Finite Group Databasebeta

← #25072899

Subgroups — #25072899

Order 11008.

918 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14583629C211yesmaximal, characteristic
2#19144975C211yesmaximal, characteristic
3#19144726C212yesmaximal
4#19133817C218yesmaximal, complemented
5#19133041C212yesmaximal
6C43×#1558C211yesmaximal, characteristic
7#14583629—24no—
8#14583629—22no—
9#14583629C2214yes—
10#14583456C2211yescharacteristic
11C2×#13063324—22no—
12C2×#13063323—22no—
13C2×C4×Dic86C2212yes—
14C2×#13063290—22no—
15#14583267—22no—
16#14583249C2214yes—
17#14583230—22no—
18#14583185C2214yes—
19#14583110C2214yes—
20#14583057—22no—
21#14583007—24no—
22#14582908—22no—
23C4×#10621877C2211yescharacteristic
24#14582629C2218yes—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#432C2212yes—
27C43×#333C2214yes—
28C22×Dic86—22no—
29C22×Dic86D412yes—
30C2×Dic172—24no—
31C2×#10621877—21no—
32#13063325C2312yes—
33#13063324—28no—
34#13063324—28no—
35#13063323—28no—
36#13063323—28no—
37#13063317—21no—
38#13063304—22no—
39C4×Dic86—22no—
40C4×Dic86—22no—
41C4×Dic86—22no—
42C4×Dic86D414yes—
43C4×Dic86C2314yes—
44#13063290—28no—
45#13063290—28no—
46#13063284—21no—
47C2×C4⋊Dic43D412yes—
48C2×Dic43⋊C4—24no—
49C2×Dic43⋊C4—22no—
50C2×C4×Dic43—22no—
51C2×C4×Dic43—22no—
52#13063257—24no—
53#13063250—24no—
54#13063250—24no—
55#13063249—28no—
56#13063236—21no—
57C4×C43⋊C8C2312yes—
58C22×Q8×C43D412yes—
59C4⋊Q8×C43—22no—
60C4⋊Q8×C43D412yes—
61C4⋊Q8×C43C2312yes—
62C2×C4⋊C4×C43—22no—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43C2314yes—
65C22⋊C8×C43—22no—
66#97×C43—22no—
67C2×Q8×C43—22no—
68C2×Q8×C43—44no—
69C2×Q8×C43C2×D414yes—
70C22×C4×C43—22no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D412yes—
73C22×Dic43—22no—
74C22×Dic43—22no—
75C2×Dic86—22no—
76C2×Dic86—28no—
77C2×Dic86—22no—
78C2×Dic86—28no—
79C2×Dic86—84no—
80C2×Dic86C2×D414yes—
81C2×C8×C43—24no—
82C4⋊C4×C43—24no—
83C4⋊C4×C43—24no—
84C42×C43C2×D411yescharacteristic
85C42×C43C2×D412yes—
86C42×C43C2411yescharacteristic
87C22⋊Dic43—41no—
88C4⋊Dic43—22no—
89C4⋊Dic43—22no—
90C4⋊Dic43—22no—
91C4⋊Dic43C2×D414yes—
92Dic43⋊C4—216no—
93Dic43⋊C4—24no—
94Dic43⋊C4—24no—
95Dic43⋊C4—42no—
96C4×Dic43—28no—
97C4×Dic43—24no—
98C4×Dic43—24no—
99C4×Dic43—41no—
100#10621877—42no—
101C2×C43⋊C8—22no—
102Dic172—48no—
103C23×C43#12011yescharacteristic
104Q8×C43—44no—
105Q8×C43—82no—
106C2×C4×C43—22no—
107C2×C4×C43—24no—
108C2×C4×C43—24no—
109C2×C4×C43—44no—
110C2×C4×C43#12012yes—
111C2×C4×C43#12011yescharacteristic
112C2×C4×C43C22×D412yes—
113C2×C4×C43C22×D411yescharacteristic
114C2×Dic43—28no—
115C2×Dic43—24no—
116C2×Dic43—24no—
117C2×Dic43—44no—
118C2×Dic43—42no—
119Dic86—28no—
120Dic86—24no—
121Dic86—44no—
122Dic86—88no—
123Dic86#13718yes—
124C8×C43—44no—
125C43⋊C8—42no—
126#18551—431nomaximal, Sylow
127C22×C43—22no—
128C22×C43#45512yes—
129C22×C43C2×#12011yescharacteristic
130C4×C43—22no—
131C4×C43—21no—
132C4×C43—21no—
133C4×C43—44no—
134C4×C43C2×#13714yes—
135Dic43—28no—
136Dic43—44no—
137Dic43—82no—
