Finite Group Databasebeta

← #25124177

Subgroups — #25124177

Order 11008.

1482 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
1C2×#14583480C211yesmaximal, characteristic
2C22×#13063256C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic, complemented
4C2×#14582893C211yesmaximal, characteristic, complemented
5C2×#14582867C211yesmaximal, characteristic, complemented
6#19137183C211yesmaximal, characteristic, complemented
7#19135794C214yesmaximal, complemented
8#19135787C214yesmaximal, complemented
9C43×#1736C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C22×#10621898C2211yescharacteristic
12C23×C43⋊C8C2211yescharacteristic
13#14583480—24no—
14#14583480—24no—
15C2×#13063305—21no—
16C2×#13063305C2212yes—
17C2×#13063300—21no—
18C2×#13063300C2212yes—
19C2×#13063299—22no—
20C22×C4⋊Dic43C2211yescharacteristic
21C2×#13063256—24no—
22C2×#13063256C2214yes—
23#14582901—24no—
24#14582893—24no—
25C2×#13063250C2212yes—
26C2×#13063248C2212yes—
27C2×#13063247C2212yes—
28C2×#13063245C2212yes—
29#14582867—24no—
30C2×(C2×D43)⋊C8C2214yes—
31#14582805—21no—
32#14582801—21no—
33#14582776—22no—
34#14582756C2214yes—
35C22×M16×C43C2211yescharacteristic
36C2×#117×C43C2211yescharacteristic
37C22×C4⋊C4×C43C2211yescharacteristic
38C43×#340C2214yes—
39C2×#10621898—22no—
40C2×#10621898—22no—
41C2×#10621898—22no—
42C2×#10621898—22no—
43C2×#10621898—22no—
44C2×#10621898—22no—
45C2×#10621898—22no—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898D414yes—
51C22×Dic86D411yescharacteristic
52C22×Dic86C2311yescharacteristic
53C22×D172—22no—
54C22×D172D411yescharacteristic
55C22×D172C2311yescharacteristic
56C22×C22⋊D43—21no—
57C22×C22⋊D43D412yes—
58C23×Dic43—21no—
59C22×C4×D43—21no—
60C22×C4×D43C2312yes—
61C22×C43⋊C8—22no—
62C22×C43⋊C8—22no—
63C22×C43⋊C8D414yescomplemented
64C22×C43⋊C8C2312yes—
65#13063305—28no—
66#13063305—24no—
67#13063305—24no—
68#13063300—28no—
69#13063300—24no—
70#13063300—24no—
71#13063299—216no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2312yes—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—22no—
79C2×(C2×D43)⋊C4—24no—
80#13063256—28no—
81#13063250—24no—
82#13063248—24no—
83#13063247—24no—
84#13063245—24no—
85(C2×D43)⋊C8—28no—
86C43⋊#95—24no—
87C23×C4×C43—21no—
88C23×C4×C43C2311yescharacteristic
89C2×M16×C43—22no—
90C2×M16×C43—22no—
91C2×M16×C43—22no—
92C22×C8×C43C2312yes—
93#117×C43—22no—
94#117×C43—22no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43D414yes—
98C2×C4⋊C4×C43C2312yes—
99C2×C4⋊C4×C43C2312yes—
100C2×C22⋊C4×C43—21no—
101C2×C42×C43—21no—
102C24×C43C2×D411yescharacteristic
103C23×D43—21no—
104C23×D43C2×D412yes—
105C22×C4×C43—24no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—82no—
109C22×C4×C43C2×D412yes—
110C22×C4×C43C2×D412yes—
111C22×C4×C43C2×D412yes—
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43#4112yes—
114C22×C4×C43#4112yes—
115C22×C4×C43#4112yes—
116C22×C4×C43C2411yescharacteristic
117C2×C22⋊D43—24no—
118C2×C22⋊D43—24no—
119C2×C22⋊D43—24no—
120C2×C22⋊D43—24no—
121C2×C22⋊D43—42no—
122C2×C22⋊D43—42no—
123C22×Dic43—21no—
124C22×Dic43—22no—
125C22×Dic43—42no—
126C22×Dic43—82no—
127C22×Dic43C2×D412yes—
128#10621898—28no—
129#10621898—28no—
130#10621898—44no—
131#10621898—44no—
132#10621898—44no—
133#10621898—44no—
134#10621898—44no—
135#10621898—44no—
136C2×D172—22no—
137C2×D172—22no—
138C2×D172—22no—
139C2×D172—21no—
140C2×D172—28no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—84no—
146C2×D172C2×D412yes—
147C2×C4×D43—24no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—22no—
161C2×Dic86—22no—
162C2×Dic86—22no—
163C2×Dic86—21no—
164C2×Dic86C2×D412yes—
165M16×C43—44no—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C2×C8×C43—22no—
169C4⋊C4×C43—24no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43C2×D414yes—
174C22⋊C4×C43—42no—
175C42×C43—42no—
176(C2×D43)⋊C4—28no—
177(C2×D43)⋊C4—28no—
178(C2×D43)⋊C4—84no—
179C4⋊Dic43—28no—
180C4⋊Dic43—22no—
181C4⋊Dic43—22no—
