Finite Group Databasebeta

← #18010557

Subgroups — #18010557

Order 4736.

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

normal subgroups only

This group has 262 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#14558612C211yesmaximal, characteristic
2#14558548C211yesmaximal, characteristic, complemented
3#14558537C211yesmaximal, characteristic, complemented
4#14558530C211yesmaximal, characteristic
5#14558416C211yesmaximal, characteristic, complemented
6#14558404C211yesmaximal, characteristic, complemented
7#104×D37C211yesmaximal, characteristic
8#11924624—21no—
9#11924623—21no—
10#11924623—22no—
11C2×#10596953—21no—
12C2×#10596953C2211yescharacteristic
13C2×#10596953C2211yescharacteristic
14D37⋊M16—21no—
15D37⋊M16C2211yescharacteristic
16#11924615C2211yescharacteristic
17#11924607—21no—
18#11924606—21no—
19C4⋊#64438—22no—
20#11924601—21no—
21#11924600—21no—
22#41×D37C2211yescharacteristic
23M16×D37C2211yescharacteristic
24C42×D37C2211yescharacteristic
25#11924464C411yescharacteristic, complemented
26#11924463C411yescharacteristic, complemented
27#11924462C411yescharacteristic, complemented
28#104×C37C411yescharacteristic, complemented
29#41×C37C2×C411yescharacteristic
30#10596966D411yescharacteristic
31Q8×D37Q811yescharacteristic
32#10596964—21no—
33#10596964D411yescharacteristic
34D4×D37—21no—
35D4×D37Q811yescharacteristic
36#10596962—21no—
37#10596962C2×C411yescharacteristic
38C2×C4×D37—21no—
39C2×C4×D37—21no—
40C2×C4×D37C2311yescharacteristic
41C22⋊#3866—21no—
42#10596957—22no—
43#10596957—21no—
44C2×#64438—22no—
45C2×#64438—21no—
46C2×#64438D412yes—
47C4⋊#3866—21no—
48C4×#3866—21no—
49#10596953—22no—
50#10596953—21no—
51#10596953—21no—
52#10596953—21no—
53#10596953—21no—
54#10596953D411yescharacteristic
55#10596953D411yescharacteristic
56D37⋊C8—22no—
57D37⋊C8—21no—
58M16×C37C2×C411yescharacteristic
59C42×C37C2×C411yescharacteristic
60C4×Dic37—21no—
61C4×Dic37C2×C411yescharacteristic
62#10596934C2×C411yescharacteristic
63#10596929—21no—
64C8×D37—21no—
65C22×D37—21no—
66C22×D37#4111yescharacteristic
67C2×#3866—41no—
68Q8×C37C4⋊C411yescharacteristic
69D4×C37—21no—
70D4×C37C4⋊C411yescharacteristic
71C2×C4×C37—21no—
72C2×C4×C37—21no—
73C2×C4×C37C22×C411yescharacteristic
74C22⋊D37—21no—
75C22⋊D37—21no—
76C22⋊D37—21no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37C2×D411yescharacteristic
80D148—21no—
81D148C4⋊C411yescharacteristic
82C4×D37—21no—
83C4×D37—21no—
84C4×D37—21no—
85C4×D37—42no—
86C4×D37C2×D411yescharacteristic
87C4×D37C2×D411yescharacteristic
88C4×D37C2×Q811yescharacteristic
89C4×D37#4111yescharacteristic
90Dic74—21no—
91Dic74C4⋊C411yescharacteristic
92#64438—21no—
93#64438—22no—
94#64438—21no—
95#64438—41no—
96C8×C37—21no—
97#64436—21no—
98C22×C37—21no—
99C22×C37C4×D411yescharacteristic
100C2×D37—21no—
101C2×D37—41no—
102C2×D37—81no—
103C2×D37C22⋊Q811yescharacteristic
104C2×D37#12311yescharacteristic
105#3866—81no—
106C4×C37—22no—
107C4×C37—21no—
108C4×C37C2×C4⋊C411yescharacteristic
