Finite Group Databasebeta

← #24988380

Subgroups — #24988380

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134898C212yesmaximal, complemented
2#19134893C211yesmaximal, characteristic, complemented
3C4×#13063240C211yesmaximal, characteristic, complemented
4#19133086C212yesmaximal, complemented
5C43×#3459C211yesmaximal, characteristic
6C22×#10621877C2211yescharacteristic, complemented
7C2×#13063252—22no—
8C2×#13063240—21no—
9C2×C22⋊(C43⋊C8)—21no—
10C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
11C4×C22⋊Dic43C2212yescomplemented
12#14582666—21no—
13#14582658—22no—
14#14582654—21no—
15#14582636—22no—
16#14582633—22no—
17C43×#543C411yescharacteristic, complemented
18C43×#539—22no—
19C43×#539C412yescomplemented
20C43×#538—22no—
21C43×#538—21no—
22C43×#534—21no—
23C43×#534C411yescharacteristic, complemented
24C43×#529—22no—
25C43×#529—21no—
26C43×#525—22no—
27C43×#525C2212yes—
28C2×C4×D4×C43—21no—
29C2×C4×D4×C43C2211yescharacteristic
30C2×#10621877—22no—
31C2×#10621877—42no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34C2×C22⋊Dic43—22no—
35C2×C4×Dic43—22no—
36#13063252—44no—
37#13063240—24no—
38C22⋊(C43⋊C8)—22no—
39C22⋊(C43⋊C8)—42no—
40C43⋊#95—22no—
41C2×#41×C43D412yes—
42C22×D4×C43—21no—
43C22×D4×C43D411yescharacteristic
44C23×C4×C43—21no—
45C23×C4×C43D411yescharacteristic
46C23×C4×C43C2311yescharacteristic
47#126×C43—22no—
48#126×C43—22no—
49#126×C43—22no—
50#125×C43—21no—
51#125×C43—22no—
52#124×C43—22no—
53#124×C43—21no—
54#123×C43—22no—
55#123×C43—22no—
56#123×C43—22no—
57#123×C43—22no—
58#123×C43—22no—
59#123×C43—22no—
60C22⋊Q8×C43—22no—
61C22⋊Q8×C43—22no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—22no—
64C22⋊Q8×C43C2×C412yes—
65C22⋊Q8×C43D412yes—
66#121×C43—22no—
67#121×C43—22no—
68#121×C43—22no—
69#121×C43—21no—
70#121×C43C2×C412yes—
71#121×C43D412yes—
72#120×C43—22no—
73#120×C43—22no—
74#120×C43—22no—
75C4×Q8×C43—21no—
76C4×D4×C43—22no—
77C4×D4×C43—22no—
78C4×D4×C43—21no—
79C4×D4×C43—22no—
80C4×D4×C43—22no—
81C4×D4×C43—22no—
82C4×D4×C43—22no—
83C4×D4×C43—22no—
84#117×C43—22no—
85#117×C43D412yes—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43C2×C411yescharacteristic
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43C2×C411yescharacteristic
91C2×C22⋊C4×C43D411yescharacteristic
92C2×C42×C43—21no—
93C2×C42×C43D411yescharacteristic
94C24×C43—21no—
95C24×C43C22⋊C411yescharacteristic
96C24×C43C2×D411yescharacteristic
97#41×C43—42no—
98#41×C43—42no—
99C2×Q8×C43—21no—
100C2×Q8×C43C22⋊C412yes—
101C2×D4×C43—22no—
102C2×D4×C43—21no—
103C2×D4×C43—22no—
104C2×D4×C43—22no—
105C2×D4×C43—22no—
106C2×D4×C43—22no—
107C2×D4×C43—22no—
108C2×D4×C43—41no—
109C2×D4×C43—42no—
110C2×D4×C43—42no—
111C2×D4×C43C22⋊C412yes—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—81no—
124C22×C4×C43—81no—
125C22×C4×C43C22⋊C411yescharacteristic
126C22×C4×C43C22⋊C411yescharacteristic
127C22×C4×C43C22⋊C411yescharacteristic
128C22×C4×C43C22×C411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D412yes—
132C22×Dic43—42no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43C22⋊C412yes—
143C4⋊C4×C43C22⋊C412yes—
144C22⋊C4×C43—22no—
145C22⋊C4×C43—22no—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—22no—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—22no—
153C22⋊C4×C43—22no—
154C22⋊C4×C43—22no—
155C22⋊C4×C43—22no—
156C42×C43—22no—
157C42×C43—22no—
158C42×C43—21no—
159C42×C43—21no—
