Finite Group Databasebeta

← #25078531

Subgroups — #25078531

Order 11008.

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

normal subgroups only

This group has 784 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
1#19145809C212yesmaximal
2#19145117C211yesmaximal, characteristic
3#19133923C218yesmaximal, complemented
4#19133233C211yesmaximal, characteristic
5#19133210C212yesmaximal
6C43×#3556C211yesmaximal, characteristic
7#14583456C2211yescharacteristic
8#14583309C2214yes—
9#14583309C2214yes—
10#14583305—22no—
11#14583269C2214yes—
12#14583240—24no—
13#14583191—22no—
14#14583181—22no—
15#14582956C2212yes—
16#14582935—22no—
17C2×#13063236C2211yescharacteristic
18#14582641C2218yes—
19#14582641C2214yes—
20C43×#564C2214yes—
21C43×#557—22no—
22C43×#557—22no—
23C43×#557—22no—
24C43×#541—22no—
25C43×#541—24no—
26C43×#533C2212yes—
27C43×#533C2211yescharacteristic
28C22×C43⋊C8—21no—
29#13063325C2312yes—
30#13063317—21no—
31#13063304—22no—
32C4×Dic86—22no—
33#13063284—21no—
34#13063258—24no—
35#13063258—24no—
36#13063256—24no—
37#13063256—24no—
38C4⋊(C43⋊C8)—22no—
39#13063248—24no—
40#13063248—24no—
41C22⋊(C43⋊C8)—22no—
42#13063236—21no—
43#13063236C2312yes—
44#13063236C2314yes—
45C4⋊Q8×C43—24no—
46C4⋊Q8×C43—22no—
47C4⋊Q8×C43D412yes—
48C4⋊Q8×C43D412yes—
49C4⋊Q8×C43D412yes—
50#126×C43—28no—
51#125×C43—24no—
52#125×C43—22no—
53#125×C43—28no—
54#125×C43—28no—
55#125×C43—28no—
56#125×C43C2312yes—
57#125×C43C2314yes—
58C22⋊Q8×C43—22no—
59C22⋊Q8×C43—22no—
60C22⋊Q8×C43—22no—
61C4×Q8×C43—24no—
62C4×Q8×C43—24no—
63C4×Q8×C43—24no—
64C4×Q8×C43—22no—
65C4×Q8×C43—22no—
66C4×Q8×C43—22no—
67#117×C43D412yes—
68#117×C43D414yes—
69C2×C42×C43C2311yescharacteristic
70C2×Q8×C43—22no—
71C2×Q8×C43—22no—
72C2×Q8×C43—22no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D412yes—
75C2×Dic86—22no—
76C4⋊C4×C43—28no—
77C4⋊C4×C43—28no—
78C4⋊C4×C43—28no—
79C4⋊C4×C43—22no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—24no—
83C4⋊C4×C43—24no—
84C4⋊C4×C43—24no—
85C4⋊C4×C43C2×D414yes—
86C4⋊C4×C43C2×D414yes—
87C4⋊C4×C43C2×D414yes—
88C22⋊C4×C43—22no—
89C22⋊C4×C43—24no—
90C42×C43—28no—
91C42×C43—24no—
92C42×C43—22no—
93C42×C43C2×D411yescharacteristic
94C42×C43C2×D412yes—
95C42×C43C2411yescharacteristic
96C22⋊Dic43—41no—
97C4⋊Dic43—22no—
98C4⋊Dic43—22no—
99Dic43⋊C4—42no—
100C4×Dic43—41no—
101C2×C43⋊C8—24no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—24no—
104C23×C43#12011yescharacteristic
105Q8×C43—44no—
106Q8×C43—44no—
107Q8×C43—44no—
108C2×C4×C43—22no—
109C2×C4×C43—24no—
110C2×C4×C43—24no—
111C2×C4×C43—24no—
112C2×C4×C43—42no—
113C2×C4×C43#12012yes—
114C2×C4×C43#12011yescharacteristic
115C2×C4×C43C22×D411yescharacteristic
116C2×C4×C43C22×D412yes—
117C2×Dic43—42no—
118Dic86—44no—
119C43⋊C8—24no—
120C43⋊C8—44no—
121#19067—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—22no—
124C22×C43C2×#12011yescharacteristic
125C4×C43—21no—
126C4×C43—22no—
127C4×C43—22no—
128C4×C43—44no—
129C4×C43—44no—
130C4×C43—44no—