182C4⋊Dic43—42no—
183C2×C43⋊C8—28no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8C2×D414yes—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43#12012yes—
190C23×C43#12112yes—
191C23×C43#12312yes—
192C23×C43C22×D411yescharacteristic
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—22no—
197C22×D43—24no—
198C22×D43—24no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—42no—
202C22×D43—42no—
203C2×C4×C43—24no—
204C2×C4×C43—44no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—84no—
209C2×C4×C43#12012yes—
210C2×C4×C43#12114yes—
211C2×C4×C43#12112yes—
212C2×C4×C43#12114yes—
213C2×C4×C43#12314yes—
214C2×C4×C43#12312yes—
215C2×C4×C43#12414yes—
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C22⋊D43—48no—
223C22⋊D43—48no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—42no—
231C2×Dic43—44no—
232C2×Dic43—84no—
233D172—22no—
234D172—22no—
235D172—41no—
236D172—41no—
237D172—44no—
238D172—88no—
239C4×D43—42no—
240C4×D43—42no—
241C4×D43—42no—
242C4×D43—42no—
243C4×D43—48no—
244Dic86—22no—
245Dic86—22no—
246Dic86—41no—
247Dic86—41no—
248Dic86—44no—
249C8×C43—42no—
250C43⋊C8—24no—
251#23489—431nomaximal, Sylow
252C22×C43—24no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—24no—
256C22×C43#39414yes—
257C22×C43C2×#12011yescharacteristic
258C22×C43C2×#12111yescharacteristic
259C22×C43C2×#12311yescharacteristic
260C22×C43#57712yes—
261C22×C43#57712yes—
262C2×D43—44no—
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—42no—
267C2×D43—42no—
268C2×D43—42no—
269C2×D43—44no—
270C2×D43—82no—
271C2×D43—82no—
272C4×C43—44no—
273C4×C43—82no—
274C4×C43#39414yes—
275C4×C43C2×#12111yescharacteristic
276C4×C43C2×#12111yescharacteristic
277C4×C43C2×#12311yescharacteristic
278C4×C43C2×#12411yescharacteristic
279Dic43—42no—
280Dic43—42no—
281Dic43—82no—
282C2×#537—431no—
283C22×#106—431no—
284C2×#417—431no—
285C2×#416—431no—
286C2×#408—431no—
287#2311—431no—
288#2035—434no—
289#2034—434no—
290#1736D4311yescharacteristic, complemented
291C2×C43—24no—
292C2×C43C2×#39411yescharacteristic
293C2×C43#300911yescharacteristic
294C2×C43#301011yescharacteristic
295C2×C43#306012yes—
296C2×C43#309912yes—
297D43—82no—
298D43—82no—
299C22×#41—431no—
300C22×#41—431no—
301C22×M16C2×D4311yescharacteristic
302C23×C8—431no—
303#537—864no—
304#537—864no—
305C2×C22⋊Q8—432no—
306C2×C22⋊Q8—861no—
307C2×#121—432no—
308C2×#121—861no—
309C2×#121—862no—
310C2×#117C2×D4311yescharacteristic
311C22×C4⋊C4—431no—
312C22×C4⋊C4C2×D4311yescharacteristic
313C2×#106—434no—
314C2×#106—864no—
315#417—864no—
316#416—864no—
317C2×#103—432no—
318C2×#103—432no—
319C2×#102—432no—
320C2×#102—432no—
321#408—864no—
322C2×C22⋊C8—434no—
323#391—861no—
324#390—861no—
325#386—862no—
326#380—434no—
327#340C2×D4314yes—
328C43#2348911yescharacteristic, complemented, Sylow
329C2×#41—434no—
330C2×#41—862no—
331C2×#41—862no—
332C2×#41—862no—
333C2×#41—862no—
334C2×#41—862no—
335C2×#41—862no—
336C2×#41—862no—
337C2×#41—862no—
338C2×#41—862no—
339C2×#41—862no—
340C2×#41—862no—
341C22×Q8—431no—
342C22×Q8—431no—
343C22×D4—432no—
344C22×D4—431no—
345C22×D4—431no—
346C22×D4—862no—
347C22×D4—861no—
348C23×C4—21no—
349C23×C4—432no—
350C23×C4—861no—
351C23×C4—861no—
352C23×C4C22×D4311yescharacteristic
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C22×C8—434no—
357C22×C8—432no—
358C22×C8—862no—
359C22×C8—862no—
360C22×C8C22×D4312yes—
361C22⋊Q8—864no—
362C22⋊Q8—868no—
363C22⋊Q8—864no—
364#121—864no—
365#121—868no—
366#121—8616no—
367#121—864no—
368#117—22no—
369#117—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—432no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4D17214yes—
378C2×C4⋊C4C22×D4312yes—
379C2×C4⋊C4C22×D4312yes—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—862no—
382C2×C22⋊C4—862no—
383C2×C22⋊C4—864no—
384C2×C42—21no—
385#106—868no—
386#103—864no—
387#103—864no—
388#102—864no—
389#102—864no—
390C22⋊C8—868no—
391#95—864no—
392C24—432no—
393C24—861no—
