Finite Group Databasebeta

← #17994955

Subgroups — #17994955

Order 4736.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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#14558331C211yesmaximal, characteristic
2#14558299C211yesmaximal, characteristic, complemented
3#14557527C211yesmaximal, characteristic, complemented
4#14557500C211yesmaximal, characteristic, complemented
5#14557303C211yesmaximal, characteristic, complemented
6#14557297C211yesmaximal, characteristic, complemented
7C37×#421C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567C412yescomplemented
10#11924566—21no—
11#11924562C412yescomplemented
12#11924561—21no—
13#11924556—22no—
14#11924544—22no—
15#11924542—22no—
16C2×#10596934C2211yescharacteristic
17C2×#10596934C2211yescharacteristic
18M16×D37—22no—
19C22×#64436C2211yescharacteristic
20#11924459—21no—
21#11924456—21no—
22C22⋊#64436—22no—
23C2×#41×C37C2211yescharacteristic
24C2×M16×C37C2211yescharacteristic
25#117×C37C2211yescharacteristic
26#104×C37—22no—
27#41×C37—21no—
28#41×C37—21no—
29#41×C37—21no—
30#41×C37—21no—
31C2×Q8×C37C2×C411yescharacteristic
32C2×D4×C37—21no—
33C2×D4×C37C2×C411yescharacteristic
34C22×C4×C37—21no—
35C22×C4×C37C2311yescharacteristic
36C2×C22⋊D37—21no—
37#10596962—21no—
38#10596962—21no—
39#10596962C2×C412yes—
40#10596962D412yes—
41C2×D148D411yescharacteristic
42C2×C4×D37—21no—
43C2×Dic74D411yescharacteristic
44M16×C37—21no—
45M16×C37D412yes—
46C2×C8×C37—21no—
47C4⋊C4×C37—21no—
48C22⋊C4×C37—21no—
49C42×C37—21no—
50#10596942—22no—
51#10596941—22no—
52#10596940—22no—
53#10596939—22no—
54#10596934—21no—
55#10596934—21no—
56#10596934—21no—
57#10596934C2×C412yes—
58C2×#64436—21no—
59C2×#64436—21no—
60C2×#64436—21no—
61C2×#64436—21no—
62C2×#64436D412yes—
63#10596929—24no—
64C8×D37—24no—
65C23×C37—21no—
66C23×C37#4111yescharacteristic
67C22×D37—21no—
68Q8×C37—21no—
69Q8×C37—21no—
70D4×C37—21no—
71D4×C37—21no—
72D4×C37—41no—
73D4×C37—41no—
74C2×C4×C37—21no—
75C2×C4×C37—41no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37C22×C411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37#4111yescharacteristic
84C22⋊D37—22no—
85C22⋊D37—22no—
86C2×Dic37—21no—
87D148—21no—
88D148C22⋊C412yes—
89C4×D37—22no—
90C4×D37—22no—
91Dic74—21no—
92Dic74C22⋊C412yes—
93C8×C37—22no—
94#64436—22no—
95#64436—22no—
96#64436—41no—
97C22×C37—41no—
98C22×C37—42no—
99C22×C37—41no—
100C22×C37C4×D411yescharacteristic
101C22×C37#12111yescharacteristic
102C22×C37#12311yescharacteristic
103C2×D37—22no—
104C2×D37—81no—
105C4×C37—41no—
106C4×C37—81no—
107C4×C37C2×C22⋊C411yescharacteristic
108C4×C37C4×D411yescharacteristic
109C4×C37#12011yescharacteristic
110C4×C37#12111yescharacteristic
111Dic37—22no—
112#1881—371nomaximal, Sylow
113C2×C37—21no—
114C2×C37—21no—
115C2×C37—21no—
116C2×C37—81no—
117C2×C37#38611yescharacteristic
118D37—42no—
119#575—371no—
120#568—371no—
121#421D3711yescharacteristic, complemented
122#416—371no—
123#408—371no—
124#344—371no—
125#341—371no—
126C37#188111yescharacteristic, complemented, Sylow
127C2×#41—371no—
128C2×#41C2×D3711yescharacteristic
129#137—372no—
130#137—741no—
131AGL(1,ℤ/8)—372no—
132AGL(1,ℤ/8)—741no—
133#135—742no—
134#131—742no—
135#131—742no—
136C2×M16—371no—
137C2×M16—371no—
138C2×M16—742no—
139C2×M16C2×D3711yescharacteristic
140C22×C8—371no—
141#117C2×D3711yescharacteristic
142#104—22no—
143#103—741no—
144#102—741no—
145C22⋊C8—742no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—372no—
151#41—372no—
152#41—741no—
153#41—741no—
154C2×Q8—371no—
155C2×Q8C4×D3711yescharacteristic
156C2×D4—21no—
157C2×D4—371no—
158C2×D4—741no—
159C2×D4C4×D3711yescharacteristic
160C22×C4—21no—
161C22×C4—741no—
162C22×C4C22×D3711yescharacteristic
163Q16—742no—
164SD16—742no—
165SD16—742no—
166D8—742no—
167M16—21no—
168M16—372no—
169M16—744no—
170M16—741no—
171M16—741no—
172M16—741no—
173M16C22⋊D3712yes—
174C2×C8—21no—
175C2×C8—372no—
176C2×C8—744no—
177C2×C8—741no—
178C2×C8—741no—
179C2×C8—741no—
180C2×C8—741no—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42—21no—
184C23—21no—
185C23—741no—
186C23#1059696411yescharacteristic
187Q8—21no—
188Q8—21no—
189Q8—372no—
190Q8—741no—
191D4—21no—
192D4—21no—
193D4—41no—
194D4—41no—
195D4—372no—
196D4—742no—
197D4—742no—
198D4—741no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—741no—
204C2×C4—742no—
205C2×C4—742no—
206C2×C4C2×C4×D3711yescharacteristic
207C2×C4#1059696211yescharacteristic
208C2×C4D4×D3711yescharacteristic
209C2×C4D4×D3711yescharacteristic
210C2×C4D4×D3711yescharacteristic
211C2×C4C2×C22⋊D3711yescharacteristic
212C8—22no—
213C8—742no—
214C8—742no—
215C8—1481no—
216C22—41no—
217C22—42no—
218C22—41no—
219C22—2961no—
220C22—742no—
221C22#1192449611yescharacteristic
222C22#1192450711yescharacteristic
223C22#1192451811yescharacteristic
224C4—41no—
225C4—81no—
226C4—742no—
227C4C22⋊C4×D3711yescharacteristic
228C4C4×C22⋊D3711yescharacteristic
229C4#1192450411yescharacteristic
230C4#1192450911yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—1482no—
236C2#1455740911yescharacteristic
subgroupG/H
centerC4#11924504
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#421C2
socleC2×C37#386
prime radical#14558331C2
cosocleC22×C4×C37C23
hypercenter#421D37
hypocenterC37#1881
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #14558299C2semidirect
3. #14557527C2semidirect
4. #14557500C2semidirect
5. #14557303C2semidirect
6. #14557297C2semidirect
7. C37×#421C2semidirect
9. #11924567C4semidirect
11. #11924562C4semidirect
121. #421D37semidirect
126. C37#1881semidirect

Maximal subgroups

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

subgroupindex
#145583312
#145582992
#145575272
#145575002
#145573032
#145572972
C37×#4212
#188137