Finite Group Databasebeta

← #25016943

Subgroups — #25016943

Order 11008.

326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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#19136257C212yesmaximal
3#19132766C211yesmaximal, characteristic, complemented
4#19132765C212yesmaximal, complemented
5C43×#1412C211yesmaximal, characteristic, complemented
6#14583455C411yescharacteristic, complemented
7#14583447C2211yescharacteristic
8#14583269C411yescharacteristic, complemented
9#14583268C411yescharacteristic, complemented
10#14583263C2211yescharacteristic
11#14583257—22no—
12#14582892—22no—
13#14582871—22no—
14#97×D43C411yescharacteristic, complemented
15#14582693—22no—
16#14582692C2212yes—
17C43×#490C2211yescharacteristic
18C43×#353C2212yes—
19C2×#10621900D412yes—
20C2×C8×D43—21no—
21#13063325C2×C411yescharacteristic
22#13063324—21no—
23#13063317C2×C411yescharacteristic
24#13063312D412yes—
25#13063303—41no—
26#13063296—41no—
27#13063290—41no—
28D4×Dic43—41no—
29#13063283—21no—
30#13063281—42no—
31C42×D43C2×C411yescharacteristic
32#13063250—22no—
33#13063248—22no—
34#13063246—22no—
35#13063240—22no—
36#13063239—42no—
37#13063236C2×C411yescharacteristic
38#13063235—21no—
39#127×C43C2311yescharacteristic
40#125×C43C2×C411yescharacteristic
41#102×C43—22no—
42#99×C43—22no—
43#97×C43C2×C411yescharacteristic
44C2×D4×C43—41no—
45C2×D4×C43C2×D412yes—
46C2×C22⋊D43—22no—
47C22×Dic43—22no—
48#10621900—42no—
49#10621900—42no—
50C2×C4×D43—21no—
51C2×C4×D43C22⋊C411yescharacteristic
52C2×Dic86—41no—
53C2×Dic86C22⋊C412yes—
54C2×C8×C43—21no—
55C4⋊C4×C43—21no—
56C4⋊C4×C43—41no—
57C22⋊C4×C43—42no—
58C42×C43C22×C411yescharacteristic
59C22⋊Dic43—42no—
60C22⋊Dic43—42no—
61(C2×D43)⋊C4—41no—
62C4⋊Dic43—21no—
63C4⋊Dic43—41no—
64Dic43⋊C4—41no—
65Dic43⋊C4—41no—
66Dic43⋊C4—82no—
67C4×Dic43—21no—
68C4×Dic43—41no—
69C4×Dic43—82no—
70C4×Dic43C22⋊C411yescharacteristic
71C2×C43⋊C8—21no—
72C8×D43—41no—
73C8×D43—41no—
74C23×C43—22no—
75C22×D43#9911yescharacteristic
76D4×C43—42no—
77D4×C43—82no—
78C2×C4×C43—21no—
79C2×C4×C43—41no—
80C2×C4×C43—82no—
81C2×C4×C43C2×C22⋊C411yescharacteristic
82C22⋊D43—82no—
83C2×Dic43—21no—
84C2×Dic43—22no—
85C2×Dic43—42no—
86C2×Dic43—42no—
87C2×Dic43—41no—
88C2×Dic43—82no—
89C2×Dic43#9911yescharacteristic
90C4×D43—21no—
91C4×D43—21no—
92C4×D43—81no—
93Dic86—42no—
94Dic86—82no—
95C8×C43—41no—
96C43⋊C8—41no—
97#13594—431nomaximal, Sylow
98C22×C43—42no—
99C22×C43—82no—
100C22×C43C2×#9911yescharacteristic
101C2×D43—21no—
102C2×D43—41no—
103C4×C43—21no—
104C4×C43—41no—
105C4×C43—81no—
106C4×C43—162no—
107Dic43—41no—
108Dic43—42no—
109Dic43—81no—
110Dic43—162no—
111Dic43#35411yescharacteristic
112Dic43#35411yescharacteristic
113#3135—431no—
114#2126—432no—
115#1412—431no—
116#1412—432no—
