Finite Group Databasebeta

← C41×#3038 #19106818

Subgroups — C41×#3038 #19106818

Order 5248.

584 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 208 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
1C2×AGL(1,ℤ/8)×C41C212yesmaximal, complemented
2C2×#127×C41C211yesmaximal, characteristic, complemented
3C4×#41×C41C211yesmaximal, characteristic, complemented
4C41×#460C214yesmaximal, complemented
5C41×#459C214yesmaximal, complemented
6C41×#423C211yesmaximal, characteristic, complemented
7C41×#418C212yesmaximal, complemented
8C2×#41×C41C2211yescharacteristic
9C22×D4×C41—22no—
10C22×D4×C41C2212yes—
11AGL(1,ℤ/8)×C41—28no—
12C2×SD16×C41C2214yescomplemented
13C2×D8×C41C2214yescomplemented
14C2×M16×C41C2212yes—
15#127×C41—21no—
16#127×C41—21no—
17#127×C41C2214yes—
18C4×Q8×C41C2212yescomplemented
19C4×D4×C41—22no—
20C4×D4×C41C2212yescomplemented
21#117×C41—21no—
22#117×C41C2211yescharacteristic
23C2×C42×C41—21no—
24C2×C42×C41C2211yescharacteristic
25C4⋊C8×C41C2214yescomplemented
26#102×C41C2218yescomplemented
27C24×C41—22no—
28#41×C41—22no—
29#41×C41D414yescomplemented
30C2×Q8×C41C2311yescharacteristic
31C2×D4×C41—21no—
32C2×D4×C41—24no—
33C2×D4×C41—22no—
34C2×D4×C41—24no—
35C2×D4×C41—24no—
36C2×D4×C41—24no—
37C2×D4×C41—48no—
38C2×D4×C41C2314yes—
39C2×D4×C41C2311yescharacteristic
40C22×C4×C41—21no—
41C22×C4×C41—22no—
42C22×C4×C41D412yes—
43C22×C4×C41C2311yescharacteristic
44SD16×C41—28no—
45D8×C41—28no—
46M16×C41—24no—
47C2×C8×C41C2314yes—
48C4⋊C4×C41—22no—
49C4⋊C4×C41C2312yes—
50C22⋊C4×C41—21no—
51C22⋊C4×C41—22no—
52C42×C41—21no—
53C42×C41—22no—
54C42×C41D411yescharacteristic
55C42×C41D411yescharacteristic
56C42×C41C2312yes—
57C23×C41—21no—
58C23×C41—24no—
59C23×C41—48no—
60C23×C41—44no—
61C23×C41C2×D411yescharacteristic
62Q8×C41—21no—
63Q8×C41C2×D412yescomplemented
64D4×C41—24no—
65D4×C41—24no—
66D4×C41—21no—
67D4×C41—24no—
68D4×C41—48no—
69D4×C41—44no—
70D4×C41—48no—
71D4×C41C2×D412yescomplemented
72C2×C4×C41—21no—
73C2×C4×C41—24no—
74C2×C4×C41—24no—
75C2×C4×C41—22no—
76C2×C4×C41—44no—
77C2×C4×C41C2×D412yes—
78C2×C4×C41C2×D411yescharacteristic
79C2×C4×C41C2×D412yes—
80C2×C4×C41C2×D412yes—
81C2×C4×C41#4112yes—
82C2×C4×C41C2411yescharacteristic
83C8×C41—24no—
84C22×C41—22no—
85C22×C41—22no—
86C22×C41—42no—
87C22×C41—44no—
88C22×C41—48no—
89C22×C41—88no—
90C22×C41#12112yes—
91C22×C41C22×D411yescharacteristic
92C4×C41—22no—
93C4×C41—22no—
94C4×C41—42no—
95C4×C41#12112yes—
96C4×C41AGL(1,ℤ/8)14yescomplemented
97C4×C41C22×D411yescharacteristic
98C4×C41C2×#4111yescharacteristic
99#3038C4111yesmaximal, characteristic, direct product factor, Sylow
100C2×C41—22no—
101C2×C41—42no—
102C2×C41—84no—
103C2×C41C2×#12111yescharacteristic
104C2×C41C2×AGL(1,ℤ/8)12yes—
105C2×AGL(1,ℤ/8)C2×C4112yescomplemented
106C2×#127C2×C4111yescharacteristic, complemented
107C4×#41C2×C4111yescharacteristic, complemented
108#460C2×C4114yescomplemented
109#459C2×C4114yescomplemented
110#423C2×C4111yescharacteristic, complemented
111#418C2×C4112yescomplemented
112C41#303811yescharacteristic, direct product factor, Sylow
113C2×#41C22×C4111yescharacteristic
114C22×D4—22no—
115C22×D4C22×C4112yes—
116AGL(1,ℤ/8)—28no—
