Finite Group Databasebeta

← C41×#19733 #23795934

Subgroups — C41×#19733 #23795934

Order 10496.

712 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3231C213yesmaximal, complemented
2C41×#3208C213yesmaximal
3C41×#1719C213yesmaximal, complemented
4C41×#1714C213yesmaximal, complemented
5C41×#1711C211yesmaximal, characteristic, complemented
6C41×#1705C211yesmaximal, characteristic, complemented
7C41×#1454C211yesmaximal, characteristic, complemented
8C41×#533C2213yes—
9C2×#127×C41C2211yescharacteristic
10C41×#500C2213yescomplemented
11C41×#498C2213yescomplemented
12C41×#492C2213yes—
13C41×#492C2213yes—
14C41×#487C2213yescomplemented
15C41×#487C2213yescomplemented
16C41×#486C2213yes—
17C41×#486C2213yes—
18C41×#485—26no—
19C41×#479—26no—
20C41×#460—26no—
21C41×#450—26no—
22C41×#431C2213yes—
23C41×#322C2213yescomplemented
24C82×C41C2211yescharacteristic, complemented
25C22×D4×C41—23no—
26C2×SD16×C41—26no—
27C2×SD16×C41—26no—
28C4⋊Q8×C41C2313yes—
29C4⋊Q8×C41C2313yes—
30#127×C41—23no—
31#127×C41C2311yescharacteristic
32#127×C41C2311yescharacteristic
33#125×C41—23no—
34C22⋊Q8×C41—23no—
35C22⋊Q8×C41—23no—
36C4×Q8×C41—23no—
37C4×Q8×C41—23no—
38#117×C41—23no—
39C2×C42×C41C2311yescharacteristic
40#107×C41—26no—
41#106×C41—26no—
42C4⋊C8×C41D416yes—
43#103×C41—26no—
44#103×C41—26no—
45#102×C41—26no—
46#102×C41—26no—
47C22⋊C8×C41D416yes—
48C4×C8×C41C2313yes—
49C4×C8×C41C2313yes—
50C24×C41—41no—
51C2×Q8×C41—23no—
52C2×Q8×C41—23no—
53C2×D4×C41—23no—
54C2×D4×C41—23no—
55C2×D4×C41—43no—
56C2×D4×C41—86no—
57C22×C4×C41C2×D413yes—
58SD16×C41—86no—
59SD16×C41—86no—
60C2×C8×C41C2×D416yes—
61C2×C8×C41C2×D416yes—
62C4⋊C4×C41—23no—
63C4⋊C4×C41—23no—
64C4⋊C4×C41—23no—
65C4⋊C4×C41—23no—
66C4⋊C4×C41—43no—
67C4⋊C4×C41—43no—
68C22⋊C4×C41—43no—
69C42×C41—43no—
70C42×C41C2×D413yes—
71C42×C41C2411yescharacteristic
72C23×C41—41no—
73C23×C41—41no—
74C23×C41—86no—
75C23×C41#12711yescharacteristic
76Q8×C41—46no—
77Q8×C41—46no—
78D4×C41—46no—
79D4×C41—46no—
80D4×C41—86no—
81C2×C4×C41—26no—
82C2×C4×C41—43no—
83C2×C4×C41—43no—
84C2×C4×C41#12713yes—
85C2×C4×C41C22×D413yes—
86C8×C41—26no—
87C8×C41—26no—
88#19733C4111yesmaximal, characteristic, direct product factor, Sylow
89C22×C41—23no—
90C22×C41—83no—
91C22×C41—83no—
92C22×C41—164no—
93C22×C41C2×#12711yescharacteristic
94C4×C41—23no—
95C4×C41—83no—
96C4×C41—83no—
97C4×C41#57716yes—
98#3231C2×C4113yescomplemented
99#3208C2×C4113yes—
100#1719C2×C4113yescomplemented
101#1714C2×C4113yescomplemented
102#1711C2×C4111yescharacteristic, complemented
103#1705C2×C4111yescharacteristic, complemented
104#1454C2×C4111yescharacteristic, complemented
105C2×C41—41no—
106C2×C41—161no—
107C2×C41—161no—
108C2×C41#315413yes—
109#533C22×C4113yes—
110C2×#127C22×C4111yescharacteristic
