Finite Group Databasebeta

← C2×#14557323 #17996232

Subgroups — C2×#14557323 #17996232

Order 4736.

278 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 77 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×#11924453C211yesmaximal, characteristic
2C2×#11924451C211yesmaximal, characteristic
3#14557323C214yesmaximal, direct product factor
4C2×#123×C37C211yesmaximal, characteristic
5C2×#10596934—21no—
6C2×C22⋊Dic37—21no—
7#11924453—21no—
8#11924453C2212yes—
9#11924451—21no—
10#11924451C2212yes—
11C22×D4×C37C2211yescharacteristic
12C23×C4×C37C411yescharacteristic, complemented
13#123×C37—21no—
14#123×C37—21no—
15#123×C37C412yescomplemented
16#123×C37C2212yes—
17C2×C4⋊C4×C37—21no—
18C2×C22⋊C4×C37—21no—
19C2×C22⋊C4×C37C411yescharacteristic, complemented
20C24×C37C2×C411yescharacteristic
21C24×C37D411yescharacteristic
22C2×D4×C37—41no—
23C2×D4×C37—41no—
24C2×D4×C37C2×C411yescharacteristic
25C2×D4×C37D411yescharacteristic
26C2×D4×C37D411yescharacteristic
27C2×D4×C37C2311yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37—21no—
30C22×C4×C37—21no—
31C22×C4×C37—41no—
32C22×C4×C37—41no—
33C22×C4×C37C2×C412yescomplemented
34C22×C4×C37D411yescharacteristic
35C22×Dic37—41no—
36C4⋊C4×C37—22no—
37C4⋊C4×C37—22no—
38C22⋊C4×C37—22no—
39C22⋊C4×C37—21no—
40C22⋊C4×C37—22no—
41C22⋊C4×C37C2×C412yescomplemented
42C22⋊Dic37—22no—
43C22⋊Dic37—41no—
44#10596934—22no—
45#10596934—41no—
46C2×#64436—41no—
47C23×C37—21no—
48C23×C37—21no—
49C23×C37—21no—
50C23×C37—21no—
51C23×C37—42no—
52C23×C37—42no—
53C23×C37C22⋊C411yescharacteristic
54C23×C37C22⋊C411yescharacteristic
55C23×C37C22⋊C411yescharacteristic
56C23×C37C22×C411yescharacteristic
57C23×C37C2×D411yescharacteristic
58D4×C37—41no—
59D4×C37—41no—
60D4×C37—41no—
61D4×C37—41no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—42no—
67C2×C4×C37—42no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37—42no—
71C2×C4×C37C22⋊C411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×Dic37—42no—
74C2×Dic37—82no—
75#64436—42no—
76C22×C37—22no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37—21no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37—42no—
86C22×C37—42no—
87C22×C37—42no—
88C22×C37—81no—
89C22×C37#9911yescharacteristic
90C22×C37#9911yescharacteristic
91C22×C37C2×C22⋊C411yescharacteristic
92C4×C37—21no—
93C4×C37—21no—
94C4×C37—42no—
95C4×C37—42no—
96Dic37—82no—
97C2×#352—371nomaximal, Sylow
98C2×C37—21no—
99C2×C37—21no—
100C2×C37—41no—
101C2×C37—41no—
102C2×C37—41no—
103C2×C37—41no—
104C2×C37#35212yescomplemented
105C2×C37C2×#9911yescharacteristic
106C2×#123D3711yescharacteristic
107C2×#100—371no—
108C2×#99—371no—
109#352—374no—
110C37C2×#35211yescharacteristic, complemented, Sylow
111C22×D4C2×D3711yescharacteristic
112C23×C4Dic3711yescharacteristic, complemented
113C2×M16—741no—
114#123—21no—
115#123—21no—
116#123Dic3712yescomplemented
117#123C2×D3712yes—
118C2×C4⋊C4—21no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—741no—
121C2×C22⋊C4Dic3711yescharacteristic, complemented
122#100—372no—
123#100—741no—
124#99—372no—
125#99—741no—
126C24C2×Dic3711yescharacteristic
127C24C22⋊D3711yescharacteristic
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C2×Dic3711yescharacteristic
131C2×D4C22⋊D3711yescharacteristic
132C2×D4C22⋊D3711yescharacteristic
133C2×D4C22×D3711yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—1481no—
140C22×C4C2×Dic3712yescomplemented
141C22×C4C22⋊D3711yescharacteristic
142M16—742no—
143M16—1481no—
144C2×C8—1481no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—21no—
149C22⋊C4—22no—
150C22⋊C4—742no—
151C22⋊C4—1481no—
152C22⋊C4C2×Dic3712yescomplemented
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23—42no—
158C23—42no—
159C23C22⋊Dic3711yescharacteristic
160C23C22⋊Dic3711yescharacteristic
161C23C22⋊Dic3711yescharacteristic
162C23C22×Dic3711yescharacteristic
163C23C2×C22⋊D3711yescharacteristic
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—2962no—
178C2×C4—1482no—
179C2×C4C22⋊Dic3711yescharacteristic
180C2×C4C2×C22⋊D3711yescharacteristic
181C8—1482no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22#1192445111yescharacteristic
196C22#1192445111yescharacteristic
197C22C2×C22⋊Dic3711yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—42no—
202C4—2962no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—41no—
208C2—41no—
209C2#1455732312yesdirect product factor
210C2C2×#1192445111yescharacteristic
subgroupG/H
centerC22#11924451
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
FittingC2×#123×C37C2
socleC22×C37#99
prime radicalC22×D4×C37C22
cosocleC2×D4×C37C23
hypercenterC2×#123D37
hypocenterC37C2×#352
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. #14557323C2direct (N × H)
12. C23×C4×C37C4semidirect
15. #123×C37C4semidirect
19. C2×C22⋊C4×C37C4semidirect
33. C22×C4×C37C2×C4semidirect
41. C22⋊C4×C37C2×C4semidirect
104. C2×C37#352semidirect
110. C37C2×#352semidirect
112. C23×C4Dic37semidirect
116. #123Dic37semidirect
121. C2×C22⋊C4Dic37semidirect
140. C22×C4C2×Dic37semidirect
152. C22⋊C4C2×Dic37semidirect
209. C2#14557323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119244532
C2×#119244512
#145573232
C2×#123×C372
C2×#35237