Finite Group Databasebeta

← #18010374

Subgroups — #18010374

Order 4736.

292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 90 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
1D37⋊#104C211yesmaximal, characteristic
2#14558523C211yesmaximal, characteristic
3#14558496C211yesmaximal, characteristic, complemented
4C2×#11924590C211yesmaximal, characteristic, complemented
5#14558408C211yesmaximal, characteristic, complemented
6#14558405C211yesmaximal, characteristic, complemented
7#131×D37C211yesmaximal, characteristic
8D37⋊M16C2211yescharacteristic
9C2×D37⋊C8C2211yescharacteristic
10#11924615C2211yescharacteristic
11C2×C4×#3866C2211yescharacteristic
12#11924601C412yescomplemented
13#11924600C412yescomplemented
14#11924599C412yescomplemented
15#11924598C412yescomplemented
16#11924590—21no—
17#11924590—21no—
18#11924590—21no—
19C8×#3866—21no—
20#41×D37C2211yescharacteristic
21#11924544—21no—
22#11924544C411yescharacteristic, complemented
23#11924543C411yescharacteristic, complemented
24#11924542—21no—
25#11924542C411yescharacteristic, complemented
26M16×D37—21no—
27M16×D37C2211yescharacteristic
28C2×C8×D37—21no—
29C2×C8×D37C2211yescharacteristic
30#131×C37C411yescharacteristic, complemented
31C22×#3866—21no—
32#41×C37C2×C411yescharacteristic
33#10596966C2×C411yescharacteristic
34Q8×D37C2×C411yescharacteristic
35#10596964—21no—
36#10596964C2×C411yescharacteristic
37D4×D37—21no—
38D4×D37C2×C411yescharacteristic
39#10596962—21no—
40#10596962C2×C411yescharacteristic
41C2×C4×D37—21no—
42C2×C4×D37C2311yescharacteristic
43C22⋊#3866—21no—
44#10596957—21no—
45C2×#64438—21no—
46C4⋊#3866C2×C412yes—
47C4×#3866—21no—
48C4×#3866—21no—
49C4×#3866C2×C412yes—
50#10596953C2×C412yes—
51D37⋊C8—21no—
52D37⋊C8—21no—
53D37⋊C8C2×C412yes—
54M16×C37—21no—
55M16×C37C2×C411yescharacteristic
56C2×C8×C37—21no—
57C2×C8×C37C2×C411yescharacteristic
58#10596934—21no—
59#10596934C2×C411yescharacteristic
60C2×#64436—21no—
61C2×#64436C2×C411yescharacteristic
62#10596929—21no—
63#10596929—21no—
64#10596929—21no—
65C8×D37—21no—
66C8×D37—21no—
67C8×D37—21no—
68C8×D37D411yescharacteristic
69C8×D37D411yescharacteristic
70C8×D37D411yescharacteristic
71C8×D37D411yescharacteristic
72C22×D37—21no—
73C22×D37#4111yescharacteristic
74C2×#3866—22no—
75C2×#3866—22no—
76C2×#3866—42no—
77Q8×C37C4211yescharacteristic
78D4×C37—21no—
79D4×C37C4211yescharacteristic
80C2×C4×C37—21no—
81C2×C4×C37C22×C411yescharacteristic
82C22⋊D37—21no—
83C22⋊D37—21no—
84C22⋊D37—21no—
85C2×Dic37—21no—
86C2×Dic37#4111yescharacteristic
87D148—21no—
88D148C4211yescharacteristic
89C4×D37—21no—
90C4×D37—21no—
91C4×D37—21no—
92C4×D37C22×C411yescharacteristic
93C4×D37C22×C411yescharacteristic
94C4×D37C2×D411yescharacteristic
95C4×D37C2×D411yescharacteristic
96Dic74—21no—
97Dic74C4211yescharacteristic
98#64438—22no—
99#64438—22no—
100C8×C37—21no—
101C8×C37C22⋊C411yescharacteristic
102C8×C37C22⋊C411yescharacteristic
103#64436—21no—
104#64436C22⋊C411yescharacteristic
105#64436C22⋊C411yescharacteristic
106C22×C37—21no—
107C22×C37#11711yescharacteristic
108C2×D37—22no—
109C2×D37—21no—
110C2×D37—42no—
111C2×D37C4×D411yescharacteristic
112C2×D37C4×D411yescharacteristic
113#3866—42no—
114#3866—42no—
115C4×C37—21no—
116C4×C37C2×C4211yescharacteristic
