Finite Group Databasebeta

← #17995635

Subgroups — #17995635

Order 4736.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11924569C211yesmaximal, characteristic
2#14558109C211yesmaximal, characteristic
3C2×#11924536C211yesmaximal, characteristic, complemented
4C2×#11924464C211yesmaximal, characteristic
5#14557541C211yesmaximal, characteristic, complemented
6C2×#11924454C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10C22×Dic74C2211yescharacteristic
11#11924569—22no—
12#11924569—22no—
13C2×Dic148—21no—
14C2×#10596930—21no—
15C2×#10596934C2211yescharacteristic
16#11924536—22no—
17#11924536—21no—
18#11924536—22no—
19#11924524—21no—
20#11924520—22no—
21#11924516—22no—
22C2×C4⋊Dic37—22no—
23#11924464—22no—
24#11924459—22no—
25#11924454—22no—
26C2×M16×C37C2211yescharacteristic
27#117×C37C2211yescharacteristic
28C2×C42×C37C2211yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C22×Dic37—21no—
33C22×Dic37D412yes—
34#10596962—21no—
35#10596962—21no—
36#10596962—21no—
37#10596962—21no—
38C2×D148D411yescharacteristic
39C2×C4×D37—21no—
40C2×Dic74—21no—
41C2×Dic74—21no—
42C2×Dic74—21no—
43C2×Dic74—21no—
44C2×Dic74—21no—
45C2×Dic74—21no—
46C2×Dic74—21no—
47C2×Dic74—21no—
48C2×Dic74—21no—
49C2×Dic74—21no—
50C2×Dic74—21no—
51C2×Dic74D411yescharacteristic
52C2×Dic74D412yes—
53M16×C37—21no—
54M16×C37D412yes—
55C2×C8×C37—21no—
56C4⋊C4×C37D412yes—
57C22⋊C4×C37—21no—
58C42×C37—21no—
59C42×C37—21no—
60C42×C37D412yes—
61#10596938—24no—
62C4⋊Dic37—28no—
63C4⋊Dic37—24no—
64#10596934—21no—
65#10596934—21no—
66C2×#64436—21no—
67Dic148—24no—
68#10596930—24no—
69C23×C37C2×D411yescharacteristic
70C22×D37—21no—
71C2×C4×C37—24no—
72C2×C4×C37—22no—
73C2×C4×C37—22no—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37#4111yescharacteristic
80C22⋊D37—41no—
81C22⋊D37—41no—
82C2×Dic37—22no—
83C2×Dic37—22no—
84C2×Dic37—21no—
85C2×Dic37—22no—
86C2×Dic37—22no—
87C2×Dic37—41no—
88C2×Dic37—41no—
89D148—21no—
90D148—21no—
91C4×D37—41no—
92C4×D37—41no—
93Dic74—22no—
94Dic74—21no—
95Dic74—22no—
96Dic74—21no—
97Dic74—41no—
98Dic74—41no—
99Dic74—41no—
100Dic74—41no—
101Dic74—41no—
102Dic74—41no—
103C8×C37—22no—
104#64436—41no—
105C22×C37—22no—
106C22×C37#12011yescharacteristic
107C22×C37#12011yescharacteristic
108C22×C37#12111yescharacteristic
109C2×D37—41no—
110C2×D37—42no—
111C4×C37—24no—
112C4×C37—42no—
113C4×C37#12011yescharacteristic
114C4×C37#12111yescharacteristic
115C4×C37#12111yescharacteristic
116C4×C37#12711yescharacteristic
117Dic37—42no—
118Dic37—41no—
119Dic37—42no—
120#2005—371nomaximal, Sylow
121C2×C37—21no—
122C2×C37—21no—
123C2×C37#39211yescharacteristic
124C2×C37#45612yes—
125D37—81no—
126C2×#137—371no—
127#536—371no—
128C2×C4⋊Q8—371no—
129C2×#104—371no—
130#419—371no—
131C2×#101—371no—
132#339D3711yescharacteristic, complemented
133C37#200511yescharacteristic, complemented, Sylow
134C2×#41—371no—
135C22×Q8—371no—
136C22×Q8—371no—
137#137—742no—
138#137—742no—
139C2×Q16—741no—
140C2×SD16—741no—
141C2×M16—371no—
142C2×M16C2×D3711yescharacteristic
143C4⋊Q8—742no—
144C4⋊Q8—741no—
145C4⋊Q8—742no—
146#124—741no—
147#123—742no—
148C22⋊Q8—742no—
149#117C2×D3711yescharacteristic
150C2×C4⋊C4—742no—
151C2×C42C2×D3711yescharacteristic
152#104—742no—
153#103—742no—
154#101—742no—
155#41—741no—
156#41—741no—
157#41—741no—
158#41—741no—
159C2×Q8—371no—
160C2×Q8—372no—
161C2×Q8—741no—
162C2×Q8—741no—
163C2×Q8—741no—
164C2×Q8—741no—
165C2×Q8—741no—
166C2×Q8—741no—
167C2×Q8—741no—
168C2×Q8—741no—
169C2×Q8—741no—
170C2×Q8—741no—
171C2×Q8—741no—
172C2×D4—371no—
173C2×D4—741no—
174C22×C4—21no—
175C22×C4—372no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4C22×D3711yescharacteristic
179Q16—744no—
180SD16—744no—
181M16—21no—
182M16—741no—
183M16—741no—
184M16D14812yes—
185C2×C8—21no—
186C2×C8—741no—
187C4⋊C4—748no—
188C4⋊C4—744no—
189C4⋊C4D14812yes—
190C22⋊C4—21no—
191C22⋊C4—744no—
192C42—21no—
193C42—21no—
194C42D14812yes—
195C23—741no—
196C23D4×D3711yescharacteristic
197Q8—742no—
198Q8—741no—
199Q8—742no—
200Q8—741no—
201Q8—1481no—
202Q8—1481no—
203Q8—1481no—
204Q8—1481no—
205Q8—1481no—
206Q8—1481no—
207D4—741no—
208D4—741no—
209D4—1481no—
210D4—1481no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—742no—
215C2×C4—742no—
216C2×C4—742no—
217C2×C4—741no—
218C2×C4—742no—
219C2×C4—1481no—
220C2×C4—1481no—
221C2×C4—1481no—
222C2×C4—1481no—
223C2×C4C2×D14811yescharacteristic
224C2×C4C2×D14811yescharacteristic
225C2×C4C2×D14811yescharacteristic
226C2×C4D4×D3711yescharacteristic
227C2×C4D4×D3711yescharacteristic
228C2×C4#1059696611yescharacteristic
229C8—22no—
230C8—1481no—
231C22—22no—
232C22—1481no—
233C22—1482no—
234C22#1192450611yescharacteristic
235C22#1192450611yescharacteristic
236C22#1192451111yescharacteristic
237C4—24no—
238C4—42no—
239C4—1482no—
240C4—1481no—
241C4—1482no—
242C4#1192450611yescharacteristic
243C4#1192451111yescharacteristic
244C4#1192451111yescharacteristic
245C4#1192453311yescharacteristic
246C2—21no—
247C2—21no—
248C2—2961no—
249C2#1455744311yescharacteristic
250C2#1455771712yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37#120
prime radicalC2×#10596962C22
hypercenter#339D37
hypocenterC37#2005
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
3. C2×#11924536C2semidirect
5. #14557541C2semidirect
6. C2×#11924454C2semidirect
7. C37×#339C2semidirect
132. #339D37semidirect
133. C37#2005semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
#145581092
C2×#119245362
C2×#119244642
#145575412
C2×#119244542
C37×#3392
#200537