Finite Group Databasebeta

← #24985495

Subgroups — #24985495

Order 11008.

416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#19135928C211yesmaximal, characteristic
2#19135928C211yesmaximal, characteristic
3#19135841C211yesmaximal, characteristic
4#19132418C211yesmaximal, characteristic
5#19132418C211yesmaximal, characteristic
6#19132418C211yesmaximal, characteristic
7C43×#2726C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×#13063256—21no—
10C2×#13063256—21no—
11C2×#13063248—21no—
12C2×#13063248—21no—
13#14582661—21no—
14#14582661—21no—
15#14582654C2211yescharacteristic
16#14582654C2211yescharacteristic
17#14582654C2211yescharacteristic
18C2×#125×C43—21no—
19C43×#398—21no—
20C43×#398—21no—
21C43×#398—21no—
22C43×#389—21no—
23C43×#389C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#389C2211yescharacteristic
26C43×#387—21no—
27C22×Dic86—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31#13063325—42no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34#13063256—42no—
35#13063256—42no—
36#13063248—42no—
37#13063248—42no—
38#125×C43—42no—
39#125×C43—42no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C42×C43—21no—
54C2×C42×C43C2311yescharacteristic
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—41no—
71C2×Dic86—22no—
72C2×Dic86—41no—
73C2×Dic86—41no—
74C2×Dic86—41no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—42no—
85C4⋊C4×C43—42no—
86C4⋊C4×C43—42no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—81no—
94C4⋊C4×C43SD1612yes—
95C4⋊C4×C43SD1612yes—
96C42×C43—41no—
97C42×C43—42no—
98C4⋊Dic43—22no—
99C4⋊Dic43—22no—
100C4⋊Dic43—41no—
101C4⋊Dic43—41no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C23×C43#12011yescharacteristic
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43C2×SD1611yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C2×Dic43—42no—
143C2×Dic43—81no—
144C2×Dic43—81no—
145Dic86—42no—
146Dic86—42no—
147Dic86—81no—
148Dic86—81no—
149C43⋊C8—42no—
150C43⋊C8—42no—
151C43⋊C8—81no—
152#7768—431nomaximal, Sylow
153C22×C43#44811yescharacteristic
154C22×C43#45011yescharacteristic
155C22×C43#45211yescharacteristic
156C22×C43#45411yescharacteristic
157C22×C43#45611yescharacteristic
158C22×C43#45611yescharacteristic
159C22×C43B(4,𝔽2)11yescharacteristic
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—42no—
167C4×C43—42no—
168C4×C43—81no—
169C4×C43—81no—
170C4×C43—81no—
171C4×C43—81no—
172Dic43—82no—
173#2726D4311yescharacteristic
174#2058—431no—
175#2058—431no—
176#2043—431no—
177#1271—431no—
178#1271—431no—
179#1271—431no—
180C2×C43#159911yescharacteristic
181C2×C43#160311yescharacteristic
182C2×C43#160411yescharacteristic
183C2×C43#163511yescharacteristic
184C2×C43#165111yescharacteristic
185C2×C43#165311yescharacteristic
186C2×C43#166311yescharacteristic
187C2×C4⋊Q8—431no—
188C2×#125—21no—
189C2×#106—861no—
190C2×#106—861no—
191C2×#103—861no—
192C2×#103—861no—
193#398—21no—
194#398—21no—
195#398—21no—
196#389—21no—
197#389C2×D4311yescharacteristic
198#389C2×D4311yescharacteristic
199#389C2×D4311yescharacteristic
200#387—21no—
201#340—861no—
202#340—861no—
203#336—431no—
204#336—431no—
205#336—431no—
206C43#776811yescharacteristic, complemented, Sylow
207C22×Q8—861no—
208C22×C8—861no—
209C22×C8—861no—
210C22×C8—861no—
211C4⋊Q8—1722no—
212#125—42no—
213#125—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4C22⋊D4311yescharacteristic
224C2×C4⋊C4C22⋊D4311yescharacteristic
225C2×C4⋊C4C22⋊D4311yescharacteristic
226C2×C4⋊C4C22⋊D4311yescharacteristic
227C2×C4⋊C4C22⋊D4311yescharacteristic
228C2×C4⋊C4C22⋊D4311yescharacteristic
229C2×C42—21no—
230C2×C42C22×D4311yescharacteristic
231#106—1722no—
232#106—1722no—
233#103—1722no—
234#103—1722no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241C2×Q8—862no—
242C2×Q8—1721no—
243C2×Q8—1721no—
244C2×Q8—1721no—
245C2×Q8—1721no—
246C2×Q8—1721no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—1721no—
254C22×C4C2×C22⋊D4311yescharacteristic
255C22×C4C2×C22⋊D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257C2×C8—862no—
258C2×C8—862no—
259C2×C8—1721no—
260C2×C8—1721no—
261C2×C8—1721no—
262C2×C8—1721no—
263C2×C8—1721no—
264C2×C8—1721no—
265C2×C8—1721no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—862no—
284C4⋊C4—862no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C4⋊C4#1062188312yes—
288C4⋊C4#1062188412yes—
289C42—41no—
290C42—42no—
291C23#1306329411yescharacteristic
292Q8—3441no—
293Q8—3441no—
294Q8—1722no—
295Q8—1722no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—1722no—
323C2×C4C2×#1062188411yescharacteristic
324C2×C4C2×#1062188311yescharacteristic
325C2×C4#1306334511yescharacteristic
326C2×C4#1306335111yescharacteristic
327C2×C4#1306335511yescharacteristic
328C2×C4#1306335611yescharacteristic
329C8—3441no—
330C8—1722no—
331C8—1722no—
332C22#1458303811yescharacteristic
333C22#1458305011yescharacteristic
334C22#1458306111yescharacteristic
335C22#1458307211yescharacteristic
336C22#1458308211yescharacteristic
337C22#1458308211yescharacteristic
338C22#1458308611yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—42no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—3442no—
352C2#1913353511yescharacteristic
353C2#1913355811yescharacteristic
354C2#1913356411yescharacteristic
355C2#1913374611yescharacteristic
356C2#1913385811yescharacteristic
357C2#1913387211yescharacteristic
358C2#1913392311yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2726C2
socle, prime radicalC23×C43#120
hypercenter#2726D43
hypocenterC43#7768
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2726

Complements

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

NH ≅ G/Ntype
206. C43#7768semidirect

Maximal subgroups

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

subgroupindex
#191359282
#191358412
#191324182
C43×#27262
#776843