Finite Group Databasebeta

← #25016946

Subgroups — #25016946

Order 11008.

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

normal subgroups only

This group has 388 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#19144968C211yesmaximal, characteristic
2#353×D43C212yesmaximal
3#19132766C211yesmaximal, characteristic, complemented
4#19132765C212yesmaximal, complemented
5C43×#1412C211yesmaximal, characteristic, complemented
6#14583455C411yescharacteristic, complemented
7#127×D43C2211yescharacteristic
8#14583265C411yescharacteristic, complemented
9#14583264C411yescharacteristic, complemented
10#14583263C2211yescharacteristic
11#14583244—22no—
12#14582902—22no—
13#99×D43—22no—
14#14582851C411yescharacteristic, complemented
15#14582692C2212yes—
16#14582691—22no—
17C43×#490C2211yescharacteristic
18C43×#353C2212yes—
19C2×D4×D43—41no—
20C2×D4×D43D412yes—
21C2×#10621872—21no—
22#13063324—21no—
23#13063322C2×C411yescharacteristic
24#13063321—41no—
25#13063321D412yes—
26#13063317C2×C411yescharacteristic, complemented
27#13063303—41no—
28#13063290—41no—
29#13063283—21no—
30C22⋊C4×D43—42no—
31C42×D43C2×C411yescharacteristic
32#13063247—22no—
33#13063246—22no—
34#13063245—22no—
35#13063240—22no—
36#13063239—42no—
37#13063236C2×C411yescharacteristic, complemented
38C8×Dic43—21no—
39#127×C43C2311yescharacteristic
40#125×C43C2×C411yescharacteristic, complemented
41#102×C43—22no—
42#99×C43—22no—
43#97×C43C2×C411yescharacteristic, complemented
44C23×D43—22no—
45C2×D4×C43—41no—
46C2×D4×C43C2×D412yes—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—42no—
49D4×D43—42no—
50D4×D43—42no—
51D4×D43—84no—
52C2×D172—41no—
53C2×D172C22⋊C412yes—
54C2×C4×D43—21no—
55C2×C4×D43—82no—
56C2×C4×D43C22⋊C411yescharacteristic
57C2×Dic86—41no—
58C2×C8×C43—21no—
59C4⋊C4×C43—21no—
60C4⋊C4×C43—41no—
61C22⋊C4×C43—42no—
62C42×C43C22×C411yescharacteristic
63C22⋊Dic43—42no—
64(C2×D43)⋊C4—41no—
65(C2×D43)⋊C4—82no—
66C4⋊Dic43—21no—
67Dic43⋊C4—41no—
68Dic43⋊C4—41no—
69C4×Dic43—21no—
70C4×Dic43—41no—
71C4×Dic43C22⋊C411yescharacteristic
72C2×C43⋊C8—21no—
73#10621872—42no—
74C23×C43—22no—
75C22×D43—22no—
76C22×D43—42no—
77C22×D43—42no—
78C22×D43—84no—
79C22×D43#9911yescharacteristic
80D4×C43—42no—
81D4×C43—82no—
82C2×C4×C43—21no—
83C2×C4×C43—41no—
84C2×C4×C43—82no—
85C2×C4×C43C2×C22⋊C411yescharacteristic
86C22⋊D43—82no—
87C22⋊D43—84no—
88C2×Dic43—21no—
89C2×Dic43—41no—
90C2×Dic43—82no—
91C2×Dic43#9911yescharacteristic
92D172—42no—
93D172—82no—
94C4×D43—22no—
95C4×D43—42no—
96C4×D43—164no—
97Dic86—82no—
98C8×C43—41no—
99C43⋊C8—41no—
100#13595—431nomaximal, Sylow
101C22×C43—42no—
102C22×C43—82no—
103C22×C43C2×#9911yescharacteristic
104C2×D43—41no—
105C2×D43—42no—
106C2×D43—84no—
107C2×D43—82no—
108C2×D43—162no—
109C2×D43#35412yes—
110C4×C43—21no—
111C4×C43—41no—
112C4×C43—81no—
113C4×C43—162no—
114Dic43—22no—
115Dic43—21no—
116Dic43—81no—
