483Q8—3444no—
484D4—862no—
485D4—862no—
486D4—1721no—
487D4—1721no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—862no—
509C2×C4—3444no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1721no—
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#41×D4311yescharacteristic
529C2×C4#41×D4311yescharacteristic
530C2×C4#41×D4311yescharacteristic
531C2×C4#41×D4311yescharacteristic
532C2×C4#1306337211yescharacteristic
533C2×C4#1306337211yescharacteristic
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—3441no—
539C22—3441no—
540C22—3441no—
541C22—3441no—
542C22—1722no—
543C22—1722no—
544C22—1722no—
545C22#1458341111yescharacteristic
546C22#1458341111yescharacteristic
547C22#1458347511yescharacteristic
548C22#1458370411yescharacteristic
549C22#1458371111yescharacteristic
550C22#1458371111yescharacteristic
551C22#1458371111yescharacteristic
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—3441no—
559C4—3441no—
560C4—3441no—
561C4—3441no—
562C4—1722no—
563C4—1722no—
564C4—1722no—
565C4#1458358511yescharacteristic
566C4#1458358511yescharacteristic
567C4#1458361611yescharacteristic
568C4#1458361611yescharacteristic
569C2—3442no—
570C2#1914017411yescharacteristic
571C2#1914478111yescharacteristic
572C2#1914478111yescharacteristic
573C2#1914487411yescharacteristic
574C2#1914488711yescharacteristic
575C2#1914585011yescharacteristic
576C2#1914589511yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1840C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1840D43
hypocenterC43#29400
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1840

Complements

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

NH ≅ G/Ntype
1. #19137343C2semidirect
3. #19136078C2semidirect
5. #19135929C2semidirect
9. #19135181C2semidirect
10. #19135181C2semidirect
11. #19135174C2semidirect
12. #19135167C2semidirect
15. C43×#1840C2semidirect
295. #1840D43semidirect
347. C43#29400semidirect

Maximal subgroups

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

subgroupindex
#191373432
#191372392
#191360782
#191360102
#191359292
#191357322
#191352232
#191351812
#191351742
#191351672
#191348592
#191348452
C43×#18402
#2940043