Finite Group Databasebeta

← #25007772

Subgroups — #25007772

Order 11008.

318 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 69 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#19144939C211yesmaximal, characteristic
2#347×D43C212yesmaximal, complemented
3#19132629C212yesmaximal, complemented
4#19132628C211yesmaximal, characteristic, complemented
5C43×#1355C211yesmaximal, characteristic, complemented
6#14583455C411yescharacteristic
7#14583447C411yescharacteristic
8M32×D43—22no—
9#14583269C411yescharacteristic
10#14583268C2211yescharacteristic
11#14583263C411yescharacteristic
12#14583257—22no—
13#14582892—22no—
14#97×D43C2211yescharacteristic
15#14582677C2212yes—
16#14582676—22no—
17C43×#490C2211yescharacteristic
18C43×#347C2212yes—
19C2×#10621900—21no—
20C2×C8×D43D412yes—
21#13063325C2×C411yescharacteristic
22#13063324—21no—
23#13063317C2×C411yescharacteristic
24#13063312—21no—
25#13063303—41no—
26#13063296—41no—
27#13063290—41no—
28D4×Dic43—41no—
29#13063283—21no—
30C42×D43C2×C411yescharacteristic
31#13063265—22no—
32#13063264—24no—
33C16×D43—24no—
34#13063250—22no—
35#13063248—22no—
36#13063246—22no—
37#13063236C2×C411yescharacteristic
38#13063235D412yes—
39#127×C43C2×C411yescharacteristic
40#125×C43C2×C411yescharacteristic
41M32×C43—22no—
42#102×C43—22no—
43#97×C43C2311yescharacteristic
44C2×D4×C43—21no—
45C2×D4×C43—41no—
46C2×C22⋊D43—41no—
47C22×Dic43—41no—
48#10621900—42no—
49#10621900—42no—
50C2×C4×D43—21no—
51C2×C4×D43C22⋊C411yescharacteristic
52C2×Dic86—21no—
53C2×Dic86—41no—
54C2×C8×C43C2×D412yes—
55C4⋊C4×C43—21no—
56C4⋊C4×C43—41no—
57C42×C43C22×C411yescharacteristic
58C22⋊Dic43—42no—
59(C2×D43)⋊C4—41no—
60C4⋊Dic43—21no—
61C4⋊Dic43—41no—
62Dic43⋊C4—41no—
63Dic43⋊C4—41no—
64C4×Dic43—21no—
65C4×Dic43—41no—
66C4×Dic43C22⋊C411yescharacteristic
67C2×C43⋊C8C22⋊C412yes—
68C8×D43—22no—
69C8×D43—22no—
70C16×C43—24no—
71C43⋊C16—24no—
72C23×C43—41no—
73C22×D43#10011yescharacteristic
74D4×C43—42no—
75D4×C43—82no—
76C2×C4×C43—21no—
77C2×C4×C43—41no—
78C2×C4×C43C2×C22⋊C411yescharacteristic
79C22⋊D43—82no—
80C2×Dic43—21no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83C2×Dic43—81no—
84C2×Dic43—81no—
85C2×Dic43#10011yescharacteristic
86C4×D43—81no—
87C4×D43#10412yes—
88C4×D43#10412yes—
89Dic86—42no—
90Dic86—82no—
91C8×C43—22no—
92C43⋊C8—22no—
93#11911—431nomaximal, Sylow
94C22×C43—82no—
95C22×C43—81no—
96C22×C43C2×#10011yescharacteristic
97C2×D43—41no—
98C2×D43#32912yes—
99C4×C43—41no—
100C4×C43—81no—
101C4×C43C2×#10412yes—
102Dic43—41no—
103Dic43—81no—
104Dic43—81no—
105Dic43#32911yescharacteristic
106Dic43#32911yescharacteristic
107#3135—431no—
108C2×#347—432no—
109#1356—432no—
110#1355—431no—
111#1355D4311yescharacteristic, complemented
112C2×C43—21no—
113C2×C43—161no—
114C2×C43C2×#32911yescharacteristic
115D43—22no—
116#533—431no—
117#532—431no—
118C2×M32—862no—
119#491—431no—
120#491—431no—
121#490—431no—
122#490C2×D4311yescharacteristic
123#489—862no—
124#416—862no—
125C2×#97—431no—
126#347—432no—
127#347—862no—
128#347C2×D4312yes—
129C43#1191111yescharacteristic, complemented, Sylow
130C2×#41—861no—
131C22×C8—432no—
132C4⋊Q8—431no—
133C4⋊Q8—861no—
134#127C4×D4311yescharacteristic
135#125—431no—
136#125C4×D4311yescharacteristic
137#124—861no—
138C22⋊Q8—1721no—
139#121—1721no—
140C4×Q8—1721no—
141C4×D4—1721no—
142#117—861no—
143C2×C42—431no—
144M32—22no—
145M32—864no—
146M32—862no—
147C2×C16—864no—
148#103—862no—
149#103—862no—
150#102—22no—
151#102—862no—
152#97—432no—
153#97—431no—
154#97C22×D4311yescharacteristic
155#41—1722no—
156#41—1722no—
157C2×Q8—861no—
158C2×Q8—1721no—
159C2×D4—21no—
160C2×D4—41no—
161C2×D4—1721no—
162C22×C4—431no—
163C22×C4—861no—
164C22×C4—1721no—
165C2×C8—432no—
166C2×C8—862no—
167C2×C8—862no—
168C2×C8D4×D4312yes—
169C4⋊C4—21no—
170C4⋊C4—41no—
171C4⋊C4—861no—
172C4⋊C4—1721no—
173C4⋊C4—1721no—
174C4⋊C4—1721no—
175C22⋊C4—1721no—
176C22⋊C4—1722no—
177C42—431no—
178C42—861no—
179C42—1721no—
180C42C2×C4×D4311yescharacteristic
181C16—24no—
182C16—864no—
183C23—41no—
184C23—431no—
185Q8—3442no—
186Q8—1722no—
187D4—42no—
188D4—82no—
189D4—3442no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—431no—
193C2×C4—432no—
194C2×C4—432no—
195C2×C4—861no—
196C2×C4—3441no—
197C2×C4—3441no—
198C2×C4—3441no—
199C2×C4—1721no—
200C2×C4—1721no—
201C2×C4C22⋊C4×D4311yescharacteristic
202C8—22no—
203C8—862no—
204C22—82no—
205C22—81no—
206C22—432no—
207C22—1721no—
208C22#100×D4311yescharacteristic
209C4—41no—
210C4—81no—
211C4—431no—
212C4—431no—
213C4—3441no—
214C4—3441no—
215C4—1721no—
216C4#104×D4312yes—
217C2—21no—
218C2—161no—
219C2—862no—
220C2#329×D4311yescharacteristic
subgroupG/H
centerC2#329×D43
commutatorC42×C43C22×C4
Frattini#97C22×D43
FittingC43×#1355C2
socleC2×C43C2×#329
prime radical#14583447C4
cosocle#97×C43C23
hypercenter#1355D43
hypocenterC43#11911
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #347×D43C2semidirect
3. #19132629C2semidirect
4. #19132628C2semidirect
5. C43×#1355C2semidirect
111. #1355D43semidirect
129. C43#11911semidirect

Maximal subgroups

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

subgroupindex
#191449392
#347×D432
#191326292
#191326282
C43×#13552
#1191143