Finite Group Databasebeta

← #24988014

Subgroups — #24988014

Order 11008.

1146 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583371C211yesmaximal, characteristic
2#19132987C211yesmaximal, characteristic, complemented
3#19132986C211yesmaximal, characteristic, complemented
4#19132985C211yesmaximal, characteristic, complemented
5#19132907C211yesmaximal, characteristic, complemented
6#19132907C211yesmaximal, characteristic, complemented
7C43×#1478C211yesmaximal, characteristic, complemented
8C22×D4×D43C411yescharacteristic
9#14583371—22no—
10#14583371—22no—
11#14583371—22no—
12#14583371—22no—
13C2×C4×D172C2211yescharacteristic
14C2×D4×Dic43C411yescharacteristic
15C2×#13063287C411yescharacteristic
16C2×C4×C22⋊D43—21no—
17C2×(C22⋊D43)⋊C4—21no—
18C2×#13063283C411yescharacteristic
19C2×#13063282C2211yescharacteristic
20C22×(C2×D43)⋊C4—21no—
21C2×C22⋊C4×D43—21no—
22#14582952C2211yescharacteristic, complemented
23#14582952C2211yescharacteristic, complemented
24#14582628—22no—
25D4⋊(C43⋊C8)—22no—
26#14582626—22no—
27#14582624—21no—
28#14582624—21no—
29#14582622—21no—
30#14582622—21no—
31C2×C4×D4×C43C2211yescharacteristic
32C43×#431C2211yescharacteristic, complemented
33C43×#431C2211yescharacteristic, complemented
34C43×D4⋊C8—22no—
35C24×D43—21no—
36C22×D172C2×C411yescharacteristic
37C22×C22⋊D43—21no—
38C2×D4×D43—22no—
39C2×D4×D43—22no—
40C2×D4×D43—22no—
41C2×D4×D43—22no—
42C2×D4×D43—22no—
43C2×D4×D43C814yescomplemented
44C23×Dic43—21no—
45C22×C4×D43—21no—
46C22×C4×D43—21no—
47C22×C4×D43C2×C411yescharacteristic
48C4×D172—21no—
49C4×D172—21no—
50C4×D172D412yes—
51C4×D172D412yes—
52D4×Dic43—22no—
53D4×Dic43—22no—
54#13063287—22no—
55#13063287—22no—
56C4×C22⋊D43—24no—
57C4×C22⋊D43—24no—
58(C22⋊D43)⋊C4—24no—
59(C22⋊D43)⋊C4—24no—
60#13063283—22no—
61#13063283—22no—
62#13063282—21no—
63#13063282—21no—
64#13063282—21no—
65#13063282—21no—
66C2×C4⋊Dic43C2×C411yescharacteristic
67C2×Dic43⋊C4D411yescharacteristic
68C2×Dic43⋊C4D411yescharacteristic
69C2×C22⋊Dic43—21no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4D411yescharacteristic
76C2×(C2×D43)⋊C4D411yescharacteristic
77C22⋊C4×D43—24no—
78C22⋊C4×D43—24no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43C2×C411yescharacteristic
81C4⋊(C43⋊C8)—21no—
82C4⋊(C43⋊C8)—21no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)—21no—
85C4×C43⋊C8—21no—
86C4×C43⋊C8—21no—
87C22×D4×C43C2×C411yescharacteristic
88C23×C4×C43—21no—
89C4×D4×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43D412yes—
92C4×D4×C43D412yes—
93C2×C4⋊C4×C43C2×C411yescharacteristic
94C2×C22⋊C4×C43—21no—
95C2×C42×C43C2311yescharacteristic
96C4⋊C8×C43—21no—
97C4⋊C8×C43—21no—
98C22⋊C8×C43—21no—
99C22⋊C8×C43—21no—
100C4×C8×C43—21no—
101C4×C8×C43—21no—
102C24×C43—21no—
103C23×D43—21no—
104C23×D43—24no—
105C23×D43—24no—
106C23×D43—24no—
107C23×D43—82no—
108C23×D43—82no—
109C23×D43C22⋊C411yescharacteristic
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43C22⋊C412yes—
114C2×D4×C43C2×C812yes—
115C2×D4×C43M1612yes—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—82no—
120C22×C4×C43C22×C411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—24no—
