Finite Group Databasebeta

← #25106047

Subgroups — #25106047

Order 11008.

1130 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583524C211yesmaximal, characteristic
2#19137192C211yesmaximal, characteristic
3#19137190C211yesmaximal, characteristic
4#19135581C211yesmaximal, characteristic, complemented
5#19135580C211yesmaximal, characteristic, complemented
6#19135579C211yesmaximal, characteristic, complemented
7#19135578C214yesmaximal, complemented
8#19134668C214yesmaximal
9C43×#1996C211yesmaximal, characteristic, complemented
10#14583524—22no—
11#14583524—22no—
12#14583524—22no—
13#14583524—22no—
14C2×#13063305C412yescomplemented
15C2×#13063304C2211yescharacteristic
16C2×#13063303C412yescomplemented
17C2×#13063303C412yescomplemented
18C2×#13063302C2212yes—
19C2×#13063301C412yescomplemented
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C2×C22⋊C4×D43C2212yes—
22#14582791—22no—
23#14582790—22no—
24#14582789—22no—
25#14582788—22no—
26#14582759C2211yescharacteristic
27#14582757C2212yes—
28#14582754C2212yes—
29#14582754C2212yes—
30C22⋊C4×Dic43C2212yes—
31C4×C22⋊Dic43C2211yescharacteristic
32#14582666C2214yes—
33#14582665C2214yes—
34#14582665C2214yes—
35C2×C22⋊Q8×C43C2211yescharacteristic
36C43×#380C2211yescharacteristic
37C4×C22⋊C4×C43C2211yescharacteristic
38C43×#342C2214yes—
39C24×D43C2311yescharacteristic
40C22×Dic86C2×C412yes—
41C22×Dic86C2×C411yescharacteristic
42C23×Dic43C2311yescharacteristic
43C22×C4×D43C2×C412yes—
44C22×C4×D43C2×C412yes—
45#13063305—24no—
46#13063305—24no—
47#13063304—21no—
48#13063304—21no—
49#13063304—21no—
50#13063304—21no—
51#13063303—24no—
52#13063303—24no—
53#13063303—24no—
54#13063303—24no—
55#13063302—24no—
56#13063302—24no—
57#13063301—24no—
58#13063301—24no—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43C2×C412yes—
61C2×C4⋊Dic43C2×C411yescharacteristic
62C2×Dic43⋊C4—22no—
63C2×Dic43⋊C4C2×C412yes—
64C2×Dic43⋊C4C2×C412yes—
65C2×Dic43⋊C4C2×C412yes—
66C2×C22⋊Dic43C2312yes—
67C2×C22⋊Dic43C2312yes—
68C2×C22⋊Dic43C2312yes—
69C2×(C2×D43)⋊C4—22no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4C2×C412yes—
74C2×(C2×D43)⋊C4C2×C412yes—
75C2×(C2×D43)⋊C4C2×C412yes—
76C2×(C2×D43)⋊C4C2×C412yes—
77C2×(C2×D43)⋊C4D412yes—
78C2×(C2×D43)⋊C4D412yes—
79C2×(C2×D43)⋊C4D412yes—
80C2×(C2×D43)⋊C4D412yes—
81C22⋊C4×D43—24no—
82C22⋊C4×D43—24no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—22no—
85C43⋊#95—21no—
86C43⋊#95—21no—
87C43⋊#95—22no—
88C43⋊#95—22no—
89C22×Q8×C43C2×C411yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43C2×C411yescharacteristic
97C2×C4⋊C4×C43C2×C412yes—
98C2×C22⋊C4×C43C2312yes—
99C2×C22⋊C4×C43C2312yes—
100C2×C22⋊C4×C43C2312yes—
101C2×C42×C43—21no—
102#95×C43—21no—
103#95×C43—21no—
104C24×C43C2411yescharacteristic
105C23×D43—22no—
106C23×D43—22no—
107C23×D43—81no—
108C23×D43—81no—
109C23×D43C22×C412yes—
110C23×D43C2×D412yes—
