Finite Group Databasebeta

← #25068874

Subgroups — #25068874

Order 11008.

1208 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147928C211yesmaximal, characteristic
2#19144626C212yesmaximal, complemented
3#19133631C212yesmaximal, complemented
4#19133614C212yesmaximal, complemented
5#19133563C212yesmaximal, complemented
6#19133546C212yesmaximal, complemented
7#19133089C212yesmaximal, complemented
8#19132909C211yesmaximal, characteristic, complemented
9C43×#2396C211yesmaximal, characteristic, complemented
10C22×#10621898—21no—
11#14583480—21no—
12#14583480C2212yes—
13#14583475—22no—
14#14583468—22no—
15#14583461—21no—
16#14583461C2212yes—
17#14583449—21no—
18#14583449C2212yes—
19#14583411—24no—
20#14583217C2214yescomplemented
21#14583184—22no—
22#14583099—22no—
23#14583038C2214yescomplemented
24C4×#10621884—24no—
25#14582952C2212yescomplemented
26#14582632C2214yescomplemented
27#14582632C2214yescomplemented
28#14582625C2212yescomplemented
29#14582623C2212yes—
30C2×C4×Q8×C43C2211yescharacteristic, complemented
31C2×#117×C43C2211yescharacteristic
32C43×#400C2211yescharacteristic, complemented
33C43×#399C2211yescharacteristic
34C43×#398—21no—
35C43×#396—21no—
36C43×#395C2211yescharacteristic, complemented
37C43×#393C2211yescharacteristic
38C4×C4⋊C4×C43—21no—
39C4×C4⋊C4×C43C2211yescharacteristic, complemented
40C4×C22⋊C4×C43—21no—
41C2×#10621898—22no—
42C2×#10621898—22no—
43C2×#10621898—22no—
44C2×#10621898—22no—
45C2×#10621898—44no—
46C2×#10621898—44no—
47C22×Dic86—21no—
48C22×D172—21no—
49C22×C22⋊D43—22no—
50C22×C4×D43—22no—
51C2×#10621884—24no—
52#13063325—21no—
53#13063325D412yes—
54#13063322—21no—
55#13063322D412yes—
56#13063313—22no—
57#13063313—22no—
58#13063309—24no—
59#13063309—24no—
60#13063305—24no—
61#13063305—24no—
62#13063300—24no—
63#13063300—24no—
64#13063299—22no—
65#13063299—22no—
66#13063299—22no—
67#13063299C2314yes—
68#13063295—24no—
69#13063295—24no—
70C4×D172—22no—
71C4×D172—22no—
72C4×D172—22no—
73C4×D172D414yes—
74#13063256—24no—
75C4⋊(C43⋊C8)—22no—
76#13063249—24no—
77#13063245—24no—
78C22⋊(C43⋊C8)C2314yes—
79C4×C43⋊C8—22no—
80C22×Q8×C43C2311yescharacteristic
81C23×C4×C43D411yescharacteristic
82C4×Q8×C43—22no—
83C4×Q8×C43—22no—
84#117×C43—22no—
85#117×C43—22no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43D411yescharacteristic
96C2×C22⋊C4×C43C2311yescharacteristic
97C2×C42×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43D411yescharacteristic
100C2×C42×C43C2311yescharacteristic
101#95×C43—21no—
102#95×C43—21no—
103#95×C43—21no—
104#95×C43—21no—
105#95×C43C2311yescharacteristic
106#95×C43C2311yescharacteristic
107C24×C43C2×D411yescharacteristic
108C23×D43—22no—
109C2×Q8×C43—22no—
110C2×Q8×C43—42no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43SD1614yescomplemented
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2411yescharacteristic
125C2×C22⋊D43—24no—
126C2×C22⋊D43—24no—
127C2×C22⋊D43—44no—
128C2×C22⋊D43—44no—
129C22×Dic43—22no—
130#10621898—44no—
131#10621898—48no—
132#10621898—48no—
133#10621898—44no—
134#10621898—44no—
135#10621898—44no—
136C2×D172—22no—
137C2×D172—22no—
138C2×D172—22no—
139C2×D172—22no—
140C2×D172—22no—
141C2×D172—44no—
142C2×D172C2×D414yes—
143C2×C4×D43—24no—
144C2×C4×D43—24no—
145C2×C4×D43—48no—
146C2×Dic86—22no—
147C2×Dic86—22no—
148C2×Dic86—44no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—42no—
153C4⋊C4×C43—42no—
154C4⋊C4×C43—42no—
155C4⋊C4×C43—42no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—42no—
159C22⋊C4×C43—42no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—41no—
163C42×C43—41no—
164C42×C43—42no—
165C42×C43C2×D412yes—
166C42×C43C2×D412yes—
167#10621884—48no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—24no—
171(C2×D43)⋊C4—24no—