117Dic43—162no—
118#3138—431no—
119C2×#353—432no—
120#1412—431no—
121#1412—432no—
122#1412D4311yescharacteristic, complemented
123C2×C43—21no—
124C2×C43—82no—
125C2×C43C2×#35411yescharacteristic
126D43—22no—
127D43—82no—
128#533—431no—
129C2×#127—431no—
130#490—431no—
131#490—431no—
132#490—431no—
133#490C2×D4311yescharacteristic
134#486—862no—
135#418—862no—
136C2×#99—862no—
137C4×M16—431no—
138#353—432no—
139#353—862no—
140#353C2×D4312yes—
141C43#1359511yescharacteristic, complemented, Sylow
142C22×D4—432no—
143C22×D4—1721no—
144C2×M16—861no—
145C4⋊Q8—861no—
146#127—432no—
147#127—431no—
148#127—1721no—
149#127C22×D4311yescharacteristic
150#125—431no—
151#125C4×D4311yescharacteristic, complemented
152C22⋊Q8—1721no—
153C4×Q8—1721no—
154#117—861no—
155C2×C22⋊C4—1722no—
156C2×C42—431no—
157#102—22no—
158#102—862no—
159#102—862no—
160#102—862no—
161#99—22no—
162#99—862no—
163#99—1722no—
164#97—431no—
165#97C4×D4311yescharacteristic, complemented
166C4×C8—861no—
167C24—862no—
168C2×Q8—1721no—
169C2×D4—41no—
170C2×D4—432no—
171C2×D4—862no—
172C2×D4—3444no—
173C2×D4—1721no—
174C2×D4—1722no—
175C2×D4—1722no—
176C2×D4—1722no—
177C2×D4D4×D4312yes—
178C22×C4—431no—
179C22×C4—861no—
180C22×C4—3442no—
181M16—1722no—
182C2×C8—21no—
183C2×C8—861no—
184C4⋊C4—21no—
185C4⋊C4—41no—
186C4⋊C4—861no—
187C4⋊C4—1721no—
188C4⋊C4—1721no—
189C22⋊C4—42no—
190C22⋊C4—3442no—
191C22⋊C4—1721no—
192C22⋊C4—1722no—
193C42—431no—
194C42—861no—
195C42—1721no—
196C42C2×C4×D4311yescharacteristic
197C23—22no—
198C23—431no—
199C23—862no—
200C23—3444no—
201C23—1722no—
202C23—1722no—
203Q8—3442no—
204D4—42no—
205D4—82no—
206D4—3442no—
207D4—3442no—
208D4—3444no—
209D4—1722no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—82no—
213C2×C4—431no—
214C2×C4—862no—
215C2×C4—861no—
216C2×C4—3442no—
217C2×C4—1722no—
218C2×C4—1721no—
219C2×C4—6884no—
220C2×C4C22⋊C4×D4311yescharacteristic
221C8—41no—
222C8—1721no—
223C22—42no—
224C22—82no—
225C22—432no—
226C22—3442no—
227C22—3444no—
228C22—1721no—
229C22—1722no—
230C22—6882no—
231C22#99×D4311yescharacteristic
232C4—21no—
233C4—41no—
234C4—81no—
235C4—162no—
236C4—862no—
237C4—861no—
238C4—3441no—
239C4—6882no—
240C2—21no—
241C2—82no—
242C2—862no—
243C2—3442no—
244C2#354×D4311yescharacteristic
subgroupG/H
centerC2#354×D43
commutatorC42×C43C22×C4
Frattini#127C22×D43
FittingC43×#1412C2
socleC2×C43C2×#354
prime radical#127×D43C22
cosocle#127×C43C23
hypercenter#1412D43
hypocenterC43#13595
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. #14583265C4semidirect
9. #14583264C4semidirect
14. #14582851C4semidirect
26. #13063317C2×C4semidirect
37. #13063236C2×C4semidirect
40. #125×C43C2×C4semidirect
43. #97×C43C2×C4semidirect
122. #1412D43semidirect
141. C43#13595semidirect
151. #125C4×D43semidirect
165. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191449682
#353×D432
#191327662
#191327652
C43×#14122
#1359543