Finite Group Databasebeta

← C2×#14534886 #17200866

Subgroups — C2×#14534886 #17200866

Order 4352.

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×#10587616C216yesmaximal, complemented
2#14534886C2116yesmaximal, direct product factor
3C2×#11762746C214yesmaximal, complemented
4C2×#11762719C214yesmaximal, complemented
5C22×C17×#95C211yesmaximal, characteristic, complemented
6C23×D68C2216yes—
7C23×C22⋊D17C2214yes—
8C2×#10587616—248no—
9C2×#10587616C22148yescomplemented
10C22×C4⋊Dic17C2216yes—
11C22×#63227C22112yes—
12#11762746C22132yescomplemented
13#11762719C22132yescomplemented
14C24×C4×C17C2213yes—
15C2×C17×#95C2214yes—
16C2×C17×#95C2218yescomplemented
17C25×C17C2311yescharacteristic
18C24×D17C2314yes—
19C23×C4×C17—412no—
20C23×C4×C17D4124yescomplemented
21C23×C4×C17C2316yes—
22C23×C4×C17C23112yes—
23C22×C22⋊D17—248no—
24C22×C22⋊D17C23116yes—
25C23×Dic17C2314yes—
26C22×D68—224no—
27C22×D68—424no—
28C22×D68C23124yes—
29#10587616—2192no—
30C2×#63227—248no—
31C2×#63227C23148yes—
32C2×C4⋊Dic17—224no—
33C2×C4⋊Dic17C23124yes—
34C17×#95C23116yes—
35C24×C17—26no—
36C24×C17—22no—
37C24×C17C2×D4112yes—
38C24×C17C2412yes—
39C24×C17C2411yescharacteristic
40C23×D17—224no—
41C23×D17—224no—
42C23×D17—28no—
43C23×D17C2418yes—
44C22×C4×C17—224no—
45C22×C4×C17—448no—
46C22×C4×C17—424no—
47C22×C4×C17C2×D4124yes—
48C22×C4×C17C2×D4148yescomplemented
49C22×C4×C17C24112yes—
50C2×C22⋊D17—296no—
51C2×C22⋊D17—464no—
52C22×Dic17—224no—
53C22×Dic17C2418yes—
54C2×D68—248no—
55C2×D68—448no—
56C2×D68—496no—
57#63227—296no—
58C4⋊Dic17—248no—
59C2×#2656—171nomaximal, Sylow
60C23×C17—224no—
61C23×C17—224no—
62C23×C17—26no—
63C23×C17—22no—
64C23×C17#127116yes—
65C23×C17C22×D4112yes—
66C23×C17C22×D416yes—
67C23×C17H(5,𝔽2)16yes—
68C23×C172−1+412yes—
69C23×C17C2511yescharacteristic
70C22×D17—224no—
71C22×D17—224no—
72C22×D17—28no—
73C22×D17—416no—
74C22×D17—448no—
75C22×D17—448no—
76C2×C4×C17—248no—
77C2×C4×C17—224no—
78C2×C4×C17—448no—
79C2×C4×C17C22×D4124yes—
80C22⋊D17—464no—
81C2×Dic17—224no—
82C2×Dic17—416no—
83D68—496no—
84C22×#121—176no—
85#2656—1716no—
86C2×#399—174no—
87C2×#392—174no—
88C22×#95D1711yescharacteristic, complemented
89C22×C17—232no—
90C22×C17—212no—
91C22×C17—212no—
92C22×C17C2×#12718yes—
93C22×C17C2×#12714yes—
94C22×C17#534112yes—
95C22×C17#537112yes—
96C22×C17C23×D413yes—
97C22×C17C2×H(5,𝔽2)13yes—
98C22×C17C2×2−1+411yescharacteristic
99C2×D17—48no—
100C2×D17—424no—
101C2×D17—424no—
102C2×D17—832no—
103C4×C17—224no—
104Dic17—48no—
105C23×D4—174no—
106C23×D4—176no—
107C24×C4C2×D1713yes—
108C2×#121—1748no—
109C2×#121—3448no—
110C22×C4⋊C4—176no—
111C22×C22⋊C4—1712no—
112#399—1732no—
113#392—1732no—
114C2×#95C2×D1714yes—
115C2×#95C2×D1718yescomplemented
