Finite Group Databasebeta

← #25068379

Subgroups — #25068379

Order 11008.

600 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#19145161C211yesmaximal, characteristic
2#19143602C211yesmaximal, characteristic, complemented
3#19143598C211yesmaximal, characteristic, complemented
4#19133489C211yesmaximal, characteristic, complemented
5#19133478C211yesmaximal, characteristic, complemented
6#19133440C211yesmaximal, characteristic, complemented
7#19133432C211yesmaximal, characteristic, complemented
8#19133430C211yesmaximal, characteristic, complemented
9C8×#10621885C211yesmaximal, characteristic, complemented
10#19133387C211yesmaximal, characteristic, complemented
11#19133340C211yesmaximal, characteristic, complemented
12#19133002C211yesmaximal, characteristic, complemented
13#19133000C211yesmaximal, characteristic, complemented
14#19132874C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16#14583436C2211yescharacteristic
17#14583431C2211yescharacteristic
18#14583299C411yescharacteristic
19#14583280C411yescharacteristic
20#14583255C411yescharacteristic
21#14583252C411yescharacteristic
22#14583139C411yescharacteristic
23#14583134C411yescharacteristic
24#14583129C411yescharacteristic
25#14583125C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583026C2211yescharacteristic
28C8×Dic86C2211yescharacteristic
29C4×#10621885C2211yescharacteristic
30C4×#10621873C2211yescharacteristic
31C4×#10621882C2211yescharacteristic
32#14582978—21no—
33#14582978C2211yescharacteristic
34#14582975—21no—
35#14582969—21no—
36#14582967—21no—
37D4×C43⋊C8C2211yescharacteristic
38#14582964C2211yescharacteristic
39#14582959—21no—
40#14582957—21no—
41#14582951C2211yescharacteristic
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582857—21no—
45#14582853—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621873C2×C411yescharacteristic
69C2×#10621882C2×C411yescharacteristic
70C2×#10621872—21no—
71C2×#10621872D411yescharacteristic
72C2×#10621872D411yescharacteristic
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43C2×C411yescharacteristic
76C2×C8×D43C2×C411yescharacteristic
77#13063320—21no—
78#13063318—21no—
79#13063316C2×C411yescharacteristic
80#13063316C2×C411yescharacteristic
81#13063314C2×C411yescharacteristic
82#13063312C2×C411yescharacteristic
83#13063310—21no—
84#13063307—21no—
85#13063305C2×C411yescharacteristic
86#13063301C2×C411yescharacteristic
87#13063300C2×C411yescharacteristic
88#13063296C2×C411yescharacteristic
89C4×Dic86C2311yescharacteristic
90C4×D172—21no—
91C4×D172C2311yescharacteristic
92C4×C22⋊D43—21no—
93#13063284—21no—
94#13063282—21no—
95C42×D43C2311yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063257C2×C411yescharacteristic
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250C2×C411yescharacteristic
106#13063249C2×C411yescharacteristic
107#13063248C2×C411yescharacteristic
108#13063247C2×C411yescharacteristic
109#13063246C2×C411yescharacteristic
110#13063245C2×C411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117#13063236—21no—
118#13063235—21no—
119#13063235D411yescharacteristic
120#13063235D411yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43C2×C411yescharacteristic
128C8×Dic43C2×C411yescharacteristic
129C2×SD16×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C2×C22⋊D43—21no—
148C2×D172—21no—
149C2×D172C22×C411yescharacteristic
150C2×C4×D43—21no—
151C2×C4×D43C22×C411yescharacteristic
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43#4111yescharacteristic
154C2×Dic86C22×C411yescharacteristic
155SD16×C43—41no—
156M16×C43—42no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C22×C411yescharacteristic
161C2×C8×C43C22×C411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43C22×C411yescharacteristic
