Finite Group Databasebeta

← #24987989

Subgroups — #24987989

Order 11008.

1118 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
1C4×#13063370C211yesmaximal, characteristic
2#19134887C212yesmaximal, complemented
3#19132913C211yesmaximal, characteristic, complemented
4#19132911C212yesmaximal, complemented
5C43×#1869C211yesmaximal, characteristic, complemented
6C2×#13063370C411yescharacteristic
7#14583380—21no—
8#14583378—22no—
9#14583374C411yescharacteristic
10#14583372—21no—
11#14583372C412yes—
12#14583371—22no—
13C4×#10621898—21no—
14C4×#10621900—22no—
15C2×C4×C22⋊D43—21no—
16C2×C4×C22⋊D43C2212yes—
17C4×D4×D43—22no—
18C2×C22⋊(C43⋊C8)C2212yescomplemented
19C2×(C2×D43)⋊C8—22no—
20#14582653—22no—
21#14582625—21no—
22#14582624—22no—
23#14582623—21no—
24#14582622—22no—
25C23×C8×C43C2211yescharacteristic, complemented
26C2×C4×D4×C43C2211yescharacteristic
27C2×C22⋊C8×C43—21no—
28C2×C22⋊C8×C43C2211yescharacteristic, complemented
29C43×#336—21no—
30#13063370—22no—
31#13063370—24no—
32#13063370C814yescomplemented
33C2×#10621898—21no—
34C2×#10621900—22no—
35C22×C22⋊D43—21no—
36C22×C22⋊D43C2×C412yes—
37C2×D4×D43—22no—
38C22×C4×D43—21no—
39C22×C4×D43D412yes—
40C22×C43⋊C8—22no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43#13063290—22no—
44C4×D172—21no—
45C4×D172—21no—
46D4×Dic43—22no—
47D4×Dic43—22no—
48#13063287—22no—
49C4×C22⋊D43—22no—
50C4×C22⋊D43—22no—
51C4×C22⋊D43—22no—
52C4×C22⋊D43—22no—
53C4×C22⋊D43—22no—
54C4×C22⋊D43—22no—
55C4×C22⋊D43—22no—
56C4×C22⋊D43—22no—
57(C22⋊D43)⋊C4—22no—
58(C22⋊D43)⋊C4—22no—
59(C22⋊D43)⋊C4—22no—
60(C22⋊D43)⋊C4—22no—
61#13063284—21no—
62#13063283—22no—
63#13063282—22no—
64#13063281—22no—
65#13063281—22no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4D412yes—
68C4⋊C4×D43—22no—
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43C2×C412yes—
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4D412yes—
73C22⋊C4×D43—22no—
74C22⋊C4×D43—22no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43D412yes—
77C42×D43—22no—
78C22⋊(C43⋊C8)—22no—
79C22⋊(C43⋊C8)—22no—
80(C2×D43)⋊C8—44no—
81C22×D4×C43C2×C411yescharacteristic
82C23×C4×C43D411yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C22×C8×C43—22no—
85C22×C8×C43—21no—
86C22×C8×C43—21no—
87C22×C8×C43—42no—
88C4×D4×C43—22no—
89C4×D4×C43—22no—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C22⋊C4×C43C2×C411yescharacteristic
92C2×C22⋊C4×C43D411yescharacteristic
93C2×C42×C43D411yescharacteristic
94C22⋊C8×C43—22no—
95C22⋊C8×C43—42no—
96C24×C43C22⋊C411yescharacteristic
97C24×C43C22×C411yescharacteristic
98C23×D43—21no—
99C23×D43C22⋊C412yes—
100C2×D4×C43—22no—
101C2×D4×C43—22no—
102C2×D4×C43C2×C812yes—
103C2×D4×C43M1612yes—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—41no—
107C22×C4×C43—41no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43C22⋊C411yescharacteristic
111C22×C4×C43C22⋊C411yescharacteristic
112C22×C4×C43C22⋊C411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D412yes—
115C22×C4×C43C2×D412yes—
116C22×C4×C43C2×D411yescharacteristic
117C2×C22⋊D43—22no—
