Finite Group Databasebeta

← #24997592

Subgroups — #24997592

Order 11008.

476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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#19144634C212yesmaximal
3#19132997C212yesmaximal
4#19132426C211yesmaximal, characteristic
5C43×#1985C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583308—22no—
8#14583308—22no—
9#14583234—22no—
10#14583194—22no—
11#14583109—22no—
12#14583055—22no—
13C4×#10621885—24no—
14#14582952C2212yes—
15#14582937—22no—
16#14582629—24no—
17C2×C4×Q8×C43C2211yescharacteristic
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×#97×C43C2211yescharacteristic
20C43×#336—22no—
21C2×#10621885—24no—
22#13063325D412yes—
23#13063325D412yes—
24#13063317—22no—
25#13063304—22no—
26#13063304—22no—
27C4×Dic86—22no—
28C4×Dic86—22no—
29#13063284—22no—
30#13063259—22no—
31#13063259—22no—
32#13063258—24no—
33#13063257—24no—
34C4⋊(C43⋊C8)—22no—
35#13063249—24no—
36#13063248—24no—
37C22⋊(C43⋊C8)—22no—
38C4×C43⋊C8D414yes—
39C22×Q8×C43D411yescharacteristic
40C22×C8×C43—21no—
41C22×C8×C43D412yes—
42C4×Q8×C43—22no—
43C4×Q8×C43—22no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C42×C43—21no—
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—22no—
49#97×C43—22no—
50C2×Q8×C43—22no—
51C2×Q8×C43—42no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43#4111yescharacteristic
57C2×Dic86—22no—
58C2×Dic86—22no—
59C2×C8×C43—22no—
60C2×C8×C43—22no—
61C2×C8×C43—41no—
62C2×C8×C43—42no—
63C2×C8×C43Q1614yescomplemented
64C4⋊C4×C43—22no—
65C4⋊C4×C43—42no—
66C42×C43—41no—
67C42×C43—41no—
68C42×C43C2×D412yes—
69C42×C43C2×D412yes—
70C22⋊Dic43—42no—
71#10621885—48no—
72C4⋊Dic43—22no—
73C4⋊Dic43—22no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76Dic43⋊C4—42no—
77Dic43⋊C4—42no—
78C4×Dic43—42no—
79C2×C43⋊C8—24no—
80C23×C43#12111yescharacteristic
81Q8×C43—24no—
82Q8×C43—42no—
83C2×C4×C43—22no—
84C2×C4×C43—41no—
85C2×C4×C43—41no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43—41no—
90C2×C4×C43#12011yescharacteristic
91C2×C4×C43#12012yes—
92C2×C4×C43#12112yes—
93C2×C4×C43#12711yescharacteristic
94C2×C4×C43C2×Q1612yes—
95C2×C4×C43#13712yes—
96C2×Dic43—42no—
97C2×Dic43—42no—
98Dic86—44no—
99Dic86—44no—
100C8×C43—24no—
101C8×C43—81no—
102C43⋊C8—44no—
103#10037—431nomaximal, Sylow
104C22×C43—21no—
105C22×C43—21no—
106C22×C43#39211yescharacteristic
107C22×C43#46212yes—
108C4×C43—22no—
109C4×C43—22no—
110C4×C43—42no—
111C4×C43—81no—
112C4×C43#45112yes—
113C4×C43#49411yescharacteristic
114C4×C43#49711yescharacteristic
115Dic43—82no—
116Dic43—82no—
117#3162—431no—
118#3104—432no—
119#1985D4311yescharacteristic
120#1481—432no—
121#1275—431no—
122C2×C43—22no—
123C2×C43#201011yescharacteristic
124C2×C43#201611yescharacteristic
125C2×C43#201711yescharacteristic
126#533—432no—
127C2×C4×Q8C2×D4311yescharacteristic
128#501—862no—
129#501—862no—
130#484—862no—
131#477—862no—
132#462—862no—
133#451—862no—
134C4×Q16—864no—
135#431—432no—
136#427—862no—
137C2×C4⋊C8C2×D4311yescharacteristic
138C2×#97C2×D4311yescharacteristic
139#336—22no—
140Q8⋊C8—864no—
141C43#1003711yescharacteristic, complemented, Sylow
142C22×Q8D17211yescharacteristic
143C2×Q16—864no—
144C22×C8—21no—
145C22×C8C22⋊D4312yes—
146C4⋊Q8—432no—
147C4⋊Q8—432no—
148#125—862no—
149C22⋊Q8—862no—
150C22⋊Q8—862no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—862no—
154C4×Q8—862no—
155#117—862no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4D17211yescharacteristic
158C2×C42—21no—
159C2×C42C22×D4311yescharacteristic
160#107—864no—
161#107—862no—
162#107—862no—
163#106—864no—
164C4⋊C8—22no—
165C4⋊C8—862no—
166#103—864no—
167#103—864no—
168C22⋊C8—862no—
169#97—22no—
170C4×C8—434no—
171C2×Q8—22no—
172C2×Q8—42no—
173C2×Q8—862no—
174C2×Q8—862no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C2×D17211yescharacteristic
178C22×C4#1062189811yescharacteristic
179C22×C4C2×C22⋊D4311yescharacteristic
180Q16—1728no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8—864no—
186C2×C8#1062188514yescomplemented
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—862no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—862no—
193C4⋊C4—1722no—
194C4⋊C4—1722no—
195C22⋊C4—1722no—
196C42—41no—
197C42—41no—
198C42—1722no—
199C42D4×D4312yes—
200C42D4×D4312yes—
201C23#1306329911yescharacteristic
202Q8—24no—
203Q8—42no—
204Q8—1724no—
205Q8—1724no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—1722no—
214C2×C4—1722no—
215C2×C4#1306329311yescharacteristic
216C2×C4#1306329512yes—
217C2×C4#1306329812yes—
218C2×C4#1306332111yescharacteristic
219C2×C4C2×#1062188512yes—
220C2×C4#1306335512yes—
221C8—24no—
222C8—81no—
223C8—1724no—
224C22—21no—
225C22—21no—
226C22#1458280811yescharacteristic
227C22#1458310912yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—81no—
232C4—3442no—
233C4—3442no—
234C4#1458305412yes—
235C4#1458327811yescharacteristic
236C4#1458329411yescharacteristic
237C2—22no—
238C2#1913566211yescharacteristic
239C2#1913569411yescharacteristic
240C2#1913569911yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1985C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#1985D43
hypocenterC43#10037
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
63. C2×C8×C43Q16semidirect
141. C43#10037semidirect
186. C2×C8#10621885semidirect

Maximal subgroups

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

subgroupindex
#191451192
#191446342
#191329972
#191324262
C43×#19852
#1003743