124C2×C22⋊D43—24no—
125C2×C22⋊D43—24no—
126C22×Dic43—24no—
127C22×Dic43—21no—
128C22×Dic43—82no—
129C22×Dic43C22⋊C411yescharacteristic
130C22×Dic43C22⋊C411yescharacteristic
131C22×Dic43C22⋊C411yescharacteristic
132D4×D43—28no—
133D4×D43—28no—
134D4×D43—28no—
135D4×D43—28no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172C22⋊C412yes—
140C2×D172C2×C812yes—
141C2×D172M1612yes—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—24no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—82no—
150C2×C4×D43—82no—
151C2×C4×D43C2×C812yes—
152C2×C4×D43M1612yes—
153C2×C8×C43—41no—
154C2×C8×C43—41no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43C22⋊C412yes—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C42×C43C2×D411yescharacteristic
160C42×C43C2×D411yescharacteristic
161C42×C43C2×D411yescharacteristic
162C42×C43C2×D411yescharacteristic
163C22⋊Dic43—24no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—21no—
167(C2×D43)⋊C4—21no—
168(C2×D43)⋊C4—21no—
169(C2×D43)⋊C4—21no—
170(C2×D43)⋊C4—22no—
171(C2×D43)⋊C4—22no—
172C4⋊Dic43—21no—
173C4⋊Dic43C22⋊C412yes—
174Dic43⋊C4—21no—
175Dic43⋊C4—21no—
176Dic43⋊C4—21no—
177Dic43⋊C4—21no—
178C4×Dic43—24no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C2×C43⋊C8—41no—
182C2×C43⋊C8—41no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43C2×C22⋊C411yescharacteristic
189C22×D43—21no—
190C22×D43—22no—
191C22×D43—22no—
192C22×D43—21no—
193C22×D43—22no—
194C22×D43—216no—
195C22×D43—42no—
196C22×D43—42no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—88no—
200C22×D43—88no—
201C22×D43—84no—
202C22×D43—84no—
203C22×D43C22⋊C812yes—
204D4×C43—22no—
205D4×C43—22no—
206D4×C43—22no—
207D4×C43C22⋊C814yes—
208C2×C4×C43—22no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—42no—
212C2×C4×C43—82no—
213C2×C4×C43—82no—
214C2×C4×C43C2×C22⋊C411yescharacteristic
215C2×C4×C43C2×C22⋊C411yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#12011yescharacteristic
220C2×C4×C43C22×C811yescharacteristic
221C2×C4×C43C2×M1611yescharacteristic
222C2×C4×C43C2×M1611yescharacteristic
223C2×C4×C43C2×M1611yescharacteristic
224C22⋊D43—216no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—22no—
230C2×Dic43—42no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—84no—
234C2×Dic43C22⋊C812yes—
235D172—22no—
236D172—22no—
237D172—22no—
238D172C22⋊C814yes—
239C4×D43—22no—
240C4×D43—22no—
241C4×D43—22no—
242C4×D43—22no—
243C4×D43—82no—
244C4×D43—82no—
245C4×D43—84no—
246C8×C43—81no—
247C8×C43—81no—
248C43⋊C8—81no—
249C43⋊C8—81no—
250#8322—431nomaximal, Sylow
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—24no—
254C22×C43—44no—
255C22×C43—44no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43#37911yescharacteristic
259C22×C43C2×C22⋊C811yescharacteristic
260C22×C43#40711yescharacteristic
261C2×D43—22no—
262C2×D43—24no—
263C2×D43—44no—
264C2×D43—44no—
265C2×D43—42no—
266C2×D43—42no—
267C2×D43—42no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—42no—
271C2×D43—816no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—42no—
277C4×C43C2×C22⋊C811yescharacteristic
278C4×C43C2×C22⋊C811yescharacteristic
279C4×C43#40711yescharacteristic