131C4×C43#45612yes—
132Dic43—82no—
133#3556D4311yescharacteristic
134#3237—432no—
135#3162—431no—
136#1663—438no—
137#1537—431no—
138#1531—432no—
139C2×C43—41no—
140C2×C43C2×#45611yescharacteristic
141C2×C43#302012yes—
142#564C2×D4314yes—
143#557—22no—
144#557—22no—
145#557—22no—
146#541—22no—
147#541—24no—
148#533—431no—
149#533C2×D4311yescharacteristic
150#533C2×D4312yes—
151#501—434no—
152#501—434no—
153#501—862no—
154#491—434no—
155#485—864no—
156#477—862no—
157#475—862no—
158#432—432no—
159#427—862no—
160C2×#97—431no—
161#330—434no—
162#330—438no—
163C43#1906711yescharacteristic, complemented, Sylow
164C22×C8—861no—
165C4⋊Q8—24no—
166C4⋊Q8—22no—
167C4⋊Q8—432no—
168C4⋊Q8C22⋊D4312yes—
169C4⋊Q8C22⋊D4312yes—
170C4⋊Q8C22⋊D4312yes—
171#126—28no—
172#125—24no—
173#125—22no—
174#125—28no—
175#125—28no—
176#125—28no—
177#125—861no—
178#125C22×D4314yes—
179#125C22×D4312yes—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—862no—
184C4×Q8—24no—
185C4×Q8—24no—
186C4×Q8—24no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—862no—
191#117—861no—
192#117C22⋊D4312yes—
193#117C22⋊D4314yes—
194C2×C42C22×D4311yescharacteristic
195#107—864no—
196#107—864no—
197#106—864no—
198#106—864no—
199C4⋊C8—862no—
200#103—864no—
201#103—864no—
202C22⋊C8—862no—
203#97—432no—
204#97—434no—
205#97—861no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—862no—
210C22×C4C2×C22⋊D4311yescharacteristic
211C22×C4C2×C22⋊D4312yes—
212C2×C8—864no—
213C2×C8—862no—
214C2×C8—864no—
215C4⋊C4—28no—
216C4⋊C4—28no—
217C4⋊C4—28no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—862no—
225C4⋊C4—862no—
226C4⋊C4—1722no—
227C4⋊C4C2×C22⋊D4314yes—
228C4⋊C4C2×C22⋊D4314yes—
229C4⋊C4C2×C22⋊D4314yes—
230C22⋊C4—22no—
231C22⋊C4—24no—
232C22⋊C4—1721no—
233C42—28no—
234C42—24no—
235C42—22no—
236C42—1721no—
237C42C2×C22⋊D4311yescharacteristic
238C42C2×C22⋊D4312yes—
239C42C23×D4311yescharacteristic
240C23#1306329411yescharacteristic
241Q8—44no—
242Q8—44no—
243Q8—44no—
244Q8—1724no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—24no—
248C2×C4—24no—
249C2×C4—42no—
250C2×C4—1722no—
251C2×C4#1306329412yes—
252C2×C4#1306329411yescharacteristic
253C2×C4C22×C22⋊D4311yescharacteristic
254C2×C4C22×C22⋊D4312yes—
255C8—864no—
256C8—1724no—
257C22—21no—
258C22—22no—
259C22C2×#1306329411yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—44no—
264C4—44no—
265C4—44no—
266C4—3442no—
267C4#1458308212yes—
268C2—41no—
269C2C2×#1458308211yescharacteristic
270C2#1914395912yes—
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3556C2
socleC22×C43C2×#120
prime radicalC23×C43#120
hypercenter#3556D43
hypocenterC43#19067
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3556

Complements

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

NH ≅ G/Ntype
3. #19133923C2semidirect
163. C43#19067semidirect

Maximal subgroups

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

subgroupindex
#191458092
#191451172
#191339232
#191332332
#191332102
C43×#35562
#1906743