Finite Group Databasebeta

← #25072898

Subgroups — #25072898

Order 11008.

918 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 195 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#19144975C211yesmaximal, characteristic
2#19144725C212yesmaximal
3#19133816C218yesmaximal, complemented
4#19133321C211yesmaximal, characteristic
5#19133042C212yesmaximal
6C2×Q82×C43C211yesmaximal, characteristic
7#14583456C2211yescharacteristic
8#14583267—22no—
9#14583249C2214yes—
10#14583229—22no—
11#14583184C2214yes—
12#14583109C2214yes—
13#14583055—22no—
14#14583004—24no—
15#14582956C2212yes—
16#14582908—22no—
17C4×#10621877C2211yescharacteristic
18#14582648C2214yes—
19Q8⋊(C43⋊C8)C2218yes—
20Q82×C43—22no—
21Q82×C43—24no—
22Q82×C43C2214yes—
23C2×C4⋊Q8×C43—22no—
24C2×C4⋊Q8×C43—22no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C2×C4×Q8×C43—22no—
27C2×C4×Q8×C43C2212yes—
28C2×#10621885—24no—
29C2×#10621877—21no—
30#13063325C2312yes—
31#13063317—21no—
32#13063304—22no—
33C4×Dic86—22no—
34#13063284—21no—
35#13063256—24no—
36C4⋊(C43⋊C8)C2314yes—
37#13063249—24no—
38#13063249—28no—
39#13063248—24no—
40C22⋊(C43⋊C8)—22no—
41#13063236—21no—
42#13063236—22no—
43C4×C43⋊C8C2312yes—
44C22×Q8×C43—22no—
45C22×Q8×C43D412yes—
46C22×Q8×C43D412yes—
47C4⋊Q8×C43—28no—
48C4⋊Q8×C43—28no—
49C4⋊Q8×C43—28no—
50C4⋊Q8×C43—28no—
51C4⋊Q8×C43—22no—
52C4⋊Q8×C43D412yes—
53C4⋊Q8×C43C2312yes—
54C4×Q8×C43—28no—
55C4×Q8×C43—28no—
56C4×Q8×C43—22no—
57C4×Q8×C43—22no—
58C4×Q8×C43D414yes—
59C4×Q8×C43C2314yes—
60C2×C4⋊C4×C43—24no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43—22no—
63C2×C4⋊C4×C43D412yes—
64C2×C42×C43—22no—
65C2×C42×C43—22no—
66C2×C42×C43C2311yescharacteristic
67C2×Q8×C43—28no—
68C2×Q8×C43—28no—
69C2×Q8×C43—22no—
70C2×Q8×C43—22no—
71C2×Q8×C43—44no—
72C2×Q8×C43—84no—
73C2×Q8×C43C2×D414yes—
74C2×Q8×C43C2×D414yes—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—22no—
78C22×C4×C43C2×D412yes—
79C22×C4×C43C2×D411yescharacteristic
80C2×Dic86—22no—
81C4⋊C4×C43—216no—
82C4⋊C4×C43—24no—
83C4⋊C4×C43—24no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—24no—
86C4⋊C4×C43—24no—
87C4⋊C4×C43C2×D414yes—
88C42×C43—28no—
89C42×C43—24no—
90C42×C43—24no—
91C42×C43C2×D411yescharacteristic
92C42×C43C2×D412yes—
93C42×C43C2411yescharacteristic
94C22⋊Dic43—41no—
95#10621885—48no—
96C4⋊Dic43—22no—
97C4⋊Dic43—22no—
98Dic43⋊C4—42no—
99C4×Dic43—41no—
100#10621877—42no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—24no—
103C23×C43#12011yescharacteristic
104Q8×C43—28no—
105Q8×C43—24no—
106Q8×C43—44no—
107Q8×C43—82no—
108Q8×C43—88no—
109Q8×C43#13718yes—
110C2×C4×C43—28no—
111C2×C4×C43—24no—
112C2×C4×C43—22no—
113C2×C4×C43—24no—
114C2×C4×C43—24no—
115C2×C4×C43—24no—
116C2×C4×C43—44no—
117C2×C4×C43—44no—
118C2×C4×C43#12011yescharacteristic
119C2×C4×C43#12012yes—
120C2×C4×C43C22×D411yescharacteristic
121C2×C4×C43C22×D412yes—
122C2×Dic43—42no—
123Dic86—44no—
124C43⋊C8—42no—
125C43⋊C8—44no—
126#18551—431nomaximal, Sylow
127C22×C43—22no—
128C22×C43#45512yes—
129C22×C43C2×#12011yescharacteristic
130C4×C43—28no—
131C4×C43—22no—
132C4×C43—21no—
