Finite Group Databasebeta

← #25071451

Subgroups — #25071451

Order 11008.

910 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 191 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#19148405C211yesmaximal, characteristic
2#19145543C212yesmaximal
3#19133568C218yesmaximal
4#19133093C212yesmaximal
5#19132919C211yesmaximal, characteristic
6C43×#2567C211yesmaximal, characteristic
7Q8×Dic86—22no—
8#14583628—22no—
9#14583625—24no—
10#14583530—21no—
11#14583530C2214yes—
12#14583456—22no—
13#14583456C2212yes—
14#14583377—21no—
15#14583278—22no—
16#14583249—22no—
17#14583106—24no—
18#14583055C2218yes—
19#14582952C2212yes—
20#14582635C2218yes—
21#14582625C2214yes—
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×C4×Q8×C43C2211yescharacteristic
24C43×#395C2214yes—
25C43×#391—21no—
26C43×#389—22no—
27C43×#384—21no—
28C4×C4⋊C4×C43C2211yescharacteristic
29C2×#10621885—28no—
30#13063325—22no—
31#13063325—22no—
32#13063325D412yes—
33#13063325D412yes—
34#13063324—24no—
35#13063324—28no—
36#13063317—24no—
37#13063317—22no—
38#13063316—24no—
39#13063316—28no—
40#13063304—22no—
41#13063304—24no—
42#13063304C2314yes—
43Q8×Dic43—24no—
44Q8×Dic43—24no—
45C4×Dic86—24no—
46C4×Dic86—24no—
47C4×Dic86—22no—
48C4×Dic86D414yes—
49#13063284—24no—
50#13063284—22no—
51C4⋊(C43⋊C8)—22no—
52#13063249—28no—
53C22⋊(C43⋊C8)C2314yes—
54C4×C43⋊C8—22no—
55C22×Q8×C43D411yescharacteristic
56C22×Q8×C43C2312yes—
57C4⋊Q8×C43—22no—
58C4⋊Q8×C43—22no—
59C4×Q8×C43—22no—
60C4×Q8×C43—22no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—24no—
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C4⋊C4×C43C2312yes—
67C2×C42×C43—21no—
68C2×C42×C43D412yes—
69C2×C42×C43C2311yescharacteristic
70#95×C43—24no—
71#95×C43C2312yes—
72C2×Q8×C43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43—24no—
75C2×Q8×C43—82no—
76C2×Q8×C43Q1614yescomplemented
77C22×C4×C43—22no—
78C22×C4×C43—22no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D412yes—
81C22×C4×C43C2×D412yes—
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2411yescharacteristic
84C2×Dic86—22no—
85C2×Dic86—24no—
86C2×Dic86C2×D414yes—
87C4⋊C4×C43—24no—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—24no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—42no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—84no—
94C42×C43—22no—
95C42×C43—22no—
96C42×C43—42no—
97C42×C43C2×D412yes—
98C42×C43C2×D412yes—
99C22⋊Dic43—24no—
100#10621885—88no—
101C4⋊Dic43—24no—
102C4⋊Dic43—24no—
103C4⋊Dic43—24no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43—22no—
107C4⋊Dic43C2×D414yes—
108Dic43⋊C4—28no—
109Dic43⋊C4—24no—
110Dic43⋊C4—24no—
111C4×Dic43—28no—
112C4×Dic43—24no—
113C2×C43⋊C8—24no—
114C23×C43C22×D411yescharacteristic
115Q8×C43—28no—
116Q8×C43—48no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—24no—
121C2×C4×C43—22no—
122C2×C4×C43—41no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—44no—
127C2×C4×C43—42no—
128C2×C4×C43#12011yescharacteristic
129C2×C4×C43#12012yes—
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43C2×Q1614yes—
132C2×C4×C43C2×Q1612yes—
133C2×C4×C43#13712yes—
134C2×C4×C43C22×D412yes—
135C2×Dic43—24no—
136C2×Dic43—24no—
137Dic86—44no—
138Dic86—44no—
139Dic86—84no—
140C43⋊C8—44no—
141#18404—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43C2×#12011yescharacteristic
145C22×C43C22×Q1611yescharacteristic
146C22×C43C2×#13711yescharacteristic
147C4×C43—24no—
148C4×C43—21no—
149C4×C43—22no—
150C4×C43—44no—
151C4×C43—42no—
152C4×C43—82no—
153C4×C43#45114yes—
154C4×C43#45612yes—