280C4×C43#40711yescharacteristic
281Dic43—22no—
282Dic43—41no—
283Dic43—42no—
284Dic43—41no—
285C2×#518—431no—
286#1478—431no—
287#1478—431no—
288#1478—431no—
289#1478D4311yescharacteristic, complemented
290#1458—431no—
291#1458—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—44no—
295C2×C43#177911yescharacteristic
296C2×C43#179511yescharacteristic
297C2×C43#179511yescharacteristic
298D43—44no—
299D43—42no—
300C23×D4—431no—
301#518—862no—
302#518—862no—
303#518—862no—
304#518—862no—
305C2×C4×D4—431no—
306C2×C4×D4—431no—
307C2×C4×D4—431no—
308C2×C4×D4—861no—
309C2×C4×D4—861no—
310C2×C4×D4C2×D4311yescharacteristic
311C2×#117—431no—
312C2×#117—431no—
313C22×C22⋊C4—861no—
314C22×C22⋊C4—861no—
315#431—431no—
316#431—431no—
317#431C2×D4311yescharacteristic, complemented
318#431C2×D4311yescharacteristic, complemented
319D4⋊C8—22no—
320D4⋊C8—862no—
321D4⋊C8—862no—
322D4⋊C8—862no—
323#324—861no—
324#324—861no—
325#323—861no—
326#323—861no—
327C43#832211yescharacteristic, complemented, Sylow
328C25—861no—
329C22×D4—434no—
330C22×D4—431no—
331C22×D4—862no—
332C22×D4—861no—
333C22×D4—862no—
334C22×D4—862no—
335C22×D4—862no—
336C22×D4—862no—
337C22×D4C4×D4311yescharacteristic
338C23×C4—21no—
339C23×C4—431no—
340C23×C4—861no—
341C23×C4—861no—
342C23×C4—861no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—432no—
346C4×D4—432no—
347C4×D4—864no—
348C4×D4—864no—
349C4×D4—862no—
350C4×D4—862no—
351C4×D4—864no—
352C4×D4—864no—
353C4×D4—862no—
354C4×D4—862no—
355C4×D4—861no—
356C4×D4—861no—
357C4×D4D17212yes—
358C4×D4C22⋊D4312yes—
359#117—862no—
360#117—862no—
361#117—861no—
362#117—861no—
363#117—861no—
364#117—861no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4C4×D4311yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—431no—
371C2×C22⋊C4—431no—
372C2×C22⋊C4—864no—
373C2×C22⋊C4—864no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C22⋊C4—864no—
377C2×C22⋊C4—864no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C42—431no—
381C2×C42—861no—
382C2×C42C22×D4311yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—861no—
386C4⋊C8—861no—
387C22⋊C8—21no—
388C22⋊C8—21no—
389C22⋊C8—861no—
390C22⋊C8—861no—
391C4×C8—21no—
392C4×C8—21no—
393C4×C8—861no—
394C4×C8—861no—
395C24—21no—
396C24—431no—
397C24—864no—
398C24—864no—
399C24—864no—
400C24—861no—
401C24—3442no—
402C24—3442no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—432no—
407C2×D4—432no—
408C2×D4—432no—
409C2×D4—864no—
410C2×D4—868no—
411C2×D4—868no—
412C2×D4—868no—
413C2×D4—864no—
414C2×D4—864no—
415C2×D4—868no—
416C2×D4—861no—
417C2×D4—861no—
418C2×D4—861no—
419C2×D4C8×D4312yes—
420C2×D4#1062187212yes—
421C2×D4(C2×D43)⋊C412yes—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—82no—
426C22×C4—431no—
427C22×C4—432no—
428C22×C4—432no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—864no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—864no—
437C22×C4—861no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—3442no—
441C22×C4—3442no—
442C22×C4—3442no—
443C22×C4C2×C4×D4311yescharacteristic
444C22×C4D4×D4311yescharacteristic
445C22×C4D4×D4311yescharacteristic
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—1721no—
