Finite Group Databasebeta

← #24985796

Subgroups — #24985796

Order 11008.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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#19142588C211yesmaximal, characteristic
2#19136138C211yesmaximal, characteristic
3#19136005C212yesmaximal
4#19132420C212yesmaximal
5C43×#1272C211yesmaximal, characteristic
6C2×#13063256—21no—
7C2×#13063250—22no—
8C2×#13063249—21no—
9#14582820—22no—
10#14582819—21no—
11#14582806—21no—
12#14582805C2212yes—
13#14582803—22no—
14#14582769C2211yescharacteristic
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C22×Dic86D412yes—
21C22×C43⋊C8—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—22no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43D412yes—
26C2×Dic43⋊C4—22no—
27C2×C4×Dic43—21no—
28#13063256—42no—
29#13063250—44no—
30#13063249—42no—
31C43⋊#95—21no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C22×Q8×C43D411yescharacteristic
36C22×C8×C43—22no—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C42×C43C2311yescharacteristic
39#95×C43—22no—
40C2×Q8×C43—21no—
41C2×Q8×C43—41no—
42C2×Q8×C43—41no—
43C2×Q8×C43Q1612yes—
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43C2×D411yescharacteristic
47C22×C4×C43C2×D412yes—
48C22×Dic43—22no—
49C22×Dic43—22no—
50C22×Dic43—41no—
51C2×Dic86—22no—
52C2×Dic86—42no—
53C2×Dic86—42no—
54C2×Dic86—81no—
55C2×Dic86—82no—
56C2×Dic86SD1614yes—
57C2×C8×C43—42no—
58C2×C8×C43—42no—
59C2×C8×C43—42no—
60C4⋊C4×C43—41no—
61C42×C43—41no—
62C4⋊Dic43—42no—
63C4⋊Dic43—41no—
64C4⋊Dic43—41no—
65C4⋊Dic43—42no—
66C4⋊Dic43—42no—
67C4⋊Dic43—81no—
68Dic43⋊C4—82no—
69C4×Dic43—81no—
70C2×C43⋊C8—22no—
71C2×C43⋊C8—41no—
72C2×C43⋊C8—41no—
73C23×C43#12011yescharacteristic
74Q8×C43—42no—
75Q8×C43—81no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—41no—
82C2×C4×C43—41no—
83C2×C4×C43—41no—
84C2×C4×C43—42no—
85C2×C4×C43C2×SD1612yes—
86C2×C4×C43C2×Q1611yescharacteristic
87C2×C4×C43#13712yes—
88C2×C4×C43#13711yescharacteristic
89C2×Dic43—24no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—82no—
96C2×Dic43—81no—
97Dic86—44no—
98Dic86—82no—
99Dic86—84no—
100C8×C43—82no—
101C43⋊C8—42no—
102#7812—431nomaximal, Sylow
103C22×C43#44812yes—
104C22×C43#45111yescharacteristic
105C22×C43#45311yescharacteristic
106C22×C43#45512yes—
107C22×C43#45811yescharacteristic
108C4×C43—22no—
109C4×C43—22no—
110C4×C43—21no—
111C4×C43—21no—
112C4×C43—42no—
113C4×C43—81no—
114Dic43—44no—
115Dic43—82no—
116Dic43—161no—
117#2811—431no—
118#2096—431no—
119#2072—432no—
120#1272—432no—
121#1272D4311yescharacteristic
122C2×C43#160812yes—
123C2×C43#161411yescharacteristic
124C2×C43#162311yescharacteristic
125C2×C43#164512yes—
126C2×C43#165911yescharacteristic
127C2×#106—861no—
128C2×#103—862no—
129C2×#103—861no—
130#395—862no—
131#395—861no—
132#391—432no—
133#391—862no—
134#391—861no—
135#391C2×D4311yescharacteristic
136#384—431no—
137#340—862no—
138#336—431no—
139#336C2×D4312yes—
140C43#781211yescharacteristic, complemented, Sylow
141C22×Q8—432no—
142C22×Q8—861no—
143C22×Q8D17211yescharacteristic
144C22×C8—22no—
145C22×C8—861no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4—862no—
148C2×C4⋊C4—861no—
149C2×C4⋊C4—861no—
150C2×C4⋊C4—862no—
151C2×C4⋊C4D17211yescharacteristic
152C2×C42—861no—
153C2×C42C22×D4311yescharacteristic
154#106—1722no—
155#103—1724no—
156#103—1722no—
157#95—22no—
158#95—862no—
159#95—861no—
160#95—862no—
161#95—862no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—434no—
166C2×Q8—862no—
167C2×Q8—3441no—
168C2×Q8—3442no—
169C2×Q8—1722no—
170C2×Q8—1722no—
171C2×Q8Dic17212yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—862no—
175C22×C4—862no—
176C22×C4—1721no—
177C22×C4C2×D17211yescharacteristic
178C22×C4D4×D4312yes—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—862no—
183C2×C8—1721no—
184C2×C8—1721no—
185C4⋊C4—41no—
186C4⋊C4—3442no—
187C4⋊C4—3441no—
188C4⋊C4—1721no—
189C4⋊C4—1721no—
190C4⋊C4—1722no—
191C4⋊C4—1722no—
192C4⋊C4—1722no—
193C42—41no—
194C42—3441no—
195C23#1306329511yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—3442no—
199Q8—3444no—
200Q8—1724no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—864no—
211C2×C4—3441no—
212C2×C4—3442no—
213C2×C4—1722no—
214C2×C4—1722no—
215C2×C4—1722no—
216C2×C4—1722no—
217C2×C4—1722no—
218C2×C4SD16×D4312yes—
219C2×C4C2×Dic17211yescharacteristic
220C2×C4#1306335712yes—
221C2×C4#1306335811yescharacteristic
222C8—82no—
223C8—1722no—
224C22#1458303912yes—
225C22#1458305711yescharacteristic
226C22#1458306911yescharacteristic
227C22#1458307812yes—
228C22#1458309011yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—42no—
234C4—81no—
235C4—3442no—
236C4—1724no—
237C4—6881no—
238C2#1913358712yes—
239C2#1913362211yescharacteristic
240C2#1913367411yescharacteristic
241C2#1913381912yes—
242C2#1913390211yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socle, prime radicalC23×C43#120
hypercenter#1272D43
hypocenterC43#7812
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
140. C43#7812semidirect

Maximal subgroups

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

subgroupindex
#191425882
#191361382
#191360052
#191324202
C43×#12722
#781243