Finite Group Databasebeta

← C41×#33227 #23809428

Subgroups — C41×#33227 #23809428

Order 10496.

986 conjugacy classes of subgroups; only the 318 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 318 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×C41×#487C212yesmaximal, complemented
2C2×C41×#486C212yesmaximal
3C41×#2862C211yesmaximal, characteristic, complemented
4C41×#2858C211yesmaximal, characteristic
5C41×#1958C218yesmaximal, complemented
6C42×C8×C41C211yesmaximal, characteristic, complemented
7C2×C4⋊Q8×C41C2211yescharacteristic
8C2×C4⋊Q8×C41C2212yes—
9C2×#127×C41C2211yescharacteristic
10C2×#124×C41C2214yes—
11C41×#487—28no—
12C41×#486—28no—
13C2×#103×C41C2218yes—
14C2×#102×C41C2218yes—
15C2×C4×C8×C41C2214yes—
16C2×C4×C8×C41C2212yes—
17C41×#391—24no—
18C41×#390—24no—
19C41×#382C2214yes—
20C43×C41C2211yescharacteristic
21C22×Q8×C41—22no—
22C22×Q8×C41C2312yes—
23C22×D4×C41—22no—
24C22×D4×C41C2312yes—
25C22×C8×C41C2314yes—
26C4⋊Q8×C41—24no—
27C4⋊Q8×C41—24no—
28C4⋊Q8×C41—24no—
29#127×C41—24no—
30#124×C41—216no—
31C2×C4⋊C4×C41—22no—
32C2×C4⋊C4×C41—22no—
33C2×C4⋊C4×C41C2314yes—
34C2×C22⋊C4×C41—28no—
35C2×C42×C41D414yes—
36C2×C42×C41C2311yescharacteristic
37C2×C42×C41C2312yes—
38#103×C41—216no—
39#102×C41—216no—
40C4×C8×C41—28no—
41C4×C8×C41D418yes—
42#95×C41—28no—
43C24×C41—22no—
44C2×Q8×C41—24no—
45C2×Q8×C41—28no—
46C2×Q8×C41—44no—
47C2×Q8×C41—48no—
48C2×D4×C41—24no—
49C2×D4×C41—28no—
50C2×D4×C41—44no—
51C2×D4×C41—48no—
52C22×C4×C41—24no—
53C22×C4×C41—22no—
54C22×C4×C41C2×D414yes—
55C22×C4×C41C2×D412yes—
56C22×C4×C41C2411yescharacteristic
57C2×C8×C41—28no—
58C2×C8×C41C2×D418yes—
59C4⋊C4×C41—24no—
60C4⋊C4×C41—24no—
61C4⋊C4×C41—44no—
62C4⋊C4×C41—44no—
63C22⋊C4×C41—416no—
64C42×C41—28no—
65C42×C41C2×D414yes—
66C42×C41#4118yes—
67C23×C41—44no—
68C23×C41—42no—
69C23×C41—48no—
70C23×C41C22×D411yescharacteristic
71Q8×C41—48no—
72Q8×C41—88no—
73D4×C41—48no—
74D4×C41—88no—
75C2×C4×C41—28no—
76C2×C4×C41—44no—
77C2×C4×C41—44no—
78C2×C4×C41—42no—
79C2×C4×C41—48no—
80C2×C4×C41#12418yes—
81C2×C4×C41#12714yes—
82C2×C4×C41#13518yes—
83C2×C4×C41C22×D412yes—
84C2×C4×C41C2×#4114yes—
85C8×C41—28no—
86#33227C4111yesmaximal, characteristic, direct product factor, Sylow
87C22×C41—82no—
88C22×C41—88no—
89C22×C41—84no—
90C22×C41C2×#12412yes—
91C22×C41C2×#12711yescharacteristic
92C22×C41C2×#13514yes—
93C4×C41—28no—
94C4×C41—82no—
95C4×C41—84no—
96C4×C41#49518yes—
97C4×C41#53214yes—
98C2×#487C2×C4112yescomplemented
99C2×#486C2×C4112yes—
100#2862C2×C4111yescharacteristic, complemented
101#2858C2×C4111yescharacteristic
102#1958C2×C4118yescomplemented
