Finite Group Databasebeta

← C2×#14558436 #18010846

Subgroups — C2×#14558436 #18010846

Order 4736.

278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 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×#11924596C211yesmaximal, characteristic
2C2×#11924594C211yesmaximal, characteristic
3#14558436C214yesmaximal, direct product factor
4C2×#11924520C211yesmaximal, characteristic
5C2×#10596957—21no—
6C2×C22⋊#3866—21no—
7#11924596—21no—
8#11924596C2212yes—
9#11924594—21no—
10#11924594C2212yes—
11C22×C22⋊D37C2211yescharacteristic
12C23×Dic37C411yescharacteristic, complemented
13#11924520—21no—
14#11924520—21no—
15#11924520C412yescomplemented
16#11924520C2212yes—
17C2×C4⋊Dic37—21no—
18C2×#10596938—21no—
19C2×C22⋊C4×C37C411yescharacteristic, complemented
20C24×C37C2×C411yescharacteristic
21C23×D37D411yescharacteristic
22C22×#3866—41no—
23C22×C4×C37—21no—
24C2×C22⋊D37—41no—
25C2×C22⋊D37—41no—
26C2×C22⋊D37C2×C411yescharacteristic
27C2×C22⋊D37D411yescharacteristic
28C2×C22⋊D37D411yescharacteristic
29C2×C22⋊D37C2311yescharacteristic
30C22×Dic37—21no—
31C22×Dic37—21no—
32C22×Dic37—41no—
33C22×Dic37—41no—
34C22×Dic37C2×C412yescomplemented
35C22×Dic37D411yescharacteristic
36C22⋊#3866—22no—
37C22⋊#3866—41no—
38#10596957—22no—
39#10596957—41no—
40C2×#64438—41no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37C2×C412yescomplemented
43#10596938—22no—
44#10596938—22no—
45C4⋊Dic37—22no—
46C4⋊Dic37—22no—
47C23×C37—21no—
48C23×C37—21no—
49C23×C37—42no—
50C23×C37C22⋊C411yescharacteristic
51C23×C37C22⋊C411yescharacteristic
52C23×C37C22×C411yescharacteristic
53C22×D37—21no—
54C22×D37—21no—
55C22×D37—42no—
56C22×D37C22⋊C411yescharacteristic
57C22×D37C2×D411yescharacteristic
58C2×#3866—42no—
59C2×#3866—82no—
60C2×C4×C37—22no—
61C2×C4×C37—42no—
62C22⋊D37—41no—
63C22⋊D37—41no—
64C22⋊D37—41no—
65C22⋊D37—41no—
66C2×Dic37—21no—
67C2×Dic37—21no—
68C2×Dic37—22no—
69C2×Dic37—42no—
70C2×Dic37—41no—
71C2×Dic37—41no—
72C2×Dic37—42no—
73C2×Dic37C22⋊C411yescharacteristic
74C2×Dic37C2×D411yescharacteristic
75#64438—42no—
76C22×C37—22no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37—42no—
82C22×C37—42no—
83C22×C37#9911yescharacteristic
84C22×C37#9911yescharacteristic
85C22×C37C2×C22⋊C411yescharacteristic
86C2×D37—21no—
87C2×D37—21no—
88C2×D37—42no—
89C2×D37—41no—
90C2×D37—41no—
91C2×D37—81no—
92#3866—82no—
93C4×C37—42no—
94Dic37—21no—
95Dic37—21no—
96Dic37—42no—
97C2×#352—371nomaximal, Sylow
98C2×C37—21no—
99C2×C37—21no—
100C2×C37—41no—
101C2×C37—41no—
102C2×C37#35212yescomplemented
103C2×C37C2×#9911yescharacteristic
104D37—41no—
105D37—41no—
106C2×#123—371no—
107C2×#100—371no—
108C2×#99—371no—
109#352—374no—
110C37C2×#35211yescharacteristic, complemented, Sylow
111C22×D4—371no—
112C23×C4—371no—
113C2×M16—741no—
114#123—372no—
115#123—372no—
116#123—741no—
117#123—741no—
118C2×C4⋊C4—741no—
119C2×C22⋊C4—741no—
120C2×C22⋊C4—741no—
121C2×C22⋊C4#386611yescharacteristic, complemented
122#100—372no—
123#100—741no—
124#99—372no—
125#99—741no—
126C24—371no—
127C24C2×#386611yescharacteristic
128C2×D4—371no—
129C2×D4—371no—
130C2×D4—371no—
131C2×D4—371no—
132C2×D4—1481no—
133C2×D4—1481no—
134C22×C4—21no—
135C22×C4—371no—
136C22×C4—372no—
137C22×C4—741no—
138C22×C4—741no—
139C22×C4—1481no—
140C22×C4—1481no—
141C22×C4—1481no—
142M16—742no—
143M16—1481no—
144C2×C8—1481no—
145C4⋊C4—742no—
146C4⋊C4—742no—
147C22⋊C4—21no—
148C22⋊C4—742no—
149C22⋊C4—742no—
150C22⋊C4—742no—
151C22⋊C4—1481no—
152C22⋊C4C2×#386612yescomplemented
153C23—21no—
154C23—21no—
155C23—42no—
156C23—371no—
157C23—371no—
158C23—741no—
159C23—741no—
160C23—1482no—
161C23C22⋊#386611yescharacteristic
162C23C22⋊#386611yescharacteristic
163C23C22×#386611yescharacteristic
164D4—1481no—
165D4—1481no—
166D4—1481no—
167D4—1481no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—2962no—
173C2×C4—741no—
174C2×C4—741no—
175C2×C4—742no—
176C2×C4—1482no—
177C2×C4—1482no—
178C2×C4—1481no—
179C2×C4—1481no—
180C2×C4—1482no—
181C8—1482no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—2961no—
190C22—741no—
191C22—741no—
192C22—1481no—
193C22—1481no—
194C22—1482no—
195C22#1192459511yescharacteristic
196C22#1192459511yescharacteristic
197C22C2×C22⋊#386611yescharacteristic
198C4—42no—
199C4—2962no—
200C4—741no—
201C4—741no—
202C4—1482no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—1481no—
208C2—1481no—
209C2#1455843612yesdirect product factor
210C2C2×#1192459511yescharacteristic
subgroupG/H
centerC22#11924595
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37#99
prime radicalC22×C22⋊D37C22
cosocleC2×C22⋊D37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37C2×#352
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #14558436C2direct (N × H)
12. C23×Dic37C4semidirect
15. #11924520C4semidirect
19. C2×C22⋊C4×C37C4semidirect
34. C22×Dic37C2×C4semidirect
42. C22⋊C4×C37C2×C4semidirect
102. C2×C37#352semidirect
110. C37C2×#352semidirect
121. C2×C22⋊C4#3866semidirect
152. C22⋊C4C2×#3866semidirect
209. C2#14558436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119245962
C2×#119245942
#145584362
C2×#119245202
C2×#35237