Finite Group Databasebeta

← #17995073

Subgroups — #17995073

Order 4736.

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

normal subgroups only

This group has 324 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
1C2×#11924562C211yesmaximal, characteristic
2#14558299C211yesmaximal, characteristic, complemented
3#14557551C211yesmaximal, characteristic, complemented
4C2×#11924453C211yesmaximal, characteristic, complemented
5#14557303C211yesmaximal, characteristic, complemented
6#14557291C211yesmaximal, characteristic, complemented
7C37×#418C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924562—22no—
10#11924562—22no—
11C2×#10596940C412yescomplemented
12C2×#10596939C412yescomplemented
13#11924544—22no—
14#11924542—22no—
15C2×#10596934C2211yescharacteristic
16C2×#10596934C2211yescharacteristic
17C2×#10596934C2211yescharacteristic
18M16×D37—22no—
19#11924464—22no—
20#11924453—22no—
21C22×D4×C37C2211yescharacteristic
22C2×M16×C37C2211yescharacteristic
23#117×C37C2211yescharacteristic
24#102×C37—22no—
25C24×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C2×D4×C37—21no—
30C2×D4×C37—21no—
31C2×D4×C37C2×C412yes—
32C22×C4×C37C2311yescharacteristic
33C2×C22⋊D37—21no—
34#10596962—21no—
35#10596962—21no—
36#10596962D412yes—
37#10596962D412yes—
38C2×D148C2×C411yescharacteristic
39C2×C4×D37—21no—
40C2×Dic74C2×C411yescharacteristic
41M16×C37—21no—
42M16×C37—21no—
43C2×C8×C37D412yes—
44C4⋊C4×C37—21no—
45C22⋊C4×C37—21no—
46C42×C37—21no—
47#10596940—24no—
48#10596939—24no—
49#10596934—21no—
50#10596934—21no—
51#10596934—21no—
52#10596934—21no—
53#10596934—21no—
54#10596934D412yes—
55C2×#64436—21no—
56C2×#64436—21no—
57C2×#64436C2×C412yes—
58#10596929—24no—
59C8×D37—24no—
60C23×C37—22no—
61C23×C37—41no—
62C23×C37—41no—
63C23×C37—82no—
64C23×C37#4111yescharacteristic
65C22×D37—21no—
66D4×C37—22no—
67D4×C37—22no—
68D4×C37—41no—
69D4×C37—41no—
70C2×C4×C37—41no—
71C2×C4×C37C22×C411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37#4111yescharacteristic
77C22⋊D37—22no—
78C22⋊D37—22no—
79C2×Dic37—21no—
80D148—21no—
81D148C22⋊C412yes—
82C4×D37—22no—
83C4×D37—22no—
84Dic74—21no—
85Dic74C22⋊C412yes—
86C8×C37—22no—
87#64436—22no—
88#64436—22no—
89#64436—41no—
90C22×C37—41no—
91C22×C37—42no—
92C22×C37—82no—
93C22×C37—82no—
94C22×C37—82no—
95C22×C37C4×D411yescharacteristic
96C22×C37#12111yescharacteristic
97C22×C37#12311yescharacteristic
98C2×D37—22no—
99C2×D37—81no—
100C4×C37—81no—
101C4×C37C2×C22⋊C411yescharacteristic
102C4×C37C4×D411yescharacteristic
103C4×C37#12011yescharacteristic
104C4×C37#12111yescharacteristic
105Dic37—22no—
106#1903—371nomaximal, Sylow
107C2×C37—21no—
108C2×C37—21no—
109C2×C37—21no—
110C2×C37—82no—
111C2×C37#38611yescharacteristic
112D37—42no—
113C2×AGL(1,ℤ/8)—371no—
114#568—371no—
115#421—371no—
116#418D3711yescharacteristic, complemented
117C2×#100—371no—
118#344—371no—
119#338—371no—
120C37#190311yescharacteristic, complemented, Sylow
121C2×#41—371no—
122C22×D4C2×D3711yescharacteristic
123AGL(1,ℤ/8)—742no—
124AGL(1,ℤ/8)—742no—
125C2×SD16—372no—
126C2×D8—372no—
127#131—742no—
128#131—742no—
129C2×M16—371no—
130C2×M16—371no—
131C2×M16—371no—
132C2×M16—742no—
133C2×M16C2×D3711yescharacteristic
134#117C2×D3711yescharacteristic
135#104—742no—
136#102—22no—
137#100—742no—
138C24—21no—
139#41—372no—
140#41—372no—
141#41—741no—
142#41—741no—
143C2×Q8—371no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—371no—
150C2×D4—741no—
151C2×D4C4×D3712yes—
152C22×C4—741no—
153C22×C4C22×D3711yescharacteristic
154SD16—744no—
155D8—744no—
156M16—21no—
157M16—21no—
158M16—372no—
159M16—744no—
160M16—741no—
161M16—741no—
162M16—741no—
163M16—741no—
164M16—741no—
165C2×C8—372no—
166C2×C8—744no—
167C2×C8—741no—
168C2×C8—741no—
169C2×C8C22⋊D3712yes—
170C4⋊C4—21no—
171C22⋊C4—21no—
172C42—21no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—82no—
177C23—741no—
178C23#1059696411yescharacteristic
179Q8—372no—
180Q8—741no—
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185D4—372no—
186D4—742no—
187D4—742no—
188D4—741no—
189C2×C4—41no—
190C2×C4—741no—
191C2×C4—742no—
192C2×C4—742no—
193C2×C4C2×C4×D3711yescharacteristic
194C2×C4#1059696211yescharacteristic
195C2×C4D4×D3711yescharacteristic
196C2×C4D4×D3711yescharacteristic
197C2×C4D4×D3711yescharacteristic
198C2×C4C2×C22⋊D3711yescharacteristic
199C8—22no—
200C8—742no—
201C8—742no—
202C8—1481no—
203C22—41no—
204C22—42no—
205C22—82no—
206C22—82no—
207C22—82no—
208C22—2961no—
209C22—742no—
210C22#1192449611yescharacteristic
211C22#1192450711yescharacteristic
212C22#1192451811yescharacteristic
213C4—81no—
214C4—742no—
215C4C22⋊C4×D3711yescharacteristic
216C4C4×C22⋊D3711yescharacteristic
217C4#1192450411yescharacteristic
218C4#1192450911yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—82no—
223C2—1482no—
224C2#1455740911yescharacteristic
subgroupG/H
centerC2#14557409
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#418C2
socleC2×C37#386
prime radicalC2×#11924562C2
cosocleC22×C4×C37C23
hypercenter#418D37
hypocenterC37#1903
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #14558299C2semidirect
3. #14557551C2semidirect
4. C2×#11924453C2semidirect
5. #14557303C2semidirect
6. #14557291C2semidirect
7. C37×#418C2semidirect
11. C2×#10596940C4semidirect
12. C2×#10596939C4semidirect
116. #418D37semidirect
120. C37#1903semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
#145582992
#145575512
C2×#119244532
#145573032
#145572912
C37×#4182
#190337