103C42×C8C2×C4111yescharacteristic, complemented
104C2×C41—162no—
105C2×C41#285811yescharacteristic
106C2×C41#313114yes—
107C2×C41C2×#49512yes—
108C2×C4⋊Q8C22×C4111yescharacteristic
109C2×C4⋊Q8C22×C4112yes—
110C2×#127C22×C4111yescharacteristic
111C2×#124C22×C4114yes—
112#487—28no—
113#486—28no—
114C2×#103C22×C4118yes—
115C2×#102C22×C4118yes—
116C2×C4×C8C22×C4114yes—
117C2×C4×C8C22×C4112yes—
118#391—24no—
119#390—24no—
120#382C22×C4114yes—
121C43C22×C4111yescharacteristic
122C41#3322711yescharacteristic, direct product factor, Sylow
123C22×Q8—22no—
124C22×Q8C23×C4112yes—
125C22×D4—22no—
126C22×D4C23×C4112yes—
127C22×C8C23×C4114yes—
128C4⋊Q8—24no—
129C4⋊Q8—24no—
130C4⋊Q8—24no—
131#127—24no—
132#124—216no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4C23×C4114yes—
136C2×C22⋊C4—28no—
137C2×C42D4×C4114yes—
138C2×C42C23×C4111yescharacteristic
139C2×C42C23×C4112yes—
140#103—216no—
141#102—216no—
142C4×C8—28no—
143C4×C8D4×C4118yes—
144#95—28no—
145C24—22no—
146C2×Q8—24no—
147C2×Q8—28no—
148C2×Q8—44no—
149C2×Q8—48no—
150C2×D4—24no—
151C2×D4—28no—
152C2×D4—44no—
153C2×D4—48no—
154C22×C4—24no—
155C22×C4—22no—
156C22×C4C2×D4×C4114yes—
157C22×C4C2×D4×C4112yes—
158C22×C4C24×C4111yescharacteristic
159C2×C8—28no—
160C2×C8C2×D4×C4118yes—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—44no—
164C4⋊C4—44no—
165C22⋊C4—416no—
166C42—28no—
167C42C2×D4×C4114yes—
168C42#41×C4118yes—
169C23—44no—
170C23—42no—
171C23—48no—
172C23C22×D4×C4111yescharacteristic
173Q8—48no—
174Q8—88no—
175D4—48no—
176D4—88no—
177C2×C4—28no—
178C2×C4—44no—
179C2×C4—44no—
180C2×C4—42no—
181C2×C4—48no—
182C2×C4#124×C4118yes—
183C2×C4#127×C4114yes—
184C2×C4#135×C4118yes—
185C2×C4C22×D4×C4112yes—
186C2×C4C2×#41×C4114yes—
187C8—28no—
188C22—82no—
189C22—88no—
190C22—84no—
191C22C2×#124×C4112yes—
192C22C2×#127×C4111yescharacteristic
193C22C2×#135×C4114yes—
194C4—28no—
195C4—82no—
196C4—84no—
197C4C41×#49518yes—
198C4C41×#53214yes—
199C2—162no—
200C2C41×#285811yescharacteristic
201C2C41×#313114yes—
202C2C2×C41×#49512yes—
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×#127×C41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C43×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#487C2semidirect
3. C41×#2862C2semidirect
5. C41×#1958C2semidirect
6. C42×C8×C41C2semidirect
86. #33227C41direct (N × H)
98. C2×#487C2×C41semidirect
100. #2862C2×C41semidirect
102. #1958C2×C41semidirect
103. C42×C8C2×C41semidirect
122. C41#33227direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4872
C2×C41×#4862
C41×#28622
C41×#28582
C41×#19582
C42×C8×C412
#3322741