116C2×C17—28no—
117C2×C17#265618yescomplemented
118C2×C17C22×#12711yescharacteristic
119C2×C17C2×#53413yes—
120C2×C17C2×#53713yes—
121D17—88no—
122C25—174no—
123C25C22×D1711yescharacteristic
124C22×D4—1716no—
125C22×D4—1724no—
126C22×D4—3448no—
127C22×D4—3424no—
128C22×D4—6824no—
129C23×C4—412no—
130C23×C4—174no—
131C23×C4D68124yescomplemented
132C23×C4C22×D1716yes—
133C23×C4C22×D17112yes—
134#121—34192no—
135C2×C4⋊C4—1724no—
136C2×C4⋊C4—3424no—
137C2×C22⋊C4—1748no—
138C2×C22⋊C4—3448no—
139#95C22×D17116yes—
140C17C2×#265611yescharacteristic, complemented, Sylow
141C24—26no—
142C24—22no—
143C24—178no—
144C24—3424no—
145C24—3424no—
146C24—348no—
147C24C2×D68112yes—
148C24C23×D1712yes—
149C24C23×D1711yescharacteristic
150C2×D4—3496no—
151C2×D4—3448no—
152C2×D4—6848no—
153C2×D4—6896no—
154C2×D4—6864no—
155C22×C4—224no—
156C22×C4—448no—
157C22×C4—424no—
158C22×C4—178no—
159C22×C4—3424no—
160C22×C4C2×D68124yes—
161C22×C4C2×D68148yescomplemented
162C22×C4C23×D17112yes—
163C4⋊C4—3448no—
164C22⋊C4—3496no—
165C23—224no—
166C23—26no—
167C23—22no—
168C23—224no—
169C23—3424no—
170C23—3424no—
171C23—348no—
172C23—6816no—
173C23—6848no—
174C23—6848no—
175C23#10587560116yes—
176C23C22×D68112yes—
177C23C22×D6816yes—
178C23#1058769116yes—
179C23#1058769412yes—
180C23C24×D1711yescharacteristic
181D4—6896no—
182D4—6864no—
183C2×C4—248no—
184C2×C4—224no—
185C2×C4—448no—
186C2×C4—3424no—
187C2×C4—6816no—
188C2×C4C22×D68124yes—
189C22—212no—
190C22—212no—
191C22—232no—
192C22—6824no—
193C22—6824no—
194C22—688no—
195C22—13632no—
196C22C2×#1058756018yes—
197C22C2×#1058756014yes—
198C22#11763371112yes—
199C22#11763390112yes—
200C22C23×D6813yes—
201C22C2×#1058769113yes—
202C22C2×#1058769411yescharacteristic
203C4—224no—
204C4—688no—
205C2—28no—
206C2—1368no—
207C2#1453488618yesdirect product factor
208C2C22×#1058756011yescharacteristic
209C2C2×#1176337113yes—
210C2C2×#1176339013yes—
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC22×C17×#95C2
socleC24×C17C24
hypercenterC22×#95D17
hypocenterC17C2×#2656
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C22×#10587616C2semidirect
2. #14534886C2direct (N × H)
3. C2×#11762746C2semidirect
4. C2×#11762719C2semidirect
5. C22×C17×#95C2semidirect
9. C2×#10587616C22semidirect
12. #11762746C22semidirect
13. #11762719C22semidirect
16. C2×C17×#95C22semidirect
20. C23×C4×C17D4semidirect
48. C22×C4×C17C2×D4semidirect
88. C22×#95D17semidirect
115. C2×#95C2×D17semidirect
117. C2×C17#2656semidirect
131. C23×C4D68semidirect
140. C17C2×#2656semidirect
161. C22×C4C2×D68semidirect
207. C2#14534886direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876162
#145348862
C2×#117627462
C2×#117627192
C22×C17×#952
C2×#265617