Finite Group Databasebeta

← #17995142

Subgroups — #17995142

Order 4736.

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

normal subgroups only

This group has 340 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#14557515C211yesmaximal, characteristic, complemented
4C2×#11924452C211yesmaximal, characteristic, complemented
5C2×#11924452C211yesmaximal, characteristic, complemented
6#14557303C211yesmaximal, characteristic, complemented
7C37×#344C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×D148C2211yescharacteristic
10#11924544—22no—
11#11924542—22no—
12C2×#10596934C2211yescharacteristic
13C2×#10596934C2211yescharacteristic
14M16×D37—22no—
15#11924533—21no—
16#11924524—21no—
17#11924511—22no—
18#11924506C414yes—
19#11924454—21no—
20#11924452—21no—
21#11924452—22no—
22#11924452—22no—
23C2×M16×C37C2211yescharacteristic
24C2×M16×C37C2211yescharacteristic
25#117×C37C2211yescharacteristic
26C23×D37C2×C412yes—
27C22×C4×C37C2311yescharacteristic
28C2×C22⋊D37C2×C412yes—
29#10596962—21no—
30#10596962—21no—
31#10596962—21no—
32#10596962—21no—
33C2×D148—21no—
34C2×D148—21no—
35C2×D148—21no—
36C2×D148—21no—
37C2×D148—21no—
38C2×D148—21no—
39C2×D148—24no—
40C2×D148D411yescharacteristic
41C2×C4×D37D412yes—
42C2×Dic74D411yescharacteristic
43M16×C37—21no—
44M16×C37—21no—
45M16×C37—21no—
46M16×C37D412yescomplemented
47C2×C8×C37—21no—
48C2×C8×C37—21no—
49C4⋊C4×C37—21no—
50C22⋊C4×C37C2×C412yes—
51C42×C37—21no—
52#10596938—24no—
53#10596934—21no—
54#10596934—21no—
55#10596934—21no—
56#10596934D412yescomplemented
57C2×#64436—21no—
58C2×#64436—21no—
59#10596929—24no—
60C8×D37—24no—
61C23×C37C22×C411yescharacteristic
62C22×D37—22no—
63C22×D37—22no—
64C22×D37—22no—
65C22×D37—82no—
66C22×D37C22⋊C412yes—
67C2×C4×C37—22no—
68C2×C4×C37C2×D411yescharacteristic
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×Dic37C22⋊C412yes—
77D148—21no—
78D148—21no—
79D148—41no—
80D148—41no—
81D148—41no—
82D148—41no—
83D148—84no—
84C4×D37—22no—
85C4×D37—22no—
86Dic74—21no—
87Dic74—21no—
88C8×C37—22no—
89C8×C37—41no—
90#64436—22no—
91#64436—41no—
92C22×C37—41no—
93C22×C37C2×C22⋊C411yescharacteristic
94C22×C37C4×D411yescharacteristic
95C22×C37C4×D411yescharacteristic
96C2×D37—22no—
97C2×D37—42no—
98C2×D37—44no—
99C2×D37—42no—
100C2×D37—82no—
101C2×D37—82no—
102C4×C37—42no—
103C4×C37#12011yescharacteristic
104C4×C37#12111yescharacteristic
105C4×C37#12111yescharacteristic
106C4×C37#12311yescharacteristic
107Dic37—22no—
108#1914—371nomaximal, Sylow
109C2×C37—21no—
110C2×C37—21no—
111C2×C37—21no—
112C2×C37#38611yescharacteristic
113D37—42no—
114D37—82no—
115#568—371no—
116#535—371no—
117#413—371no—
118C2×#100—371no—
119C2×#100—371no—
120#344—371no—
121#344D3711yescharacteristic, complemented
122C37#191411yescharacteristic, complemented, Sylow
123C2×#41—371no—
124C22×D4—371no—
125#131—742no—
126#131—742no—
127C2×M16—371no—
128C2×M16—371no—
129C2×M16—742no—
130C2×M16C2×D3711yescharacteristic
131C2×M16C2×D3711yescharacteristic
132#127—741no—
133#124—741no—
134#121—742no—
135#120—374no—
136#117C2×D3711yescharacteristic
137#101—741no—
138#100—742no—
139#100—741no—
140#100—742no—
141C24—372no—
142#41—741no—
143#41—741no—
144#41—741no—
145#41—741no—
146C2×Q8—371no—
147C2×D4—372no—
148C2×D4—371no—
149C2×D4—744no—
150C2×D4—741no—
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—21no—
161M16—372no—
162M16—744no—
163M16—741no—
164M16—741no—
165M16—741no—
166M16D14812yescomplemented
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—744no—
170C2×C8—741no—
171C2×C8—741no—
172C4⋊C4—21no—
173C22⋊C4—744no—
174C22⋊C4C4×D3712yes—
175C42—21no—
176C23—372no—
177C23—2962no—
178C23—742no—
179C23—742no—
180C23—742no—
181C23C2×C4×D3711yescharacteristic
182Q8—741no—
183Q8—741no—
184D4—2964no—
185D4—742no—
186D4—742no—
187D4—741no—
188D4—741no—
189D4—1481no—
190D4—1481no—
191D4—1481no—
192D4—1481no—
193C2×C4—22no—
194C2×C4—372no—
195C2×C4—742no—
196C2×C4—742no—
197C2×C4C2×D14811yescharacteristic
198C2×C4#1059696211yescharacteristic
199C2×C4D4×D3711yescharacteristic
200C2×C4D4×D3711yescharacteristic
201C2×C4D4×D3711yescharacteristic
202C2×C4#1059696611yescharacteristic
203C8—22no—
204C8—41no—
205C8—742no—
206C8—1481no—
207C22—41no—
208C22—2962no—
209C22—2962no—
210C22—742no—
211C22—1484no—
212C22—1482no—
213C22—1482no—
214C22C22⋊C4×D3711yescharacteristic
215C22#1192449811yescharacteristic
216C22C4×D14811yescharacteristic
217C4—42no—
218C4—742no—
219C4#1192450611yescharacteristic
220C4#1192450911yescharacteristic
221C4#1192451111yescharacteristic
222C4#1192452111yescharacteristic
223C2—21no—
224C2—21no—
225C2—21no—
226C2—2962no—
227C2—1482no—
228C2#1455741111yescharacteristic
subgroupG/H
centerC2#14557411
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#344C2
socleC2×C37#386
prime radical#14558102C2
cosocleC22×C4×C37C23
hypercenter#344D37
hypocenterC37#1914
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #14558299C2semidirect
3. #14557515C2semidirect
4. C2×#11924452C2semidirect
5. C2×#11924452C2semidirect
6. #14557303C2semidirect
7. C37×#344C2semidirect
46. M16×C37D4semidirect
56. #10596934D4semidirect
121. #344D37semidirect
122. C37#1914semidirect
166. M16D148semidirect

Maximal subgroups

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

subgroupindex
#145582992
#145581022
#145575152
C2×#119244522
#145573032
C37×#3442
#191437