Finite Group Databasebeta

← C2×#23766681 #34454535

Subgroups — C2×#23766681 #34454535

Order 20224.

5150 conjugacy classes of subgroups; only the 939 normal subgroups are shown.

normal subgroups only

This group has 5150 conjugacy classes of subgroups — too many to draw. Only its 939 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
1C22×C4×D316C216yesmaximal, complemented
2#23766681C2116yesmaximal, direct product factor
3C2×#19098500C214yesmaximal, complemented
4C2×#19098473C214yesmaximal, complemented
5C2×#376×C79C211yesmaximal, characteristic, complemented
6C23×D316C2216yes—
7C23×C4×D79C2214yes—
8C2×C4×D316—248no—
9C2×C4×D316C22148yescomplemented
10C22×C4⋊Dic79C2216yes—
11C22×(C2×D79)⋊C4C22112yes—
12#19098500C22132yescomplemented
13#19098473C22132yescomplemented
14C22×C42×C79C2213yes—
15#376×C79C2218yescomplemented
16C2×#95×C79C2214yes—
17C24×D79C2314yes—
18C22×D316—224no—
19C22×D316—248no—
20C22×D316C23124yes—
21C23×Dic79C2314yes—
22C22×C4×D79—248no—
23C22×C4×D79C23116yes—
24C4×D316—2192no—
25C2×C4⋊Dic79—224no—
26C2×C4⋊Dic79C23124yes—
27C2×(C2×D79)⋊C4—248no—
28C2×(C2×D79)⋊C4C23148yes—
29C23×C4×C79C2316yes—
30C23×C4×C79C2311yescharacteristic
31C2×C42×C79D4124yescomplemented
32C2×C42×C79C23112yes—
33#95×C79C23116yes—
34C23×D79—224no—
35C23×D79—224no—
36C23×D79#41116yes—
37C23×D79C2418yes—
38C2×D316—2192no—
39C2×D316—296no—
40C2×D316—248no—
41C22×Dic79—224no—
42C22×Dic79C2418yes—
43C2×C4×D79—296no—
44C2×C4×D79—464no—
45C4⋊Dic79—248no—
46(C2×D79)⋊C4—296no—
47C24×C79C2411yescharacteristic
48C22×C4×C79—224no—
49C22×C4×C79C2×D4124yes—
50C22×C4×C79C2×D4112yes—
51C22×C4×C79C24112yes—
52C22×C4×C79C2412yes—
53C42×C79C2×D4148yescomplemented
54C23×C79C22×D416yes—
55C23×C79C2×#4118yes—
56C23×C79C2511yescharacteristic
57C22×D79—296no—
58C22×D79—224no—
59C22×D79—224no—
60C22×D79—448no—
61C22×D79—416no—
62C22×D79C2×#41116yes—
63C2×C4×C79—248no—
64C2×C4×C79—224no—
65C2×C4×C79#127116yes—
66C2×C4×C79C22×D4124yes—
67C2×C4×C79C22×D4112yes—
68C2×Dic79—224no—
69C2×Dic79—416no—
70D316—2192no—
71C4×D79—464no—
72C22×C79#525124yes—
73C22×C79C2×#12714yes—
74C22×C79C23×D413yes—
75C22×C79C22×#4114yes—
76C2×D79—248no—
77C2×D79—464no—
78C2×D79—424no—
79C2×D79—48no—
80C4×C79—224no—
81C4×C79C2×#12718yes—
82Dic79—48no—
83C2×#2397—791nomaximal, Sylow
84C2×C79#239718yescomplemented
85C2×C79C2×#52516yes—
86C2×C79C22×#12711yescharacteristic
87D79—416no—
88C22×C4×D4—796no—
89#2397—7916no—
90C2×#399—794no—
91C2×#392—794no—
92C2×#376D7911yescharacteristic, complemented
93C79C2×#239711yescharacteristic, complemented, Sylow
94C23×D4—796no—
95C24×C4—794no—
96C2×C4×D4—7948no—
97C2×C4×D4—15848no—
98C22×C4⋊C4—796no—
99C22×C22⋊C4—7912no—
100C22×C42C2×D7913yes—
101#399—7932no—
102#392—7932no—
103#376C2×D7918yescomplemented
104C2×#95C2×D7914yes—
105C25—794no—
106C22×D4—7924no—
107C22×D4—15848no—
108C22×D4—15824no—
109C23×C4—794no—
110C23×C4—7916no—
111C23×C4—15848no—
112C23×C4C22×D7916yes—
113C23×C4C22×D7911yescharacteristic
114C4×D4—158192no—
115C2×C4⋊C4—7924no—
116C2×C4⋊C4—15824no—
117C2×C22⋊C4—7948no—
118C2×C22⋊C4—15848no—
119C2×C42D316124yescomplemented
120C2×C42C22×D79112yes—
121#95C22×D79116yes—
122C24—7916no—
123C24—798no—
124C24—15824no—
125C24—15824no—
126C24C23×D7911yescharacteristic
127C2×D4—15896no—
128C2×D4—158192no—
129C2×D4—15848no—
130C22×C4—224no—
131C22×C4—31664no—
132C22×C4—798no—
133C22×C4—15824no—
134C22×C4—15896no—
135C22×C4C2×D316124yes—
136C22×C4C2×D316112yes—
137C22×C4C23×D79112yes—
138C22×C4C23×D7912yes—
139C4⋊C4—15848no—
140C22⋊C4—15896no—
141C42C2×D316148yescomplemented
142C23—31648no—
143C23—31616no—
144C23—7916no—
145C23—15896no—
146C23—15824no—
147C23—15824no—
148C23C22×D31616yes—
149C23#41×D7918yes—
150C23C24×D7911yescharacteristic
151D4—158192no—
152C2×C4—248no—
153C2×C4—224no—
154C2×C4—31616no—
155C2×C4—31664no—
156C2×C4—15824no—
157C2×C4#14579158116yes—
158C2×C4C22×D316124yes—
159C2×C4C22×D316112yes—
160C22—31624no—
161C22—31664no—
162C22—3168no—
163C22—15848no—
164C22#19099075124yes—
165C22C2×#1457915814yes—
166C22C23×D31613yes—
167C22C2×#41×D7914yes—
168C4—224no—
169C4—3168no—
170C4C2×#1457915818yes—
171C2—31616no—
172C2#2376668118yesdirect product factor
173C2C2×#1909907516yes—
174C2C22×#1457915811yescharacteristic
subgroupG/H
centerC23×C4C22×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#376×C79C2
socleC24×C79C24
hypercenterC2×#376D79
hypocenterC79C2×#2397
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23×C4 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
1. C22×C4×D316C2semidirect
2. #23766681C2direct (N × H)
3. C2×#19098500C2semidirect
4. C2×#19098473C2semidirect
5. C2×#376×C79C2semidirect
9. C2×C4×D316C22semidirect
12. #19098500C22semidirect
13. #19098473C22semidirect
15. #376×C79C22semidirect
31. C2×C42×C79D4semidirect
53. C42×C79C2×D4semidirect
84. C2×C79#2397semidirect
92. C2×#376D79semidirect
93. C79C2×#2397semidirect
103. #376C2×D79semidirect
119. C2×C42D316semidirect
141. C42C2×D316semidirect
172. C2#23766681direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D3162
#237666812
C2×#190985002
C2×#190984732
C2×#376×C792
C2×#239779