Finite Group Databasebeta

← #18010628

Subgroups — #18010628

Order 4736.

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

normal subgroups only

This group has 324 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#14558613C211yesmaximal, characteristic, complemented
2#14558532C211yesmaximal, characteristic, complemented
3#14558525C211yesmaximal, characteristic, complemented
4D37⋊#100C211yesmaximal, characteristic, complemented
5#14558415C211yesmaximal, characteristic, complemented
6#14558402C211yesmaximal, characteristic, complemented
7C2×#11924563C211yesmaximal, characteristic
8#11924624—22no—
9#11924624—22no—
10D37⋊M16—22no—
11D37⋊M16C2211yescharacteristic
12D37⋊M16C2211yescharacteristic
13D37⋊M16C2211yescharacteristic
14#11924615C2211yescharacteristic
15#11924601—22no—
16#11924598—22no—
17#11924596—22no—
18C2×#10596966C2211yescharacteristic
19C2×D4×D37C2211yescharacteristic
20#11924563—22no—
21#11924563—22no—
22C2×#10596941C411yescharacteristic, complemented
23C2×D296C411yescharacteristic, complemented
24C2×#10596939C411yescharacteristic, complemented
25C2×#10596929C2211yescharacteristic
26C2×SD16×C37C411yescharacteristic, complemented
27C23×D37—21no—
28C2×Q8×C37C2×C411yescharacteristic
29C2×D4×C37C2×C411yescharacteristic
30C2×C22⋊D37—21no—
31#10596966—21no—
32#10596966—21no—
33#10596966D412yes—
34#10596966D412yes—
35D4×D37—21no—
36D4×D37—21no—
37D4×D37—21no—
38D4×D37—21no—
39C2×D148—21no—
40C2×D148C2×C411yescharacteristic
41C2×D148C2×C411yescharacteristic
42C2×C4×D37—21no—
43C2×C4×D37C2311yescharacteristic
44C22⋊#3866—21no—
45#10596957—21no—
46#10596957—21no—
47#10596957D412yes—
48C4⋊#3866—21no—
49C4×#3866—21no—
50#10596953—24no—
51#10596953—21no—
52#10596953—21no—
53#10596953—21no—
54D37⋊C8—24no—
55D37⋊C8—21no—
56D37⋊C8—21no—
57D37⋊C8D412yes—
58SD16×C37—22no—
59C2×C8×C37C2×C411yescharacteristic
60#10596941—22no—
61#10596939—22no—
62C2×#64436C2×C411yescharacteristic
63D296—22no—
64#10596929—21no—
65#10596929—21no—
66C23×C37—21no—
67C22×D37—21no—
68C22×D37—21no—
69C22×D37—41no—
70C22×D37—41no—
71C22×D37—82no—
72C22×D37#4111yescharacteristic
73C2×#3866—41no—
74Q8×C37—21no—
75Q8×C37C22⋊C412yes—
76D4×C37—21no—
77D4×C37—21no—
78C2×C4×C37—21no—
79C2×C4×C37C22×C411yescharacteristic
80C22⋊D37—41no—
81C22⋊D37—41no—
82C2×Dic37C2×D411yescharacteristic
83D148—22no—
84D148—22no—
85D148—21no—
86D148—21no—
87D148—21no—
88D148C22⋊C412yes—
89C4×D37—22no—
90C4×D37—22no—
91C4×D37C2×D411yescharacteristic
92C4×D37C2×D411yescharacteristic
93C4×D37C2×D411yescharacteristic
94C4×D37#4111yescharacteristic
95#64438—22no—
96#64438—22no—
97#64438—41no—
98C8×C37—21no—
99#64436—21no—
100C22×C37—41no—
101C22×C37—81no—
102C22×C37C4×D411yescharacteristic
103C2×D37—22no—
104C2×D37—41no—
105C2×D37—41no—
106C2×D37—82no—
107C2×D37—82no—
108C2×D37—81no—
109C2×D37—81no—
110C2×D37#12111yescharacteristic
111C2×D37#12311yescharacteristic
112#3866—81no—
113C4×C37—22no—
114C4×C37C2×C22⋊C411yescharacteristic
115C4×C37C4×D411yescharacteristic