160C22⋊Dic43—24no—
161C22⋊Dic43—42no—
162C4×Dic43—42no—
163C4×Dic43—42no—
164#10621877—24no—
165#10621877—42no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8—41no—
168C2×C43⋊C8—41no—
169C2×C43⋊C8—41no—
170C2×C43⋊C8—41no—
171C2×C43⋊C8—41no—
172C23×C43—21no—
173C23×C43—21no—
174C23×C43—21no—
175C23×C43—21no—
176C23×C43—22no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—42no—
182C23×C43—81no—
183C23×C43—81no—
184C23×C43#10412yescomplemented
185C23×C43C2×C22⋊C411yescharacteristic
186C23×C43#12012yes—
187Q8×C43—42no—
188Q8×C43—81no—
189D4×C43—42no—
190D4×C43—44no—
191D4×C43—44no—
192D4×C43—42no—
193D4×C43—42no—
194D4×C43—82no—
195D4×C43—82no—
196D4×C43—81no—
197C2×C4×C43—21no—
198C2×C4×C43—22no—
199C2×C4×C43—21no—
200C2×C4×C43—22no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—21no—
206C2×C4×C43—22no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—41no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—81no—
219C2×C4×C43—81no—
220C2×C4×C43—82no—
221C2×C4×C43—81no—
222C2×C4×C43C2×C22⋊C412yes—
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43#12011yescharacteristic
225C2×Dic43—44no—
226C2×Dic43—82no—
227C2×Dic43—82no—
228C43⋊C8—42no—
229C43⋊C8—81no—
230#8399—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—22no—
234C22×C43—22no—
235C22×C43—22no—
236C22×C43—22no—
237C22×C43—42no—
238C22×C43—41no—
239C22×C43—41no—
240C22×C43—42no—
241C22×C43—42no—
242C22×C43—42no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43—81no—
246C22×C43—84no—
247C22×C43#37911yescharacteristic
248C22×C43C2×#10411yescharacteristic
249C22×C43#42111yescharacteristic
250C4×C43—21no—
251C4×C43—22no—
252C4×C43—41no—
253C4×C43—42no—
254C4×C43—41no—
255C4×C43—42no—
256C4×C43—41no—
257C4×C43—42no—
258C4×C43B(4,𝔽2)11yescharacteristic
259C4×C43#45811yescharacteristic
260Dic43—84no—
261#3459D4311yescharacteristic
262#1871—432no—
263#1870—431no—
264C4×#99—431no—
265#1501—432no—
266C2×C43—21no—
267C2×C43—21no—
268C2×C43—42no—
269C2×C43—42no—
270C2×C43—82no—
271C2×C43#178911yescharacteristic
272C2×C43#179011yescharacteristic
273C2×C43#179411yescharacteristic
274C22×M16—431no—
275#543Dic4311yescharacteristic, complemented
276#539—22no—
277#539Dic4312yescomplemented
278#538—22no—
279#538—21no—
280#534—21no—
281#534Dic4311yescharacteristic, complemented
282#529—22no—
283#529—21no—
284#525—22no—
285#525C2×D4312yes—
286C2×C4×D4—21no—
287C2×C4×D4C2×D4311yescharacteristic
288C2×#104—862no—
289C2×#99—861no—
290C2×C22⋊C8—431no—
291C2×C22⋊C8—861no—
292C4×C22⋊C4—432no—
293#342—861no—
294#339—862no—
295#336—861no—
296#328—862no—
297#327—862no—
298C43#839911yescharacteristic, complemented, Sylow
299C2×#41C22⋊D4312yes—
300C22×D4—21no—
301C22×D4C22⋊D4311yescharacteristic
302C23×C4—21no—
303C23×C4C22⋊D4311yescharacteristic
304C23×C4C22×D4311yescharacteristic
305C2×M16—862no—
306C2×M16—1722no—
307C22×C8—861no—
308C22×C8—861no—
309#126—22no—
310#126—22no—
311#126—22no—
312#125—21no—
313#125—22no—
314#124—22no—
315#124—21no—
316#123—22no—
317#123—22no—
318#123—22no—
319#123—22no—
320#123—22no—
321#123—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—21no—
325C22⋊Q8—22no—
326C22⋊Q8C2×Dic4312yes—
327C22⋊Q8C22⋊D4312yes—
328#121—22no—
329#121—22no—
330#121—22no—
331#121—21no—
332#121C2×Dic4312yes—
333#121C22⋊D4312yes—
334#120—22no—
335#120—22no—
336#120—22no—
337C4×Q8—21no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—21no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346#117—22no—