172C4⋊Dic43—22no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43C2×D414yes—
176C2×C43⋊C8—24no—
177C23×C43—21no—
178C23×C43—21no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43C2×SD1612yes—
182C23×C43C22×D411yescharacteristic
183C22×D43—24no—
184C22×D43—44no—
185C22×D43—82no—
186C22×D43—82no—
187Q8×C43—24no—
188Q8×C43—42no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—24no—
192C2×C4×C43—24no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
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—41no—
211C2×C4×C43#12012yes—
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#12011yescharacteristic
214C2×C4×C43C2×SD1612yes—
215C2×C4×C43C2×SD1612yes—
216C2×C4×C43AGL(1,ℤ/8)12yes—
217C2×C4×C43C22×D412yes—
218C22⋊D43—48no—
219C22⋊D43—44no—
220C22⋊D43—44no—
221C2×Dic43—24no—
222C2×Dic43—44no—
223D172—44no—
224D172—44no—
225D172—44no—
226D172—82no—
227D172—82no—
228D172—82no—
229C4×D43—48no—
230C4×D43—48no—
231Dic86—44no—
232Dic86—44no—
233C43⋊C8—44no—
234#18123—431nomaximal, Sylow
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—22no—
238C22×C43—42no—
239C22×C43—41no—
240C22×C43—41no—
241C22×C43—81no—
242C22×C43C2×#12011yescharacteristic
243C22×C43C22×SD1611yescharacteristic
244C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
245C2×D43—44no—
246C2×D43—44no—
247C2×D43—44no—
248C2×D43—88no—
249C4×C43—22no—
250C4×C43—22no—
251C4×C43—22no—
252C4×C43—42no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—42no—
256C4×C43—81no—
257C4×C43—81no—
258C4×C43#45012yes—
259C4×C43#45012yes—
260Dic43—44no—
261#3449—431no—
262#3103—432no—
263#2396D4311yescharacteristic, complemented
264#1616—432no—
265#1613—432no—
266#1604—432no—
267#1601—432no—
268#1502—432no—
269#1458—431no—
270C2×C43—21no—
271C2×C43—21no—
272C2×C43—42no—
273C2×C43C2×#45011yescharacteristic
274C2×C43#301811yescharacteristic
275C2×C43#302511yescharacteristic
276D43—84no—
277C22×#41—861no—
278#537—432no—
279#537—861no—
280#536—862no—
281#535—862no—
282#534—432no—
283#534—861no—
284#532—432no—
285#532—861no—
286#525—864no—
287C2×C4×Q8C2×D4311yescharacteristic, complemented
288C2×#117C2×D4311yescharacteristic
289#481—434no—
290#475—862no—
291#460—862no—
292#448—434no—
293C4×SD16—864no—
294#431—432no—
295#400C2×D4311yescharacteristic, complemented
296#399C2×D4311yescharacteristic
297#398—21no—
298#396—21no—
299#395C2×D4311yescharacteristic, complemented
300#393C2×D4311yescharacteristic
301C4×C4⋊C4—21no—
302C4×C4⋊C4C2×D4311yescharacteristic, complemented
303C4×C22⋊C4—21no—
304#327—434no—
305#327—434no—
306#324—432no—
307#323—432no—
308C43#1812311yescharacteristic, complemented, Sylow
309C2×#41—862no—
310C2×#41—862no—
311C2×#41—862no—
312C2×#41—862no—
313C2×#41—1724no—
314C2×#41—1724no—
315C22×Q8—861no—
316C22×Q8C22×D4311yescharacteristic
317C22×D4—861no—
318C22×D4—862no—
319C23×C4—862no—
320C23×C4C22⋊D4311yescharacteristic
321C2×SD16—864no—
322C4⋊Q8—432no—
323C4⋊Q8—861no—
324#127—432no—
325#127—861no—
326#124—862no—
327#124—862no—
328#123—864no—
329#123—864no—
330C22⋊Q8—864no—
331C22⋊Q8—864no—
332#121—434no—
333#121—864no—
334#121—864no—
335#121—862no—
336#121—862no—
337#121—862no—
338#120—864no—
339#120—864no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×D4—434no—
343C4×D4—862no—
344C4×D4—862no—
345C4×D4—862no—
346#117—22no—
347#117—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4C22⋊D4311yescharacteristic
353C2×C4⋊C4C22×D4311yescharacteristic
354C2×C4⋊C4C22×D4311yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4C22⋊D4311yescharacteristic
358C2×C22⋊C4C22×D4311yescharacteristic
359C2×C42—21no—
360C2×C42—21no—
361C2×C42C22⋊D4311yescharacteristic
362C2×C42C22×D4311yescharacteristic
363#106—864no—
364C4⋊C8—862no—
365#103—864no—
366#102—864no—
367C22⋊C8—434no—