111C23×D43C2×D412yes—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—81no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—81no—
118C22×C4×C43C22×C412yes—
119C22×C4×C43C22×C412yes—
120C22×C4×C43C22×C411yescharacteristic
121C22×C4×C43C22×C411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—81no—
129C22×Dic43C22×C412yes—
130C22×Dic43C22×C412yes—
131C22×Dic43C22×C412yes—
132C22×Dic43C2×D412yes—
133C22×Dic43C2×D412yes—
134C2×C4×D43—24no—
135C2×C4×D43—24no—
136C2×C4×D43—82no—
137C2×C4×D43—82no—
138C2×Dic86—21no—
139C2×Dic86—21no—
140C2×Dic86—24no—
141C2×Dic86—82no—
142C2×Dic86—81no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—81no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—22no—
151C22⋊C4×C43—24no—
152C22⋊C4×C43—22no—
153C42×C43—81no—
154C22⋊Dic43—22no—
155C22⋊Dic43—22no—
156C22⋊Dic43—22no—
157C22⋊Dic43—22no—
158C22⋊Dic43—24no—
159(C2×D43)⋊C4—24no—
160(C2×D43)⋊C4—24no—
161(C2×D43)⋊C4—82no—
162(C2×D43)⋊C4—82no—
163(C2×D43)⋊C4—82no—
164(C2×D43)⋊C4—82no—
165(C2×D43)⋊C4C22⋊C414yes—
166(C2×D43)⋊C4C22⋊C414yes—
167(C2×D43)⋊C4C22⋊C414yes—
168(C2×D43)⋊C4C22⋊C414yes—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—24no—
172C4⋊Dic43—81no—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175Dic43⋊C4—24no—
176Dic43⋊C4—24no—
177Dic43⋊C4—82no—
178C4×Dic43—82no—
179C4×Dic43—81no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43C23×C411yescharacteristic
183C23×C43C22×D411yescharacteristic
184C23×C43C22×D411yescharacteristic
185C23×C432−1+412yes—
186C23×C432−1+412yes—
187C22×D43—24no—
188C22×D43—22no—
189C22×D43—24no—
190C22×D43—22no—
191C22×D43—42no—
192C22×D43—42no—
193C22×D43—42no—
194C22×D43—42no—
195C22×D43—42no—
196C22×D43—42no—
197C22×D43—84no—
198C22×D43—84no—
199C22×D43C2×C22⋊C414yes—
200Q8×C43—81no—
201Q8×C43—81no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
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—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43C2×C22⋊C411yescharacteristic
219C2×C4×C43C2×C22⋊C411yescharacteristic
220C2×C4×C43C2×C22⋊C411yescharacteristic
221C2×C4×C43C2×C22⋊C411yescharacteristic
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43C2×C22⋊C414yes—
236C4×D43—84no—
237C4×D43—84no—
238Dic86—84no—
239Dic86—81no—
240Dic86—81no—
241#21827—431nomaximal, Sylow
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43C22×C22⋊C411yescharacteristic
251C22×C43#51912yes—
252C22×C43#53611yescharacteristic
253C22×C43#53612yes—
254C22×C43#53611yescharacteristic
255C2×D43—24no—
256C2×D43—24no—
257C2×D43—24no—
258C2×D43—48no—
259C2×D43—82no—
260C2×D43—84no—
261C2×D43—82no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—42no—
267C4×C43—42no—
268C4×C43—82no—
269C4×C43—82no—
270Dic43—24no—
271Dic43—42no—
272Dic43—42no—
273Dic43—82no—
274Dic43—82no—
275C2×#543—431no—
276#2312—431no—
277#2312—431no—
278#1996—431no—