111#500C22×C4113yescomplemented
112#498C22×C4113yescomplemented
113#492C22×C4113yes—
114#492C22×C4113yes—
115#487C22×C4113yescomplemented
116#487C22×C4113yescomplemented
117#486C22×C4113yes—
118#486C22×C4113yes—
119#485—26no—
120#479—26no—
121#460—26no—
122#450—26no—
123#431C22×C4113yes—
124#322C22×C4113yescomplemented
125C82C22×C4111yescharacteristic, complemented
126C41#1973311yescharacteristic, direct product factor, Sylow
127C22×D4—23no—
128C2×SD16—26no—
129C2×SD16—26no—
130C4⋊Q8C23×C4113yes—
131C4⋊Q8C23×C4113yes—
132#127—23no—
133#127C23×C4111yescharacteristic
134#127C23×C4111yescharacteristic
135#125—23no—
136C22⋊Q8—23no—
137C22⋊Q8—23no—
138C4×Q8—23no—
139C4×Q8—23no—
140#117—23no—
141C2×C42C23×C4111yescharacteristic
142#107—26no—
143#106—26no—
144C4⋊C8D4×C4116yes—
145#103—26no—
146#103—26no—
147#102—26no—
148#102—26no—
149C22⋊C8D4×C4116yes—
150C4×C8C23×C4113yes—
151C4×C8C23×C4113yes—
152C24—41no—
153C2×Q8—23no—
154C2×Q8—23no—
155C2×D4—23no—
156C2×D4—23no—
157C2×D4—43no—
158C2×D4—86no—
159C22×C4C2×D4×C4113yes—
160SD16—86no—
161SD16—86no—
162C2×C8C2×D4×C4116yes—
163C2×C8C2×D4×C4116yes—
164C4⋊C4—23no—
165C4⋊C4—23no—
166C4⋊C4—23no—
167C4⋊C4—23no—
168C4⋊C4—43no—
169C4⋊C4—43no—
170C22⋊C4—43no—
171C42—43no—
172C42C2×D4×C4113yes—
173C42C24×C4111yescharacteristic
174C23—41no—
175C23—41no—
176C23—86no—
177C23#127×C4111yescharacteristic
178Q8—46no—
179Q8—46no—
180D4—46no—
181D4—46no—
182D4—86no—
183C2×C4—26no—
184C2×C4—43no—
185C2×C4—43no—
186C2×C4#127×C4113yes—
187C2×C4C22×D4×C4113yes—
188C8—26no—
189C8—26no—
190C22—23no—
191C22—83no—
192C22—83no—
193C22—164no—
194C22C2×#127×C4111yescharacteristic
195C4—23no—
196C4—83no—
197C4—83no—
198C4C41×#57716yes—
199C2—41no—
200C2—161no—
201C2—161no—
202C2C41×#315413yes—
subgroupG/H
center, socleC22×C41C2×#127
commutator, Frattini, cosocleC42C24×C41
prime radicalC2×#127×C41C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3231C2semidirect
3. C41×#1719C2semidirect
4. C41×#1714C2semidirect
5. C41×#1711C2semidirect
6. C41×#1705C2semidirect
7. C41×#1454C2semidirect
10. C41×#500C22semidirect
11. C41×#498C22semidirect
14. C41×#487C22semidirect
15. C41×#487C22semidirect
23. C41×#322C22semidirect
24. C82×C41C22semidirect
88. #19733C41direct (N × H)
98. #3231C2×C41semidirect
100. #1719C2×C41semidirect
101. #1714C2×C41semidirect
102. #1711C2×C41semidirect
103. #1705C2×C41semidirect
104. #1454C2×C41semidirect
111. #500C22×C41semidirect
112. #498C22×C41semidirect
115. #487C22×C41semidirect
116. #487C22×C41semidirect
124. #322C22×C41semidirect
125. C82C22×C41semidirect
126. C41#19733direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#32312
C41×#32082
C41×#17192
C41×#17142
C41×#17112
C41×#17052
C41×#14542
#1973341