Finite Group Databasebeta

← #24990642

Subgroups — #24990642

Order 11008.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137295C211yesmaximal, characteristic
2#19134912C211yesmaximal, characteristic
3C2×#14582634C211yesmaximal, characteristic
4#19132858C211yesmaximal, characteristic, complemented
5#19132473C211yesmaximal, characteristic, complemented
6#19132437C211yesmaximal, characteristic, complemented
7C43×#1852C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×(C22⋊D43)⋊C4—21no—
10C22×Dic43⋊C4—21no—
11C2×#13063245—21no—
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13#14582789—21no—
14#14582782—21no—
15#14582777—21no—
16#14582776—21no—
17#14582770—21no—
18C2×C43⋊#95—21no—
19C2×C43⋊#95C2211yescharacteristic
20C2×C43⋊#95C2211yescharacteristic
21#14582661—21no—
22#14582634C414yescomplemented
23C22×C4⋊C4×C43C2211yescharacteristic
24C2×#107×C43—21no—
25C2×C22⋊C8×C43C2211yescharacteristic
26C43×#380C2211yescharacteristic
27C43×#340—21no—
28C22×D172D411yescharacteristic
29C22×C22⋊D43—21no—
30C23×Dic43—21no—
31C23×Dic43D411yescharacteristic
32C23×Dic43D411yescharacteristic
33C22×C4×D43—21no—
34C22×C43⋊C8—21no—
35#13063299—21no—
36#13063299—21no—
37#13063299C2×C412yes—
38#13063299Q812yes—
39(C22⋊D43)⋊C4—42no—
40(C22⋊D43)⋊C4—42no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—42no—
44C2×Dic43⋊C4—42no—
45C2×Dic43⋊C4—42no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×C4×Dic43—21no—
51#13063245—42no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—42no—
60C43⋊#95C2×C412yescomplemented
61C23×C4×C43—21no—
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—42no—
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43—21no—
70#107×C43—42no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43C2×C412yescomplemented
73#95×C43—21no—
74C24×C43C2×D411yescharacteristic
75C23×D43—21no—
76C22×C4×C43—22no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—41no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×Q811yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C2×C22⋊D43—22no—
94C2×C22⋊D43—22no—
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C2×C22⋊D43—41no—
99C22×Dic43—22no—
100C22×Dic43—22no—
101C22×Dic43—22no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—41no—
109C22×Dic43—41no—
110C22×Dic43—41no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C22×Dic43D812yes—
117C2×D172—21no—
118C2×D172—41no—
119C2×D172—41no—
120C2×D172C4⋊C412yescomplemented
121C2×C4×D43—42no—
122C2×C4×D43—81no—
123C2×C4×D43—81no—
124C2×C8×C43—22no—
125C2×C8×C43—41no—
126C2×C8×C43—41no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—41no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135(C2×D43)⋊C4—22no—
136(C2×D43)⋊C4—22no—
137(C2×D43)⋊C4—42no—
138(C2×D43)⋊C4—81no—
139(C2×D43)⋊C4—81no—
140C4⋊Dic43—21no—
141C4⋊Dic43C4⋊C412yescomplemented
142Dic43⋊C4—42no—
143Dic43⋊C4—48no—
144C4×Dic43—42no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—41no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43C4×D411yescharacteristic
153C23×C43#12011yescharacteristic
154C23×C43C22⋊Q811yescharacteristic
155C23×C43C2×D811yescharacteristic
156C23×C43#13511yescharacteristic
157C23×C43AGL(1,ℤ/8)11yescharacteristic
158C23×C43#13711yescharacteristic
159C22×D43—22no—
160C22×D43—41no—
161C22×D43—41no—
162C22×D43—41no—
163C22×D43—41no—
164C22×D43—41no—
165C22×D43—41no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—42no—
175C2×C4×C43—42no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—42no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—81no—