279#1996—431no—
280#1996—434no—
281#1996—431no—
282#1996D4311yescharacteristic, complemented
283#1819—434no—
284C2×C43—21no—
285C2×C43—22no—
286C2×C43—21no—
287C2×C43—22no—
288C2×C43#231011yescharacteristic
289C2×C43#288311yescharacteristic
290C2×C43#288311yescharacteristic
291D43—44no—
292#543—862no—
293#543—862no—
294#543—862no—
295#543—862no—
296C2×C22⋊Q8—432no—
297C2×C22⋊Q8—431no—
298C2×C22⋊Q8—432no—
299C2×C22⋊Q8—432no—
300C2×C22⋊Q8—432no—
301C2×C22⋊Q8—432no—
302C2×C22⋊Q8C2×D4311yescharacteristic
303C22×C22⋊C4—431no—
304C22×C22⋊C4—432no—
305#388—862no—
306#388—862no—
307#388—862no—
308#388—862no—
309#380—431no—
310#380—432no—
311#380C2×D4311yescharacteristic
312#379—432no—
313#379—432no—
314C4×C22⋊C4—431no—
315C4×C22⋊C4—432no—
316C4×C22⋊C4C2×D4311yescharacteristic
317#342—434no—
318#342—434no—
319#342—434no—
320#342C2×D4314yes—
321C43#2182711yescharacteristic, complemented, Sylow
322C25—431no—
323C22×Q8—432no—
324C22×Q8—431no—
325C22×Q8C4×D4311yescharacteristic
326C23×C4—431no—
327C23×C4—432no—
328C23×C4—432no—
329C23×C4C22×D4311yescharacteristic
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—864no—
335C22⋊Q8—864no—
336C22⋊Q8—864no—
337C22⋊Q8—864no—
338C22⋊Q8—864no—
339C22⋊Q8—864no—
340C22⋊Q8—864no—
341C22⋊Q8—864no—
342C22⋊Q8—864no—
343C22⋊Q8—864no—
344C22⋊Q8—861no—
345C22⋊Q8—861no—
346C22⋊Q8—861no—
347C22⋊Q8—861no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—432no—
350C2×C4⋊C4—432no—
351C2×C4⋊C4—432no—
352C2×C4⋊C4—432no—
353C2×C4⋊C4—431no—
354C2×C4⋊C4—862no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4C4×D4312yes—
357C2×C4⋊C4C4×D4311yescharacteristic
358C2×C22⋊C4—432no—
359C2×C22⋊C4—432no—
360C2×C22⋊C4—432no—
361C2×C22⋊C4—432no—
362C2×C22⋊C4—432no—
363C2×C22⋊C4—432no—
364C2×C22⋊C4—432no—
365C2×C22⋊C4—432no—
366C2×C22⋊C4—432no—
367C2×C22⋊C4—432no—
368C2×C22⋊C4—432no—
369C2×C22⋊C4—864no—
370C2×C22⋊C4—864no—
371C2×C22⋊C4—862no—
372C2×C22⋊C4—862no—
373C2×C22⋊C4—862no—
374C2×C22⋊C4—862no—
375C2×C22⋊C4C22×D4312yes—
376C2×C22⋊C4C22×D4312yes—
377C2×C22⋊C4C22×D4312yes—
378C2×C42—21no—
379C2×C42—862no—
380C2×C42—861no—
381#95—21no—
382#95—21no—
383#95—862no—
384#95—862no—
385#95—861no—
386#95—861no—
387C24—432no—
388C24—432no—
389C24—432no—
390C24—862no—
391C24—862no—
392C24—3441no—
393C24—3441no—
394C24C23×D4311yescharacteristic
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—81no—
398C2×Q8—864no—
399C2×Q8—861no—
400C2×Q8—861no—
401C2×Q8—3441no—
402C2×Q8—3442no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—81no—
406C22×C4—432no—
407C22×C4—432no—
408C22×C4—432no—
409C22×C4—432no—
410C22×C4—432no—
411C22×C4—864no—
412C22×C4—864no—
413C22×C4—862no—
414C22×C4—862no—
415C22×C4—3442no—
416C22×C4—3442no—
417C22×C4—3441no—
418C22×C4C2×C4×D4312yes—
419C22×C4C2×C4×D4312yes—
420C22×C4C2×C4×D4311yescharacteristic
421C22×C4C2×C4×D4311yescharacteristic
