Finite Group Databasebeta

← C2×#23769502 #34454811

Subgroups — C2×#23769502 #34454811

Order 20224.

4886 conjugacy classes of subgroups; only the 907 normal subgroups are shown.

normal subgroups only

This group has 4886 conjugacy classes of subgroups — too many to draw. Only its 907 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×#14579135C216yesmaximal, complemented
2#23769502C2116yesmaximal, direct product factor
3C2×#19098500C214yesmaximal, complemented
4C2×#19098473C214yesmaximal, complemented
5C22×#95×C79C211yesmaximal, characteristic, complemented
6C23×D316C2216yes—
7C23×C22⋊D79C2214yes—
8C2×#14579135—248no—
9C2×#14579135C22148yescomplemented
10C22×C4⋊Dic79C2216yes—
11C22×(C2×D79)⋊C4C22112yes—
12#19098500C22132yescomplemented
13#19098473C22132yescomplemented
14C24×C4×C79C2213yes—
15C2×#95×C79C2214yes—
16C2×#95×C79C2218yescomplemented
17C24×D79C2314yes—
18C22×D316—224no—
19C22×D316—424no—
20C22×D316C23124yes—
21C22×C22⋊D79—248no—
22C22×C22⋊D79C23116yes—
23C23×Dic79C2314yes—
24#14579135—2192no—
25C2×C4⋊Dic79—224no—
26C2×C4⋊Dic79C23124yes—
27C2×(C2×D79)⋊C4—248no—
28C2×(C2×D79)⋊C4C23148yes—
29C25×C79C2311yescharacteristic
30C23×C4×C79—412no—
31C23×C4×C79D4124yescomplemented
32C23×C4×C79C2316yes—
33C23×C4×C79C23112yes—
34#95×C79C23116yes—
35C23×D79—224no—
36C23×D79—224no—
37C23×D79—28no—
38C23×D79C2418yes—
39C2×D316—248no—
40C2×D316—448no—
41C2×D316—496no—
42C2×C22⋊D79—296no—
43C2×C22⋊D79—464no—
44C22×Dic79—224no—
45C22×Dic79C2418yes—
46C4⋊Dic79—248no—
47(C2×D79)⋊C4—296no—
48C24×C79—26no—
49C24×C79—22no—
50C24×C79C2×D4112yes—
51C24×C79C2412yes—
52C24×C79C2411yescharacteristic
53C22×C4×C79—224no—
54C22×C4×C79—448no—
55C22×C4×C79—424no—
56C22×C4×C79C2×D4124yes—
57C22×C4×C79C2×D4148yescomplemented
58C22×C4×C79C24112yes—
59C23×C79—224no—
60C23×C79—224no—
61C23×C79—26no—
62C23×C79—22no—
63C23×C79#127116yes—
64C23×C79C22×D4112yes—
65C23×C79C22×D416yes—
66C23×C79H(5,𝔽2)16yes—
67C23×C792−1+412yes—
68C23×C79C2511yescharacteristic
69C22×D79—224no—
70C22×D79—224no—
71C22×D79—28no—
72C22×D79—416no—
73C22×D79—448no—
74C22×D79—448no—
75C2×C4×C79—248no—
76C2×C4×C79—224no—
77C2×C4×C79—448no—
78C2×C4×C79C22×D4124yes—
79C22⋊D79—464no—
80C2×Dic79—224no—
81C2×Dic79—416no—
82D316—496no—
83C22×C79—232no—
84C22×C79—212no—
85C22×C79—212no—
86C22×C79C2×#12718yes—
87C22×C79C2×#12714yes—
88C22×C79#534112yes—
89C22×C79#537112yes—
90C22×C79C23×D413yes—
91C22×C79C2×H(5,𝔽2)13yes—
92C22×C79C2×2−1+411yescharacteristic
93C2×D79—48no—
94C2×D79—424no—
95C2×D79—424no—
96C2×D79—832no—
97C4×C79—224no—
98Dic79—48no—
99C2×#2656—791nomaximal, Sylow
100C2×C79—28no—
101C2×C79#265618yescomplemented
102C2×C79C22×#12711yescharacteristic
103C2×C79C2×#53413yes—
104C2×C79C2×#53713yes—
105D79—88no—
106C22×#121—796no—
107#2656—7916no—
108C2×#399—794no—
109C2×#392—794no—
110C22×#95D7911yescharacteristic, complemented
