Finite Group Databasebeta

← C41×#1598 #19105378

Subgroups — C41×#1598 #19105378

Order 5248.

310 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 68 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×#537C211yesmaximal, characteristic, complemented
2C41×#447C212yesmaximal, complemented
3C41×#394C211yesmaximal, characteristic, complemented
4C41×#327C212yesmaximal, complemented
5C41×#324C211yesmaximal, characteristic, complemented
6C2×#41×C41—21no—
7C22×D4×C41C2211yescharacteristic
8C2×D8×C41—22no—
9C22⋊Q8×C41—22no—
10#121×C41—22no—
11#121×C41—21no—
12#121×C41C2212yes—
13C2×C4⋊C4×C41C2211yescharacteristic
14C2×C22⋊C4×C41—21no—
15C2×C22⋊C4×C41—21no—
16#102×C41—22no—
17C22⋊C8×C41C2212yes—
18#95×C41C2211yescharacteristic
19C24×C41—21no—
20#41×C41—42no—
21#41×C41—42no—
22C2×Q8×C41—21no—
23C2×D4×C41—21no—
24C2×D4×C41—22no—
25C2×D4×C41—21no—
26C2×D4×C41—22no—
27C2×D4×C41—42no—
28C2×D4×C41D412yes—
29C22×C4×C41—22no—
30C22×C4×C41—21no—
31C22×C4×C41D411yescharacteristic
32C22×C4×C41D411yescharacteristic
33C22×C4×C41C2311yescharacteristic
34D8×C41—44no—
35C2×C8×C41—22no—
36C4⋊C4×C41—21no—
37C4⋊C4×C41—22no—
38C4⋊C4×C41D412yes—
39C22⋊C4×C41—22no—
40C22⋊C4×C41—22no—
41C22⋊C4×C41—42no—
42C22⋊C4×C41—42no—
43C23×C41—22no—
44C23×C41—22no—
45C23×C41—41no—
46C23×C41—41no—
47C23×C41—41no—
48C23×C41—41no—
49C23×C41—41no—
50C23×C41—41no—
51C23×C41C2×D411yescharacteristic
52Q8×C41—42no—
53D4×C41—24no—
54D4×C41—42no—
55D4×C41—42no—
56D4×C41—42no—
57D4×C41—42no—
58D4×C41—42no—
59D4×C41—81no—
60C2×C4×C41—21no—
61C2×C4×C41—21no—
62C2×C4×C41—21no—
63C2×C4×C41—22no—
64C2×C4×C41—41no—
65C2×C4×C41—44no—
66C2×C4×C41—41no—
67C2×C4×C41—41no—
68C2×C4×C41—41no—
69C2×C4×C41—41no—
70C2×C4×C41D812yescomplemented
71C2×C4×C41C2×D412yes—
72C8×C41—42no—
73C22×C41—21no—
74C22×C41—21no—
75C22×C41—42no—
76C22×C41—42no—
77C22×C41—42no—
78C22×C41—42no—
79C22×C41—42no—
80C22×C41—42no—
81C22×C41—81no—
82C22×C41—81no—
83C22×C41—81no—
84C22×C41—81no—
85C22×C41#12011yescharacteristic
86C22×C41C2×D811yescharacteristic
87C22×C41AGL(1,ℤ/8)11yescharacteristic
88C4×C41—22no—
89C4×C41—22no—
90C4×C41—42no—
91C4×C41—41no—
92C4×C41—81no—
93#1598C4111yesmaximal, characteristic, direct product factor, Sylow
94C2×C41—21no—
95C2×C41—21no—
96C2×C41—82no—
97C2×C41—82no—
98C2×C41#44711yescharacteristic
99C2×C41#45411yescharacteristic
100C2×C41B(4,𝔽2)11yescharacteristic
101#537C2×C4111yescharacteristic, complemented
102#447C2×C4112yescomplemented
103#394C2×C4111yescharacteristic, complemented
104#327C2×C4112yescomplemented
105#324C2×C4111yescharacteristic, complemented
106C41#159811yescharacteristic, direct product factor, Sylow
107C2×#41—21no—
108C22×D4C22×C4111yescharacteristic
109C2×D8—22no—
110C22⋊Q8—22no—
111#121—22no—
112#121—21no—
113#121C22×C4112yes—
114C2×C4⋊C4C22×C4111yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—21no—
117#102—22no—
118C22⋊C8C22×C4112yes—
119#95C22×C4111yescharacteristic
120C24—21no—
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×D4—21no—
125C2×D4—22no—
126C2×D4—21no—
127C2×D4—22no—
128C2×D4—42no—
129C2×D4D4×C4112yes—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4D4×C4111yescharacteristic
133C22×C4D4×C4111yescharacteristic
134C22×C4C23×C4111yescharacteristic
135D8—44no—
136C2×C8—22no—
137C4⋊C4—21no—
138C4⋊C4—22no—
139C4⋊C4D4×C4112yes—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—42no—
143C22⋊C4—42no—
144C23—22no—
145C23—22no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—41no—
152C23C2×D4×C4111yescharacteristic
153Q8—42no—
154D4—24no—
155D4—42no—
156D4—42no—
157D4—42no—
158D4—42no—
159D4—42no—
160D4—81no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—44no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4D8×C4112yescomplemented
172C2×C4C2×D4×C4112yes—
173C8—42no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—42no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—81no—
186C22#120×C4111yescharacteristic
187C22C2×D8×C4111yescharacteristic
188C22AGL(1,ℤ/8)×C4111yescharacteristic
189C4—22no—
190C4—22no—
191C4—42no—
192C4—41no—
193C4—81no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—82no—
198C2C41×#44711yescharacteristic
199C2C41×#45411yescharacteristic
200C2C41×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C41#120
commutator, Frattini, cosocleC22×C4C23×C41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#537C2semidirect
2. C41×#447C2semidirect
3. C41×#394C2semidirect
4. C41×#327C2semidirect
5. C41×#324C2semidirect
70. C2×C4×C41D8semidirect
93. #1598C41direct (N × H)
101. #537C2×C41semidirect
102. #447C2×C41semidirect
103. #394C2×C41semidirect
104. #327C2×C41semidirect
105. #324C2×C41semidirect
106. C41#1598direct (N × H)
171. C2×C4D8×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#5372
C41×#4472
C41×#3942
C41×#3272
C41×#3242
#159841