118C2×C22⋊D43—24no—
119C2×C22⋊D43—24no—
120C2×C22⋊D43—22no—
121C2×C22⋊D43—22no—
122C2×C22⋊D43—22no—
123C2×C22⋊D43—22no—
124C2×C22⋊D43C2×C814yes—
125C2×C22⋊D43M1614yes—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43C22⋊C412yes—
130C22×Dic43C22⋊C412yes—
131C22×Dic43C22⋊C412yes—
132#10621900—28no—
133#10621900—28no—
134D4×D43—28no—
135D4×D43—28no—
136#10621898—24no—
137#10621898—24no—
138C2×D172—21no—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—42no—
145C2×C4×D43—42no—
146C2×C4×D43—81no—
147C2×C4×D43—81no—
148C2×Dic86—21no—
149C2×C8×C43—22no—
150C2×C8×C43—24no—
151C2×C8×C43—42no—
152C2×C8×C43—41no—
153C2×C8×C43—41no—
154C2×C8×C43—41no—
155C2×C8×C43—41no—
156C2×C8×C43—41no—
157C4⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C42×C43—21no—
161C42×C43—21no—
162C22⋊Dic43—22no—
163C22⋊Dic43—22no—
164C22⋊Dic43—22no—
165(C2×D43)⋊C4—22no—
166(C2×D43)⋊C4—22no—
167(C2×D43)⋊C4—22no—
168(C2×D43)⋊C4—22no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171Dic43⋊C4—22no—
172Dic43⋊C4—22no—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175C4×Dic43—22no—
176C4×Dic43—22no—
177C4×Dic43—22no—
178C4×Dic43—22no—
179C4×Dic43—22no—
180C2×C43⋊C8—42no—
181C2×C43⋊C8—42no—
182C2×C43⋊C8—42no—
183C23×C43—21no—
184C23×C43—21no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43C22⋊C812yescomplemented
190C23×C43C2×C22⋊C412yes—
191C23×C43C2×C22⋊C411yescharacteristic
192C23×C43C22×C811yescharacteristic
193C23×C43C2×M1612yes—
194C23×C43C2×M1611yescharacteristic
195C22×D43—22no—
196C22×D43—24no—
197C22×D43—22no—
198C22×D43—42no—
199C22×D43—42no—
200C22×D43—81no—
201C22×D43—81no—
202C22×D43C22⋊C814yescomplemented
203D4×C43—24no—
204D4×C43—24no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—22no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—41no—
214C2×C4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—81no—
220C2×C4×C43C22⋊C812yescomplemented
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12012yes—
224C22⋊D43—28no—
225C22⋊D43—24no—
226C22⋊D43—24no—
227C22⋊D43—24no—
228C22⋊D43—24no—
229C2×Dic43—24no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—81no—
237C2×Dic43—81no—
238C2×Dic43C22⋊C814yescomplemented
239D172—24no—
240C4×D43—28no—
241C4×D43—42no—
242C4×D43—42no—
243C4×D43—82no—
244C4×D43—82no—
245C4×D43—82no—
246Dic86—24no—
247C8×C43—42no—
248C8×C43—81no—
249C43⋊C8—82no—
250#8316—431nomaximal, Sylow
251C22×C43—22no—
252C22×C43—21no—
253C22×C43—22no—
254C22×C43—21no—
255C22×C43—22no—
256C22×C43—41no—
257C22×C43—42no—
258C22×C43—41no—
259C22×C43—42no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—81no—
263C22×C43#37911yescharacteristic
264C22×C43C2×C22⋊C812yes—
265C22×C43C2×C22⋊C811yescharacteristic
266C22×C43#40712yes—
267C22×C43#40711yescharacteristic
268C2×D43—24no—
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—44no—
272C2×D43—82no—
273C2×D43—84no—
274C4×C43—22no—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43B(4,𝔽2)11yescharacteristic
280C4×C43#45811yescharacteristic
281Dic43—24no—
282Dic43—42no—
283Dic43—42no—
284C4×H(5,𝔽2)—431no—