166C4⋊C4×C43C22×C411yescharacteristic
167C22⋊C4×C43—21no—
168C42×C43—21no—
169C42×C43C2411yescharacteristic
170C22⋊Dic43—21no—
171C22⋊Dic43—21no—
172C22⋊Dic43—21no—
173#10621885—22no—
174#10621882—22no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C411yescharacteristic
185C4⋊Dic43C22×C411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43C22×C411yescharacteristic
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43#4111yescharacteristic
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—42no—
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202#10621873—41no—
203#10621872—22no—
204#10621872—22no—
205#10621872—42no—
206C8×D43—22no—
207C8×D43—41no—
208C8×D43—42no—
209C23×C43—21no—
210C22×D43—21no—
211C22×D43C4×D411yescharacteristic
212Q8×C43—21no—
213Q8×C43—21no—
214D4×C43—21no—
215D4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43C23×C411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C22⋊D43—81no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43C4×D411yescharacteristic
229C2×Dic43C4×D411yescharacteristic
230C2×Dic43C4×D411yescharacteristic
231D172—21no—
232D172—21no—
233D172—81no—
234C4×D43—21no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—41no—
239C4×D43—41no—
240C4×D43—41no—
241Dic86—21no—
242Dic86—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43#13512yes—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8#13112yes—
256C43⋊C8#13512yes—
257#18069—431nomaximal, Sylow
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43C2×C4×D411yescharacteristic
262C2×D43—21no—
263C2×D43—21no—
264C2×D43—21no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43C2×#13111yescharacteristic
273C4×C43#56811yescharacteristic
274C4×C43C2×#13511yescharacteristic
275C4×C43C2×#13511yescharacteristic
276Dic43—21no—
277Dic43—21no—
278Dic43—21no—
279Dic43—41no—
280Dic43—41no—
281Dic43—41no—
282#3168—431no—
283#2969—431no—
284#2969—431no—
285#1591—431no—
286#1589—431no—
287#1583—431no—
288#1583D4311yescharacteristic, complemented
289#1582—431no—
290#1582—431no—
291C8×Q16—431no—
292C8×D8—431no—
293#1564—431no—
294#1482—431no—
295#1482—431no—
296C8×M16—431no—
297C2×C43—81no—
298C2×C43#293511yescharacteristic
299C2×C43C4×#13511yescharacteristic
300C2×C43#295711yescharacteristic
301D43—41no—
302D43—81no—
303#529—431no—
304#529—431no—
305#499—431no—
306#495—431no—
307#488—431no—
308#488—431no—
309#467—431no—
310#466—431no—
311#465—431no—
312#465—431no—
313#446—431no—
314#446—431no—
315C8×Q8—431no—
316C8×Q8C2×D4311yescharacteristic
317C4×Q16—431no—
318C4×SD16—431no—
319C4×SD16C2×D4311yescharacteristic
320C4×D8—431no—
321#436—431no—
322#436—861no—
323#436—861no—
324#436C2×D4311yescharacteristic
325#435—861no—
326#435—861no—
327C8×D4—431no—
328C8×D4—431no—
329#433—861no—
330#433—861no—
331#431—431no—
332#431—431no—
333#431—431no—
334#405—861no—
335#405—861no—
336C4×M16—431no—
337C2×C4×C8—431no—
338#335—431no—
339#335—431no—
340#334—431no—
341#334C2×D4311yescharacteristic
342Q8⋊C8—431no—
343Q8⋊C8—431no—
344Q8⋊C8—431no—
345Q8⋊C8C2×D4311yescharacteristic
346D4⋊C8—431no—
347D4⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8C2×D4311yescharacteristic
350#322—431no—
351#322C2×D4311yescharacteristic
352C82—431no—
353C82—431no—
354C43#1806911yescharacteristic, complemented, Sylow
355C2×Q16—431no—
356C2×SD16—431no—
357C2×SD16C4×D4311yescharacteristic
358C2×D8—431no—
359C2×M16—21no—
360C2×M16—431no—
361C2×M16—431no—
362C2×M16—861no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8—861no—
366C22×C8—861no—
367#126—861no—
368#126—861no—
369#125—431no—
370#125—431no—
371#124—431no—
372#124—431no—
373#123—861no—
374#123—861no—
375C22⋊Q8—431no—
