Finite Group Databasebeta

← #17995117

Subgroups — #17995117

Order 4736.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#14558299C211yesmaximal, characteristic
2#14558109C211yesmaximal, characteristic
3#14557543C211yesmaximal, characteristic, complemented
4#14557541C211yesmaximal, characteristic, complemented
5#14557506C211yesmaximal, characteristic
6#14557289C211yesmaximal, characteristic, complemented
7C37×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924544—22no—
11#11924542—22no—
12C2×#10596934C2211yescharacteristic
13M16×D37—22no—
14#11924536C412yescomplemented
15#11924524C412yescomplemented
16#11924520—22no—
17#11924516—22no—
18#11924495C2211yescharacteristic
19#11924461—22no—
20#11924459—22no—
21#11924450—22no—
22C2×M16×C37C2211yescharacteristic
23#117×C37C2211yescharacteristic
24#117×C37C2211yescharacteristic
25C22×C4×C37C2311yescharacteristic
26C2×C22⋊D37D412yes—
27C22×Dic37—21no—
28#10596962—21no—
29#10596962—21no—
30#10596962—21no—
31#10596962—21no—
32C2×D148C2×C411yescharacteristic
33C2×C4×D37D412yes—
34C2×Dic74—21no—
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74—21no—
39C2×Dic74C2×C412yes—
40C2×Dic74C2×C411yescharacteristic
41M16×C37—21no—
42M16×C37—21no—
43C2×C8×C37D412yes—
44C4⋊C4×C37—21no—
45C4⋊C4×C37—21no—
46C22⋊C4×C37—21no—
47C22⋊C4×C37—21no—
48C42×C37—21no—
49C42×C37C2×C412yes—
50C22⋊Dic37—21no—
51#10596938—24no—
52C4⋊Dic37—24no—
53C4⋊Dic37—21no—
54C4×Dic37—21no—
55#10596934—21no—
56#10596934—21no—
57C2×#64436D412yes—
58#10596929—24no—
59C8×D37—24no—
60C23×C37C2×D411yescharacteristic
61C22×D37C22⋊C412yes—
62C2×C4×C37—22no—
63C2×C4×C37—41no—
64C2×C4×C37C22×C411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37#4111yescharacteristic
69C2×C4×C37#4111yescharacteristic
70C22⋊D37—22no—
71C22⋊D37—22no—
72C2×Dic37—22no—
73C2×Dic37—41no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37C22⋊C412yes—
77D148—21no—
78D148—21no—
79C4×D37—22no—
80C4×D37—22no—
81Dic74—21no—
82Dic74—21no—
83Dic74—22no—
84Dic74—22no—
85Dic74—41no—
86Dic74—41no—
87C8×C37—22no—
88#64436—22no—
89C22×C37—41no—
90C22×C37C2×C22⋊C411yescharacteristic
91C22×C37#12111yescharacteristic
92C22×C37#12111yescharacteristic
93C2×D37—22no—
94C2×D37—42no—
95C4×C37—42no—
96C4×C37—81no—
97C4×C37C4×D411yescharacteristic
98C4×C37C4×D411yescharacteristic
99C4×C37#12011yescharacteristic
100C4×C37#12311yescharacteristic
101Dic37—22no—
102Dic37—42no—
103Dic37—81no—
104#1909—371nomaximal, Sylow
105C2×C37—21no—
106C2×C37—21no—
107C2×C37—21no—
108C2×C37#38611yescharacteristic
109D37—42no—
110#568—371no—
111#536—371no—
112#419—371no—
113#419—371no—
114#410—371no—
115H(3,ℤ/4)—371no—
116H(3,ℤ/4)D3711yescharacteristic, complemented
117C37#190911yescharacteristic, complemented, Sylow
118C2×#41—371no—
119C22×Q8—371no—
120#131—742no—
121#131—742no—
122C2×M16—371no—
123C2×M16—742no—
124C2×M16C2×D3711yescharacteristic
125C4⋊Q8—372no—
126#124—372no—
127#123—742no—
128C22⋊Q8—742no—
129#117—371no—
130#117C2×D3711yescharacteristic
131#117C2×D3711yescharacteristic
132#103—742no—
133#103—742no—
134#99—742no—
135#41—741no—
136#41—741no—
137#41—741no—
138#41—741no—
139C2×Q8—371no—
140C2×Q8—372no—
141C2×Q8—741no—
142C2×Q8—741no—
143C2×Q8—741no—
144C2×Q8—741no—
145C2×Q8—741no—
146C2×D4—372no—
147C2×D4—371no—
148C22×C4—372no—
149C22×C4—741no—
150C22×C4C22×D3711yescharacteristic
151M16—21no—
152M16—21no—
153M16—744no—
154M16—741no—
155M16—741no—
156C2×C8—372no—
157C2×C8—744no—
158C2×C8D14812yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—744no—
162C4⋊C4—741no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—744no—
166C22⋊C4—741no—
167C42—21no—
168C42—741no—
169C42C4×D3712yes—
170C23—372no—
171C23D4×D3711yescharacteristic
172Q8—741no—
173Q8—741no—
174Q8—742no—
175Q8—742no—
176Q8—1481no—
177Q8—1481no—
178D4—742no—
179D4—742no—
180D4—741no—
181D4—741no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—372no—
185C2×C4—742no—
186C2×C4—742no—
187C2×C4—742no—
188C2×C4—1481no—
189C2×C4—1481no—
190C2×C4—1481no—
191C2×C4C2×C4×D3711yescharacteristic
192C2×C4C2×D14811yescharacteristic
193C2×C4#1059696211yescharacteristic
194C2×C4D4×D3711yescharacteristic
195C2×C4D4×D3711yescharacteristic
196C2×C4#1059696611yescharacteristic
197C8—22no—
198C8—742no—
199C22—41no—
200C22—742no—
201C22—1482no—
202C22C22⋊C4×D3711yescharacteristic
203C22#1192450911yescharacteristic
204C22#1192451111yescharacteristic
205C4—42no—
206C4—81no—
207C4—2961no—
208C4—742no—
209C4—1482no—
210C4#1192449811yescharacteristic
211C4C4×D14811yescharacteristic
212C4#1192450611yescharacteristic
213C4#1192452111yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—1482no—
218C2#1455741111yescharacteristic
subgroupG/H
centerC2#14557411
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×H(3,ℤ/4)C2
socleC2×C37#386
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenterH(3,ℤ/4)D37
hypocenterC37#1909
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
3. #14557543C2semidirect
4. #14557541C2semidirect
6. #14557289C2semidirect
7. C37×H(3,ℤ/4)C2semidirect
14. #11924536C4semidirect
15. #11924524C4semidirect
116. H(3,ℤ/4)D37semidirect
117. C37#1909semidirect

Maximal subgroups

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

subgroupindex
#145582992
#145581092
#145575432
#145575412
#145575062
#145572892
C37×H(3,ℤ/4)2
#190937