117C4×C37C2×C22⋊C411yescharacteristic
118Dic37—21no—
119Dic37C4×D411yescharacteristic
120Dic37C4×D411yescharacteristic
121#1765—371nomaximal, Sylow
122C2×C37—21no—
123C2×C37—41no—
124C2×C37C4×C22⋊C411yescharacteristic
125D37—21no—
126D37—41no—
127D37#44412yes—
128C2×#131—371no—
129C2×#104—371no—
130#416—371no—
131#405—371no—
132C2×#97—371no—
133#341—371no—
134#339—371no—
135C37#176511yescharacteristic, complemented, Sylow
136C2×#41—371no—
137#131—371no—
138#131—371no—
139#131—371no—
140#131—741no—
141#131—741no—
142#131#386611yescharacteristic, complemented
143C2×M16—371no—
144C2×M16—371no—
145C2×M16—741no—
146C22×C8—371no—
147C22×C8—371no—
148C22×C8—741no—
149#117—371no—
150C2×C42—371no—
151#104—372no—
152#104—372no—
153#103—372no—
154#102—372no—
155#97—741no—
156#97—741no—
157#97—741no—
158C4×C8—741no—
159#41—371no—
160#41—371no—
161#41—371no—
162#41—741no—
163#41—741no—
164#41C2×#386611yescharacteristic
165C2×Q8—371no—
166C2×D4—371no—
167C2×D4—741no—
168C22×C4—371no—
169C22×C4—741no—
170C22×C4—741no—
171M16—21no—
172M16—372no—
173M16—371no—
174M16—741no—
175M16—741no—
176M16—741no—
177M16—741no—
178M16—741no—
179M16C2×#386611yescharacteristic
180C2×C8—21no—
181C2×C8—371no—
182C2×C8—371no—
183C2×C8—371no—
184C2×C8—371no—
185C2×C8—371no—
186C2×C8—372no—
187C2×C8—741no—
188C2×C8—741no—
189C2×C8—741no—
190C2×C8—741no—
191C2×C8—741no—
192C2×C8—741no—
193C2×C8—741no—
194C2×C8C2×#386611yescharacteristic
195C4⋊C4—372no—
196C22⋊C4—741no—
197C42—372no—
198C42—741no—
199C42—741no—
200C23—371no—
201C23—741no—
202Q8—371no—
203Q8—741no—
204Q8C4×#386611yescharacteristic
205D4—21no—
206D4—371no—
207D4—741no—
208D4—741no—
209D4—741no—
210D4—741no—
211D4C4×#386611yescharacteristic
212C2×C4—21no—
213C2×C4—371no—
214C2×C4—371no—
215C2×C4—371no—
216C2×C4—371no—
217C2×C4—371no—
218C2×C4—741no—
219C2×C4—741no—
220C2×C4—741no—
221C2×C4—741no—
222C2×C4—742no—
223C2×C4—742no—
224C2×C4—1482no—
225C2×C4C22×#386611yescharacteristic
226C8—21no—
227C8—371no—
228C8—371no—
229C8—742no—
230C8—742no—
231C8—741no—
232C8C22⋊#386611yescharacteristic
233C8C22⋊#386611yescharacteristic
234C22—21no—
235C22—371no—
236C22—371no—
237C22—742no—
238C22—741no—
239C22—1482no—
240C22#1192461511yescharacteristic
241C4—21no—
242C4—371no—
243C4—371no—
244C4—741no—
245C4—1482no—
246C4—1482no—
247C4C2×C4×#386611yescharacteristic
248C4C2×C22⋊#386611yescharacteristic
249C2—21no—
250C2—41no—
251C2—372no—
252C2—741no—
253C2—1481no—
254C2C4×C22⋊#386611yescharacteristic
subgroupG/H
centerC4C2×C22⋊#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
Fitting#131×C37C4
socleC2×C37C4×C22⋊C4
prime radical#41×D37C22
cosocleC2×C4×D37C23
hypercenter#131#3866
hypocenterC37#1765
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
3. #14558496C2semidirect
4. C2×#11924590C2semidirect
5. #14558408C2semidirect
6. #14558405C2semidirect
12. #11924601C4semidirect
13. #11924600C4semidirect
14. #11924599C4semidirect
15. #11924598C4semidirect
22. #11924544C4semidirect
23. #11924543C4semidirect
25. #11924542C4semidirect
30. #131×C37C4semidirect
135. C37#1765semidirect
142. #131#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1042
#145585232
#145584962
C2×#119245902
#145584082
#145584052
#131×D372
#176537