376C22⋊Q8—431no—
377#121—431no—
378#121—431no—
379C4×Q8—431no—
380C4×Q8C22×D4311yescharacteristic
381C4×D4—431no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4C22×D4311yescharacteristic
385#117—861no—
386#117—861no—
387C2×C42—431no—
388#107—431no—
389#107—431no—
390#106—431no—
391#106C4×D4311yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401#103—431no—
402#103—431no—
403#103—431no—
404#103C4×D4311yescharacteristic
405#102—431no—
406#102—431no—
407#102—431no—
408#102C4×D4311yescharacteristic
409C22⋊C8—21no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—431no—
417#97—431no—
418#97—861no—
419#97—861no—
420C4×C8—21no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8C22×D4311yescharacteristic
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432C2×Q8—431no—
433C2×Q8C2×C4×D4311yescharacteristic
434C2×D4—431no—
435C2×D4—861no—
436C2×D4—861no—
437C2×D4C2×C4×D4311yescharacteristic
438C22×C4—21no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—861no—
443Q16—862no—
444SD16—41no—
445SD16—1721no—
446D8—862no—
447M16—42no—
448M16—862no—
449M16—862no—
450M16—1722no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—862no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—1721no—
463C2×C8—1722no—
464C2×C8—1722no—
465C2×C8C2×C4×D4311yescharacteristic
466C2×C8C2×C4×D4311yescharacteristic
467C2×C8D4×D4311yescharacteristic
468C2×C8D4×D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—431no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4C2×C4×D4311yescharacteristic
480C4⋊C4C2×C4×D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C42—21no—
492C42—431no—
493C42—431no—
494C42—431no—
495C42—861no—
496C42C23×D4311yescharacteristic
497C23—21no—
498C23—431no—
499C23—861no—
500Q8—21no—
501Q8—21no—
502Q8—861no—
503Q8—861no—
504D4—21no—
505D4—21no—
506D4—861no—
507D4—861no—
508D4—3441no—
509D4—3441no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—431no—
516C2×C4—431no—
517C2×C4—431no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4C22×C4×D4311yescharacteristic
529C2×C4C2×D4×D4311yescharacteristic
530C2×C4#41×D4311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—432no—
538C8—432no—
539C8—861no—
540C8—861no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8#1306334612yes—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—861no—
549C22—861no—
550C22—861no—
551C22—1721no—
552C22—1721no—
553C22—1721no—
554C22C4×D4×D4311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—861no—
560C4—861no—
561C4—861no—
562C4—1721no—
563C4—1721no—
564C4—1721no—
565C4#131×D4311yescharacteristic
566C4#1458366511yescharacteristic
567C4#135×D4311yescharacteristic
568C4C2×#1306334611yescharacteristic
569C2—81no—
570C2—3441no—
571C2—1721no—
572C2#1914333611yescharacteristic
573C2C4×#1306334611yescharacteristic
574C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1583C2
socleC22×C43C2×C4×D4
prime radical#14583134C4
cosocleC42×C43C24
hypercenter#1583D43
hypocenterC43#18069
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #19143602C2semidirect
3. #19143598C2semidirect
4. #19133489C2semidirect
5. #19133478C2semidirect
6. #19133440C2semidirect
7. #19133432C2semidirect
8. #19133430C2semidirect
9. C8×#10621885C2semidirect
10. #19133387C2semidirect
11. #19133340C2semidirect
12. #19133002C2semidirect
13. #19133000C2semidirect
14. #19132874C2semidirect
15. C43×#1583C2semidirect
288. #1583D43semidirect
354. C43#18069semidirect

Maximal subgroups

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

subgroupindex
#191451612
#191436022
#191435982
#191334892
#191334782
#191334402
#191334322
#191334302
C8×#106218852
#191333872
#191333402
#191330022
#191330002
#191328742
C43×#15832
#1806943