Finite Group Databasebeta

← C41×#7403 #23783604

Subgroups — C41×#7403 #23783604

Order 10496.

282 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C41×#2013C211yesmaximal, characteristic
2C41×#1393C211yesmaximal, characteristic
3C41×#1318C211yesmaximal, characteristic
4C22×SD16×C41—21no—
5C2×C4⋊Q8×C41C411yescharacteristic, complemented
6C2×#103×C41—21no—
7C2×#99×C41—21no—
8C41×#390C2211yescharacteristic
9C41×#336C411yescharacteristic, complemented
10C41×#324—21no—
11C22×Q8×C41—21no—
12C22×D4×C41D411yescharacteristic
13C2×SD16×C41—42no—
14C2×SD16×C41—42no—
15C2×SD16×C41—41no—
16C2×SD16×C41—41no—
17C22×C8×C41—21no—
18C4⋊Q8×C41—42no—
19C2×C4⋊C4×C41—41no—
20C2×C4⋊C4×C41D411yescharacteristic
21C2×C22⋊C4×C41—41no—
22C2×C22⋊C4×C41—41no—
23C2×C42×C41C2×C411yescharacteristic
24#103×C41—42no—
25#99×C41—22no—
26#99×C41—41no—
27C22⋊C8×C41—41no—
28C24×C41—21no—
29C2×Q8×C41—22no—
30C2×Q8×C41—41no—
31C2×Q8×C41—41no—
32C2×Q8×C41—41no—
33C2×Q8×C41—41no—
34C2×Q8×C41—41no—
35C2×D4×C41—21no—
36C2×D4×C41—41no—
37C2×D4×C41—41no—
38C2×D4×C41D811yescharacteristic
39C2×D4×C41SD1611yescharacteristic
40C22×C4×C41—21no—
41C22×C4×C41—21no—
42C22×C4×C41—41no—
43C22×C4×C41—81no—
44C22×C4×C41C22⋊C411yescharacteristic
45SD16×C41—44no—
46SD16×C41—44no—
47C2×C8×C41—22no—
48C2×C8×C41—41no—
49C2×C8×C41—41no—
50C2×C8×C41—81no—
51C4⋊C4×C41—41no—
52C4⋊C4×C41—42no—
53C4⋊C4×C41—42no—
54C22⋊C4×C41—42no—
55C22⋊C4×C41—82no—
56C22⋊C4×C41—81no—
57C42×C41—41no—
58C23×C41—21no—
59C23×C41—21no—
60C23×C41—41no—
61C23×C41—41no—
62C23×C41—81no—
63C23×C41—81no—
64C23×C41#9911yescharacteristic
65Q8×C41—42no—
66Q8×C41—42no—
67Q8×C41—81no—
68Q8×C41—81no—
69D4×C41—41no—
70D4×C41—41no—
71D4×C41—81no—
72C2×C4×C41—21no—
73C2×C4×C41—21no—
74C2×C4×C41—22no—
75C2×C4×C41—41no—
76C2×C4×C41—41no—
77C2×C4×C41—42no—
78C2×C4×C41—41no—
79C2×C4×C41—81no—
80C2×C4×C41—81no—
81C2×C4×C41—81no—
82C2×C4×C41—82no—
83C2×C4×C41—161no—
84C2×C4×C41—161no—
85C2×C4×C41#10211yescharacteristic
86C2×C4×C41#10411yescharacteristic
87C8×C41—42no—
88C8×C41—161no—
89#7403C4111yesmaximal, characteristic, direct product factor, Sylow
90C22×C41—21no—
91C22×C41—21no—
92C22×C41—41no—
93C22×C41—41no—
94C22×C41—81no—
95C22×C41—81no—
96C22×C41—81no—
97C22×C41—81no—
98C22×C41—161no—
99C22×C41#32711yescharacteristic
100C22×C41AΣL(1,𝔽16)11yescharacteristic
101C22×C41#35311yescharacteristic
102C4×C41—21no—
103C4×C41—21no—
104C4×C41—42no—
105C4×C41—82no—
106C4×C41—81no—
107C4×C41—162no—
108#2013C2×C4111yescharacteristic
109#1393C2×C4111yescharacteristic
110#1318C2×C4111yescharacteristic
111C2×C41—21no—
112C2×C41—21no—
113C2×C41—81no—
114C2×C41—81no—
115C2×C41#134311yescharacteristic
116C2×C41#140711yescharacteristic
117C2×C41#140911yescharacteristic
118C22×SD16—21no—
119C2×C4⋊Q8C4×C4111yescharacteristic, complemented
120C2×#103—21no—
121C2×#99—21no—
122#390C22×C4111yescharacteristic
123#336C4×C4111yescharacteristic, complemented
124#324—21no—
125C41#740311yescharacteristic, direct product factor, Sylow
126C22×Q8—21no—
127C22×D4D4×C4111yescharacteristic
128C2×SD16—42no—
129C2×SD16—42no—
130C2×SD16—41no—
131C2×SD16—41no—
132C22×C8—21no—
133C4⋊Q8—42no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4D4×C4111yescharacteristic
136C2×C22⋊C4—41no—
137C2×C22⋊C4—41no—
138C2×C42C2×C4×C4111yescharacteristic
139#103—42no—
140#99—22no—
141#99—41no—
142C22⋊C8—41no—
143C24—21no—
144C2×Q8—22no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—41no—
153C2×D4D8×C4111yescharacteristic
154C2×D4SD16×C4111yescharacteristic
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—41no—
158C22×C4—81no—
159C22×C4C22⋊C4×C4111yescharacteristic
160SD16—44no—
161SD16—44no—
162C2×C8—22no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—81no—
166C4⋊C4—41no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C22⋊C4—42no—
170C22⋊C4—82no—
171C22⋊C4—81no—
172C42—41no—
173C23—21no—
174C23—21no—
175C23—41no—
176C23—41no—
177C23—81no—
178C23—81no—
179C23#99×C4111yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—81no—
183Q8—81no—
184D4—41no—
185D4—41no—
186D4—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—161no—
199C2×C4—161no—
200C2×C4#102×C4111yescharacteristic
201C2×C4#104×C4111yescharacteristic
202C8—42no—
203C8—161no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—161no—
213C22C41×#32711yescharacteristic
214C22C41×AΣL(1,𝔽16)11yescharacteristic
215C22C41×#35311yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—82no—
220C4—81no—
221C4—162no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—81no—
226C2C41×#134311yescharacteristic
227C2C41×#140711yescharacteristic
228C2C41×#140911yescharacteristic
subgroupG/H
center, socleC22×C41#353
commutatorC2×C42C2×C4×C41
Frattini, cosocle#390C22×C41
prime radicalC22×D4×C41D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C41 ◁ C22×C4×C41 ◁ C41×#390 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C41C4semidirect
9. C41×#336C4semidirect
89. #7403C41direct (N × H)
119. C2×C4⋊Q8C4×C41semidirect
123. #336C4×C41semidirect
125. C41#7403direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#20132
C41×#13932
C41×#13182
#740341