Finite Group Databasebeta

← C2×#21451921 #29846555

Subgroups — C2×#21451921 #29846555

Order 15616.

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×#14519751C216yesmaximal, complemented
2#21451921C2116yesmaximal, direct product factor
3C2×#16839699C214yesmaximal, complemented
4C2×#16839672C214yesmaximal, complemented
5C22×#95×C61C211yesmaximal, characteristic, complemented
6C23×D244C2216yes—
7C23×C22⋊D61C2214yes—
8C2×#14519751—248no—
9C2×#14519751C22148yescomplemented
10C22×C4⋊Dic61C2216yes—
11C22×#11758198C22112yes—
12#16839699C22132yescomplemented
13#16839672C22132yescomplemented
14C24×C4×C61C2213yes—
15C2×#95×C61C2214yes—
16C2×#95×C61C2218yescomplemented
17C24×D61C2314yes—
18C22×D244—224no—
19C22×D244—424no—
20C22×D244C23124yes—
21C22×C22⋊D61—248no—
22C22×C22⋊D61C23116yes—
23C23×Dic61C2314yes—
24#14519751—2192no—
25C2×C4⋊Dic61—224no—
26C2×C4⋊Dic61C23124yes—
27C2×#11758198—248no—
28C2×#11758198C23148yes—
29C25×C61C2311yescharacteristic
30C23×C4×C61—412no—
31C23×C4×C61D4124yescomplemented
32C23×C4×C61C2316yes—
33C23×C4×C61C23112yes—
34#95×C61C23116yes—
35C24×C61—26no—
36C24×C61—22no—
37C24×C61C2×D4112yes—
38C24×C61C2412yes—
39C24×C61C2411yescharacteristic
40C23×D61—224no—
41C23×D61—224no—
42C23×D61—28no—
43C23×D61C2418yes—
44C22×C4×C61—224no—
45C22×C4×C61—448no—
46C22×C4×C61—424no—
47C22×C4×C61C2×D4124yes—
48C22×C4×C61C2×D4148yescomplemented
49C22×C4×C61C24112yes—
50C2×C22⋊D61—296no—
51C2×C22⋊D61—464no—
52C22×Dic61—224no—
53C22×Dic61C2418yes—
54C2×D244—248no—
55C2×D244—448no—
56C2×D244—496no—
57#11758198—296no—
58C4⋊Dic61—248no—
59C23×C61—224no—
60C23×C61—224no—
61C23×C61—26no—
62C23×C61—22no—
63C23×C61#127116yes—
64C23×C61C22×D4112yes—
65C23×C61C22×D416yes—
66C23×C61H(5,𝔽2)16yes—
67C23×C612−1+412yes—
68C23×C61C2511yescharacteristic
69C22×D61—224no—
70C22×D61—224no—
71C22×D61—28no—
72C22×D61—416no—
73C22×D61—448no—
74C22×D61—448no—
75C2×C4×C61—248no—
76C2×C4×C61—224no—
77C2×C4×C61—448no—
78C2×C4×C61C22×D4124yes—
79C22⋊D61—464no—
80C2×Dic61—224no—
81C2×Dic61—416no—
82D244—496no—
83C2×#2656—611nomaximal, Sylow
84C22×C61—232no—
85C22×C61—212no—
86C22×C61—212no—
87C22×C61C2×#12718yes—
88C22×C61C2×#12714yes—
89C22×C61#534112yes—
90C22×C61#537112yes—
91C22×C61C23×D413yes—
92C22×C61C2×H(5,𝔽2)13yes—
93C22×C61C2×2−1+411yescharacteristic
94C2×D61—48no—
95C2×D61—424no—
96C2×D61—424no—
97C2×D61—832no—
98C4×C61—224no—
99Dic61—48no—
100C22×#121—616no—
101#2656—6116no—
102C2×#399—614no—
103C2×#392—614no—
104C22×#95D6111yescharacteristic, complemented
105C2×C61—28no—
106C2×C61#265618yescomplemented
107C2×C61C22×#12711yescharacteristic
108C2×C61C2×#53413yes—
109C2×C61C2×#53713yes—
110D61—88no—
111C23×D4—614no—
112C23×D4—616no—
113C24×C4C2×D6113yes—
114C2×#121—6148no—
