Finite Group Databasebeta

← C41×#7409 #23783610

Subgroups — C41×#7409 #23783610

Order 10496.

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

normal subgroups only

This group has 268 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×#2007C211yesmaximal, characteristic
2C41×#1394C211yesmaximal, characteristic, complemented
3C41×#1272C211yesmaximal, characteristic, complemented
4C2×#137×C41—21no—
5C41×#537C411yescharacteristic
6C2×#104×C41—21no—
7C2×#101×C41—21no—
8C41×#391C2211yescharacteristic
9C41×#343C411yescharacteristic
10C41×#336—21no—
11C2×#41×C41—21no—
12C22×Q8×C41D411yescharacteristic
13#137×C41—42no—
14#137×C41—41no—
15#137×C41—41no—
16C2×Q16×C41—41no—
17C2×SD16×C41—41no—
18C2×M16×C41—21no—
19C2×M16×C41—41no—
20C22×C8×C41—41no—
21C22⋊Q8×C41—41no—
22#121×C41—41no—
23#121×C41—41no—
24C2×C4⋊C4×C41C2×C411yescharacteristic
25C2×C42×C41D411yescharacteristic
26#104×C41—42no—
27#101×C41—22no—
28#101×C41—41no—
29#95×C41—41no—
30#41×C41—41no—
31#41×C41—41no—
32#41×C41—41no—
33#41×C41—41no—
34C2×Q8×C41—21no—
35C2×Q8×C41—21no—
36C2×Q8×C41—41no—
37C2×Q8×C41—41no—
38C2×Q8×C41D811yescharacteristic
39C2×Q8×C41SD1611yescharacteristic
40C2×D4×C41—21no—
41C2×D4×C41—41no—
42C2×D4×C41—41no—
43C22×C4×C41—21no—
44C22×C4×C41—21no—
45C22×C4×C41—21no—
46C22×C4×C41—41no—
47C22×C4×C41C22⋊C411yescharacteristic
48Q16×C41—42no—
49Q16×C41—42no—
50SD16×C41—42no—
51SD16×C41—42no—
52M16×C41—22no—
53M16×C41—41no—
54M16×C41—42no—
55M16×C41—81no—
56C2×C8×C41—41no—
57C2×C8×C41—42no—
58C2×C8×C41—81no—
59C2×C8×C41—81no—
60C2×C8×C41—81no—
61C4⋊C4×C41—41no—
62C4⋊C4×C41—41no—
63C22⋊C4×C41—42no—
64C42×C41—41no—
65C23×C41—41no—
66C23×C41#9911yescharacteristic
67Q8×C41—41no—
68Q8×C41—41no—
69Q8×C41—41no—
70Q8×C41—41no—
71Q8×C41—81no—
72D4×C41—41no—
73D4×C41—41no—
74D4×C41—81no—
75D4×C41—81no—
76D4×C41—161no—
77C2×C4×C41—21no—
78C2×C4×C41—21no—
79C2×C4×C41—21no—
80C2×C4×C41—21no—
81C2×C4×C41—21no—
82C2×C4×C41—21no—
83C2×C4×C41—41no—
84C2×C4×C41—41no—
85C2×C4×C41—41no—
86C2×C4×C41—41no—
87C2×C4×C41—41no—
88C2×C4×C41—41no—
89C2×C4×C41—81no—
90C2×C4×C41—81no—
91C2×C4×C41—81no—
92C2×C4×C41#10211yescharacteristic
93C2×C4×C41#10411yescharacteristic
94C8×C41—42no—
95C8×C41—82no—
96C8×C41—82no—
97#7409C4111yesmaximal, characteristic, direct product factor, Sylow
98C22×C41—21no—
99C22×C41—21no—
100C22×C41—81no—
101C22×C41—81no—
102C22×C41—81no—
103C22×C41#32711yescharacteristic
104C22×C41AΣL(1,𝔽16)11yescharacteristic
105C22×C41#35311yescharacteristic
106C4×C41—21no—
107C4×C41—21no—
108C4×C41—41no—
109C4×C41—41no—
110C4×C41—41no—
111C4×C41—41no—
112C4×C41—81no—
113C4×C41—81no—
114#2007C2×C4111yescharacteristic
115#1394C2×C4111yescharacteristic, complemented
116#1272C2×C4111yescharacteristic, complemented
117C2×C41—21no—
118C2×C41—21no—
119C2×C41—161no—
120C2×C41#134311yescharacteristic
121C2×C41#140311yescharacteristic
122C2×C41#140511yescharacteristic
123C2×#137—21no—
124#537C4×C4111yescharacteristic
125C2×#104—21no—
126C2×#101—21no—
127#391C22×C4111yescharacteristic
128#343C4×C4111yescharacteristic
129#336—21no—
130C41#740911yescharacteristic, direct product factor, Sylow
131C2×#41—21no—
132C22×Q8D4×C4111yescharacteristic
133#137—42no—
134#137—41no—
135#137—41no—
136C2×Q16—41no—
137C2×SD16—41no—
138C2×M16—21no—
139C2×M16—41no—
140C22×C8—41no—
141C22⋊Q8—41no—
142#121—41no—
143#121—41no—
144C2×C4⋊C4C2×C4×C4111yescharacteristic
145C2×C42D4×C4111yescharacteristic
146#104—42no—
147#101—22no—
148#101—41no—
149#95—41no—
150#41—41no—
151#41—41no—
152#41—41no—
153#41—41no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8D8×C4111yescharacteristic
159C2×Q8SD16×C4111yescharacteristic
160C2×D4—21no—
161C2×D4—41no—
162C2×D4—41no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—41no—
167C22×C4C22⋊C4×C4111yescharacteristic
168Q16—42no—
169Q16—42no—
170SD16—42no—
171SD16—42no—
172M16—22no—
173M16—41no—
174M16—42no—
175M16—81no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C22⋊C4—42no—
184C42—41no—
185C23—41no—
186C23#99×C4111yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—81no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196D4—161no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—81no—
212C2×C4#102×C4111yescharacteristic
213C2×C4#104×C4111yescharacteristic
214C8—42no—
215C8—82no—
216C8—82no—
217C22—21no—
218C22—21no—
219C22—81no—
220C22—81no—
221C22—81no—
222C22C41×#32711yescharacteristic
223C22C41×AΣL(1,𝔽16)11yescharacteristic
224C22C41×#35311yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—81no—
233C2—21no—
234C2—21no—
235C2—161no—
236C2C41×#134311yescharacteristic
237C2C41×#140311yescharacteristic
238C2C41×#140511yescharacteristic
subgroupG/H
center, socleC22×C41AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C41
Frattini, cosocle#391C22×C41
prime radicalC41×#537C4
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C41 ◁ C22×C4×C41 ◁ C41×#391 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1394C2semidirect
3. C41×#1272C2semidirect
97. #7409C41direct (N × H)
115. #1394C2×C41semidirect
116. #1272C2×C41semidirect
130. C41#7409direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#20072
C41×#13942
C41×#12722
#740941