117C2×SD16C22×C4114yescomplemented
118C2×D8C22×C4114yescomplemented
119C2×M16C22×C4112yes—
120#127—21no—
121#127—21no—
122#127C22×C4114yes—
123C4×Q8C22×C4112yescomplemented
124C4×D4—22no—
125C4×D4C22×C4112yescomplemented
126#117—21no—
127#117C22×C4111yescharacteristic
128C2×C42—21no—
129C2×C42C22×C4111yescharacteristic
130C4⋊C8C22×C4114yescomplemented
131#102C22×C4118yescomplemented
132C24—22no—
133#41—22no—
134#41D4×C4114yescomplemented
135C2×Q8C23×C4111yescharacteristic
136C2×D4—21no—
137C2×D4—24no—
138C2×D4—22no—
139C2×D4—24no—
140C2×D4—24no—
141C2×D4—24no—
142C2×D4—48no—
143C2×D4C23×C4114yes—
144C2×D4C23×C4111yescharacteristic
145C22×C4—21no—
146C22×C4—22no—
147C22×C4D4×C4112yes—
148C22×C4C23×C4111yescharacteristic
149SD16—28no—
150D8—28no—
151M16—24no—
152C2×C8C23×C4114yes—
153C4⋊C4—22no—
154C4⋊C4C23×C4112yes—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C42—21no—
158C42—22no—
159C42D4×C4111yescharacteristic
160C42D4×C4111yescharacteristic
161C42C23×C4112yes—
162C23—21no—
163C23—24no—
164C23—48no—
165C23—44no—
166C23C2×D4×C4111yescharacteristic
167Q8—21no—
168Q8C2×D4×C4112yescomplemented
169D4—24no—
170D4—24no—
171D4—21no—
172D4—24no—
173D4—48no—
174D4—44no—
175D4—48no—
176D4C2×D4×C4112yescomplemented
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—44no—
182C2×C4C2×D4×C4112yes—
183C2×C4C2×D4×C4111yescharacteristic
184C2×C4C2×D4×C4112yes—
185C2×C4C2×D4×C4112yes—
186C2×C4#41×C4112yes—
187C2×C4C24×C4111yescharacteristic
188C8—24no—
189C22—22no—
190C22—22no—
191C22—42no—
192C22—44no—
193C22—48no—
194C22—88no—
195C22#121×C4112yes—
196C22C22×D4×C4111yescharacteristic
197C4—22no—
198C4—22no—
199C4—42no—
200C4#121×C4112yes—
201C4AGL(1,ℤ/8)×C4114yescomplemented
202C4C22×D4×C4111yescharacteristic
203C4C2×#41×C4111yescharacteristic
204C2—22no—
205C2—42no—
206C2—84no—
207C2C2×#121×C4111yescharacteristic
208C2C2×AGL(1,ℤ/8)×C4112yes—
subgroupG/H
center, socleC22×C41C22×D4
commutator, Frattini, cosocleC2×C4C24×C41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×AGL(1,ℤ/8)×C41C2semidirect
2. C2×#127×C41C2semidirect
3. C4×#41×C41C2semidirect
4. C41×#460C2semidirect
5. C41×#459C2semidirect
6. C41×#423C2semidirect
7. C41×#418C2semidirect
12. C2×SD16×C41C22semidirect
13. C2×D8×C41C22semidirect
18. C4×Q8×C41C22semidirect
20. C4×D4×C41C22semidirect
25. C4⋊C8×C41C22semidirect
26. #102×C41C22semidirect
29. #41×C41D4semidirect
63. Q8×C41C2×D4semidirect
71. D4×C41C2×D4semidirect
96. C4×C41AGL(1,ℤ/8)semidirect
99. #3038C41direct (N × H)
105. C2×AGL(1,ℤ/8)C2×C41semidirect
106. C2×#127C2×C41semidirect
107. C4×#41C2×C41semidirect
108. #460C2×C41semidirect
109. #459C2×C41semidirect
110. #423C2×C41semidirect
111. #418C2×C41semidirect
112. C41#3038direct (N × H)
117. C2×SD16C22×C41semidirect
118. C2×D8C22×C41semidirect
123. C4×Q8C22×C41semidirect
125. C4×D4C22×C41semidirect
130. C4⋊C8C22×C41semidirect
131. #102C22×C41semidirect
134. #41D4×C41semidirect
168. Q8C2×D4×C41semidirect
176. D4C2×D4×C41semidirect
201. C4AGL(1,ℤ/8)×C41semidirect

Maximal subgroups

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

subgroupindex
C2×AGL(1,ℤ/8)×C412
C2×#127×C412
C4×#41×C412
C41×#4602
C41×#4592
C41×#4232
C41×#4182
#303841