184C2×C4×C43—81no—
185C2×C4×C43—81no—
186C2×C4×C43—81no—
187C2×C4×C43C2×C4⋊C411yescharacteristic
188C2×C4×C43C4×D411yescharacteristic
189C2×C4×C43C22⋊Q811yescharacteristic
190C2×C4×C43#12311yescharacteristic
191C22⋊D43—42no—
192C22⋊D43—42no—
193C22⋊D43—42no—
194C22⋊D43—42no—
195C2×Dic43—24no—
196C2×Dic43—22no—
197C2×Dic43—22no—
198C2×Dic43—42no—
199C2×Dic43—42no—
200C2×Dic43—42no—
201C2×Dic43—42no—
202C2×Dic43—42no—
203C2×Dic43—42no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—42no—
209C2×Dic43—42no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—81no—
214C2×Dic43—81no—
215D172—42no—
216D172—81no—
217C4×D43—84no—
218C8×C43—42no—
219C43⋊C8—81no—
220#8866—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43#38511yescharacteristic
234C22×C43C4×D811yescharacteristic
235C22×C43#44011yescharacteristic
236C22×C43#44711yescharacteristic
237C22×C43#45211yescharacteristic
238C22×C43#45311yescharacteristic
239C22×C43#45611yescharacteristic
240C22×C43B(4,𝔽2)11yescharacteristic
241C22×C43#45811yescharacteristic
242C22×C43#47411yescharacteristic
243C22×C43#47811yescharacteristic
244C2×D43—42no—
245C2×D43—42no—
246C2×D43—42no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—81no—
250C2×D43—81no—
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—81no—
256C4×C43—82no—
257C4×C43—81no—
258Dic43—44no—
259Dic43—42no—
260Dic43—42no—
261Dic43—81no—
262#2325—431no—
263#1874—431no—
264#1852D4311yescharacteristic, complemented
265C2×#327—431no—
266#1444—431no—
267#1294—431no—
268#1280—431no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43—21no—
272C2×C43—21no—
273C2×C43#159511yescharacteristic
274C2×C43#160311yescharacteristic
275C2×C43#161011yescharacteristic
276C2×C43#161811yescharacteristic
277C2×C43#185911yescharacteristic
278C2×C43#186211yescharacteristic
279C2×C43#186711yescharacteristic
280D43—82no—
281C2×#121—431no—
282C2×C4×D4—861no—
283C22×C4⋊C4—861no—
284C22×C4⋊C4C2×D4311yescharacteristic
285C2×#107—21no—
286C2×#102—861no—
287C2×C22⋊C8—431no—
288C2×C22⋊C8C2×D4311yescharacteristic
289#388—861no—
290#387—861no—
291#386—861no—
292#386—861no—
293#385—861no—
294#380C2×D4311yescharacteristic
295C2×#95—431no—
296C2×#95—431no—
297C2×#95—861no—
298#340—21no—
299#340—861no—
300#327—434no—
301C43#886611yescharacteristic, complemented, Sylow
302C22×D4—431no—
303C22×D4—861no—
304C23×C4—21no—
305C23×C4—431no—
306C23×C4—431no—
307C23×C4—861no—
308C23×C4—861no—
309C23×C4C22×D4311yescharacteristic
310C22×C8—21no—
311C22×C8—861no—
312#121—432no—
313#121—432no—
314#121—861no—
315#121—861no—
316C4×D4—1722no—
317C4×D4—1722no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—431no—
322C2×C4⋊C4—861no—
323C2×C4⋊C4—1722no—
324C2×C4⋊C4—1722no—
325C2×C4⋊C4—1722no—
326C2×C4⋊C4C22⋊D4311yescharacteristic
327C2×C4⋊C4C22⋊D4311yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—861no—
330C2×C22⋊C4—861no—
331C2×C22⋊C4—861no—
332C2×C22⋊C4—861no—
333C2×C42—861no—
334#107—42no—
335#102—1722no—
336C22⋊C8—21no—
337C22⋊C8—861no—
338C22⋊C8—861no—
339C22⋊C8C4×D4312yescomplemented
340#95—21no—
341#95—432no—
342#95—861no—
343#95—861no—
344#95—861no—
345#95—861no—
346#95—861no—
347#95—1722no—
348C24—861no—
349C24D4×D4311yescharacteristic
350C2×D4—432no—
351C2×D4—862no—
352C2×D4—862no—
353C2×D4—861no—
354C2×D4—1721no—
355C2×D4—1721no—
356C2×D4—1721no—
357C2×D4—1721no—
358C2×D4—1721no—
359C2×D4—1721no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—432no—
372C22×C4—861no—
373C22×C4—862no—
