Finite Group Databasebeta

← #17995122

Subgroups — #17995122

Order 4736.

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

normal subgroups only

This group has 344 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, complemented
2#14558102C211yesmaximal, characteristic
3#14557539C211yesmaximal, characteristic, complemented
4#14557537C211yesmaximal, characteristic, complemented
5#14557506C211yesmaximal, characteristic, complemented
6#14557289C211yesmaximal, characteristic, complemented
7C37×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×D148C2211yescharacteristic
10#11924544—22no—
11#11924542—22no—
12C2×#10596934C2211yescharacteristic
13M16×D37—22no—
14#11924533C412yescomplemented
15#11924524C412yescomplemented
16#11924511—22no—
17#11924506—22no—
18#11924495C2211yescharacteristic
19#11924458—22no—
20#11924456—22no—
21#11924450—22no—
22C2×M16×C37C2211yescharacteristic
23#117×C37C2211yescharacteristic
24#117×C37C2211yescharacteristic
25C23×D37—21no—
26C22×C4×C37C2311yescharacteristic
27C2×C22⋊D37D412yes—
28#10596962—21no—
29#10596962—21no—
30#10596962—21no—
31#10596962—21no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148—21no—
35C2×D148—21no—
36C2×D148—21no—
37C2×D148—24no—
38C2×D148C2×C412yes—
39C2×D148C2×C411yescharacteristic
40C2×C4×D37D412yes—
41C2×Dic74C2×C411yescharacteristic
42M16×C37—21no—
43M16×C37—21no—
44C2×C8×C37D412yescomplemented
45C4⋊C4×C37—21no—
46C4⋊C4×C37—21no—
47C22⋊C4×C37—21no—
48C22⋊C4×C37—21no—
49C42×C37—21no—
50C42×C37C2×C412yes—
51C22⋊Dic37—21no—
52#10596938—24no—
53C4⋊Dic37—21no—
54C4×Dic37—21no—
55#10596934—21no—
56#10596934—21no—
57C2×#64436D412yescomplemented
58#10596929—24no—
59C8×D37—24no—
60C23×C37C2×D411yescharacteristic
61C22×D37—22no—
62C22×D37—41no—
63C22×D37—41no—
64C22×D37—82no—
65C22×D37C22⋊C412yes—
66C2×C4×C37—22no—
67C2×C4×C37—41no—
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37#4111yescharacteristic
73C2×C4×C37#4111yescharacteristic
74C22⋊D37—22no—
75C22⋊D37—22no—
76C2×Dic37—41no—
77C2×Dic37C22⋊C412yes—
78D148—21no—
79D148—21no—
80D148—22no—
81D148—22no—
82D148—41no—
83D148—41no—
84D148—84no—
85C4×D37—22no—
86C4×D37—22no—
87Dic74—21no—
88Dic74—21no—
89C8×C37—22no—
90#64436—22no—
91C22×C37—41no—
92C22×C37C2×C22⋊C411yescharacteristic
93C22×C37#12111yescharacteristic
94C22×C37#12111yescharacteristic
95C2×D37—22no—
96C2×D37—42no—
97C2×D37—44no—
98C2×D37—42no—
99C2×D37—82no—
100C2×D37—82no—
101C4×C37—42no—
102C4×C37—81no—
103C4×C37C4×D411yescharacteristic
104C4×C37C4×D411yescharacteristic
105C4×C37#12011yescharacteristic
106C4×C37#12311yescharacteristic
107Dic37—22no—
108Dic37—81no—
109#1910—371nomaximal, Sylow
110C2×C37—21no—
111C2×C37—21no—
112C2×C37—21no—
113C2×C37#38611yescharacteristic
114D37—42no—
115D37—82no—
116#568—371no—
117#535—371no—
118#418—371no—
119#418—371no—
120#410—371no—
121H(3,ℤ/4)—371no—
122H(3,ℤ/4)D3711yescharacteristic, complemented
123C37#191011yescharacteristic, complemented, Sylow
124C2×#41—371no—
125C22×D4—371no—
126#131—742no—
127#131—742no—
128C2×M16—371no—
129C2×M16—742no—
130C2×M16C2×D3711yescharacteristic
131#127—372no—
132#124—372no—
133#121—742no—
134#120—742no—
135#117—371no—
136#117C2×D3711yescharacteristic
137#117C2×D3711yescharacteristic
138#102—742no—
139#102—742no—
140#99—742no—
141C24—741no—
142#41—741no—
143#41—741no—
144#41—741no—
145#41—741no—
146C2×Q8—371no—
147C2×D4—372no—
148C2×D4—371no—
149C2×D4—372no—
150C2×D4—744no—
151C2×D4—741no—
152C2×D4—741no—
153C2×D4—741no—
154C2×D4—741no—
155C2×D4—741no—
156C22×C4—372no—
157C22×C4C22×D3711yescharacteristic
158M16—21no—
159M16—21no—
160M16—744no—
161M16—741no—
162M16—741no—
163C2×C8—372no—
164C2×C8—744no—
165C2×C8D14812yescomplemented
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—741no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—744no—
172C22⋊C4—741no—
173C42—21no—
174C42—741no—
175C42C4×D3712yes—
176C23—372no—
177C23—2962no—
178C23—742no—
179C23—1481no—
180C23—1481no—
181C23D4×D3711yescharacteristic
182Q8—741no—
183Q8—741no—
184D4—2964no—
185D4—742no—
186D4—742no—
187D4—741no—
188D4—742no—
189D4—741no—
190D4—742no—
191D4—1481no—
192D4—1481no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—372no—
196C2×C4—742no—
197C2×C4—742no—
198C2×C4—1481no—
199C2×C4C2×C4×D3711yescharacteristic
200C2×C4C2×D14811yescharacteristic
201C2×C4#1059696211yescharacteristic
202C2×C4D4×D3711yescharacteristic
203C2×C4D4×D3711yescharacteristic
204C2×C4#1059696611yescharacteristic
205C8—22no—
206C8—742no—
207C22—41no—
208C22—2962no—
209C22—2962no—
210C22—742no—
211C22—1484no—
212C22—1482no—
213C22—1482no—
214C22C22⋊C4×D3711yescharacteristic
215C22#1192450911yescharacteristic
216C22#1192451111yescharacteristic
217C4—42no—
218C4—81no—
219C4—2961no—
220C4—742no—
221C4#1192449811yescharacteristic
222C4C4×D14811yescharacteristic
223C4#1192450611yescharacteristic
224C4#1192452111yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—2962no—
229C2—1482no—
230C2#1455741111yescharacteristic
subgroupG/H
centerC2#14557411
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×H(3,ℤ/4)C2
socleC2×C37#386
prime radical#14558102C2
cosocleC22×C4×C37C23
hypercenterH(3,ℤ/4)D37
hypocenterC37#1910
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
1. #14558299C2semidirect
3. #14557539C2semidirect
4. #14557537C2semidirect
5. #14557506C2semidirect
6. #14557289C2semidirect
7. C37×H(3,ℤ/4)C2semidirect
14. #11924533C4semidirect
15. #11924524C4semidirect
44. C2×C8×C37D4semidirect
57. C2×#64436D4semidirect
122. H(3,ℤ/4)D37semidirect
123. C37#1910semidirect
165. C2×C8D148semidirect

Maximal subgroups

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

subgroupindex
#145582992
#145581022
#145575392
#145575372
#145575062
#145572892
C37×H(3,ℤ/4)2
#191037