Finite Group Databasebeta

← #25069005

Subgroups — #25069005

Order 11008.

1398 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1398 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583461C211yesmaximal, characteristic
2#19144535C212yesmaximal, complemented
3#19133614C214yesmaximal, complemented
4#19133580C214yesmaximal, complemented
5#19133123C212yesmaximal, complemented
6#19132922C211yesmaximal, characteristic, complemented
7C43×#2482C211yesmaximal, characteristic, complemented
8C23×C22⋊D43—21no—
9#14583461—24no—
10#14583461—22no—
11#14583461C2214yes—
12C2×#13063309—22no—
13C2×#13063299—21no—
14C2×#13063299C2212yes—
15C2×#13063295—22no—
16#14583223—24no—
17#14583217C2214yescomplemented
18#14583212C2214yescomplemented
19#14582942—22no—
20#14582903—22no—
21#14582863C2212yescomplemented
22#14582632C2218yescomplemented
23#14582623C2214yescomplemented
24C2×#117×C43C2211yescharacteristic, complemented
25C22×C22⋊C4×C43C2211yescharacteristic
26C43×#399C2212yescomplemented
27C43×#397C2212yescomplemented
28C43×#388—22no—
29C43×#385—21no—
30C43×#381C2211yescharacteristic, complemented
31C43×#379—21no—
32C24×D43—21no—
33C22×D172—21no—
34C22×D172D412yes—
35C22×C22⋊D43—22no—
36C22×C22⋊D43—24no—
37C22×C22⋊D43—22no—
38C22×C22⋊D43—24no—
39C22×C22⋊D43—48no—
40C23×Dic43—21no—
41C2×#10621877—22no—
42#13063309—28no—
43#13063309—28no—
44#13063299—24no—
45#13063299—24no—
46#13063299—22no—
47#13063299—22no—
48#13063299D414yes—
49#13063299C2314yes—
50#13063295—28no—
51#13063295—28no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43D412yes—
54C2×(C2×D43)⋊C4—22no—
55C2×(C2×D43)⋊C4—22no—
56#13063258—24no—
57#13063256—24no—
58#13063245—24no—
59#13063245—24no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)C2314yescomplemented
62C25×C43D411yescharacteristic
63C23×C4×C43D411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65#117×C43—22no—
66#117×C43—22no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43C2311yescharacteristic, complemented
69C2×C4⋊C4×C43C2311yescharacteristic, complemented
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43—22no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—22no—
76C2×C22⋊C4×C43D412yes—
77C2×C22⋊C4×C43C2312yes—
78C2×C42×C43—21no—
79#95×C43—21no—
80#95×C43—22no—
81#95×C43C2312yescomplemented
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—24no—
85C24×C43—42no—
86C24×C43—81no—
87C24×C43C2×D411yescharacteristic
88C24×C43C2×D412yes—
89C23×D43—22no—
90C23×D43—24no—
91C23×D43—44no—
92C23×D43—82no—
93C23×D43—82no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—22no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—42no—
100C22×C4×C43—81no—
101C22×C4×C43C2×D412yes—
102C22×C4×C43C2×D412yes—
103C22×C4×C43C2×D412yes—
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2411yescharacteristic
106C2×C22⋊D43—28no—
107C2×C22⋊D43—24no—
108C2×C22⋊D43—24no—
109C2×C22⋊D43—48no—
110C2×C22⋊D43—416no—
111C2×C22⋊D43—48no—
112C2×C22⋊D43—48no—
113C2×C22⋊D43—48no—
114C22×Dic43—24no—
115C22×Dic43—22no—
116C22×Dic43—44no—
117C2×D172—24no—
118C2×D172—22no—
119C2×D172—44no—
120C2×D172—82no—
121C2×D172C2×D414yes—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—82no—
125C22⋊C4×C43—24no—
126C22⋊C4×C43—24no—
127C22⋊C4×C43—42no—
128C22⋊C4×C43—41no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—44no—
131C22⋊C4×C43—82no—
132C42×C43—42no—
133(C2×D43)⋊C4—28no—
134(C2×D43)⋊C4—24no—