449C2×C8—1721no—
450C4⋊C4—21no—
451C4⋊C4—432no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4(C2×D43)⋊C412yes—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—864no—
461C22⋊C4—864no—
462C22⋊C4—864no—
463C22⋊C4—861no—
464C22⋊C4—861no—
465C22⋊C4—862no—
466C22⋊C4—861no—
467C22⋊C4—861no—
468C22⋊C4—862no—
469C42—864no—
470C42—861no—
471C42—861no—
472C42C2×D17211yescharacteristic
473C42D4×D4311yescharacteristic
474C42D4×D4311yescharacteristic
475C42C2×C22⋊D4311yescharacteristic
476C23—22no—
477C23—22no—
478C23—22no—
479C23—42no—
480C23—42no—
481C23—432no—
482C23—8616no—
483C23—862no—
484C23—861no—
485C23—862no—
486C23—861no—
487C23—862no—
488C23—3448no—
489C23—3448no—
490C23—3444no—
491C23—3444no—
492C23—1721no—
493C23—1721no—
494C23—1722no—
495C23—1722no—
496C23C22⋊C4×D4311yescharacteristic
497D4—22no—
498D4—22no—
499D4—22no—
500D4—434no—
501D4—8616no—
502D4—862no—
503D4—862no—
504D4—862no—
505D4(C2×D43)⋊C814yes—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—432no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—3442no—
523C2×C4—3442no—
524C2×C4—3444no—
525C2×C4—3444no—
526C2×C4—1722no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4C22⋊C4×D4311yescharacteristic
530C2×C4C2×(C2×D43)⋊C411yescharacteristic
531C2×C4#1306329311yescharacteristic
532C2×C4#1306329311yescharacteristic
533C2×C4#1306329511yescharacteristic
534C2×C4#1306329511yescharacteristic
535C2×C4C2×C8×D4311yescharacteristic
536C2×C4M16×D4311yescharacteristic
537C2×C4M16×D4311yescharacteristic
538C2×C4C2×#1062187211yescharacteristic
539C8—81no—
540C8—81no—
541C8—3441no—
542C8—3441no—
543C22—21no—
544C22—21no—
545C22—24no—
546C22—44no—
547C22—44no—
548C22—42no—
549C22—42no—
550C22—862no—
551C22—864no—
552C22—34416no—
553C22—1722no—
554C22—1722no—
555C22—1724no—
556C22—1724no—
557C22—1722no—
558C22—1721no—
559C22—1722no—
560C22—1721no—
561C22#1458275411yescharacteristic
562C22C22⋊C8×D4311yescharacteristic
563C22#1458286111yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—42no—
569C4—862no—
570C4—1721no—
571C4—1722no—
572C4—1721no—
573C4C22⋊C8×D4311yescharacteristic
574C4C2×(C2×D43)⋊C811yescharacteristic
575C4#1458286111yescharacteristic
576C4#1458286211yescharacteristic
577C2—21no—
578C2—21no—
579C2—44no—
580C2—1722no—
581C2—1724no—
582C2#1913450411yescharacteristic
583C2#1913456211yescharacteristic
584C2#1913456411yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1478C2
socleC22×C43#379
prime radicalC22×D4×D43C4
cosocleC2×C42×C43C23
hypercenter#1478D43
hypocenterC43#8322
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #19132987C2semidirect
3. #19132986C2semidirect
4. #19132985C2semidirect
5. #19132907C2semidirect
6. #19132907C2semidirect
7. C43×#1478C2semidirect
22. #14582952C22semidirect
23. #14582952C22semidirect
32. C43×#431C22semidirect
33. C43×#431C22semidirect
43. C2×D4×D43C8semidirect
289. #1478D43semidirect
317. #431C2×D43semidirect
318. #431C2×D43semidirect
327. C43#8322semidirect

Maximal subgroups

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

subgroupindex
C2×#145833712
#191329872
#191329862
#191329852
#191329072
C43×#14782
#832243