116Dic37#12011yescharacteristic
117Dic37#12111yescharacteristic
118#1903—371nomaximal, Sylow
119C2×C37—21no—
120C2×C37—81no—
121C2×C37#38611yescharacteristic
122D37—21no—
123D37—21no—
124D37—42no—
125D37—81no—
126C2×AGL(1,ℤ/8)—371no—
127#568—371no—
128#421—371no—
129#418—371no—
130C2×#100—371no—
131#344—371no—
132#338—371no—
133C37#190311yescharacteristic, complemented, Sylow
134C2×#41—371no—
135C22×D4—371no—
136AGL(1,ℤ/8)—742no—
137AGL(1,ℤ/8)—742no—
138C2×SD16—371no—
139C2×SD16#386611yescharacteristic, complemented
140C2×D8—371no—
141C2×D8—371no—
142#131—742no—
143#131—742no—
144C2×M16—371no—
145C2×M16—371no—
146C2×M16—371no—
147C2×M16—371no—
148C2×M16—742no—
149#117—371no—
150#104—742no—
151#102—742no—
152#100—742no—
153C24—741no—
154#41—372no—
155#41—372no—
156#41—741no—
157#41—741no—
158C2×Q8C2×#386611yescharacteristic
159C2×D4—371no—
160C2×D4—371no—
161C2×D4—741no—
162C2×D4—741no—
163C2×D4—741no—
164C2×D4—741no—
165C2×D4—741no—
166C2×D4—741no—
167C2×D4C2×#386611yescharacteristic
168C22×C4—371no—
169C22×C4—741no—
170SD16—22no—
171SD16—742no—
172D8—742no—
173D8—742no—
174M16—372no—
175M16—741no—
176M16—741no—
177M16—741no—
178M16—741no—
179M16—741no—
180M16—744no—
181M16—741no—
182M16—741no—
183C2×C8—372no—
184C2×C8—371no—
185C2×C8—741no—
186C2×C8—744no—
187C2×C8—741no—
188C2×C8C2×#386611yescharacteristic
189C4⋊C4—741no—
190C22⋊C4—741no—
191C42—741no—
192C23—21no—
193C23—371no—
194C23—2962no—
195C23—741no—
196C23—741no—
197C23—1481no—
198C23—1481no—
199Q8—21no—
200Q8C22⋊#386612yes—
201D4—21no—
202D4—21no—
203D4—372no—
204D4—742no—
205D4—742no—
206D4—741no—
207D4—741no—
208D4—741no—
209D4—1481no—
210D4—1481no—
211C2×C4—21no—
212C2×C4—371no—
213C2×C4—371no—
214C2×C4—371no—
215C2×C4—371no—
216C2×C4—371no—
217C2×C4—742no—
218C2×C4—742no—
219C2×C4—1481no—
220C2×C4C22×#386611yescharacteristic
221C8—21no—
222C8—742no—
223C8—742no—
224C8—741no—
225C8—1481no—
226C22—41no—
227C22—81no—
228C22—371no—
229C22—371no—
230C22—2961no—
231C22—2961no—
232C22—2962no—
233C22—2962no—
234C22—742no—
235C22—1481no—
236C22—1481no—
237C22D4×#386611yescharacteristic
238C4—22no—
239C4—371no—
240C4—371no—
241C4—2961no—
242C4C2×C22⋊#386611yescharacteristic
243C4D4×#386611yescharacteristic
244C2—21no—
245C2—81no—
246C2—2961no—
247C2—741no—
248C2—741no—
249C2—1482no—
250C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×SD16×C37C4
socleC2×C37#386
prime radicalC2×#11924563C2
cosocleC2×C4×D37C23
hypercenterC2×SD16#3866
hypocenterC37#1903
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. #14558613C2semidirect
2. #14558532C2semidirect
3. #14558525C2semidirect
4. D37⋊#100C2semidirect
5. #14558415C2semidirect
6. #14558402C2semidirect
22. C2×#10596941C4semidirect
23. C2×D296C4semidirect
24. C2×#10596939C4semidirect
26. C2×SD16×C37C4semidirect
133. C37#1903semidirect
139. C2×SD16#3866semidirect

Maximal subgroups

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

subgroupindex
#145586132
#145585322
#145585252
D37⋊#1002
#145584152
#145584022
C2×#119245632
#190337