285#1869—432no—
286#1869D4311yescharacteristic, complemented
287#1459—432no—
288#1459—431no—
289C2×C43—22no—
290C2×C43—22no—
291C2×C43—21no—
292C2×C43—21no—
293C2×C43—42no—
294C2×C43#177911yescharacteristic
295C2×C43#179011yescharacteristic
296C2×C43#179111yescharacteristic
297D43—44no—
298C2×H(5,𝔽2)—431no—
299C23×C8C2×D4311yescharacteristic, complemented
300#520—862no—
301#520—861no—
302#518—431no—
303#518—432no—
304#518—862no—
305#518—861no—
306C4×#41—862no—
307C4×#41—861no—
308C2×C4×D4—432no—
309C2×C4×D4—862no—
310C2×C4×D4—861no—
311C2×C4×D4C2×D4311yescharacteristic
312C2×C22⋊C8—21no—
313C2×C22⋊C8—432no—
314C2×C22⋊C8—862no—
315C2×C22⋊C8C2×D4311yescharacteristic, complemented
316#336—21no—
317#336—862no—
318#324—862no—
319#324—861no—
320#323—862no—
321#323—861no—
322C43#831611yescharacteristic, complemented, Sylow
323H(5,𝔽2)—434no—
324H(5,𝔽2)—864no—
325H(5,𝔽2)—862no—
326C2×#41—862no—
327C2×#41—861no—
328C22×D4—432no—
329C22×D4—862no—
330C22×D4—861no—
331C22×D4C4×D4311yescharacteristic
332C23×C4—432no—
333C23×C4—861no—
334C23×C4C22⋊D4311yescharacteristic
335C23×C4C22×D4311yescharacteristic
336C22×C8—22no—
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—42no—
340C22×C8—862no—
341C4×Q8—861no—
342C4×Q8—861no—
343C4×Q8—862no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—861no—
347C4×D4—861no—
348C4×D4—862no—
349C4×D4—862no—
350C4×D4—862no—
351C4×D4—862no—
352C4×D4—862no—
353C4×D4—862no—
354C4×D4—862no—
355C4×D4—862no—
356C4×D4—862no—
357C4×D4—862no—
358C4×D4—862no—
359C4×D4—862no—
360C4×D4—862no—
361C4×D4—862no—
362C4×D4—862no—
363#117—862no—
364#117—862no—
365#117—862no—
366#117—862no—
367#117—861no—
368C2×C4⋊C4—432no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4D17211yescharacteristic
372C2×C22⋊C4—432no—
373C2×C22⋊C4—432no—
374C2×C22⋊C4—862no—
375C2×C22⋊C4—862no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4C4×D4311yescharacteristic
379C2×C22⋊C4D17211yescharacteristic
380C2×C42—432no—
381C2×C42—862no—
382C2×C42—861no—
383C2×C42C22⋊D4311yescharacteristic
384C22⋊C8—22no—
385C22⋊C8—42no—
386C22⋊C8—862no—
387C22⋊C8—862no—
388C22⋊C8—1724no—
389C24—432no—
390C24—861no—
391C24(C2×D43)⋊C411yescharacteristic
392C24C2×C4×D4311yescharacteristic
393#41—864no—
394#41—868no—
395#41—868no—
396#41—864no—
397C2×Q8—861no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—434no—
401C2×D4—434no—
402C2×D4—861no—
403C2×D4—868no—
404C2×D4—868no—
405C2×D4—862no—
406C2×D4—864no—
407C2×D4—864no—
408C2×D4—862no—
409C2×D4—862no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4C8×D4312yes—
413C2×D4#1062187212yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—432no—
421C22×C4—432no—
422C22×C4—432no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—3441no—
432C22×C4—3441no—
433C22×C4—1722no—
434C22×C4—1722no—
435C22×C4(C2×D43)⋊C411yescharacteristic
436C22×C4(C2×D43)⋊C411yescharacteristic
437C22×C4(C2×D43)⋊C411yescharacteristic
438C22×C4C2×D17211yescharacteristic
439C22×C4D4×D4312yes—
440C22×C4D4×D4312yes—
441C22×C4C2×C22⋊D4311yescharacteristic
442C2×C8—22no—
