Finite Group Databasebeta

← #17995633

Subgroups — #17995633

Order 4736.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11924567C211yesmaximal, characteristic
2#14558109C211yesmaximal, characteristic
3C2×#11924534C211yesmaximal, characteristic, complemented
4C2×#11924462C211yesmaximal, characteristic
5C2×#11924454C211yesmaximal, characteristic, complemented
6#14557292C211yesmaximal, characteristic, complemented
7C37×#419C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924567—22no—
11#11924567—22no—
12C2×#10596942—21no—
13C2×#10596941—21no—
14C2×#10596934C2211yescharacteristic
15#11924536—21no—
16#11924534—22no—
17#11924534—22no—
18#11924524—21no—
19#11924520—22no—
20#11924516—22no—
21C2×#10596936—22no—
22C2×C4×Dic37C2211yescharacteristic
23#11924462—22no—
24#11924454—22no—
25C22×Q8×C37C2211yescharacteristic
26C2×M16×C37C2211yescharacteristic
27#117×C37C2211yescharacteristic
28#103×C37—22no—
29C2×Q8×C37—21no—
30C2×Q8×C37—21no—
31C2×Q8×C37—21no—
32C2×Q8×C37—21no—
33C2×Q8×C37—21no—
34C2×Q8×C37D412yes—
35C22×C4×C37—21no—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—21no—
38C22×Dic37—21no—
39C22×Dic37D412yes—
40#10596962—21no—
41#10596962—21no—
42#10596962—21no—
43#10596962—21no—
44C2×D148D411yescharacteristic
45C2×C4×D37—21no—
46C2×Dic74—21no—
47C2×Dic74—21no—
48C2×Dic74—21no—
49C2×Dic74—21no—
50C2×Dic74—21no—
51C2×Dic74—21no—
52C2×Dic74D411yescharacteristic
53M16×C37—21no—
54M16×C37—21no—
55C2×C8×C37—21no—
56C4⋊C4×C37D412yes—
57C22⋊C4×C37—21no—
58C42×C37—21no—
59#10596942—24no—
60#10596941—24no—
61#10596938—24no—
62C4⋊Dic37—24no—
63#10596936—28no—
64C4×Dic37—21no—
65C4×Dic37D412yes—
66#10596934—21no—
67#10596934D412yes—
68C2×#64436—21no—
69C23×C37C2×D411yescharacteristic
70C22×D37—21no—
71Q8×C37—22no—
72Q8×C37—22no—
73Q8×C37—41no—
74Q8×C37—41no—
75C2×C4×C37—22no—
76C2×C4×C37—22no—
77C2×C4×C37—41no—
78C2×C4×C37—41no—
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37#4111yescharacteristic
85C22⋊D37—41no—
86C22⋊D37—41no—
87C2×Dic37—24no—
88C2×Dic37—22no—
89C2×Dic37—22no—
90C2×Dic37—21no—
91C2×Dic37—22no—
92C2×Dic37—22no—
93D148—21no—
94D148—21no—
95C4×D37—41no—
96C4×D37—41no—
97Dic74—21no—
98Dic74—21no—
99Dic74—41no—
100Dic74—41no—
101Dic74—41no—
102Dic74—41no—
103C8×C37—41no—
104#64436—22no—
105C22×C37—22no—
106C22×C37#12011yescharacteristic
107C22×C37#12011yescharacteristic
108C22×C37#12111yescharacteristic
109C2×D37—41no—
110C2×D37—42no—
111C4×C37—42no—
112C4×C37—42no—
113C4×C37#12011yescharacteristic
114C4×C37#12111yescharacteristic
115C4×C37#12111yescharacteristic
116C4×C37#12711yescharacteristic
117Dic37—24no—
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#419D3711yescharacteristic, complemented
131C2×#101—371no—
132#339—371no—
133C37#200511yescharacteristic, complemented, Sylow
134C2×#41—371no—
135C22×Q8—371no—
136C22×Q8C2×D3711yescharacteristic
137#137—742no—
138#137—742no—
139C2×Q16—741no—
140C2×SD16—741no—
141C2×M16—371no—
142C2×M16C2×D3711yescharacteristic
143C4⋊Q8—741no—
144C4⋊Q8—742no—
145C4⋊Q8—742no—
146#124—741no—
147#123—742no—
148C22⋊Q8—742no—
149#117C2×D3711yescharacteristic
150C2×C4⋊C4—742no—
151C2×C42—371no—
152#104—742no—
153#103—22no—
154#101—742no—
155#41—741no—
156#41—741no—
157#41—741no—
158#41—741no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—371no—
165C2×Q8—741no—
166C2×Q8—741no—
167C2×Q8—741no—
168C2×Q8—741no—
169C2×Q8—741no—
170C2×Q8—741no—
171C2×Q8D14812yes—
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—21no—
183M16—372no—
184M16—741no—
185C2×C8—21no—
186C2×C8—741no—
187C4⋊C4—748no—
188C4⋊C4—744no—
189C4⋊C4C22⋊D3712yes—
190C22⋊C4—21no—
191C22⋊C4—744no—
192C42—21no—
193C42—372no—
194C42—741no—
195C23—741no—
196C23D4×D3711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201Q8—741no—
202Q8—741no—
203Q8—1481no—
204Q8—1481no—
205Q8—1481no—
206Q8—1481no—
207D4—741no—
208D4—741no—
209D4—1481no—
210D4—1481no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—744no—
216C2×C4—742no—
217C2×C4—742no—
218C2×C4—741no—
219C2×C4—742no—
220C2×C4—742no—
221C2×C4—1481no—
222C2×C4—1481no—
223C2×C4C2×D14811yescharacteristic
224C2×C4#1059696211yescharacteristic
225C2×C4D4×D3711yescharacteristic
226C2×C4D4×D3711yescharacteristic
227C2×C4D4×D3711yescharacteristic
228C2×C4C2×C22⋊D3711yescharacteristic
229C8—41no—
230C8—742no—
231C22—22no—
232C22—1481no—
233C22—1482no—
234C22#1192450411yescharacteristic
235C22#1192450611yescharacteristic
236C22#1192450911yescharacteristic
237C4—42no—
238C4—42no—
239C4—744no—
240C4—1482no—
241C4—1481no—
242C4#1192450611yescharacteristic
243C4#1192450911yescharacteristic
244C4#1192451011yescharacteristic
245C4#1192453211yescharacteristic
246C2—21no—
247C2—21no—
248C2—2961no—
249C2#1455744211yescharacteristic
250C2#1455771412yes—
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#419C2
socleC22×C37#120
prime radicalC2×#10596962C22
hypercenter#419D37
hypocenterC37#2005
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C2×#11924534C2semidirect
5. C2×#11924454C2semidirect
6. #14557292C2semidirect
7. C37×#419C2semidirect
130. #419D37semidirect
133. C37#2005semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
#145581092
C2×#119245342
C2×#119244622
C2×#119244542
#145572922
C37×#4192
#200537