368C4×C8—862no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95C22×D4311yescharacteristic
374#95C22×D4311yescharacteristic
375C24—862no—
376C24C2×C22⋊D4311yescharacteristic
377#41—1724no—
378#41—1728no—
379#41—1728no—
380#41—1724no—
381#41—1724no—
382#41—1724no—
383C2×Q8—22no—
384C2×Q8—42no—
385C2×Q8—862no—
386C2×Q8—862no—
387C2×Q8—1724no—
388C2×D4—434no—
389C2×D4—862no—
390C2×D4—862no—
391C2×D4—862no—
392C2×D4—864no—
393C2×D4—864no—
394C2×D4—862no—
395C2×D4—862no—
396C2×D4—1724no—
397C2×D4—1724no—
398C2×D4—1724no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—864no—
407C22×C4—862no—
408C22×C4—864no—
409C22×C4—1728no—
410C22×C4#1062188414yescomplemented
411C22×C4C2×C22⋊D4311yescharacteristic
412C22×C4C2×C22⋊D4311yescharacteristic
413C22×C4C2×C22⋊D4311yescharacteristic
414C22×C4C2×C22⋊D4311yescharacteristic
415C22×C4C2×C22⋊D4311yescharacteristic
416C22×C4C23×D4311yescharacteristic
417SD16—1728no—
418C2×C8—864no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C4⋊C4—42no—
425C4⋊C4—42no—
426C4⋊C4—434no—
427C4⋊C4—862no—
428C4⋊C4—862no—
429C4⋊C4—862no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—42no—
433C22⋊C4—42no—
434C22⋊C4—864no—
435C22⋊C4—864no—
436C22⋊C4—864no—
437C22⋊C4—864no—
438C42—21no—
439C42—21no—
440C42—41no—
441C42—41no—
442C42—42no—
443C42D4×D4312yes—
444C42D4×D4312yes—
445C23—21no—
446C23—21no—
447C23—41no—
448C23—41no—
449C23—864no—
450C23—3442no—
451C23—3442no—
452C23—1724no—
453C23C2×#1062188412yes—
454C23C22×C22⋊D4311yescharacteristic
455Q8—24no—
456Q8—42no—
457Q8—1724no—
458Q8—1724no—
459D4—3442no—
460D4—3442no—
461D4—3442no—
462D4—1724no—
463D4—1724no—
464D4—1728no—
465D4—1724no—
466D4—1724no—
467D4—1724no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—864no—
491C2×C4—1728no—
492C2×C4—1724no—
493C2×C4—1728no—
494C2×C4#1306329312yes—
495C2×C4#1306329311yescharacteristic
496C2×C4#1306329311yescharacteristic
497C2×C4C2×#1062188412yes—
498C2×C4C2×#1062188412yes—
499C2×C4#1306335012yes—
500C2×C4C2×D4×D4312yes—
501C8—1724no—
502C22—21no—
503C22—21no—
504C22—22no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—81no—
509C22—3448no—
510C22—1724no—
511C22—1724no—
512C22—1724no—
513C22C2×#1306329311yescharacteristic
514C22C22×#1062188411yescharacteristic
515C22C2×#1306335011yescharacteristic
516C4—22no—
517C4—22no—
518C4—22no—
519C4—42no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—81no—
524C4—81no—
525C4—1724no—
526C4#1458304912yes—
527C4#1458304912yes—
528C2—21no—
529C2—21no—
530C2—42no—
531C2—3444no—
532C2C2×#1458304911yescharacteristic
533C2#1914394311yescharacteristic
534C2#1914398611yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2396C2
socleC22×C43C2×#120
prime radical#19147928C2
hypercenter#2396D43
hypocenterC43#18123
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2396

Complements

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

NH ≅ G/Ntype
2. #19144626C2semidirect
3. #19133631C2semidirect
4. #19133614C2semidirect
5. #19133563C2semidirect
6. #19133546C2semidirect
7. #19133089C2semidirect
8. #19132909C2semidirect
9. C43×#2396C2semidirect
20. #14583217C22semidirect
23. #14583038C22semidirect
25. #14582952C22semidirect
26. #14582632C22semidirect
27. #14582632C22semidirect
28. #14582625C22semidirect
30. C2×C4×Q8×C43C22semidirect
32. C43×#400C22semidirect
36. C43×#395C22semidirect
39. C4×C4⋊C4×C43C22semidirect
118. C22×C4×C43SD16semidirect
263. #2396D43semidirect
287. C2×C4×Q8C2×D43semidirect
295. #400C2×D43semidirect
299. #395C2×D43semidirect
302. C4×C4⋊C4C2×D43semidirect
308. C43#18123semidirect
410. C22×C4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191479282
#191446262
#191336312
#191336142
#191335632
#191335462
#191330892
#191329092
C43×#23962
#1812343