422C22×C4D4×D4311yescharacteristic
423C22×C4D4×D4311yescharacteristic
424C22×C4D4×D4311yescharacteristic
425C22×C4D4×D4311yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—81no—
431C4⋊C4—864no—
432C4⋊C4—864no—
433C4⋊C4—864no—
434C4⋊C4—862no—
435C4⋊C4—862no—
436C4⋊C4—861no—
437C4⋊C4—861no—
438C4⋊C4—3442no—
439C4⋊C4—3441no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—434no—
446C22⋊C4—434no—
447C22⋊C4—434no—
448C22⋊C4—434no—
449C22⋊C4—864no—
450C22⋊C4—864no—
451C22⋊C4—862no—
452C22⋊C4—862no—
453C22⋊C4—862no—
454C22⋊C4—862no—
455C22⋊C4—864no—
456C22⋊C4—3442no—
457C22⋊C4—3442no—
458C22⋊C4—3442no—
459C22⋊C4—3442no—
460C42—81no—
461C42—3441no—
462C42—3442no—
463C23—41no—
464C23—41no—
465C23—434no—
466C23—862no—
467C23—864no—
468C23—862no—
469C23—864no—
470C23—3444no—
471C23—3444no—
472C23—1722no—
473C23—1722no—
474C23—1722no—
475C23—1722no—
476C23—1722no—
477C23—1722no—
478C23C22×C4×D4311yescharacteristic
479C23C2×D4×D4311yescharacteristic
480C23C2×D4×D4311yescharacteristic
481C23#1306337212yes—
482C23#1306337312yes—
483Q8—81no—
484Q8—81no—
485Q8—3441no—
486Q8—3441no—
487Q8—3444no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—434no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—3444no—
508C2×C4—3444no—
509C2×C4—1722no—
510C2×C4—1722no—
511C2×C4—1722no—
512C2×C4—1722no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4C22⋊C4×D4311yescharacteristic
521C2×C4C22⋊C4×D4311yescharacteristic
522C2×C4C22⋊C4×D4311yescharacteristic
523C2×C4C22⋊C4×D4311yescharacteristic
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—42no—
531C22—42no—
532C22—864no—
533C22—864no—
534C22—864no—
535C22—3442no—
536C22—3444no—
537C22—3442no—
538C22—1728no—
539C22C2×C22⋊C4×D4311yescharacteristic
540C22#1458337512yes—
541C22#1458346911yescharacteristic
542C22#1458347212yes—
543C22#1458347411yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—42no—
549C4—42no—
550C4—82no—
551C4—82no—
552C4—864no—
553C4—3442no—
554C4—3442no—
555C4—1722no—
556C4—1722no—
557C2—21no—
558C2—22no—
559C2—21no—
560C2—22no—
561C2—1724no—
562C2#1913717811yescharacteristic
563C2#1914305311yescharacteristic
564C2#1914305411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1996C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43C23
cosocleC24×C43C24
hypercenter#1996D43
hypocenterC43#21827
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
4. #19135581C2semidirect
5. #19135580C2semidirect
6. #19135579C2semidirect
7. #19135578C2semidirect
9. C43×#1996C2semidirect
14. C2×#13063305C4semidirect
16. C2×#13063303C4semidirect
17. C2×#13063303C4semidirect
19. C2×#13063301C4semidirect
282. #1996D43semidirect
321. C43#21827semidirect

Maximal subgroups

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

subgroupindex
C2×#145835242
#191371922
#191371902
#191355812
#191355802
#191355792
#191355782
#191346682
C43×#19962
#2182743