347#117C22⋊D4312yes—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C2×Dic4311yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—862no—
353C2×C22⋊C4C2×Dic4311yescharacteristic
354C2×C22⋊C4C22⋊D4311yescharacteristic
355C2×C42—21no—
356C2×C42—862no—
357C2×C42C22⋊D4311yescharacteristic
358#104—1724no—
359#99—864no—
360C22⋊C8—862no—
361C22⋊C8—1722no—
362#95—862no—
363C24—21no—
364C24C22⋊Dic4311yescharacteristic
365C24C2×C22⋊D4311yescharacteristic
366#41—42no—
367#41—42no—
368C2×Q8—21no—
369C2×Q8C22⋊Dic4312yes—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—41no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4C22⋊Dic4312yes—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—81no—
393C22×C4—81no—
394C22×C4—1722no—
395C22×C4C22⋊Dic4311yescharacteristic
396C22×C4C22⋊Dic4311yescharacteristic
397C22×C4C22⋊Dic4311yescharacteristic
398C22×C4C22×Dic4311yescharacteristic
399C22×C4C2×C22⋊D4312yes—
400C22×C4C2×C22⋊D4311yescharacteristic
401C22×C4C2×C22⋊D4312yes—
402M16—864no—
403M16—1722no—
404C2×C8—862no—
405C2×C8—1721no—
406C2×C8—1721no—
407C2×C8—1721no—
408C2×C8—1721no—
409C2×C8—1721no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4C22⋊Dic4312yes—
420C4⋊C4C22⋊Dic4312yes—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—864no—
434C22⋊C4—1722no—
435C42—22no—
436C42—21no—
437C42—22no—
438C42—21no—
439C42—1722no—
440C42—1722no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—81no—
452C23—81no—
453C23#1306325212yescomplemented
454C23C2×C22⋊Dic4311yescharacteristic
455C23#1306329412yes—
456Q8—42no—
457Q8—81no—
458D4—42no—
459D4—44no—
460D4—44no—
461D4—42no—
462D4—42no—
463D4—82no—
464D4—82no—
465D4—81no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—81no—
488C2×C4—82no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—3442no—
492C2×C4—3442no—
493C2×C4—1724no—
494C2×C4C2×C22⋊Dic4312yes—
495C2×C4#1306329411yescharacteristic
496C2×C4#1306329411yescharacteristic
497C8—3441no—
498C8—1722no—
499C22—21no—
500C22—21no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—84no—
515C22#1458275511yescharacteristic
516C22C2×#1306325211yescharacteristic
517C22#1458291611yescharacteristic
518C4—21no—
519C4—22no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—42no—
524C4—41no—
525C4—42no—
526C4—3444no—
527C4#1458308611yescharacteristic
528C4#1458308911yescharacteristic
529C2—21no—
530C2—21no—
531C2—42no—
532C2—42no—
533C2—82no—
534C2#1913453911yescharacteristic
535C2#1913454311yescharacteristic
536C2#1913455911yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#3459C2
socleC22×C43#379
cosocleC23×C4×C43C23
hypercenter#3459D43
hypocenterC43#8399
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3459

Complements

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

NH ≅ G/Ntype
1. #19134898C2semidirect
2. #19134893C2semidirect
3. C4×#13063240C2semidirect
4. #19133086C2semidirect
6. C22×#10621877C22semidirect
10. C2×C22⋊(C43⋊C8)C22semidirect
11. C4×C22⋊Dic43C22semidirect
17. C43×#543C4semidirect
19. C43×#539C4semidirect
23. C43×#534C4semidirect
184. C23×C43#104semidirect
275. #543Dic43semidirect
277. #539Dic43semidirect
281. #534Dic43semidirect
298. C43#8399semidirect
453. C23#13063252semidirect

Maximal subgroups

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

subgroupindex
#191348982
#191348932
C4×#130632402
#191330862
C43×#34592
#839943