Finite Group Databasebeta

← #18010754

Subgroups — #18010754

Order 4736.

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558543C211yesmaximal, characteristic, complemented
2#14558532C211yesmaximal, characteristic, complemented
3#14558531C211yesmaximal, characteristic, complemented
4#14558514C211yesmaximal, characteristic, complemented
5#14558513C211yesmaximal, characteristic, complemented
6#14558496C211yesmaximal, characteristic, complemented
7C2×#11924557C211yesmaximal, characteristic
8D37⋊M16C2211yescharacteristic
9#11924615C2211yescharacteristic
10#11924615C2211yescharacteristic
11#11924615C2211yescharacteristic
12#11924605—21no—
13#11924604—21no—
14#11924601—22no—
15#11924600—22no—
16#11924595—22no—
17#11924594—22no—
18#11924590—21no—
19C8×#3866—21no—
20C2×#10596966C2211yescharacteristic
21C2×#10596964C2211yescharacteristic
22#11924557—21no—
23#11924557—21no—
24#11924557—21no—
25#11924557—21no—
26C2×#10596942C411yescharacteristic, complemented
27C2×#10596930C411yescharacteristic, complemented
28C2×#10596939C411yescharacteristic, complemented
29C2×C8×D37C2211yescharacteristic
30C2×SD16×C37C411yescharacteristic, complemented
31C2×Q8×C37C2×C411yescharacteristic
32C2×D4×C37C2×C411yescharacteristic
33C2×C22⋊D37—21no—
34C22×Dic37—21no—
35#10596966—21no—
36#10596966—21no—
37#10596966—21no—
38#10596966—21no—
39#10596964—21no—
40#10596964—21no—
41#10596964—21no—
42#10596964—21no—
43C2×D148—21no—
44C2×D148C2×C411yescharacteristic
45C2×C4×D37—21no—
46C2×C4×D37C2311yescharacteristic
47C2×Dic74C2×C411yescharacteristic
48C22⋊#3866—21no—
49C22⋊#3866—21no—
50C22⋊#3866D412yes—
51#10596957—21no—
52C4⋊#3866—21no—
53C4⋊#3866—21no—
54C4⋊#3866—21no—
55C4×#3866—21no—
56C4×#3866—21no—
57C4×#3866—21no—
58#10596953D412yes—
59D37⋊C8—21no—
60SD16×C37—21no—
61SD16×C37—21no—
62C2×C8×C37C2×C411yescharacteristic
63#10596942—21no—
64#10596942—21no—
65#10596939—21no—
66#10596939—21no—
67C2×#64436C2×C411yescharacteristic
68#10596930—21no—
69#10596930—21no—
70C8×D37D411yescharacteristic
71C8×D37D411yescharacteristic
72C8×D37D411yescharacteristic
73C8×D37D411yescharacteristic
74C23×C37—21no—
75C22×D37—21no—
76C22×D37C2×D411yescharacteristic
77C2×#3866—22no—
78C2×#3866—41no—
79C2×#3866—41no—
80Q8×C37—21no—
81Q8×C37—21no—
82D4×C37—21no—
83D4×C37—21no—
84C2×C4×C37—21no—
85C2×C4×C37C22×C411yescharacteristic
86C22⋊D37—41no—
87C22⋊D37—41no—
88C2×Dic37—21no—
89C2×Dic37—41no—
90C2×Dic37—41no—
91C2×Dic37#4111yescharacteristic
92D148—21no—
93D148—21no—
94D148—41no—
95D148—41no—
96C4×D37—41no—
97C4×D37—41no—
98C4×D37C2×D411yescharacteristic
99C4×D37C2×D411yescharacteristic
100C4×D37C2×D411yescharacteristic
101C4×D37#4111yescharacteristic
102Dic74—21no—
103Dic74—21no—
104#64438—22no—
105C8×C37C22⋊C411yescharacteristic
106C8×C37C22⋊C411yescharacteristic
107#64436C22⋊C411yescharacteristic
108#64436C22⋊C411yescharacteristic
109C22×C37—41no—
110C22×C37—81no—
111C22×C37C4×D411yescharacteristic
112C2×D37—41no—
113C2×D37—41no—
114C2×D37—81no—
115C2×D37#12111yescharacteristic
116C2×D37#12711yescharacteristic
117#3866—42no—
118#3866—81no—
119#3866—81no—
120C4×C37—41no—
121C4×C37C2×C22⋊C411yescharacteristic
122C4×C37C4×D411yescharacteristic
123Dic37—41no—
