Finite Group Databasebeta

← C2×#14557708 #18003934

Subgroups — C2×#14557708 #18003934

Order 4736.

728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#11924584C211yesmaximal, characteristic, complemented
2C2×#11924564C212yesmaximal, complemented
3C2×#11924525C211yesmaximal, characteristic, complemented
4#14557708C218yesmaximal, direct product factor
5C2×#11924462C212yesmaximal, complemented
6C2×#101×C37C211yesmaximal, characteristic, complemented
7#11924584—22no—
8#11924584—24no—
9#11924584C2214yescomplemented
10C2×#10596966—22no—
11C2×#10596962—22no—
12C2×#10596962C2212yes—
13C2×Q8×D37—22no—
14C22×D148C2211yescharacteristic
15#11924564—24no—
16#11924564C2218yescomplemented
17C2×#10596930—22no—
18C2×D296—22no—
19#11924525—22no—
20#11924525C2214yescomplemented
21C2×#10596938—22no—
22C2×C4×Dic37C2211yescharacteristic
23#11924462C2218yescomplemented
24C22×Q8×C37C2211yescharacteristic
25C2×M16×C37C2212yes—
26#101×C37C2214yescomplemented
27C23×D37—21no—
28C2×Q8×C37—22no—
29C2×Q8×C37—22no—
30C2×Q8×C37D412yes—
31C2×Q8×C37C2312yes—
32C22×C4×C37D412yes—
33C22×C4×C37C2311yescharacteristic
34C2×C22⋊D37—22no—
35C22×Dic37—21no—
36#10596966—28no—
37#10596966—28no—
38Q8×D37—28no—
39Q8×D37—28no—
40#10596962—28no—
41#10596962—28no—
42#10596962—22no—
43#10596962—22no—
44#10596962D414yes—
45#10596962C2314yes—
46C2×D148—22no—
47C2×D148—22no—
48C2×D148—22no—
49C2×D148—21no—
50C2×D148D412yes—
51C2×D148C2312yes—
52C2×C4×D37—24no—
53C2×C4×D37—22no—
54C2×Dic74—22no—
55C2×Dic74D412yes—
56M16×C37—22no—
57M16×C37C2314yes—
58C2×C8×C37—22no—
59#10596938—28no—
60C4×Dic37—21no—
61C4×Dic37C2312yes—
62D296—28no—
63#10596930—28no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66C22×D37—22no—
67C22×D37—44no—
68C22×D37—41no—
69C22×D37—41no—
70Q8×C37—24no—
71Q8×C37—24no—
72C2×C4×C37—22no—
73C2×C4×C37—22no—
74C2×C4×C37C2×D414yes—
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D412yes—
77C2×C4×C37C2×D412yes—
78C2×C4×C37C2411yescharacteristic
79C22⋊D37—24no—
80C22⋊D37—24no—
81C2×Dic37—22no—
82C2×Dic37—22no—
83C2×Dic37—42no—
84D148—28no—
85D148—22no—
86D148—24no—
87D148—42no—
88D148C2×D414yes—
89C4×D37—216no—
90C4×D37—24no—
91C4×D37—24no—
92Dic74—28no—
93Dic74—22no—
94Dic74C2×D414yes—
95C8×C37—24no—
96C22×C37—22no—
97C22×C37#12011yescharacteristic
98C22×C37#12011yescharacteristic
99C22×C37C22×D411yescharacteristic
100C2×D37—24no—
101C2×D37—44no—
102C2×D37—44no—
103C2×D37—42no—
104C2×D37—82no—
105C2×D37—82no—
106C4×C37—24no—
107C4×C37#12012yes—
108C4×C37C22×D412yes—
109Dic37—24no—
110Dic37—42no—
111C2×#454—371nomaximal, Sylow
112C2×C37—21no—
113C2×C37—21no—
114C2×C37#45412yescomplemented
115C2×C37C2×#12011yescharacteristic
116D37—44no—
117D37—82no—
118C2×2−1+4—371no—
119C2×AGL(1,ℤ/8)—372no—
120C2×#124—371no—
121#454—378no—
122C2×#104—372no—
