Finite Group Databasebeta

← C41×#7484 #23783685

Subgroups — C41×#7484 #23783685

Order 10496.

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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×#2132C211yesmaximal, characteristic
2C41×#1884C211yesmaximal, characteristic
3C41×#1536C211yesmaximal, characteristic
4C41×#568C411yescharacteristic
5C41×#532C2211yescharacteristic
6C41×#432—21no—
7C41×#421—21no—
8C41×#413—21no—
9C41×#410C411yescharacteristic
10C41×#356C412yescomplemented
11C41×#355—21no—
12C41×#339—21no—
13C41×#329—21no—
14C41×#329C412yescomplemented
15C2×#41×C41C2×C411yescharacteristic
16C2×#41×C41D411yescharacteristic
17#131×C41—42no—
18C2×M16×C41—21no—
19C2×M16×C41—41no—
20C2×M16×C41—41no—
21C4⋊Q8×C41C2×C411yescharacteristic
22#127×C41Q811yescharacteristic
23#124×C41C2×C411yescharacteristic
24#124×C41D411yescharacteristic
25#121×C41—41no—
26C4×D4×C41—41no—
27#117×C41—21no—
28C2×C42×C41D411yescharacteristic
29C4⋊C8×C41—41no—
30#104×C41—42no—
31#101×C41—22no—
32#100×C41—41no—
33#99×C41—41no—
34C22⋊C8×C41—41no—
35#97×C41—22no—
36#41×C41—41no—
37#41×C41—41no—
38#41×C41—41no—
39#41×C41—41no—
40C2×Q8×C41C4211yescharacteristic
41C2×Q8×C41C22⋊C411yescharacteristic
42C2×D4×C41—21no—
43C2×D4×C41—21no—
44C2×D4×C41—41no—
45C2×D4×C41C4⋊C411yescharacteristic
46C2×D4×C41C4⋊C411yescharacteristic
47C22×C4×C41—21no—
48C22×C4×C41—21no—
49C22×C4×C41—21no—
50C22×C4×C41C22⋊C411yescharacteristic
51M16×C41—22no—
52M16×C41—42no—
53M16×C41—41no—
54M16×C41—42no—
55M16×C41—81no—
56C2×C8×C41—41no—
57C2×C8×C41—42no—
58C2×C8×C41—42no—
59C2×C8×C41—81no—
60C4⋊C4×C41—41no—
61C4⋊C4×C41—41no—
62C22⋊C4×C41—41no—
63C22⋊C4×C41—41no—
64C22⋊C4×C41—41no—
65C42×C41—21no—
66C42×C41—41no—
67C42×C41C22⋊C411yescharacteristic
68C42×C41C4⋊C411yescharacteristic
69C23×C41—21no—
70C23×C41—21no—
71C23×C41#9911yescharacteristic
72Q8×C41—41no—
73Q8×C41—41no—
74D4×C41—41no—
75D4×C41—41no—
76D4×C41—42no—
77D4×C41—81no—
78D4×C41—82no—
79C2×C4×C41—21no—
80C2×C4×C41—21no—
81C2×C4×C41—21no—
82C2×C4×C41—21no—
83C2×C4×C41—21no—
84C2×C4×C41—21no—
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#9511yescharacteristic
92C2×C4×C41#9911yescharacteristic
93C8×C41—42no—
94C8×C41—82no—
95C8×C41—82no—
96#7484C4111yesmaximal, characteristic, direct product factor, Sylow
97C22×C41—21no—
98C22×C41—41no—
99C22×C41—41no—
100C22×C41—41no—
101C22×C41—81no—
102C22×C41—81no—
103C22×C41#34211yescharacteristic
104C4×C41—21no—
105C4×C41—41no—
106C4×C41—41no—
107C4×C41—41no—
108C4×C41—41no—
109C4×C41—161no—
110C4×C41AΣL(1,𝔽16)11yescharacteristic
111C4×C41#35211yescharacteristic
112#2132C2×C4111yescharacteristic
113#1884C2×C4111yescharacteristic
114#1536C2×C4111yescharacteristic
115C2×C41—21no—
116C2×C41—41no—
117C2×C41—81no—
118C2×C41—81no—
119C2×C41#139011yescharacteristic
120#568C4×C4111yescharacteristic
121#532C22×C4111yescharacteristic
122#432—21no—
123#421—21no—
124#413—21no—
125#410C4×C4111yescharacteristic
126#356C4×C4112yescomplemented
127#355—21no—
128#339—21no—
129#329—21no—
130#329C4×C4112yescomplemented
131C41#748411yescharacteristic, direct product factor, Sylow
132C2×#41C2×C4×C4111yescharacteristic
133C2×#41D4×C4111yescharacteristic
134#131—42no—
135C2×M16—21no—
136C2×M16—41no—
137C2×M16—41no—
138C4⋊Q8C2×C4×C4111yescharacteristic
139#127Q8×C4111yescharacteristic
140#124C2×C4×C4111yescharacteristic
141#124D4×C4111yescharacteristic
142#121—41no—
143C4×D4—41no—
144#117—21no—
145C2×C42D4×C4111yescharacteristic
146C4⋊C8—41no—
147#104—42no—
148#101—22no—
149#100—41no—
150#99—41no—
151C22⋊C8—41no—
152#97—22no—
153#41—41no—
154#41—41no—
155#41—41no—
156#41—41no—
157C2×Q8C42×C4111yescharacteristic
158C2×Q8C22⋊C4×C4111yescharacteristic
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4C4⋊C4×C4111yescharacteristic
163C2×D4C4⋊C4×C4111yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C22⋊C4×C4111yescharacteristic
168M16—22no—
169M16—42no—
170M16—41no—
171M16—42no—
172M16—81no—
173C2×C8—41no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—81no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C42—21no—
183C42—41no—
184C42C22⋊C4×C4111yescharacteristic
185C42C4⋊C4×C4111yescharacteristic
186C23—21no—
187C23—21no—
188C23#99×C4111yescharacteristic
189Q8—41no—
190Q8—41no—
191D4—41no—
192D4—41no—
193D4—42no—
194D4—81no—
195D4—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—81no—
207C2×C4—81no—
208C2×C4#95×C4111yescharacteristic
209C2×C4#99×C4111yescharacteristic
210C8—42no—
211C8—82no—
212C8—82no—
213C22—21no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22—81no—
219C22C41×#34211yescharacteristic
220C4—21no—
221C4—41no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—161no—
226C4C41×AΣL(1,𝔽16)11yescharacteristic
227C4C41×#35211yescharacteristic
228C2—21no—
229C2—41no—
230C2—81no—
231C2—81no—
232C2C41×#139011yescharacteristic
subgroupG/H
center, socleC2×C41#1390
commutatorC2×Q8C42×C41
Frattini, cosocle#532C22×C41
prime radicalC41×#532C22
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C22×C4×C41 ◁ C41×#532 ◁ G

Complements

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

NH ≅ G/Ntype
10. C41×#356C4semidirect
14. C41×#329C4semidirect
96. #7484C41direct (N × H)
126. #356C4×C41semidirect
130. #329C4×C41semidirect
131. C41#7484direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#21322
C41×#18842
C41×#15362
#748441