Finite Group Databasebeta

← #18010626

Subgroups — #18010626

Order 4736.

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

normal subgroups only

This group has 304 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
2#14558532C211yesmaximal, characteristic
3#14558526C211yesmaximal, characteristic, complemented
4D37⋊#101C211yesmaximal, characteristic, complemented
5#14558415C211yesmaximal, characteristic, complemented
6#14558402C211yesmaximal, characteristic, complemented
7C2×#11924568C211yesmaximal, characteristic
8#11924624—22no—
9#11924624—22no—
10D37⋊M16—22no—
11D37⋊M16C2211yescharacteristic
12D37⋊M16C2211yescharacteristic
13D37⋊M16C2211yescharacteristic
14#11924615C2211yescharacteristic
15#11924601—22no—
16#11924599—22no—
17#11924597—22no—
18C2×#10596966C2211yescharacteristic
19C2×Q8×D37C2211yescharacteristic
20#11924568—22no—
21#11924568—22no—
22C2×#10596942C411yescharacteristic, complemented
23C2×#10596930C411yescharacteristic, complemented
24C2×#10596941C411yescharacteristic, complemented
25C2×#10596929C2211yescharacteristic
26C2×Q16×C37C411yescharacteristic, complemented
27C2×Q8×C37C2×C411yescharacteristic
28C2×Q8×C37C2×C411yescharacteristic
29#10596966—21no—
30#10596966—21no—
31#10596966D412yes—
32#10596966D412yes—
33Q8×D37—21no—
34Q8×D37—21no—
35Q8×D37—21no—
36Q8×D37—21no—
37C2×D148—21no—
38C2×D148C2×C411yescharacteristic
39C2×C4×D37—21no—
40C2×C4×D37—21no—
41C2×C4×D37C2311yescharacteristic
42C2×Dic74—21no—
43C2×Dic74C2×C411yescharacteristic
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—
58Q16×C37—22no—
59C2×C8×C37C2×C411yescharacteristic
60#10596942—22no—
61#10596941—22no—
62C2×#64436C2×C411yescharacteristic
63#10596930—22no—
64#10596929—21no—
65#10596929—21no—
66C22×D37—21no—
67C22×D37#4111yescharacteristic
68C2×#3866—41no—
69Q8×C37—21no—
70Q8×C37—21no—
71Q8×C37—21no—
72Q8×C37C22⋊C412yes—
73C2×C4×C37—21no—
74C2×C4×C37—21no—
75C2×C4×C37C22×C411yescharacteristic
76C2×Dic37—21no—
77C2×Dic37C2×D411yescharacteristic
78D148—22no—
79D148—22no—
80D148—21no—
81D148C22⋊C412yes—
82C4×D37—22no—
83C4×D37—22no—
84C4×D37—41no—
85C4×D37—41no—
86C4×D37C2×D411yescharacteristic
87C4×D37C2×D411yescharacteristic
88C4×D37C2×D411yescharacteristic
89C4×D37#4111yescharacteristic
90Dic74—21no—
91Dic74—21no—
92Dic74—41no—
93Dic74—41no—
94#64438—22no—
95#64438—22no—
96#64438—41no—
97C8×C37—21no—
98#64436—21no—
99C22×C37C4×D411yescharacteristic
100C2×D37—22no—
101C2×D37—41no—
102C2×D37—81no—
103C2×D37#12111yescharacteristic
104C2×D37#12311yescharacteristic
105#3866—81no—
106C4×C37—22no—
107C4×C37—41no—
108C4×C37C2×C22⋊C411yescharacteristic
109C4×C37C4×D411yescharacteristic
110Dic37—41no—
111Dic37#12011yescharacteristic
112Dic37#12111yescharacteristic
113#1902—371nomaximal, Sylow
114C2×C37—21no—
115C2×C37#38611yescharacteristic
116D37—21no—
117D37—21no—
118D37—42no—
119C2×#137—371no—
120#568—371no—
121#421—371no—
122#419—371no—
123C2×#101—371no—
124#344—371no—
125#338—371no—
126C37#190211yescharacteristic, complemented, Sylow
127C2×#41—371no—
128C22×Q8—371no—
129#137—742no—
130#137—742no—
131C2×Q16—371no—
132C2×Q16#386611yescharacteristic, complemented
133C2×SD16—371no—
134C2×SD16—371no—
135#131—742no—
136#131—742no—
137C2×M16—371no—
138C2×M16—371no—
139C2×M16—371no—
140C2×M16—371no—
141C2×M16—742no—
142#117—371no—
143#104—742no—
144#103—742no—
145#101—742no—
146#41—372no—
147#41—372no—
148#41—741no—
149#41—741no—
150C2×Q8—371no—
151C2×Q8—741no—
152C2×Q8—741no—
153C2×Q8—741no—
154C2×Q8—741no—
155C2×Q8—741no—
156C2×Q8C2×#386611yescharacteristic
157C2×Q8C2×#386611yescharacteristic
158C2×D4—371no—
159C2×D4—741no—
160C22×C4—371no—
161C22×C4—741no—
162C22×C4—741no—
163Q16—22no—
164Q16—742no—
165SD16—742no—
166SD16—742no—
167M16—372no—
168M16—741no—
169M16—741no—
170M16—741no—
171M16—741no—
172M16—741no—
173M16—744no—
174M16—741no—
175M16—741no—
176C2×C8—372no—
177C2×C8—371no—
178C2×C8—741no—
179C2×C8—744no—
180C2×C8—741no—
181C2×C8C2×#386611yescharacteristic
182C4⋊C4—741no—
183C22⋊C4—741no—
184C42—741no—
185C23—371no—
186C23—741no—
187Q8—21no—
188Q8—21no—
189Q8—21no—
190Q8—741no—
191Q8—741no—
192Q8—1481no—
193Q8—1481no—
194Q8C22⋊#386612yes—
195D4—372no—
196D4—742no—
197D4—742no—
198D4—741no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—371no—
202C2×C4—371no—
203C2×C4—371no—
204C2×C4—371no—
205C2×C4—371no—
206C2×C4—742no—
207C2×C4—742no—
208C2×C4—741no—
209C2×C4—1481no—
210C2×C4—1481no—
211C2×C4—1481no—
212C2×C4C22×#386611yescharacteristic
213C8—21no—
214C8—742no—
215C8—742no—
216C8—741no—
217C8—1481no—
218C22—371no—
219C22—371no—
220C22—2961no—
221C22—742no—
222C22—1481no—
223C22D4×#386611yescharacteristic
224C4—22no—
225C4—41no—
226C4—371no—
227C4—371no—
228C4—2961no—
229C4—1481no—
230C4C2×C22⋊#386611yescharacteristic
231C4D4×#386611yescharacteristic
232C2—21no—
233C2—741no—
234C2—741no—
235C2—1482no—
236C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×Q16×C37C4
socleC2×C37#386
prime radicalC2×#10596966C22
cosocleC2×C4×D37C23
hypercenterC2×Q16#3866
hypocenterC37#1902
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #14558526C2semidirect
4. D37⋊#101C2semidirect
5. #14558415C2semidirect
6. #14558402C2semidirect
22. C2×#10596942C4semidirect
23. C2×#10596930C4semidirect
24. C2×#10596941C4semidirect
26. C2×Q16×C37C4semidirect
126. C37#1902semidirect
132. C2×Q16#3866semidirect

Maximal subgroups

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

subgroupindex
#145586132
#145585322
#145585262
D37⋊#1012
#145584152
#145584022
C2×#119245682
#190237