115C2×#121—12248no—
116C22×C4⋊C4—616no—
117C22×C22⋊C4—6112no—
118#399—6132no—
119#392—6132no—
120C2×#95C2×D6114yes—
121C2×#95C2×D6118yescomplemented
122C61C2×#265611yescharacteristic, complemented, Sylow
123C25—614no—
124C25C22×D6111yescharacteristic
125C22×D4—6116no—
126C22×D4—6124no—
127C22×D4—12248no—
128C22×D4—12224no—
129C22×D4—24424no—
130C23×C4—412no—
131C23×C4—614no—
132C23×C4D244124yescomplemented
133C23×C4C22×D6116yes—
134C23×C4C22×D61112yes—
135#121—122192no—
136C2×C4⋊C4—6124no—
137C2×C4⋊C4—12224no—
138C2×C22⋊C4—6148no—
139C2×C22⋊C4—12248no—
140#95C22×D61116yes—
141C24—26no—
142C24—22no—
143C24—618no—
144C24—12224no—
145C24—12224no—
146C24—1228no—
147C24C2×D244112yes—
148C24C23×D6112yes—
149C24C23×D6111yescharacteristic
150C2×D4—12296no—
151C2×D4—12248no—
152C2×D4—24448no—
153C2×D4—24496no—
154C2×D4—24464no—
155C22×C4—224no—
156C22×C4—448no—
157C22×C4—424no—
158C22×C4—618no—
159C22×C4—12224no—
160C22×C4C2×D244124yes—
161C22×C4C2×D244148yescomplemented
162C22×C4C23×D61112yes—
163C4⋊C4—12248no—
164C22⋊C4—12296no—
165C23—224no—
166C23—26no—
167C23—22no—
168C23—224no—
169C23—12224no—
170C23—12224no—
171C23—1228no—
172C23—24416no—
173C23—24448no—
174C23—24448no—
175C23#14519774116yes—
176C23C22×D244112yes—
177C23C22×D24416yes—
178C23#1451982216yes—
179C23#1451982512yes—
180C23C24×D6111yescharacteristic
181D4—24496no—
182D4—24464no—
183C2×C4—248no—
184C2×C4—224no—
185C2×C4—448no—
186C2×C4—12224no—
187C2×C4—24416no—
188C2×C4C22×D244124yes—
189C22—232no—
190C22—212no—
191C22—212no—
192C22—48832no—
193C22—2448no—
194C22—24424no—
195C22—24424no—
196C22C2×#1451977418yes—
197C22C2×#1451977414yes—
198C22#16840324112yes—
199C22#16840343112yes—
200C22C23×D24413yes—
201C22C2×#1451982213yes—
202C22C2×#1451982511yescharacteristic
203C4—224no—
204C4—2448no—
205C2—28no—
206C2—4888no—
207C2#2145192118yesdirect product factor
208C2C22×#1451977411yescharacteristic
209C2C2×#1684032413yes—
210C2C2×#1684034313yes—
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×#95×C61C2
socleC24×C61C24
hypercenterC22×#95D61
hypocenterC61C2×#2656
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C22×#14519751C2semidirect
2. #21451921C2direct (N × H)
3. C2×#16839699C2semidirect
4. C2×#16839672C2semidirect
5. C22×#95×C61C2semidirect
9. C2×#14519751C22semidirect
12. #16839699C22semidirect
13. #16839672C22semidirect
16. C2×#95×C61C22semidirect
31. C23×C4×C61D4semidirect
48. C22×C4×C61C2×D4semidirect
104. C22×#95D61semidirect
106. C2×C61#2656semidirect
121. C2×#95C2×D61semidirect
122. C61C2×#2656semidirect
132. C23×C4D244semidirect
161. C22×C4C2×D244semidirect
207. C2#21451921direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197512
#214519212
C2×#168396992
C2×#168396722
C22×#95×C612
C2×#265661