155Dic43—44no—
156Dic43—44no—
157#3502—431no—
158#3209—432no—
159#2567D4311yescharacteristic
160#1605—438no—
161#1503—432no—
162#1461—431no—
163C2×C43—21no—
164C2×C43—21no—
165C2×C43C2×#45111yescharacteristic
166C2×C43C2×#45611yescharacteristic
167C2×C43#302711yescharacteristic
168Q82—862no—
169#557—864no—
170#557—862no—
171#544—434no—
172#544—861no—
173#533—432no—
174#533—862no—
175C2×C4⋊Q8C2×D4311yescharacteristic
176#519—861no—
177C2×C4×Q8C2×D4311yescharacteristic
178#494—862no—
179#487—862no—
180#462—864no—
181#451—438no—
182#431—432no—
183#395C2×D4314yes—
184#391—21no—
185#389—22no—
186#384—21no—
187C4×C4⋊C4C2×D4311yescharacteristic
188#328—438no—
189#324—434no—
190C43#1840411yescharacteristic, complemented, Sylow
191C22×Q8C22⋊D4311yescharacteristic
192C22×Q8C22×D4312yes—
193C2×Q16—868no—
194C4⋊Q8—22no—
195C4⋊Q8—22no—
196C4⋊Q8—432no—
197C4⋊Q8—432no—
198C4⋊Q8—862no—
199C4⋊Q8—862no—
200C4⋊Q8—868no—
201C4⋊Q8—864no—
202#125—864no—
203#125—868no—
204#125—864no—
205#125—862no—
206C22⋊Q8—434no—
207C22⋊Q8—862no—
208C22⋊Q8—864no—
209C4×Q8—22no—
210C4×Q8—22no—
211C4×Q8—434no—
212C4×Q8—864no—
213C4×Q8—864no—
214C4×Q8—864no—
215C4×Q8—864no—
216C4×Q8—862no—
217#117—862no—
218#117—864no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4C22⋊D4311yescharacteristic
224C2×C4⋊C4C22×D4312yes—
225C2×C42—21no—
226C2×C42C22⋊D4312yes—
227C2×C42C22×D4311yescharacteristic
228C4⋊C8—862no—
229#103—868no—
230C22⋊C8—434no—
231C4×C8—862no—
232#95—24no—
233#95C22×D4312yes—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—24no—
237C2×Q8—82no—
238C2×Q8—434no—
239C2×Q8—864no—
240C2×Q8—862no—
241C2×Q8#1062188514yescomplemented
242C22×C4—22no—
243C22×C4—22no—
244C22×C4C2×C22⋊D4311yescharacteristic
245C22×C4C2×C22⋊D4312yes—
246C22×C4C2×C22⋊D4312yes—
247C22×C4C2×C22⋊D4311yescharacteristic
248C22×C4C23×D4311yescharacteristic
249Q16—3448no—
250C2×C8—864no—
251C4⋊C4—24no—
252C4⋊C4—22no—
253C4⋊C4—24no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—84no—
258C4⋊C4—434no—
259C4⋊C4—864no—
260C4⋊C4—864no—
261C4⋊C4—864no—
262C4⋊C4—868no—
263C4⋊C4—862no—
264C4⋊C4—862no—
265C4⋊C4—864no—
266C4⋊C4—862no—
267C4⋊C4—864no—
268C22⋊C4—864no—
269C42—22no—
270C42—22no—
271C42—42no—
272C42—868no—
273C42—864no—
274C42D4×D4312yes—
275C42D4×D4312yes—
276C23C22×C22⋊D4311yescharacteristic
277Q8—28no—
278Q8—48no—
279Q8—3444no—
280Q8—1724no—
281Q8—1724no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—864no—
294C2×C4—864no—
295C2×C4#1306329311yescharacteristic
296C2×C4#1306329312yes—
297C2×C4#1306329311yescharacteristic
298C2×C4C2×#1062188514yes—
299C2×C4C2×#1062188512yes—
300C2×C4#1306335512yes—
301C2×C4C2×D4×D4312yes—
302C8—1724no—
303C22—21no—
304C22—21no—
305C22C2×#1306329311yescharacteristic
306C22C22×#1062188511yescharacteristic
307C22C2×#1306335511yescharacteristic
308C4—21no—
309C4—22no—
310C4—24no—
311C4—44no—
312C4—42no—
313C4—82no—
314C4—1724no—
315C4—1724no—
316C4#1458305414yes—
317C4#1458308112yes—
318C2—21no—
319C2—21no—
320C2C2×#1458305411yescharacteristic
321C2C2×#1458308111yescharacteristic
322C2#1914399611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2567C2
socleC22×C43C2×#120
prime radicalC23×C43C22×D4
hypercenter#2567D43
hypocenterC43#18404
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2567

Complements

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

NH ≅ G/Ntype
76. C2×Q8×C43Q16semidirect
190. C43#18404semidirect
241. C2×Q8#10621885semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191455432
#191335682
#191330932
#191329192
C43×#25672
#1840443