123C2×#101D3711yescharacteristic, complemented
124C37C2×#45411yescharacteristic, complemented, Sylow
1252−1+4—374no—
1262−1+4—744no—
1272−1+4—742no—
128C2×#41—372no—
129C2×#41—742no—
130C2×#41—742no—
131C22×Q8—742no—
132C22×Q8C2×D3711yescharacteristic
133C22×D4—371no—
134AGL(1,ℤ/8)—378no—
135AGL(1,ℤ/8)—744no—
136C2×SD16—742no—
137C2×D8—742no—
138C2×M16C2×D3712yes—
139#124—374no—
140#124—742no—
141C2×C22⋊C4—742no—
142C2×C42—371no—
143#104—378no—
144#101C2×D3714yescomplemented
145C24—741no—
146#41—374no—
147#41—374no—
148#41—748no—
149#41—748no—
150#41—748no—
151#41—742no—
152#41—748no—
153#41—742no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—372no—
157C2×Q8—742no—
158C2×Q8—748no—
159C2×Q8—748no—
160C2×Q8D14812yes—
161C2×Q8C22×D3712yes—
162C2×D4—372no—
163C2×D4—372no—
164C2×D4—742no—
165C2×D4—742no—
166C2×D4—741no—
167C2×D4—742no—
168C2×D4—742no—
169C22×C4—744no—
170C22×C4—742no—
171C22×C4—741no—
172C22×C4D14812yes—
173C22×C4C22×D3711yescharacteristic
174SD16—748no—
175D8—748no—
176M16—22no—
177M16C22×D3714yes—
178C2×C8—22no—
179C22⋊C4—748no—
180C42—372no—
181C42—741no—
182C23—742no—
183C23—742no—
184C23—1484no—
185C23—1481no—
186C23—1481no—
187C23C2×D14811yescharacteristic
188Q8—24no—
189Q8—24no—
190Q8—374no—
191Q8—748no—
192Q8—742no—
193D4—374no—
194D4—748no—
195D4—744no—
196D4—744no—
197D4—742no—
198D4—744no—
199D4—1482no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—7416no—
203C2×C4—742no—
204C2×C4—744no—
205C2×C4—744no—
206C2×C4—742no—
207C2×C4—1482no—
208C2×C4C2×D14814yes—
209C2×C4C2×D14811yescharacteristic
210C2×C4D4×D3712yes—
211C2×C4D4×D3712yes—
212C2×C4C23×D3711yescharacteristic
213C8—24no—
214C22—22no—
215C22—2962no—
216C22—2962no—
217C22—744no—
218C22—1484no—
219C22—1482no—
220C22—1484no—
221C22#1192450611yescharacteristic
222C22#1192450611yescharacteristic
223C22C22×D14811yescharacteristic
224C4—24no—
225C4—744no—
226C4—1482no—
227C4#1192450612yes—
228C4C2×D4×D3712yes—
229C2—21no—
230C2—21no—
231C2—2962no—
232C2—1484no—
233C2#1455770812yesdirect product factor
234C2C2×#1192450611yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#101×C37C2
socleC22×C37#120
hypercenterC2×#101D37
hypocenterC37C2×#454
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#11924584C2semidirect
2. C2×#11924564C2semidirect
3. C2×#11924525C2semidirect
4. #14557708C2direct (N × H)
5. C2×#11924462C2semidirect
6. C2×#101×C37C2semidirect
9. #11924584C22semidirect
16. #11924564C22semidirect
20. #11924525C22semidirect
23. #11924462C22semidirect
26. #101×C37C22semidirect
114. C2×C37#454semidirect
123. C2×#101D37semidirect
124. C37C2×#454semidirect
144. #101C2×D37semidirect
233. C2#14557708direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119245842
C2×#119245642
C2×#119245252
#145577082
C2×#119244622
C2×#101×C372
C2×#45437