Finite Group Databasebeta

← C41×#12299 #23788500

Subgroups — C41×#12299 #23788500

Order 10496.

324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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×#3195C211yesmaximal, characteristic
2C41×#2239C212yesmaximal, complemented
3C41×#2091C211yesmaximal, characteristic
4C41×#1342C212yesmaximal, complemented
5C41×#1320C211yesmaximal, characteristic
6C2×C22⋊Q8×C41—21no—
7C41×#483—22no—
8C41×#470—21no—
9C41×#470C2212yes—
10C41×#451—22no—
11C41×#430—21no—
12C41×#430C2211yescharacteristic
13C41×#407—21no—
14C41×#407C2211yescharacteristic
15C41×#365—22no—
16C41×#362—22no—
17C41×#349C2212yes—
18C41×#338C2211yescharacteristic
19C22×Q8×C41—21no—
20C23×C4×C41D411yescharacteristic
21C2×Q16×C41—21no—
22C2×Q16×C41D412yes—
23C2×M16×C41—21no—
24C2×M16×C41—21no—
25C2×M16×C41D411yescharacteristic
26C2×M16×C41C2311yescharacteristic
27C22⋊Q8×C41—22no—
28C22⋊Q8×C41—22no—
29C22⋊Q8×C41—41no—
30C22⋊Q8×C41—41no—
31C2×C4⋊C4×C41—21no—
32C2×C4⋊C4×C41—41no—
33C2×C22⋊C4×C41—41no—
34M32×C41—22no—
35#108×C41—22no—
36#108×C41—42no—
37#106×C41—21no—
38#106×C41D412yes—
39#103×C41—22no—
40#103×C41—22no—
41C22⋊C8×C41—22no—
42C22⋊C8×C41—42no—
43C24×C41SD1611yescharacteristic
44C2×Q8×C41—22no—
45C2×Q8×C41—41no—
46C2×Q8×C41—81no—
47C2×Q8×C41—81no—
48C22×C4×C41—21no—
49C22×C4×C41—21no—
50C22×C4×C41—41no—
51C22×C4×C41—41no—
52C22×C4×C41—41no—
53C22×C4×C41—41no—
54C22×C4×C41SD1611yescharacteristic
55C22×C4×C41C2×D411yescharacteristic
56Q16×C41—42no—
57Q16×C41—81no—
58M16×C41—41no—
59M16×C41—41no—
60M16×C41—41no—
61M16×C41—41no—
62M16×C41—41no—
63M16×C41—41no—
64C2×C8×C41—22no—
65C2×C8×C41—21no—
66C2×C8×C41—41no—
67C2×C8×C41C2×D412yes—
68C4⋊C4×C41—22no—
69C4⋊C4×C41—41no—
70C4⋊C4×C41—42no—
71C4⋊C4×C41—42no—
72C22⋊C4×C41—42no—
73C22⋊C4×C41—42no—
74C16×C41—42no—
75C23×C41—21no—
76C23×C41—41no—
77C23×C41—42no—
78C23×C41C2×SD1611yescharacteristic
79Q8×C41—42no—
80Q8×C41—42no—
81Q8×C41—82no—
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—42no—
89C2×C4×C41—42no—
90C2×C4×C41—81no—
91C2×C4×C41—82no—
92C2×C4×C41—82no—
93C2×C4×C41#12011yescharacteristic
94C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
95C8×C41—22no—
96C8×C41—42no—
97C8×C41—41no—
98C8×C41—81no—
99#12299C4111yesmaximal, characteristic, direct product factor, Sylow
100C22×C41—22no—
101C22×C41—21no—
102C22×C41—41no—
103C22×C41—41no—
104C22×C41—42no—
105C22×C41—41no—
106C22×C41—81no—
107C22×C41#45011yescharacteristic
108C4×C41—21no—
109C4×C41—41no—
110C4×C41—82no—
111C4×C41—82no—
112C4×C41#45311yescharacteristic
113C4×C41#45811yescharacteristic
114#3195C2×C4111yescharacteristic
115#2239C2×C4112yescomplemented
116#2091C2×C4111yescharacteristic
117#1342C2×C4112yescomplemented
118#1320C2×C4111yescharacteristic
119C2×C41—21no—
120C2×C41—42no—
121C2×C41—41no—
122C2×C41#161311yescharacteristic
123C2×C22⋊Q8—21no—
124#483—22no—
125#470—21no—
126#470C22×C4112yes—
127#451—22no—
128#430—21no—
129#430C22×C4111yescharacteristic
130#407—21no—
131#407C22×C4111yescharacteristic
132#365—22no—
133#362—22no—
134#349C22×C4112yes—
135#338C22×C4111yescharacteristic
136C41#1229911yescharacteristic, direct product factor, Sylow
137C22×Q8—21no—
138C23×C4D4×C4111yescharacteristic
139C2×Q16—21no—
140C2×Q16D4×C4112yes—
141C2×M16—21no—
142C2×M16—21no—
143C2×M16D4×C4111yescharacteristic
144C2×M16C23×C4111yescharacteristic
145C22⋊Q8—22no—
146C22⋊Q8—22no—
147C22⋊Q8—41no—
148C22⋊Q8—41no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—41no—
151C2×C22⋊C4—41no—
152M32—22no—
153#108—22no—
154#108—42no—
155#106—21no—
156#106D4×C4112yes—
157#103—22no—
158#103—22no—
159C22⋊C8—22no—
160C22⋊C8—42no—
161C24SD16×C4111yescharacteristic
162C2×Q8—22no—
163C2×Q8—41no—
164C2×Q8—81no—
165C2×Q8—81no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4SD16×C4111yescharacteristic
173C22×C4C2×D4×C4111yescharacteristic
174Q16—42no—
175Q16—81no—
176M16—41no—
177M16—41no—
178M16—41no—
179M16—41no—
180M16—41no—
181M16—41no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8C2×D4×C4112yes—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C22⋊C4—42no—
191C22⋊C4—42no—
192C16—42no—
193C23—21no—
194C23—41no—
195C23—42no—
196C23C2×SD16×C4111yescharacteristic
197Q8—42no—
198Q8—42no—
199Q8—82no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—81no—
209C2×C4—82no—
210C2×C4—82no—
211C2×C4#120×C4111yescharacteristic
212C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
213C8—22no—
214C8—42no—
215C8—41no—
216C8—81no—
217C22—22no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22C41×#45011yescharacteristic
225C4—21no—
226C4—41no—
227C4—82no—
228C4—82no—
229C4C41×#45311yescharacteristic
230C4C41×#45811yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2C41×#161311yescharacteristic
subgroupG/H
center, socleC2×C41#1613
commutator, Frattini, cosocleC2×M16C23×C41
prime radicalC24×C41SD16
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C2×M16×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2239C2semidirect
4. C41×#1342C2semidirect
99. #12299C41direct (N × H)
115. #2239C2×C41semidirect
117. #1342C2×C41semidirect
136. C41#12299direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31952
C41×#22392
C41×#20912
C41×#13422
C41×#13202
#1229941