117#1412D4311yescharacteristic, complemented
118C2×C43—21no—
119C2×C43—82no—
120C2×C43C2×#35411yescharacteristic
121D43—41no—
122#533—431no—
123#532—431no—
124#491—431no—
125#491—431no—
126#490—431no—
127#490C2×D4311yescharacteristic
128#489—862no—
129#416—862no—
130#410—862no—
131C2×#97—431no—
132#354—862no—
133#353—432no—
134#353C2×D4312yes—
135C43#1359411yescharacteristic, complemented, Sylow
136C2×#41—432no—
137C22×C8—861no—
138C4⋊Q8—431no—
139C4⋊Q8—861no—
140#127C22×D4311yescharacteristic
141#125—431no—
142#125C4×D4311yescharacteristic
143#124—432no—
144C22⋊Q8—1721no—
145#121—1721no—
146C4×Q8—1721no—
147C4×D4—1721no—
148#117—861no—
149#117—1722no—
150C2×C42—431no—
151#103—862no—
152#103—862no—
153#102—22no—
154#102—862no—
155#99—22no—
156#99—862no—
157#99—1722no—
158#97—431no—
159#97—861no—
160#97C4×D4311yescharacteristic
161#41—1722no—
162#41—1722no—
163C2×Q8—432no—
164C2×Q8—1721no—
165C2×D4—41no—
166C2×D4—862no—
167C2×D4D4×D4312yes—
168C22×C4—431no—
169C22×C4—861no—
170C22×C4—862no—
171C2×C8—21no—
172C2×C8—861no—
173C2×C8—1721no—
174C2×C8—1721no—
175C4⋊C4—21no—
176C4⋊C4—41no—
177C4⋊C4—861no—
178C4⋊C4—3442no—
179C4⋊C4—1721no—
180C4⋊C4—1721no—
181C4⋊C4—1721no—
182C22⋊C4—42no—
183C22⋊C4—1721no—
184C22⋊C4—1722no—
185C22⋊C4—1722no—
186C42—431no—
187C42—861no—
188C42—3442no—
189C42—1721no—
190C42C2×C4×D4311yescharacteristic
191C23—22no—
192C23—431no—
193Q8—3442no—
194Q8—1722no—
195D4—42no—
196D4—82no—
197D4—3442no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—82no—
201C2×C4—431no—
202C2×C4—861no—
203C2×C4—861no—
204C2×C4—861no—
205C2×C4—862no—
206C2×C4—3441no—
207C2×C4—3442no—
208C2×C4—1722no—
209C2×C4—1722no—
210C2×C4—1721no—
211C2×C4C22⋊C4×D4311yescharacteristic
212C8—41no—
213C8—1721no—
214C22—42no—
215C22—82no—
216C22—861no—
217C22—1721no—
218C22#99×D4311yescharacteristic
219C4—21no—
220C4—41no—
221C4—81no—
222C4—162no—
223C4—431no—
224C4—431no—
225C4—3441no—
226C4—1721no—
227C4—1722no—
228C4—6882no—
229C2—21no—
230C2—82no—
231C2—1721no—
232C2#354×D4311yescharacteristic
subgroupG/H
centerC2#354×D43
commutatorC42×C43C22×C4
Frattini#127C22×D43
FittingC43×#1412C2
socleC2×C43C2×#354
prime radical#14583447C22
cosocle#127×C43C23
hypercenter#1412D43
hypocenterC43#13594
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1412

Complements

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

NH ≅ G/Ntype
3. #19132766C2semidirect
4. #19132765C2semidirect
5. C43×#1412C2semidirect
6. #14583455C4semidirect
8. #14583269C4semidirect
9. #14583268C4semidirect
14. #97×D43C4semidirect
117. #1412D43semidirect
135. C43#13594semidirect

Maximal subgroups

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

subgroupindex
#191449392
#191362572
#191327662
#191327652
C43×#14122
#1359443