Finite Group Databasebeta

← #17995619

Subgroups — #17995619

Order 4736.

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

normal subgroups only

This group has 382 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×#11924562C211yesmaximal, characteristic
2#14558109C211yesmaximal, characteristic, complemented
3C2×#11924523C211yesmaximal, characteristic, complemented
4C2×#11924462C211yesmaximal, characteristic, complemented
5C2×#11924454C211yesmaximal, characteristic, complemented
6#14557292C211yesmaximal, characteristic, complemented
7C37×#418C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924562—22no—
11#11924562—22no—
12C2×#10596940—21no—
13C2×#10596939—21no—
14C2×#10596934C2211yescharacteristic
15#11924536—21no—
16#11924524—21no—
17#11924523—22no—
18#11924523—22no—
19#11924520—22no—
20#11924516—22no—
21C2×C22⋊Dic37—22no—
22C2×C4×Dic37C2211yescharacteristic
23#11924462—22no—
24#11924454—22no—
25C22×D4×C37C2211yescharacteristic
26C2×M16×C37C2211yescharacteristic
27#117×C37C2211yescharacteristic
28#102×C37—22no—
29C24×C37—21no—
30C2×D4×C37—21no—
31C2×D4×C37—21no—
32C2×D4×C37—21no—
33C2×D4×C37—21no—
34C2×D4×C37—21no—
35C2×D4×C37D412yes—
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—
59C22⋊Dic37—28no—
60#10596940—24no—
61#10596939—24no—
62#10596938—24no—
63C4⋊Dic37—24no—
64C4×Dic37—21no—
65C4×Dic37D412yes—
66#10596934—21no—
67#10596934D412yes—
68C2×#64436—21no—
69C23×C37—22no—
70C23×C37—44no—
71C23×C37—41no—
72C23×C37—41no—
73C23×C37C2×D411yescharacteristic
74C22×D37—21no—
75D4×C37—22no—
76D4×C37—22no—
77D4×C37—41no—
78D4×C37—41no—
79C2×C4×C37—22no—
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37#4111yescharacteristic
86C22⋊D37—41no—
87C22⋊D37—41no—
88C2×Dic37—22no—
89C2×Dic37—21no—
90C2×Dic37—22no—
91C2×Dic37—22no—
92C2×Dic37—22no—
93C2×Dic37—42no—
94D148—21no—
95D148—21no—
96C4×D37—41no—
97C4×D37—41no—
98Dic74—21no—
99Dic74—21no—
100Dic74—41no—
101Dic74—41no—
102Dic74—41no—
103Dic74—41no—
104C8×C37—41no—
105#64436—22no—
106C22×C37—22no—
107C22×C37—44no—
108C22×C37—42no—
109C22×C37—82no—
110C22×C37—82no—
111C22×C37#12011yescharacteristic
112C22×C37#12011yescharacteristic
113C22×C37#12111yescharacteristic
114C2×D37—41no—
115C2×D37—42no—
116C4×C37—42no—
117C4×C37#12011yescharacteristic
118C4×C37#12111yescharacteristic
119C4×C37#12111yescharacteristic
120C4×C37#12711yescharacteristic
121Dic37—42no—
122Dic37—41no—
123Dic37—42no—
124#2003—371nomaximal, Sylow
125C2×C37—21no—
126C2×C37—21no—
127C2×C37—82no—
128C2×C37#39211yescharacteristic
129C2×C37#45412yes—
130D37—81no—
131C2×AGL(1,ℤ/8)—371no—
132#536—371no—
133C2×#124—371no—
134C2×#104—371no—
135#418D3711yescharacteristic, complemented
136C2×#101—371no—
137#339—371no—
138C37#200311yescharacteristic, complemented, Sylow
139C2×#41—371no—
140C22×Q8—371no—
141C22×D4C2×D3711yescharacteristic
142AGL(1,ℤ/8)—742no—
143AGL(1,ℤ/8)—742no—
144C2×SD16—741no—
145C2×D8—741no—
146C2×M16—371no—
147C2×M16C2×D3711yescharacteristic
148C4⋊Q8—741no—
149#124—741no—
150#124—742no—
151#124—742no—
152#123—742no—
153C22⋊Q8—742no—
154#117C2×D3711yescharacteristic
155C2×C22⋊C4—742no—
156C2×C42—371no—
157#104—742no—
158#102—22no—
159#101—742no—
160C24—21no—
161#41—741no—
162#41—741no—
163#41—741no—
164#41—741no—
165C2×Q8—371no—
166C2×Q8—741no—
167C2×Q8—741no—
168C2×Q8—741no—
169C2×Q8—741no—
170C2×Q8—741no—
171C2×Q8—741no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—371no—
178C2×D4—741no—
179C2×D4D14812yes—
180C22×C4—372no—
181C22×C4—741no—
182C22×C4—741no—
183C22×C4C22×D3711yescharacteristic
184SD16—744no—
185D8—744no—
186M16—21no—
187M16—21no—
188M16—372no—
189M16—741no—
190C2×C8—21no—
191C2×C8—741no—
192C4⋊C4—744no—
193C4⋊C4C22⋊D3712yes—
194C22⋊C4—21no—
195C22⋊C4—744no—
196C22⋊C4—748no—
197C42—21no—
198C42—372no—
199C42—741no—
200C23—22no—
201C23—44no—
202C23—41no—
203C23—41no—
204C23—741no—
205C23D4×D3711yescharacteristic
206Q8—741no—
207Q8—741no—
208Q8—1481no—
209Q8—1481no—
210Q8—1481no—
211Q8—1481no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—741no—
217D4—741no—
218D4—1481no—
219D4—1481no—
220C2×C4—22no—
221C2×C4—742no—
222C2×C4—741no—
223C2×C4—742no—
224C2×C4—742no—
225C2×C4—742no—
226C2×C4—1482no—
227C2×C4—1481no—
228C2×C4—1481no—
229C2×C4C2×D14811yescharacteristic
230C2×C4#1059696211yescharacteristic
231C2×C4D4×D3711yescharacteristic
232C2×C4D4×D3711yescharacteristic
233C2×C4D4×D3711yescharacteristic
234C2×C4C2×C22⋊D3711yescharacteristic
235C8—41no—
236C8—742no—
237C22—22no—
238C22—44no—
239C22—42no—
240C22—82no—
241C22—82no—
242C22—1481no—
243C22—1482no—
244C22#1192450411yescharacteristic
245C22#1192450611yescharacteristic
246C22#1192450911yescharacteristic
247C4—42no—
248C4—1482no—
249C4—1482no—
250C4—1481no—
251C4#1192450611yescharacteristic
252C4#1192450911yescharacteristic
253C4#1192451011yescharacteristic
254C4#1192453211yescharacteristic
255C2—21no—
256C2—21no—
257C2—82no—
258C2—2961no—
259C2#1455744211yescharacteristic
260C2#1455770412yes—
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#418C2
socleC22×C37#120
prime radicalC2×#11924562C2
hypercenter#418D37
hypocenterC37#2003
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #14558109C2semidirect
3. C2×#11924523C2semidirect
4. C2×#11924462C2semidirect
5. C2×#11924454C2semidirect
6. #14557292C2semidirect
7. C37×#418C2semidirect
135. #418D37semidirect
138. C37#2003semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
#145581092
C2×#119245232
C2×#119244622
C2×#119244542
#145572922
C37×#4182
#200337