Finite Group Databasebeta

← #25009943

Subgroups — #25009943

Order 11008.

310 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 55 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#19145490C211yesmaximal, characteristic
2#19136814C212yesmaximal, complemented
3#19132582C212yesmaximal, complemented
4#19132533C211yesmaximal, characteristic
5C43×#2098C211yesmaximal, characteristic
6#14583470—21no—
7#14583241—22no—
8#14583157C2212yes—
9#14583140—21no—
10#14583057—22no—
11#14582723—22no—
12#14582714—22no—
13#14582681C2212yes—
14C43×#430C2211yescharacteristic
15C43×#424—21no—
16C43×#421—21no—
17C43×#408C2211yescharacteristic
18C43×H(3,ℤ/4)C2211yescharacteristic
19C22×Dic86—21no—
20C2×Dic172—21no—
21C2×Dic172D412yes—
22#13063323—41no—
23#13063312—41no—
24#13063306—41no—
25#13063306—41no—
26#13063304—22no—
27#13063304—22no—
28#13063284—21no—
29#13063265—22no—
30#13063259—21no—
31#13063257D412yes—
32#13063250—22no—
33#13063250—22no—
34C2×#41×C43D411yescharacteristic
35C2×M16×C43—21no—
36C2×M16×C43C2311yescharacteristic
37C22×C8×C43D411yescharacteristic
38#117×C43—21no—
39#108×C43—22no—
40C4⋊C8×C43—42no—
41#104×C43—42no—
42C22⋊C8×C43—22no—
43#41×C43—41no—
44#41×C43—41no—
45C2×Q8×C43SD1611yescharacteristic
46C2×D4×C43—21no—
47C2×D4×C43SD1611yescharacteristic
48C22×C4×C43—21no—
49C22×C4×C43C2×D411yescharacteristic
50C22×Dic43—41no—
51C2×Dic86—22no—
52C2×Dic86—41no—
53C2×Dic86—81no—
54C2×Dic86—81no—
55M16×C43—41no—
56M16×C43—41no—
57M16×C43—41no—
58C2×C8×C43—21no—
59C2×C8×C43—41no—
60C2×C8×C43—41no—
61C2×C8×C43C2×D412yes—
62C4⋊C4×C43—41no—
63C22⋊C4×C43—41no—
64C42×C43—22no—
65C22⋊Dic43—41no—
66C22⋊Dic43—42no—
67C22⋊Dic43—42no—
68C4⋊Dic43—22no—
69Dic43⋊C4—42no—
70Dic43⋊C4—42no—
71C4×Dic43—41no—
72Dic172—42no—
73Dic172—81no—
74C43⋊C16—42no—
75C23×C43—21no—
76C23×C43AGL(1,ℤ/8)11yescharacteristic
77Q8×C43—41no—
78D4×C43—41no—
79D4×C43—81no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—41no—
84C2×C4×C43—41no—
85C2×C4×C43—42no—
86C2×C4×C43#12011yescharacteristic
87C2×C4×C43C2×SD1611yescharacteristic
88C2×Dic43—42no—
89C2×Dic43—42no—
90C2×Dic43—82no—
91Dic86—42no—
92Dic86—42no—
93Dic86—82no—
94C8×C43—22no—
95C8×C43—41no—
96C8×C43—81no—
97#12302—431nomaximal, Sylow
98C22×C43—21no—
99C22×C43—41no—
100C22×C43—42no—
101C22×C43—41no—
102C22×C43#45011yescharacteristic
103C4×C43—21no—
104C4×C43—41no—
105C4×C43—82no—
106C4×C43#45311yescharacteristic
107C4×C43#45811yescharacteristic
108Dic43—82no—
109Dic43—82no—
110#3202—431no—
111#2239—432no—
112#2098D4311yescharacteristic
113#1340—432no—
114#1321—431no—
115C2×C43—21no—
116C2×C43—41no—
117C2×C43—81no—
118C2×C43#161311yescharacteristic
119#536—861no—
120#485—862no—
121#470—432no—
122#467—861no—
123#451—862no—
124#430C2×D4311yescharacteristic
125#424—21no—
126#421—21no—
127#408C2×D4311yescharacteristic
128#365—862no—
129#362—862no—
130#349—432no—
131H(3,ℤ/4)C2×D4311yescharacteristic
132C43#1230211yescharacteristic, complemented, Sylow
133C2×#41C22⋊D4311yescharacteristic
134C22×Q8—861no—
135C2×Q16—432no—
136C2×Q16—861no—
137C2×M16—21no—
138C2×M16C22×D4311yescharacteristic
139C22×C8C22⋊D4311yescharacteristic
140C4⋊Q8—1721no—
141#124—1721no—
142#123—1721no—
143#123—1721no—
144C22⋊Q8—862no—
145C22⋊Q8—862no—
146#117—21no—
147#117—861no—
148M32—862no—
149#108—22no—
150#107—861no—
151#106—432no—
152C4⋊C8—42no—
153#104—42no—
154#103—862no—
155#103—862no—
156C22⋊C8—22no—
157#41—41no—
158#41—41no—
159C2×Q8—862no—
160C2×Q8—3441no—
161C2×Q8—3441no—
162C2×Q8—1721no—
163C2×Q8#1062188411yescharacteristic
164C2×D4—21no—
165C2×D4#1062188411yescharacteristic
166C22×C4—21no—
167C22×C4—1721no—
168C22×C4C2×C22⋊D4311yescharacteristic
169Q16—3441no—
170Q16—1722no—
171M16—41no—
172M16—41no—
173M16—41no—
174C2×C8—21no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8D4×D4312yes—
178C4⋊C4—41no—
179C4⋊C4—862no—
180C4⋊C4—1722no—
181C4⋊C4—1722no—
182C22⋊C4—41no—
183C22⋊C4—1721no—
184C22⋊C4—1722no—
185C22⋊C4—1722no—
186C42—22no—
187C42—1721no—
188C16—1722no—
189C23—21no—
190C23#1306335011yescharacteristic
191Q8—41no—
192Q8—3442no—
193Q8—1722no—
194Q8—1722no—
195D4—41no—
196D4—81no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—3442no—
204C2×C4—1722no—
205C2×C4—1722no—
206C2×C4#1306329311yescharacteristic
207C2×C4C2×#1062188411yescharacteristic
208C8—22no—
209C8—41no—
210C8—81no—
211C22—21no—
212C22—41no—
213C22—42no—
214C22—41no—
215C22#1458304911yescharacteristic
216C4—21no—
217C4—41no—
218C4—82no—
219C4—3442no—
220C4—3442no—
221C4#1458306611yescharacteristic
222C4#1458308811yescharacteristic
223C2—21no—
224C2—41no—
225C2—81no—
226C2#1913361411yescharacteristic
subgroupG/H
centerC2#19133614
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#2098C2
socleC2×C43#1613
prime radicalC2×#41×C43D4
hypercenter#2098D43
hypocenterC43#12302
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2098

Complements

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

NH ≅ G/Ntype
2. #19136814C2semidirect
3. #19132582C2semidirect
132. C43#12302semidirect

Maximal subgroups

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

subgroupindex
#191454902
#191368142
#191325822
#191325332
C43×#20982
#1230243