Finite Group Databasebeta

← #24997590

Subgroups — #24997590

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#19144630C212yesmaximal
2#19135535C211yesmaximal, characteristic
3#19132998C212yesmaximal
4#19132426C211yesmaximal, characteristic
5C43×#3162C211yesmaximal, characteristic
6C2×C4×Dic86C2211yescharacteristic
7#14583232—22no—
8#14583191—22no—
9#14583106—22no—
10#14583054—22no—
11C4×#10621885—24no—
12#14582952C2212yes—
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14#14582653—22no—
15Q8⋊(C43⋊C8)—24no—
16C43×#533C2212yes—
17C43×#501—22no—
18C43×#501—22no—
19C43×#427—22no—
20C2×#97×C43C2211yescharacteristic
21C22×Dic86D411yescharacteristic
22C2×#10621885—24no—
23C22×C43⋊C8—21no—
24C4×Dic86—22no—
25C4×Dic86—22no—
26C2×C4⋊Dic43D411yescharacteristic
27C2×Dic43⋊C4—21no—
28C2×C4×Dic43—21no—
29#13063258—24no—
30C4⋊(C43⋊C8)—22no—
31C4⋊(C43⋊C8)—22no—
32#13063249—24no—
33#13063248—24no—
34C22⋊(C43⋊C8)—22no—
35C4×C43⋊C8D414yes—
36C22×C8×C43D412yes—
37C4⋊Q8×C43D412yes—
38C4⋊Q8×C43D412yes—
39#125×C43—22no—
40C22⋊Q8×C43—22no—
41C22⋊Q8×C43—22no—
42C4×Q8×C43—22no—
43C4×Q8×C43—22no—
44#117×C43—22no—
45C2×C42×C43C2311yescharacteristic
46#107×C43—22no—
47#107×C43—22no—
48#106×C43—24no—
49#97×C43—22no—
50C2×Q8×C43—22no—
51C2×Q8×C43—22no—
52C22×C4×C43C2×D411yescharacteristic
53C22×C4×C43C2×D411yescharacteristic
54C22×C4×C43#4111yescharacteristic
55C22×Dic43—21no—
56C22×Dic43—21no—
57C2×Dic86—22no—
58C2×Dic86—42no—
59C2×C8×C43—22no—
60C2×C8×C43—22no—
61C2×C8×C43Q1614yescomplemented
62C4⋊C4×C43—22no—
63C4⋊C4×C43—22no—
64C4⋊C4×C43—22no—
65C4⋊C4×C43—22no—
66C4⋊C4×C43—42no—
67C4⋊C4×C43—42no—
68C22⋊C4×C43—42no—
69C42×C43—42no—
70C42×C43C2×D412yes—
71C42×C43C2×D412yes—
72#10621885—48no—
73C4⋊Dic43—22no—
74Dic43⋊C4—42no—
75C4×Dic43—41no—
76C4×Dic43—41no—
77C2×C43⋊C8—24no—
78C2×C43⋊C8—41no—
79C2×C43⋊C8—42no—
80C23×C43#12111yescharacteristic
81Q8×C43—44no—
82Q8×C43—44no—
83C2×C4×C43—41no—
84C2×C4×C43—41no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43#12012yes—
88C2×C4×C43#12011yescharacteristic
89C2×C4×C43#12112yes—
90C2×C4×C43#12711yescharacteristic
91C2×C4×C43C2×Q1612yes—
92C2×C4×C43#13712yes—
93C2×Dic43—22no—
94C2×Dic43—41no—
95C2×Dic43—41no—
96C2×Dic43—42no—
97C2×Dic43—41no—
98Dic86—24no—
99Dic86—42no—
100C8×C43—24no—
101C43⋊C8—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—82no—
111C4×C43—82no—
112C4×C43#45112yes—
113C4×C43#49411yescharacteristic
114C4×C43#49711yescharacteristic
115Dic43—42no—
116Dic43—81no—
117#3162D4311yescharacteristic
118#3104—432no—
119#1985—431no—
120#1481—432no—
121#1275—431no—
122C2×C43—22no—
123C2×C43#201011yescharacteristic
124C2×C43#201611yescharacteristic
125C2×C43#201711yescharacteristic
126#533C2×D4312yes—
127C2×C4×Q8—431no—
128#501—22no—
129#501—22no—
130#484—862no—
131#477—862no—
132#462—862no—
133#451—862no—
134C4×Q16—864no—
135#431—432no—
136#427—22no—
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×C8C22⋊D4312yes—
146C4⋊Q8C22⋊D4312yes—
147C4⋊Q8C22⋊D4312yes—
148#125—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—862no—
154C4×Q8—862no—
155#117—22no—
156C2×C4⋊C4—431no—
157C2×C4⋊C4—861no—
158C2×C42—861no—
159C2×C42C22×D4311yescharacteristic
160#107—22no—
161#107—22no—
162#107—864no—
163#106—24no—
164C4⋊C8—862no—
165C4⋊C8—862no—
166#103—864no—
167#103—864no—
168C22⋊C8—862no—
169#97—22no—
170C4×C8—434no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—862no—
174C2×Q8—1722no—
175C22×C4—861no—
176C22×C4—861no—
177C22×C4D4×D4311yescharacteristic
178C22×C4#1062190011yescharacteristic
179C22×C4C2×C22⋊D4311yescharacteristic
180Q16—1728no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—864no—
184C2×C8—1721no—
185C2×C8—1722no—
186C2×C8#1062188514yescomplemented
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—862no—
194C4⋊C4—1722no—
195C22⋊C4—42no—
196C42—42no—
197C42—1721no—
198C42—1721no—
199C42D4×D4312yes—
200C42C2×C22⋊D4312yes—
201C23#1306329611yescharacteristic
202Q8—44no—
203Q8—44no—
204Q8—864no—
205Q8—1722no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—862no—
211C2×C4—1722no—
212C2×C4—1721no—
213C2×C4—1721no—
214C2×C4—1721no—
215C2×C4#1306329312yes—
216C2×C4#1306329411yescharacteristic
217C2×C4#1306329712yes—
218C2×C4#1306332111yescharacteristic
219C2×C4C2×#1062188512yes—
220C2×C4#1306335612yes—
221C8—24no—
222C8—3441no—
223C8—1724no—
224C22—21no—
225C22—21no—
226C22#1458280711yescharacteristic
227C22#1458310612yes—
228C4—22no—
229C4—22no—
230C4—82no—
231C4—82no—
232C4—3441no—
233C4—1722no—
234C4#1458305512yes—
235C4#1458327811yescharacteristic
236C4#1458329111yescharacteristic
237C2—22no—
238C2#1913565911yescharacteristic
239C2#1913569511yescharacteristic
240C2#1913569811yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3162C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#3162D43
hypocenterC43#10037
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
61. 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
#191446302
#191355352
#191329982
#191324262
C43×#31622
#1003743