394C24D4×D4311yescharacteristic
395#41—868no—
396#41—868no—
397#41—1724no—
398#41—1724no—
399#41—1724no—
400#41—1724no—
401#41—1724no—
402#41—1724no—
403C2×Q8—432no—
404C2×Q8—862no—
405C2×Q8—862no—
406C2×Q8—862no—
407C2×Q8—861no—
408C2×Q8—861no—
409C2×Q8—861no—
410C2×Q8—861no—
411C2×Q8—861no—
412C2×D4—432no—
413C2×D4—868no—
414C2×D4—864no—
415C2×D4—864no—
416C2×D4—864no—
417C2×D4—864no—
418C2×D4—862no—
419C2×D4—862no—
420C2×D4—862no—
421C2×D4—861no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—3444no—
427C2×D4—1722no—
428C2×D4—1722no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—82no—
433C22×C4—432no—
434C22×C4—861no—
435C22×C4—864no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—3442no—
444C22×C4—1722no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4C2×D17212yes—
448C22×C4#1062189812yes—
449C22×C4#1062189812yes—
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4312yes—
452C22×C4D4×D4312yes—
453C22×C4#1062190212yes—
454C22×C4C23×D4311yescharacteristic
455M16—44no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—434no—
460C2×C8—868no—
461C2×C8—862no—
462C2×C8—862no—
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—868no—
468C4⋊C4—862no—
469C4⋊C4—862no—
470C4⋊C4—1722no—
471C4⋊C4C2×D17214yes—
472C22⋊C4—42no—
473C22⋊C4—868no—
474C22⋊C4—868no—
475C22⋊C4—3444no—
476C42—42no—
477C23—22no—
478C23—22no—
479C23—862no—
480C23—862no—
481C23—862no—
482C23—862no—
483C23—864no—
484C23—864no—
485C23—1721no—
486C23—1721no—
487C23—1722no—
488C23—1722no—
489C23#1306329512yes—
490C23#1306329812yes—
491C23#1306331012yes—
492C23C2×D4×D4311yescharacteristic
493Q8—862no—
494Q8—862no—
495Q8—1724no—
496Q8—1721no—
497Q8—1721no—
498D4—862no—
499D4—862no—
500D4—3448no—
501D4—1728no—
502D4—1728no—
503D4—1724no—
504D4—1721no—
505D4—1721no—
506C2×C4—24no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—84no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—3444no—
517C2×C4—1722no—
518C2×C4—1724no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1728no—
522C2×C4—1722no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4#1306329512yes—
527C2×C4#1306329812yes—
528C2×C4#1306329814yes—
529C2×C4#1306330014yes—
530C2×C4#1306331012yes—
531C2×C4#1306331014yes—
532C2×C4#1306331314yes—
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4C22×D17211yescharacteristic
536C2×C4C2×#1062189811yescharacteristic
537C2×C4C2×#1062189811yescharacteristic
538C2×C4C2×#1062190211yescharacteristic
539C8—42no—
540C8—864no—
541C22—24no—
542C22—24no—
543C22—22no—
544C22—22no—
545C22—3442no—
546C22—3442no—
547C22—1722no—
548C22—1722no—
549C22—1724no—
550C22—1724no—
551C22—1722no—
552C22—1722no—
553C22—1722no—
554C22—1722no—
555C22#1458281714yes—
556C22C2×#1306329511yescharacteristic
557C22C2×#1306329811yescharacteristic
558C22C2×#1306331011yescharacteristic
559C22#1458370812yes—
560C22#1458370912yes—
561C4—44no—
562C4—82no—
563C4—3442no—
564C4—1722no—
565C4—1722no—
566C4#1458281714yes—
567C4C2×#1306329811yescharacteristic
568C4C2×#1306330011yescharacteristic
569C4C2×#1306331011yescharacteristic
570C4C2×#1306331311yescharacteristic
571C2—24no—
572C2—3442no—
573C2—3442no—
574C2C2×#1458281711yescharacteristic
575C2#1914387311yescharacteristic
576C2#1914388211yescharacteristic
577C2#1914425612yes—
578C2#1914458812yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC2×#14583480C2
hypercenter#1736D43
hypocenterC43#23489
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C22×#13063256C2semidirect
3. C2×#14582901C2semidirect
4. C2×#14582893C2semidirect
5. C2×#14582867C2semidirect
6. #19137183C2semidirect
7. #19135794C2semidirect
8. #19135787C2semidirect
9. C43×#1736C2semidirect
63. C22×C43⋊C8D4semidirect
290. #1736D43semidirect
328. C43#23489semidirect

Maximal subgroups

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

subgroupindex
C2×#145834802
C22×#130632562
C2×#145829012
C2×#145828932
C2×#145828672
#191371832
#191357942
#191357872
C43×#17362
#2348943