111C79C2×#265611yescharacteristic, complemented, Sylow
112C23×D4—794no—
113C23×D4—796no—
114C24×C4C2×D7913yes—
115C2×#121—7948no—
116C2×#121—15848no—
117C22×C4⋊C4—796no—
118C22×C22⋊C4—7912no—
119#399—7932no—
120#392—7932no—
121C2×#95C2×D7914yes—
122C2×#95C2×D7918yescomplemented
123C25—794no—
124C25C22×D7911yescharacteristic
125C22×D4—31624no—
126C22×D4—7916no—
127C22×D4—7924no—
128C22×D4—15848no—
129C22×D4—15824no—
130C23×C4—412no—
131C23×C4—794no—
132C23×C4D316124yescomplemented
133C23×C4C22×D7916yes—
134C23×C4C22×D79112yes—
135#121—158192no—
136C2×C4⋊C4—7924no—
137C2×C4⋊C4—15824no—
138C2×C22⋊C4—7948no—
139C2×C22⋊C4—15848no—
140#95C22×D79116yes—
141C24—26no—
142C24—22no—
143C24—798no—
144C24—15824no—
145C24—1588no—
146C24—15824no—
147C24C2×D316112yes—
148C24C23×D7912yes—
149C24C23×D7911yescharacteristic
150C2×D4—31696no—
151C2×D4—31648no—
152C2×D4—31664no—
153C2×D4—15896no—
154C2×D4—15848no—
155C22×C4—224no—
156C22×C4—424no—
157C22×C4—448no—
158C22×C4—798no—
159C22×C4—15824no—
160C22×C4C2×D316124yes—
161C22×C4C2×D316148yescomplemented
162C22×C4C23×D79112yes—
163C4⋊C4—15848no—
164C22⋊C4—15896no—
165C23—26no—
166C23—22no—
167C23—224no—
168C23—224no—
169C23—31648no—
170C23—31616no—
171C23—31648no—
172C23—15824no—
173C23—1588no—
174C23—15824no—
175C23#14579158116yes—
176C23C22×D316112yes—
177C23C22×D31616yes—
178C23#1457920616yes—
179C23#1457920912yes—
180C23C24×D7911yescharacteristic
181D4—31696no—
182D4—31664no—
183C2×C4—224no—
184C2×C4—248no—
185C2×C4—448no—
186C2×C4—31616no—
187C2×C4—15824no—
188C2×C4C22×D316124yes—
189C22—232no—
190C22—212no—
191C22—212no—
192C22—3168no—
193C22—31624no—
194C22—31624no—
195C22—63232no—
196C22C2×#1457915818yes—
197C22C2×#1457915814yes—
198C22#19099125112yes—
199C22#19099144112yes—
200C22C23×D31613yes—
201C22C2×#1457920613yes—
202C22C2×#1457920911yescharacteristic
203C4—224no—
204C4—3168no—
205C2—28no—
206C2—6328no—
207C2#2376950218yesdirect product factor
208C2C22×#1457915811yescharacteristic
209C2C2×#1909912513yes—
210C2C2×#1909914413yes—
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC22×#95×C79C2
socleC24×C79C24
hypercenterC22×#95D79
hypocenterC79C2×#2656
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C22×#14579135C2semidirect
2. #23769502C2direct (N × H)
3. C2×#19098500C2semidirect
4. C2×#19098473C2semidirect
5. C22×#95×C79C2semidirect
9. C2×#14579135C22semidirect
12. #19098500C22semidirect
13. #19098473C22semidirect
16. C2×#95×C79C22semidirect
31. C23×C4×C79D4semidirect
57. C22×C4×C79C2×D4semidirect
101. C2×C79#2656semidirect
110. C22×#95D79semidirect
111. C79C2×#2656semidirect
122. C2×#95C2×D79semidirect
132. C23×C4D316semidirect
161. C22×C4C2×D316semidirect
207. C2#23769502direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791352
#237695022
C2×#190985002
C2×#190984732
C22×#95×C792
C2×#265679