374C22×C4—862no—
375C22×C4—862no—
376C22×C4—861no—
377C22×C4—861no—
378C22×C4—861no—
379C22×C4—861no—
380C22×C4—861no—
381C22×C4—3441no—
382C22×C4—3441no—
383C22×C4—1722no—
384C22×C4—1721no—
385C22×C4—1721no—
386C22×C4—1721no—
387C22×C4—1721no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4C2×C4×D4311yescharacteristic
393C22×C4#1062189811yescharacteristic
394C22×C4D4×D4311yescharacteristic
395C22×C4Q8×D4311yescharacteristic
396C22×C4#1062190211yescharacteristic
397C22×C4C2×C22⋊D4311yescharacteristic
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—1721no—
402C2×C8—1721no—
403C2×C8—1721no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—432no—
411C4⋊C4—861no—
412C4⋊C4—1722no—
413C4⋊C4—1728no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—862no—
417C22⋊C4—862no—
418C22⋊C4—3441no—
419C22⋊C4—3441no—
420C22⋊C4—1722no—
421C42—1722no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—862no—
427C23—1721no—
428C23—1721no—
429C23—1721no—
430C23—1721no—
431C23—1721no—
432C23—1721no—
433C23#1306328711yescharacteristic
434C23#1306329311yescharacteristic
435C23#1306330311yescharacteristic
436C23D8×D4311yescharacteristic
437C23#1306334811yescharacteristic
438C23#1306334911yescharacteristic
439C23#1306335711yescharacteristic
440D4—3441no—
441D4—1722no—
442D4—1722no—
443D4—1722no—
444D4—1722no—
445D4—1722no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—864no—
468C2×C4—862no—
469C2×C4—862no—
470C2×C4—3444no—
471C2×C4—3441no—
472C2×C4—3441no—
473C2×C4—1722no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—1722no—
478C2×C4—1722no—
479C2×C4—1722no—
480C2×C4—1722no—
481C2×C4—1722no—
482C2×C4—1721no—
483C2×C4—1721no—
484C2×C4—1721no—
485C2×C4—1722no—
486C2×C4—1721no—
487C2×C4—1722no—
488C2×C4C4⋊C4×D4311yescharacteristic
489C2×C4C4×C22⋊D4311yescharacteristic
490C2×C4#1306330111yescharacteristic
491C2×C4#1306331011yescharacteristic
492C8—42no—
493C8—3441no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—3441no—
507C22—3441no—
508C22—3441no—
509C22—3441no—
510C22—1722no—
511C22—1722no—
512C22—1722no—
513C22#1458277011yescharacteristic
514C22#1458298111yescharacteristic
515C22#1458299811yescharacteristic
516C22#1458303111yescharacteristic
517C22#1458306011yescharacteristic
518C22#1458306511yescharacteristic
519C22#1458308011yescharacteristic
520C22#1458308511yescharacteristic
521C22#1458308811yescharacteristic
522C22#1458317811yescharacteristic
523C22#1458320211yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—82no—
529C4—81no—
530C4—81no—
531C4—3441no—
532C4—1724no—
533C4—1722no—
534C4—1722no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—3442no—
540C2#1913351111yescharacteristic
541C2#1913355711yescharacteristic
542C2#1913359611yescharacteristic
543C2#1913364211yescharacteristic
544C2#1913481811yescharacteristic
545C2#1913483911yescharacteristic
546C2#1913487411yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1852C2
socleC23×C43#120
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1852D43
hypocenterC43#8866
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
4. #19132858C2semidirect
5. #19132473C2semidirect
6. #19132437C2semidirect
7. C43×#1852C2semidirect
22. #14582634C4semidirect
60. C43⋊#95C2×C4semidirect
72. C22⋊C8×C43C2×C4semidirect
120. C2×D172C4⋊C4semidirect
141. C4⋊Dic43C4⋊C4semidirect
264. #1852D43semidirect
301. C43#8866semidirect
339. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191372952
#191349122
C2×#145826342
#191328582
#191324732
#191324372
C43×#18522
#886643