443C2×C8—24no—
444C2×C8—41no—
445C2×C8—42no—
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—41no—
449C2×C8—41no—
450C2×C8—1722no—
451C2×C8—1722no—
452C2×C8—1722no—
453C4⋊C4—22no—
454C4⋊C4—862no—
455C4⋊C4—861no—
456C4⋊C4—862no—
457C4⋊C4—861no—
458C4⋊C4—862no—
459C4⋊C4—862no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—862no—
463C22⋊C4—862no—
464C22⋊C4—862no—
465C22⋊C4—862no—
466C22⋊C4—862no—
467C22⋊C4—862no—
468C22⋊C4—862no—
469C42—21no—
470C42—21no—
471C42—862no—
472C42—862no—
473C42—862no—
474C42—862no—
475C42—862no—
476C23—21no—
477C23—21no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—434no—
483C23—864no—
484C23—862no—
485C23—862no—
486C23—3441no—
487C23—3441no—
488C23—1722no—
489C23—1722no—
490C23(C2×D43)⋊C812yescomplemented
491C23C22⋊C4×D4312yes—
492C23C2×(C2×D43)⋊C411yescharacteristic
493C23C2×C8×D4311yescharacteristic
494C23M16×D4312yes—
495C23C2×#1062187211yescharacteristic
496Q8—864no—
497D4—24no—
498D4—24no—
499D4—864no—
500D4—868no—
501D4—864no—
502D4—864no—
503D4—864no—
504D4—864no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4—434no—
521C2×C4—868no—
522C2×C4—864no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—3442no—
528C2×C4—3442no—
529C2×C4—3442no—
530C2×C4—3441no—
531C2×C4—3441no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4(C2×D43)⋊C812yescomplemented
537C2×C4#1306329311yescharacteristic
538C2×C4#1306329311yescharacteristic
539C2×C4#1306329512yes—
540C8—42no—
541C8—81no—
542C8—3442no—
543C22—21no—
544C22—22no—
545C22—21no—
546C22—22no—
547C22—22no—
548C22—41no—
549C22—42no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—41no—
554C22—81no—
555C22—864no—
556C22—3442no—
557C22—3444no—
558C22—1724no—
559C22—1722no—
560C22—1722no—
561C22#1458275411yescharacteristic
562C22C22⋊C8×D4312yes—
563C22C2×(C2×D43)⋊C811yescharacteristic
564C22#1458286112yes—
565C22#1458286211yescharacteristic
566C4—22no—
567C4—21no—
568C4—22no—
569C4—41no—
570C4—41no—
571C4—864no—
572C4—1722no—
573C4—1722no—
574C4#1458308511yescharacteristic
575C4#1458308811yescharacteristic
576C2—21no—
577C2—21no—
578C2—22no—
579C2—22no—
580C2—42no—
581C2—1724no—
582C2#1913450411yescharacteristic
583C2#1913454211yescharacteristic
584C2#1913454511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#1869C2
socleC22×C43#379
prime radicalC2×#13063370C4
cosocleC23×C4×C43C23
hypercenter#1869D43
hypocenterC43#8316
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #19134887C2semidirect
3. #19132913C2semidirect
4. #19132911C2semidirect
5. C43×#1869C2semidirect
18. C2×C22⋊(C43⋊C8)C22semidirect
25. C23×C8×C43C22semidirect
28. C2×C22⋊C8×C43C22semidirect
32. #13063370C8semidirect
189. C23×C43C22⋊C8semidirect
202. C22×D43C22⋊C8semidirect
220. C2×C4×C43C22⋊C8semidirect
238. C2×Dic43C22⋊C8semidirect
286. #1869D43semidirect
299. C23×C8C2×D43semidirect
315. C2×C22⋊C8C2×D43semidirect
322. C43#8316semidirect
490. C23(C2×D43)⋊C8semidirect
536. C2×C4(C2×D43)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×#130633702
#191348872
#191329132
#191329112
C43×#18692
#831643