124Dic37#12111yescharacteristic
125Dic37#12411yescharacteristic
126#1976—371nomaximal, Sylow
127C2×C37—21no—
128C2×C37—81no—
129C2×C37#39011yescharacteristic
130D37—21no—
131D37—21no—
132D37—81no—
133C2×#135—371no—
134#427—371no—
135#421—371no—
136#421—371no—
137#410—371no—
138#410—371no—
139#405—371no—
140C37#197611yescharacteristic, complemented, Sylow
141C2×#41—371no—
142C2×#41—371no—
143#135—741no—
144#135—741no—
145#135—741no—
146#135—741no—
147C2×Q16—371no—
148C2×SD16—371no—
149C2×SD16#386611yescharacteristic, complemented
150C2×D8—371no—
151C2×M16—371no—
152C22×C8—371no—
153#117—371no—
154#117—371no—
155#117—371no—
156#107—741no—
157#106—741no—
158#104—742no—
159#104—742no—
160#99—742no—
161#99—742no—
162#97—741no—
163C4×C8—741no—
164#41—741no—
165#41—741no—
166#41—741no—
167#41—741no—
168#41—741no—
169#41—741no—
170#41—741no—
171#41—741no—
172C2×Q8—371no—
173C2×Q8C2×#386611yescharacteristic
174C2×D4—371no—
175C2×D4—741no—
176C2×D4—741no—
177C2×D4C2×#386611yescharacteristic
178C22×C4—371no—
179C22×C4—741no—
180C22×C4—741no—
181Q16—741no—
182Q16—741no—
183SD16—21no—
184SD16—21no—
185SD16—741no—
186SD16—741no—
187D8—741no—
188D8—741no—
189M16—372no—
190M16—741no—
191C2×C8—371no—
192C2×C8—371no—
193C2×C8—371no—
194C2×C8—371no—
195C2×C8—371no—
196C2×C8—741no—
197C2×C8C2×#386611yescharacteristic
198C4⋊C4—741no—
199C4⋊C4—741no—
200C4⋊C4—741no—
201C22⋊C4—372no—
202C22⋊C4—741no—
203C22⋊C4—741no—
204C42—741no—
205C42—741no—
206C42—741no—
207C23—21no—
208C23—371no—
209C23—741no—
210Q8—21no—
211Q8—21no—
212Q8—741no—
213Q8—741no—
214D4—21no—
215D4—21no—
216D4—741no—
217D4—741no—
218D4—1481no—
219D4—1481no—
220D4—1481no—
221D4—1481no—
222C2×C4—21no—
223C2×C4—371no—
224C2×C4—371no—
225C2×C4—371no—
226C2×C4—371no—
227C2×C4—371no—
228C2×C4—742no—
229C2×C4—741no—
230C2×C4—1481no—
231C2×C4—1481no—
232C2×C4—1481no—
233C2×C4—1481no—
234C2×C4—1481no—
235C2×C4—1481no—
236C2×C4C22×#386611yescharacteristic
237C8—371no—
238C8—371no—
239C8—742no—
240C8C22⋊#386611yescharacteristic
241C8C22⋊#386611yescharacteristic
242C22—41no—
243C22—81no—
244C22—371no—
245C22—371no—
246C22—2961no—
247C22—1481no—
248C22—1481no—
249C22D4×#386611yescharacteristic
250C4—41no—
251C4—371no—
252C4—371no—
253C4—2961no—
254C4—2961no—
255C4—1482no—
256C4—1481no—
257C4C2×C22⋊#386611yescharacteristic
258C4D4×#386611yescharacteristic
259C2—21no—
260C2—81no—
261C2—2961no—
262C2—741no—
263C2—741no—
264C2#1455848511yescharacteristic
subgroupG/H
centerC2#14558485
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×SD16×C37C4
socleC2×C37#390
prime radicalC2×#11924557C2
cosocleC2×C4×D37C23
hypercenterC2×SD16#3866
hypocenterC37#1976
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #14558543C2semidirect
2. #14558532C2semidirect
3. #14558531C2semidirect
4. #14558514C2semidirect
5. #14558513C2semidirect
6. #14558496C2semidirect
26. C2×#10596942C4semidirect
27. C2×#10596930C4semidirect
28. C2×#10596939C4semidirect
30. C2×SD16×C37C4semidirect
140. C37#1976semidirect
149. C2×SD16#3866semidirect

Maximal subgroups

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

subgroupindex
#145585432
#145585322
#145585312
#145585142
#145585132
#145584962
C2×#119245572
#197637