109C4×C37C4×D411yescharacteristic
110Dic37—21no—
111Dic37—41no—
112Dic37#12011yescharacteristic
113Dic37C22⋊Q811yescharacteristic
114#1861—371nomaximal, Sylow
115C2×C37—21no—
116C2×C37—41no—
117C2×C37#38511yescharacteristic
118D37—21no—
119D37—21no—
120D37—41no—
121#568—371no—
122#430—371no—
123#423—371no—
124#421—371no—
125C2×#104—371no—
126#344—371no—
127#339—371no—
128C37#186111yescharacteristic, complemented, Sylow
129C2×#41—371no—
130#131—742no—
131#131—741no—
132#131—741no—
133C2×M16—371no—
134C2×M16—371no—
135C2×M16—371no—
136C2×M16—371no—
137C2×M16—741no—
138C2×M16—741no—
139#117—371no—
140C2×C42—371no—
141#108—741no—
142#108—741no—
143C4⋊C8—742no—
144#104—371no—
145#104—371no—
146#104—371no—
147#104—741no—
148#104—741no—
149#104#386611yescharacteristic, complemented
150#41—371no—
151#41—371no—
152#41—371no—
153#41—741no—
154#41—741no—
155#41C2×#386611yescharacteristic
156C2×Q8—371no—
157C2×D4—371no—
158C2×D4—741no—
159C22×C4—371no—
160C22×C4—741no—
161C22×C4—741no—
162M16—371no—
163M16—371no—
164M16—371no—
165M16—741no—
166M16—741no—
167M16—741no—
168M16—741no—
169M16—742no—
170M16—742no—
171M16—741no—
172M16—741no—
173M16C2×#386611yescharacteristic
174C2×C8—372no—
175C2×C8—741no—
176C2×C8—741no—
177C2×C8—742no—
178C2×C8—742no—
179C2×C8—741no—
180C4⋊C4—741no—
181C22⋊C4—741no—
182C42—371no—
183C42—741no—
184C42—741no—
185C42C2×#386611yescharacteristic
186C23—371no—
187C23—741no—
188Q8—371no—
189Q8—741no—
190Q8C4⋊#386611yescharacteristic
191D4—21no—
192D4—371no—
193D4—741no—
194D4—741no—
195D4—741no—
196D4—741no—
197D4C4⋊#386611yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—371no—
201C2×C4—371no—
202C2×C4—371no—
203C2×C4—371no—
204C2×C4—371no—
205C2×C4—741no—
206C2×C4—741no—
207C2×C4—741no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—1482no—
211C2×C4—1481no—
212C2×C4C22×#386611yescharacteristic
213C8—21no—
214C8—742no—
215C8—741no—
216C8—741no—
217C8—741no—
218C8—1481no—
219C22—21no—
220C22—371no—
221C22—371no—
222C22—2961no—
223C22—741no—
224C22—1481no—
225C22D4×#386611yescharacteristic
226C4—22no—
227C4—21no—
228C4—371no—
229C4—371no—
230C4—2961no—
231C4—741no—
232C4—1481no—
233C4C2×C4⋊#386611yescharacteristic
234C4D4×#386611yescharacteristic
235C2—21no—
236C2—41no—
237C2—741no—
238C2—741no—
239C2—1481no—
240C2#1455848011yescharacteristic
subgroupG/H
centerC2#14558480
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#104×C37C4
socleC2×C37#385
prime radical#41×D37C22
cosocleC2×C4×D37C23
hypercenter#104#3866
hypocenterC37#1861
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #14558548C2semidirect
3. #14558537C2semidirect
5. #14558416C2semidirect
6. #14558404C2semidirect
25. #11924464C4semidirect
26. #11924463C4semidirect
27. #11924462C4semidirect
28. #104×C37C4semidirect
128. C37#1861semidirect
149. #104#3866semidirect

Maximal subgroups

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

subgroupindex
#145586122
#145585482
#145585372
#145585302
#145584162
#145584042
#104×D372
#186137