Finite Group Databasebeta

← #24997593

Subgroups — #24997593

Order 11008.

476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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#19145119C211yesmaximal, characteristic
2#19144635C212yesmaximal
3#19135535C211yesmaximal, characteristic
4#19132999C212yesmaximal
5C43×#1275C211yesmaximal, characteristic
6#14583456C2212yes—
7C2×C4×Dic86C2211yescharacteristic
8#14583308—22no—
9#14583308—22no—
10#14583235—22no—
11#14583195—22no—
12#14583110—22no—
13#14583057—22no—
14C4×Dic172—24no—
15#14582937—22no—
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17#14582653—22no—
18#14582631—24no—
19C43×#431C2212yes—
20C2×#97×C43C2211yescharacteristic
21C22×Dic86D411yescharacteristic
22C2×Dic172—24no—
23C22×C43⋊C8—21no—
24#13063325D412yes—
25#13063325D412yes—
26#13063317—22no—
27#13063304—22no—
28#13063304—22no—
29C4×Dic86—22no—
30C4×Dic86—22no—
31C4×Dic86—22no—
32C4×Dic86—22no—
33#13063284—22no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×C4×Dic43—21no—
37#13063259—22no—
38#13063259—22no—
39#13063259—24no—
40#13063257—24no—
41C4⋊(C43⋊C8)—22no—
42#13063250—24no—
43#13063250—24no—
44C22×C8×C43D412yes—
45C2×C42×C43C2311yescharacteristic
46C4⋊C8×C43—22no—
47C22⋊C8×C43—22no—
48#97×C43—22no—
49C4×C8×C43D414yes—
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43#4111yescharacteristic
53C22×Dic43—21no—
54C22×Dic43—21no—
55C2×Dic86—22no—
56C2×Dic86—22no—
57C2×Dic86—22no—
58C2×Dic86—42no—
59C2×C8×C43—22no—
60C2×C8×C43—22no—
61C2×C8×C43—24no—
62C2×C8×C43Q1614yescomplemented
63C42×C43C2×D412yes—
64C42×C43C2×D412yes—
65C22⋊Dic43—42no—
66C4⋊Dic43—22no—
67C4⋊Dic43—22no—
68C4⋊Dic43—22no—
69C4⋊Dic43—22no—
70C4⋊Dic43—22no—
71Dic43⋊C4—42no—
72Dic43⋊C4—42no—
73Dic43⋊C4—42no—
74C4×Dic43—41no—
75C4×Dic43—41no—
76C4×Dic43—42no—
77C2×C43⋊C8—41no—
78C2×C43⋊C8—42no—
79Dic172—48no—
80C23×C43#12111yescharacteristic
81C2×C4×C43—41no—
82C2×C4×C43—41no—
83C2×C4×C43#12012yes—
84C2×C4×C43#12011yescharacteristic
85C2×C4×C43#12112yes—
86C2×C4×C43#12711yescharacteristic
87C2×C4×C43C2×Q1612yes—
88C2×C4×C43#13712yes—
89C2×Dic43—22no—
90C2×Dic43—41no—
91C2×Dic43—41no—
92C2×Dic43—42no—
93C2×Dic43—41no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96Dic86—24no—
97Dic86—42no—
98Dic86—44no—
99Dic86—44no—
100C8×C43—24no—
101C8×C43—44no—
102C43⋊C8—81no—
103#10037—431nomaximal, Sylow
104C22×C43—21no—
105C22×C43—21no—
106C22×C43#39211yescharacteristic
107C22×C43#46212yes—
108C4×C43—22no—
109C4×C43—22no—
110C4×C43#45112yes—
111C4×C43#49411yescharacteristic
112C4×C43#49711yescharacteristic
113Dic43—42no—
114Dic43—82no—
115Dic43—82no—
116Dic43—81no—
117#3162—431no—
118#3104—432no—
119#1985—431no—
120#1481—432no—
121#1275D4311yescharacteristic
122C2×C43—22no—
123C2×C43#201011yescharacteristic
124C2×C43#201611yescharacteristic
125C2×C43#201711yescharacteristic
126#533—432no—
127C2×C4×Q8—431no—
128#501—862no—
129#501—862no—
130#484—862no—
131#477—862no—
132#462—862no—
133#451—862no—
134C4×Q16—864no—
135#431C2×D4312yes—
136#427—862no—
137C2×C4⋊C8—431no—
138C2×#97C2×D4311yescharacteristic
139#336—862no—
140Q8⋊C8—864no—
141C43#1003711yescharacteristic, complemented, Sylow
142C22×Q8—431no—
143C2×Q16—864no—
144C22×C8—861no—
145C22×C8D17212yes—
146C4⋊Q8—432no—
147C4⋊Q8—432no—
148#125—862no—
149C22⋊Q8—862no—
150C22⋊Q8—862no—
151C4×Q8—862no—
152C4×Q8—862no—
153C4×Q8—862no—
154C4×Q8—862no—
155#117—862no—
156C2×C4⋊C4—431no—
157C2×C4⋊C4—861no—
158C2×C42—861no—
159C2×C42C22×D4311yescharacteristic
160#107—862no—
161#107—862no—
162#107—864no—
163#106—864no—
164C4⋊C8—22no—
165C4⋊C8—862no—
166#103—864no—
167#103—864no—
168C22⋊C8—22no—
169#97—22no—
170C4×C8D17214yes—
171C2×Q8—862no—
172C2×Q8—862no—
173C2×Q8—862no—
174C2×Q8—1722no—
175C22×C4—861no—
176C22×C4—861no—
177C22×C4C2×D17211yescharacteristic
178C22×C4D4×D4311yescharacteristic
179C22×C4#1062190211yescharacteristic
180Q16—1728no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—24no—
184C2×C8—1721no—
185C2×C8—1722no—
186C2×C8Dic17214yescomplemented
187C4⋊C4—862no—
188C4⋊C4—862no—
189C4⋊C4—862no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—1722no—
193C4⋊C4—1722no—
194C4⋊C4—1722no—
195C22⋊C4—1722no—
196C42—1721no—
197C42—1721no—
198C42—1722no—
199C42C2×D17212yes—
200C42D4×D4312yes—
201C23#1306330011yescharacteristic
202Q8—864no—
203Q8—1724no—
204Q8—1724no—
205Q8—1722no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—862no—
209C2×C4—1722no—
210C2×C4—1721no—
211C2×C4—1722no—
212C2×C4—1722no—
213C2×C4—1721no—
214C2×C4—1721no—
215C2×C4#1306329512yes—
216C2×C4#1306329511yescharacteristic
217C2×C4#1306330012yes—
218C2×C4#1306332211yescharacteristic
219C2×C4C2×Dic17212yes—
220C2×C4#1306335812yes—
221C8—24no—
222C8—44no—
223C8—3441no—
224C22—21no—
225C22—21no—
226C22#1458280911yescharacteristic
227C22#1458311012yes—
228C4—22no—
229C4—22no—
230C4—3442no—
231C4—3441no—
232C4—3442no—
233C4—1722no—
234C4#1458305712yes—
235C4#1458327911yescharacteristic
236C4#1458329311yescharacteristic
237C2—22no—
238C2#1913566311yescharacteristic
239C2#1913569711yescharacteristic
240C2#1913570011yescharacteristic
subgroupG/H
centerC2×C4#13063322
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1275C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#1275D43
hypocenterC43#10037
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
62. C2×C8×C43Q16semidirect
141. C43#10037semidirect
186. C2×C8Dic172semidirect

Maximal subgroups

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

subgroupindex
#191451192
#191446352
#191355352
#191329992
C43×#12752
#1003743