Finite Group Databasebeta

← #18010013

Subgroups — #18010013

Order 4736.

286 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558504C211yesmaximal, characteristic, complemented
2#14558475C211yesmaximal, characteristic, complemented
3#14558386C212yesmaximal, complemented
4#14558385C212yesmaximal, complemented
5#14558045C211yesmaximal, characteristic
6C2×#10596953—21no—
7C2×C4⋊#3866—21no—
8C2×C22⋊#3866—21no—
9#11924593C2212yes—
10C22⋊#64438—21no—
11(C2×#3866)⋊C4C2212yes—
12C2×#10596962C411yescharacteristic, complemented
13C22×C4×D37C2211yescharacteristic
14#11924520—21no—
15#11924516C411yescharacteristic, complemented
16#11924516C2211yescharacteristic
17#11924511C411yescharacteristic, complemented
18#11924511C2211yescharacteristic
19#11924506—21no—
20C4×D148—21no—
21C4×D148—21no—
22#117×C37C411yescharacteristic, complemented
23C23×D37D411yescharacteristic
24C22×#3866—22no—
25C22×C4×C37C2×C411yescharacteristic
26C2×C22⋊D37—21no—
27C22×Dic37D411yescharacteristic
28#10596962—42no—
29C2×D148—21no—
30C2×D148—21no—
31C2×D148C2×C411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37—42no—
34C2×C4×D37C2×C411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37C2311yescharacteristic
38C2×Dic74C2×C411yescharacteristic
39C22⋊#3866—42no—
40C2×#64438—22no—
41C4⋊#3866—42no—
42#10596953—42no—
43C4⋊C4×C37C2×C411yescharacteristic
44C4⋊C4×C37C2×C411yescharacteristic
45C22⋊C4×C37—21no—
46C42×C37—21no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—21no—
51C4⋊Dic37—21no—
52C4⋊Dic37—21no—
53C23×C37C22⋊C411yescharacteristic
54C22×D37—21no—
55C22×D37—21no—
56C22×D37—21no—
57C22×D37—41no—
58C22×D37—41no—
59C22×D37C22⋊C411yescharacteristic
60C22×D37C2×D411yescharacteristic
61C2×#3866—42no—
62C2×#3866—42no—
63C2×#3866—42no—
64C2×C4×C37—22no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37C22⋊C411yescharacteristic
68C2×C4×C37C22×C411yescharacteristic
69C22⋊D37—42no—
70C2×Dic37—21no—
71C2×Dic37—41no—
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C2×D411yescharacteristic
74D148—41no—
75D148—42no—
76D148—41no—
77D148—41no—
78C4×D37—22no—
79C4×D37—22no—
80C4×D37—41no—
81C4×D37—41no—
82C4×D37—42no—
83Dic74—41no—
84#64438—42no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37C2×C22⋊C411yescharacteristic
89C2×D37—21no—
90C2×D37—21no—
91C2×D37—21no—
92C2×D37—21no—
93C2×D37—21no—
94C2×D37—42no—
95C2×D37—42no—
96C2×D37—41no—
97C2×D37—41no—
98C2×D37—41no—
99C2×D37AGL(1,ℤ/8)11yescharacteristic
100C2×D37#13711yescharacteristic
101#3866—82no—
102C4×C37—21no—
103C4×C37—41no—
104C4×C37—41no—
105C4×C37#9912yes—
106Dic37—21no—
107Dic37—21no—
108Dic37—41no—
109#1513—371nomaximal, Sylow
110C2×C37—41no—
111C2×C37C2×#9911yescharacteristic
112C2×C37#41711yescharacteristic
113C2×C37#42111yescharacteristic
114D37—21no—
115D37—21no—
116D37—41no—
117D37—81no—
118#525—371no—
119#407—371no—
120#380—371no—
121#328—372no—
122#327—372no—
123C37#151311yescharacteristic, complemented, Sylow
124C2×#41—371no—
125C23×C4—371no—
126C2×M16—741no—
127#123—741no—
128C22⋊Q8—371no—
129C22⋊Q8—371no—
130#121—371no—
131#121—371no—
132#120—741no—
133C4×D4—741no—
134C4×D4—741no—
135#117#386611yescharacteristic, complemented
136C2×C4⋊C4—741no—
137C2×C22⋊C4—741no—
138C22⋊C8—372no—
139C22⋊C8—741no—
140#95—372no—
141C24—371no—
142#41—1482no—
143C2×Q8—371no—
144C2×D4—371no—
145C2×D4—741no—
146C2×D4—741no—
147C2×D4—741no—
148C22×C4—371no—
149C22×C4—371no—
150C22×C4—371no—
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—741no—
154C22×C4—742no—
155C22×C4—1482no—
156C22×C4C2×#386611yescharacteristic
157M16—1482no—
158C2×C8—742no—
159C4⋊C4—741no—
160C4⋊C4—741no—
161C4⋊C4—1482no—
162C4⋊C4C2×#386611yescharacteristic
163C4⋊C4C2×#386611yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—741no—
166C22⋊C4—741no—
167C22⋊C4—741no—
168C22⋊C4—741no—
169C22⋊C4—1482no—
170C42—21no—
171C23—371no—
172C23—371no—
173C23—741no—
174C23—741no—
175C23—741no—
176C23—1481no—
177C23—1481no—
178C23C22⋊#386611yescharacteristic
179Q8—1481no—
180D4—1481no—
181D4—1481no—
182D4—1481no—
183D4—1482no—
184D4—1482no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—742no—
191C2×C4—742no—
192C2×C4—741no—
193C2×C4—1481no—
194C2×C4—1481no—
195C2×C4—1482no—
196C2×C4—1482no—
197C2×C4—1482no—
198C2×C4—1481no—
199C2×C4—1482no—
200C2×C4C22⋊#386611yescharacteristic
201C2×C4C22×#386611yescharacteristic
202C8—1482no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—371no—
207C22—371no—
208C22—741no—
209C22—741no—
210C22—741no—
211C22—741no—
212C22—741no—
213C22—1482no—
214C22—1482no—
215C22—1481no—
216C22—1481no—
217C22—1481no—
218C22C2×C22⋊#386611yescharacteristic
219C4—21no—
220C4—41no—
221C4—41no—
222C4—2962no—
223C4—741no—
224C4—741no—
225C4—1481no—
226C4#1192459512yes—
227C2—41no—
228C2—2961no—
229C2—741no—
230C2—741no—
231C2—1481no—
232C2C2×#1192459511yescharacteristic
233C2#1455852411yescharacteristic
234C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#117×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558045C2
cosocleC2×C4×D37C23
hypercenter#117#3866
hypocenterC37#1513
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #14558504C2semidirect
2. #14558475C2semidirect
3. #14558386C2semidirect
4. #14558385C2semidirect
12. C2×#10596962C4semidirect
15. #11924516C4semidirect
17. #11924511C4semidirect
22. #117×C37C4semidirect
123. C37#1513semidirect
135. #117#3866semidirect

Maximal subgroups

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

subgroupindex
#145585042
#145584752
#145583862
#145583852
#145580452
#151337