Finite Group Databasebeta

← C2×#14557715 #18003937

Subgroups — C2×#14557715 #18003937

Order 4736.

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

normal subgroups only

This group has 708 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
2C2×#11924567C212yesmaximal, complemented
3#14557715C218yesmaximal, direct product factor
4C2×#11924464C212yesmaximal, complemented
5C2×#11924455C211yesmaximal, characteristic, complemented
6C2×C4⋊Q8×C37C211yesmaximal, characteristic, complemented
7#11924584—22no—
8#11924584—24no—
9#11924584C2214yes—
10C2×#10596966—22no—
11C2×#10596962—22no—
12C2×#10596962C2212yes—
13C2×Q8×D37—22no—
14#11924567—24no—
15#11924567C2218yescomplemented
16C2×#10596942—22no—
17C2×#10596941—22no—
18C2×#10596934C2212yes—
19#11924464C2218yescomplemented
20#11924455C2214yescomplemented
21C22×Q8×C37C2211yescharacteristic
22C22×Q8×C37C2211yescharacteristic
23C4⋊Q8×C37—22no—
24C4⋊Q8×C37C2214yescomplemented
25C2×C4⋊C4×C37—22no—
26C2×C42×C37C2211yescharacteristic
27C2×Q8×C37—22no—
28C2×Q8×C37—22no—
29C2×Q8×C37—21no—
30C2×Q8×C37—22no—
31C2×Q8×C37—22no—
32C2×Q8×C37D412yes—
33C2×Q8×C37C2312yes—
34C2×Q8×C37C2312yes—
35C22×C4×C37—21no—
36C22×C4×C37—21no—
37C22×C4×C37D412yes—
38C22×C4×C37C2311yescharacteristic
39C2×C22⋊D37—22no—
40#10596966—28no—
41#10596966—28no—
42Q8×D37—28no—
43Q8×D37—28no—
44#10596962—28no—
45#10596962—28no—
46#10596962—22no—
47#10596962—22no—
48#10596962D414yes—
49#10596962C2314yes—
50C2×D148—22no—
51C2×D148D412yes—
52C2×C4×D37—24no—
53C2×C4×D37—22no—
54C2×Dic74—22no—
55C2×Dic74D412yes—
56C4⋊C4×C37—28no—
57C42×C37—21no—
58C42×C37C2312yes—
59#10596942—28no—
60#10596941—28no—
61#10596934—22no—
62#10596934C2314yes—
63C2×#64436—22no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66Q8×C37—24no—
67Q8×C37—24no—
68Q8×C37—24no—
69Q8×C37—42no—
70C2×C4×C37—24no—
71C2×C4×C37—22no—
72C2×C4×C37—22no—
73C2×C4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37—41no—
76C2×C4×C37—41no—
77C2×C4×C37C2×D412yes—
78C2×C4×C37C2×D412yes—
79C2×C4×C37C2×D414yes—
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2411yescharacteristic
82C22⋊D37—24no—
83C22⋊D37—24no—
84C2×Dic37—22no—
85D148—28no—
86D148—22no—
87D148C2×D414yes—
88C4×D37—216no—
89C4×D37—24no—
90C4×D37—24no—
91Dic74—28no—
92Dic74—22no—
93Dic74C2×D414yes—
94#64436—24no—
95C22×C37—22no—
96C22×C37#12011yescharacteristic
97C22×C37#12011yescharacteristic
98C22×C37C22×D411yescharacteristic
99C2×D37—24no—
100C2×D37—44no—
101C4×C37—24no—
102C4×C37—24no—
103C4×C37—42no—
104C4×C37#12012yes—
105C4×C37C22×D412yes—
106Dic37—24no—
107C2×#456—371nomaximal, Sylow
108C2×C37—21no—
109C2×C37—21no—
110C2×C37#45612yescomplemented
111C2×C37C2×#12011yescharacteristic
112D37—44no—
113C2×2−1+4—371no—
114C2×#137—372no—
115C2×C4⋊Q8D3711yescharacteristic, complemented
116#456—378no—
117C2×#104—372no—
118C2×#101—371no—
119C37C2×#45611yescharacteristic, complemented, Sylow
1202−1+4—374no—
1212−1+4—744no—
1222−1+4—742no—
123C2×#41—372no—
124C2×#41—742no—
125C2×#41—742no—
126C22×Q8—742no—
127C22×Q8C2×D3711yescharacteristic
128C22×Q8C2×D3711yescharacteristic
129#137—378no—
130#137—744no—
131C2×Q16—742no—
132C2×SD16—742no—
133C2×M16—372no—
134C4⋊Q8—22no—
135C4⋊Q8C2×D3714yescomplemented
136C2×C4⋊C4—22no—
137C2×C42C2×D3711yescharacteristic
138#104—378no—
139#101—374no—
140#41—374no—
141#41—374no—
142#41—748no—
143#41—748no—
144#41—748no—
145#41—742no—
146#41—742no—
147#41—748no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—372no—
154C2×Q8—742no—
155C2×Q8—748no—
156C2×Q8—748no—
157C2×Q8C22⋊D3712yes—
158C2×Q8C22×D3712yes—
159C2×Q8C22×D3712yes—
160C2×D4—372no—
161C2×D4—742no—
162C2×D4—742no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—744no—
166C22×C4—742no—
167C22×C4C22⋊D3712yes—
168C22×C4C22×D3711yescharacteristic
169Q16—748no—
170SD16—748no—
171M16—374no—
172M16—742no—
173C2×C8—742no—
174C4⋊C4—28no—
175C42—21no—
176C42C22×D3712yes—
177C23—742no—
178C23C2×C22⋊D3711yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—24no—
182Q8—42no—
183Q8—374no—
184Q8—748no—
185Q8—742no—
186D4—374no—
187D4—748no—
188D4—744no—
189D4—744no—
190D4—742no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—7416no—
199C2×C4—742no—
200C2×C4—744no—
201C2×C4—744no—
202C2×C4D4×D3712yes—
203C2×C4D4×D3712yes—
204C2×C4C2×C22⋊D3714yes—
205C2×C4C2×C22⋊D3711yescharacteristic
206C2×C4C23×D3711yescharacteristic
207C8—744no—
208C22—22no—
209C22—744no—
210C22—1484no—
211C22#1192450411yescharacteristic
212C22#1192450411yescharacteristic
213C22C22×C22⋊D3711yescharacteristic
214C4—24no—
215C4—24no—
216C4—42no—
217C4—744no—
218C4#1192450412yes—
219C4C2×D4×D3712yes—
220C2—21no—
221C2—21no—
222C2—1484no—
223C2#1455771512yesdirect product factor
224C2C2×#1192450411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×C4⋊Q8×C37C2
socleC22×C37#120
prime radicalC2×#11924584C2
hypercenterC2×C4⋊Q8D37
hypocenterC37C2×#456
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11924567C2semidirect
3. #14557715C2direct (N × H)
4. C2×#11924464C2semidirect
5. C2×#11924455C2semidirect
6. C2×C4⋊Q8×C37C2semidirect
15. #11924567C22semidirect
19. #11924464C22semidirect
20. #11924455C22semidirect
24. C4⋊Q8×C37C22semidirect
110. C2×C37#456semidirect
115. C2×C4⋊Q8D37semidirect
119. C37C2×#456semidirect
135. C4⋊Q8C2×D37semidirect
223. C2#14557715direct (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×#119245672
#145577152
C2×#119244642
C2×#119244552
C2×C4⋊Q8×C372
C2×#45637