133C4×C43—21no—
134C4×C43—44no—
135C4×C43—44no—
136C4×C43C2×#13714yes—
137Dic43—82no—
138C2×Q82D4311yescharacteristic
139#3139—431no—
140#3113—432no—
141#1645—438no—
142#1558—431no—
143#1491—432no—
144C2×C43—22no—
145C2×C43#300412yes—
146C2×C43C2×#45511yescharacteristic
147Q82—22no—
148Q82—24no—
149Q82C2×D4314yes—
150#533—431no—
151C2×C4⋊Q8—22no—
152C2×C4⋊Q8—22no—
153C2×C4⋊Q8C2×D4311yescharacteristic
154C2×C4×Q8—22no—
155C2×C4×Q8C2×D4312yes—
156#491—862no—
157#487—434no—
158#483—862no—
159#475—434no—
160#462—434no—
161#451—862no—
162#441—864no—
163#432—432no—
164#419—862no—
165C4×M16—431no—
166#333—434no—
167Q8⋊C8—438no—
168C43#1855111yescharacteristic, complemented, Sylow
169C22×Q8—22no—
170C22×Q8C22⋊D4312yes—
171C22×Q8C22⋊D4312yes—
172C2×Q16—864no—
173C2×M16—861no—
174C4⋊Q8—28no—
175C4⋊Q8—28no—
176C4⋊Q8—28no—
177C4⋊Q8—28no—
178C4⋊Q8—22no—
179C4⋊Q8—432no—
180C4⋊Q8C22⋊D4312yes—
181C4⋊Q8C22×D4312yes—
182#125—861no—
183C22⋊Q8—862no—
184C4×Q8—28no—
185C4×Q8—28no—
186C4×Q8—22no—
187C4×Q8—22no—
188C4×Q8—862no—
189C4×Q8C22⋊D4314yes—
190C4×Q8C22×D4314yes—
191#117—861no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4C22⋊D4312yes—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42C22×D4311yescharacteristic
199#106—864no—
200C4⋊C8—434no—
201#103—868no—
202#103—864no—
203#103—864no—
204C22⋊C8—862no—
205#97—861no—
206#97—862no—
207C4×C8—432no—
208C2×Q8—28no—
209C2×Q8—28no—
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—44no—
213C2×Q8—84no—
214C2×Q8—862no—
215C2×Q8C2×C22⋊D4314yes—
216C2×Q8C2×C22⋊D4314yes—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4C2×C22⋊D4312yes—
221C22×C4C2×C22⋊D4311yescharacteristic
222Q16—1728no—
223M16—1722no—
224C2×C8—862no—
225C2×C8—864no—
226C4⋊C4—216no—
227C4⋊C4—24no—
228C4⋊C4—24no—
229C4⋊C4—22no—
230C4⋊C4—24no—
231C4⋊C4—24no—
232C4⋊C4—862no—
233C4⋊C4—862no—
234C4⋊C4—1722no—
235C4⋊C4C2×C22⋊D4314yes—
236C22⋊C4—1721no—
237C42—28no—
238C42—24no—
239C42—24no—
240C42—1721no—
241C42C2×C22⋊D4311yescharacteristic
242C42C2×C22⋊D4312yes—
243C42C23×D4311yescharacteristic
244C23#1306329411yescharacteristic
245Q8—28no—
246Q8—24no—
247Q8—44no—
248Q8—82no—
249Q8—88no—
250Q8—1724no—
251Q8#1306335618yes—
252C2×C4—28no—
253C2×C4—22no—
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—1722no—
261C2×C4#1306329412yes—
262C2×C4#1306329411yescharacteristic
263C2×C4C22×C22⋊D4311yescharacteristic
264C2×C4C22×C22⋊D4312yes—
265C8—1722no—
266C8—1724no—
267C22—22no—
268C22#1458307712yes—
269C22C2×#1306329411yescharacteristic
270C4—28no—
271C4—22no—
272C4—21no—
273C4—21no—
274C4—44no—
275C4—44no—
276C4—3442no—
277C4C2×#1306335614yes—
278C2—22no—
279C2#1914382912yes—
280C2C2×#1458307711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×Q82×C43C2
socleC22×C43C2×#120
prime radicalC23×C43#120
hypercenterC2×Q82D43
hypocenterC43#18551
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
3. #19133816C2semidirect
168. C43#18551semidirect

Maximal subgroups

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

subgroupindex
#191449752
#191447252
#191338162
#191333212
#191330422
C2×Q82×C432
#1855143