135(C2×D43)⋊C4—24no—
136C4⋊Dic43—24no—
137C4⋊Dic43—22no—
138C4⋊Dic43C2×D414yes—
139#10621877—44no—
140C2×C43⋊C8—24no—
141C23×C43—24no—
142C23×C43—24no—
143C23×C43—22no—
144C23×C43—22no—
145C23×C43—22no—
146C23×C43—22no—
147C23×C43—41no—
148C23×C43—42no—
149C23×C43—42no—
150C23×C43—42no—
151C23×C43—42no—
152C23×C43—81no—
153C23×C43—81no—
154C23×C43—88no—
155C23×C43#12011yescharacteristic
156C23×C43#12011yescharacteristic
157C23×C43AGL(1,ℤ/8)14yes—
158C23×C43C22×D411yescharacteristic
159C22×D43—24no—
160C22×D43—44no—
161C22×D43—44no—
162C22×D43—48no—
163C22×D43—44no—
164C22×D43—84no—
165C22×D43—84no—
166C22×D43—816no—
167C2×C4×C43—24no—
168C2×C4×C43—22no—
169C2×C4×C43—42no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—42no—
174C2×C4×C43—42no—
175C2×C4×C43—42no—
176C2×C4×C43—42no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—42no—
180C2×C4×C43—42no—
181C2×C4×C43—81no—
182C2×C4×C43#12012yes—
183C2×C4×C43C22×D412yes—
184C22⋊D43—416no—
185C22⋊D43—48no—
186C22⋊D43—48no—
187C2×Dic43—24no—
188C2×Dic43—44no—
189C2×Dic43—48no—
190D172—44no—
191D172—82no—
192D172—84no—
193C43⋊C8—44no—
194#18137—431nomaximal, Sylow
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—24no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—44no—
204C22×C43—44no—
205C22×C43—48no—
206C22×C43—42no—
207C22×C43—42no—
208C22×C43—82no—
209C22×C43—84no—
210C22×C43#45812yes—
211C22×C43C2×#12011yescharacteristic
212C22×C43C2×AGL(1,ℤ/8)12yes—
213C2×D43—44no—
214C2×D43—44no—
215C2×D43—44no—
216C2×D43—88no—
217C2×D43—816no—
218C4×C43—22no—
219C4×C43—22no—
220C4×C43—42no—
221C4×C43—82no—
222C4×C43—81no—
223C4×C43—81no—
224Dic43—44no—
225C2×#534—431no—
226#3094—432no—
227#2482D4311yescharacteristic, complemented
228#1613—434no—
229#1607—434no—
230#1510—432no—
231#1462—431no—
232C2×C43—22no—
233C2×C43—22no—
234C2×C43—44no—
235C2×C43—41no—
236C2×C43#300311yescharacteristic
237C2×C43#301911yescharacteristic
238C2×C43C2×#45811yescharacteristic
239D43—84no—
240C23×D4—861no—
241#534—434no—
242#534—864no—
243#534—862no—
244C2×#123—862no—
245C2×#121—432no—
246C2×#121—861no—
247C2×#120—862no—
248C2×#117C2×D4311yescharacteristic, complemented
249C22×C22⋊C4C2×D4311yescharacteristic
250#482—864no—
251#481—434no—
252#480—434no—
253#428—862no—
254#418—862no—
255#407—432no—
256#399C2×D4312yescomplemented
257#397C2×D4312yescomplemented
258#388—22no—
259#385—21no—
260#381C2×D4311yescharacteristic, complemented
261#379—21no—
262#327—438no—
263#323—434no—
264C43#1813711yescharacteristic, complemented, Sylow
265C25—861no—
266C25C22⋊D4311yescharacteristic
267C22×D4—432no—
268C22×D4—861no—
269C22×D4—862no—
270C22×D4—864no—
271C22×D4—862no—
272C22×D4—864no—
273C22×D4—1728no—
274C23×C4—861no—
275C23×C4C22⋊D4311yescharacteristic
276C23×C4C22×D4311yescharacteristic
277C2×M16—862no—
278#123—868no—
279#123—868no—
280#121—434no—
281#121—434no—
282#121—864no—
283#121—862no—
284#121—862no—
285#121—864no—
286#120—868no—
287#120—868no—
288#117—22no—
289#117—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—432no—
292C2×C4⋊C4—861no—
293C2×C4⋊C4C22×D4311yescharacteristic, complemented
294C2×C4⋊C4C22×D4311yescharacteristic, complemented
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—862no—
302C2×C22⋊C4—862no—
303C2×C22⋊C4C22⋊D4312yes—
304C2×C22⋊C4C22×D4312yes—
305C2×C42—21no—
306#107—864no—
307#106—864no—
308#102—864no—
309#102—864no—