138C2×Q82—431no—
139#3139—431no—
140#3113—432no—
141#1645—438no—
142#1558D4311yescharacteristic
143#1491—432no—
144C2×C43—22no—
145C2×C43#300412yes—
146C2×C43C2×#45511yescharacteristic
147Q82—434no—
148Q82—864no—
149Q82—862no—
150#533—431no—
151C2×C4⋊Q8—862no—
152C2×C4⋊Q8—862no—
153C2×C4⋊Q8C2×D4311yescharacteristic
154C2×C4×Q8—432no—
155C2×C4×Q8—862no—
156#491—862no—
157#487—434no—
158#483—862no—
159#475—434no—
160#462—434no—
161#451—862no—
162#441—864no—
163#432C2×D4312yes—
164#419—862no—
165C4×M16—431no—
166#333C2×D4314yes—
167Q8⋊C8—438no—
168C43#1855111yescharacteristic, complemented, Sylow
169C22×Q8—432no—
170C22×Q8—862no—
171C22×Q8D17212yes—
172C2×Q16—864no—
173C2×M16—861no—
174C4⋊Q8—22no—
175C4⋊Q8—432no—
176C4⋊Q8—868no—
177C4⋊Q8—868no—
178C4⋊Q8—868no—
179C4⋊Q8—868no—
180C4⋊Q8D17212yes—
181C4⋊Q8C22×D4312yes—
182#125—861no—
183C22⋊Q8—862no—
184C4×Q8—434no—
185C4×Q8—434no—
186C4×Q8—868no—
187C4×Q8—868no—
188C4×Q8—862no—
189C4×Q8—862no—
190C4×Q8—862no—
191#117—861no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—432no—
194C2×C4⋊C4—864no—
195C2×C4⋊C4—862no—
196C2×C42—862no—
197C2×C42—862no—
198C2×C42C22×D4311yescharacteristic
199#106—864no—
200C4⋊C8C22×D4314yes—
201#103—864no—
202#103—864no—
203#103—868no—
204C22⋊C8—22no—
205#97—22no—
206#97—861no—
207C4×C8—432no—
208C2×Q8—22no—
209C2×Q8—44no—
210C2×Q8—434no—
211C2×Q8—868no—
212C2×Q8—868no—
213C2×Q8—862no—
214C2×Q8—862no—
215C2×Q8—3444no—
216C2×Q8C2×D17214yes—
217C22×C4—22no—
218C22×C4—862no—
219C22×C4—862no—
220C22×C4C2×D17211yescharacteristic
221C22×C4D4×D4312yes—
222Q16—1728no—
223M16—1722no—
224C2×C8—24no—
225C2×C8—862no—
226C4⋊C4—24no—
227C4⋊C4—24no—
228C4⋊C4—434no—
229C4⋊C4—8616no—
230C4⋊C4—862no—
231C4⋊C4—864no—
232C4⋊C4—864no—
233C4⋊C4—862no—
234C4⋊C4—862no—
235C4⋊C4—1722no—
236C22⋊C4—1721no—
237C42—868no—
238C42—864no—
239C42—864no—
240C42—1721no—
241C42C2×D17211yescharacteristic
242C42D4×D4312yes—
243C42C23×D4311yescharacteristic
244C23#1306329511yescharacteristic
245Q8—44no—
246Q8—82no—
247Q8—438no—
248Q8—868no—
249Q8—864no—
250Q8—3448no—
251Q8—1724no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—44no—
256C2×C4—868no—
257C2×C4—864no—
258C2×C4—864no—
259C2×C4—1722no—
260C2×C4—1724no—
261C2×C4#1306329512yes—
262C2×C4#1306329511yescharacteristic
263C2×C4C2×D4×D4312yes—
264C2×C4C22×D17211yescharacteristic
265C8—44no—
266C8—1722no—
267C22—22no—
268C22#1458307912yes—
269C22C2×#1306329511yescharacteristic
270C4—22no—
271C4—21no—
272C4—21no—
273C4—44no—
274C4—868no—
275C4—3442no—
276C4—1724no—
277C4#137×D4314yes—
278C2—22no—
279C2#1914383112yes—
280C2C2×#1458307911yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1558C2
socleC22×C43C2×#120
prime radicalC23×C43#120
hypercenter#1558D43
hypocenterC43#18551
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
4. #19133817C2semidirect
168. C43#18551semidirect

Maximal subgroups

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

subgroupindex
C2×#145836292
#191449752
#191447262
#191338172
#191330412
C43×#15582
#1855143