310C22⋊C8—434no—
311C22⋊C8—862no—
312#95—21no—
313#95—22no—
314#95C22×D4312yescomplemented
315C24—21no—
316C24—21no—
317C24—24no—
318C24—42no—
319C24—81no—
320C24—864no—
321C24—862no—
322C24—3442no—
323C24—3442no—
324C24—1724no—
325C24C2×C22⋊D4311yescharacteristic
326C24C2×C22⋊D4312yes—
327C2×D4—434no—
328C2×D4—864no—
329C2×D4—868no—
330C2×D4—864no—
331C2×D4—864no—
332C2×D4—862no—
333C2×D4—3442no—
334C2×D4—1724no—
335C2×D4—1728no—
336C2×D4—17216no—
337C2×D4—1728no—
338C2×D4—1728no—
339C2×D4—1728no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—42no—
346C22×C4—81no—
347C22×C4—864no—
348C22×C4—862no—
349C22×C4—1724no—
350C22×C4D4×D4312yes—
351C22×C4D4×D4312yes—
352C22×C4C2×C22⋊D4312yes—
353C22×C4C2×C22⋊D4311yescharacteristic
354C22×C4C23×D4311yescharacteristic
355M16—1724no—
356C2×C8—864no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—82no—
360C4⋊C4—434no—
361C4⋊C4—864no—
362C4⋊C4—862no—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—42no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—44no—
369C22⋊C4—82no—
370C22⋊C4—868no—
371C22⋊C4—864no—
372C22⋊C4—864no—
373C42—42no—
374C23—24no—
375C23—24no—
376C23—22no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23—81no—
386C23—81no—
387C23—88no—
388C23—864no—
389C23—34416no—
390C23—3444no—
391C23—3444no—
392C23—1724no—
393C23—1724no—
394C23—1728no—
395C23—1724no—
396C23#1306329311yescharacteristic
397C23#1306329311yescharacteristic
398C23#1306335014yes—
399C23C22×C22⋊D4311yescharacteristic
400D4—3442no—
401D4—3444no—
402D4—1724no—
403D4—17216no—
404D4—1728no—
405D4—1728no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—81no—
421C2×C4—864no—
422C2×C4—1724no—
423C2×C4—1728no—
424C2×C4#1306329312yes—
425C2×C4C2×D4×D4312yes—
426C8—1724no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—24no—
434C22—21no—
435C22—44no—
436C22—44no—
437C22—48no—
438C22—42no—
439C22—42no—
440C22—82no—
441C22—84no—
442C22—3448no—
443C22—34416no—
444C22—1724no—
445C22—1724no—
446C22—1724no—
447C22#1458308812yes—
448C22C2×#1306329311yescharacteristic
449C22C2×#1306335012yes—
450C4—22no—
451C4—22no—
452C4—42no—
453C4—82no—
454C4—81no—
455C4—81no—
456C4—1724no—
457C2—22no—
458C2—22no—
459C2—41no—
460C2—44no—
461C2—3444no—
462C2#1914382111yescharacteristic
463C2#1914395111yescharacteristic
464C2C2×#1458308811yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2482C2
socleC22×C43C2×#120
prime radicalC2×#14583461C2
hypercenter#2482D43
hypocenterC43#18137
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
2. #19144535C2semidirect
3. #19133614C2semidirect
4. #19133580C2semidirect
5. #19133123C2semidirect
6. #19132922C2semidirect
7. C43×#2482C2semidirect
17. #14583217C22semidirect
18. #14583212C22semidirect
21. #14582863C22semidirect
22. #14582632C22semidirect
23. #14582623C22semidirect
24. C2×#117×C43C22semidirect
26. C43×#399C22semidirect
27. C43×#397C22semidirect
30. C43×#381C22semidirect
61. C22⋊(C43⋊C8)C23semidirect
68. C2×C4⋊C4×C43C23semidirect
69. C2×C4⋊C4×C43C23semidirect
81. #95×C43C23semidirect
227. #2482D43semidirect
248. C2×#117C2×D43semidirect
256. #399C2×D43semidirect
257. #397C2×D43semidirect
260. #381C2×D43semidirect
264. C43#18137semidirect
293. C2×C4⋊C4C22×D43semidirect
294. C2×C4⋊C4C22×D43semidirect
314. #95C22×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834612
#191445352
#191336142
#191335802
#191331232
#191329222
C43×#24822
#1813743