Finite Group Databasebeta

← #17994957

Subgroups — #17994957

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#14558333C211yesmaximal, characteristic
2#14558299C211yesmaximal, characteristic, complemented
3#14557551C211yesmaximal, characteristic, complemented
4#14557527C211yesmaximal, characteristic, complemented
5#14557501C211yesmaximal, characteristic, complemented
6#14557297C211yesmaximal, characteristic, complemented
7C37×#344C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596962C2211yescharacteristic
10#11924569—21no—
11#11924569C412yescomplemented
12#11924564—21no—
13#11924564C412yescomplemented
14#11924558—22no—
15#11924544—22no—
16#11924542—22no—
17C2×#10596934C2211yescharacteristic
18M16×D37—22no—
19C22×#64436C2211yescharacteristic
20#11924464—22no—
21#11924459—21no—
22#11924456—21no—
23#11924448—22no—
24C2×M16×C37C2211yescharacteristic
25C2×M16×C37C2211yescharacteristic
26#117×C37C2211yescharacteristic
27C22×C4×C37C2311yescharacteristic
28C2×C22⋊D37—21no—
29C2×C22⋊D37—21no—
30#10596962—21no—
31#10596962—21no—
32#10596962—21no—
33#10596962—21no—
34#10596962—21no—
35#10596962—21no—
36#10596962C2×C412yes—
37#10596962D412yes—
38C2×D148C2×C411yescharacteristic
39C2×D148D411yescharacteristic
40C2×C4×D37—21no—
41C2×C4×D37—21no—
42C2×Dic74C2×C411yescharacteristic
43C2×Dic74D411yescharacteristic
44M16×C37—21no—
45M16×C37—21no—
46M16×C37—21no—
47M16×C37C2×C412yes—
48C2×C8×C37—21no—
49C2×C8×C37D412yes—
50C4⋊C4×C37—21no—
51C22⋊C4×C37—21no—
52C42×C37—21no—
53#10596934—21no—
54#10596934D412yes—
55C2×#64436—21no—
56C2×#64436—21no—
57C2×#64436—21no—
58C2×#64436—21no—
59Dic148—22no—
60D296—22no—
61#10596930—22no—
62#10596930—22no—
63#10596929—24no—
64C8×D37—24no—
65C23×C37#4111yescharacteristic
66C22×D37—21no—
67C22×D37—21no—
68C2×C4×C37—41no—
69C2×C4×C37C22×C411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37#4111yescharacteristic
75C22⋊D37—22no—
76C22⋊D37—22no—
77C22⋊D37—41no—
78C22⋊D37—41no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81D148—21no—
82D148—21no—
83D148—21no—
84D148C22⋊C412yes—
85C4×D37—22no—
86C4×D37—22no—
87C4×D37—41no—
88C4×D37—41no—
89Dic74—21no—
90Dic74—21no—
91Dic74—21no—
92Dic74C22⋊C412yes—
93C8×C37—22no—
94C8×C37—22no—
95#64436—22no—
96#64436—41no—
97C22×C37—41no—
98C22×C37C4×D411yescharacteristic
99C22×C37#12111yescharacteristic
100C22×C37#12311yescharacteristic
101C2×D37—22no—
102C2×D37—42no—
103C2×D37—41no—
104C2×D37—81no—
105C4×C37—81no—
106C4×C37C2×C22⋊C411yescharacteristic
107C4×C37C4×D411yescharacteristic
108C4×C37#12011yescharacteristic
109C4×C37#12111yescharacteristic
110Dic37—22no—
111Dic37—41no—
112#1881—371nomaximal, Sylow
113C2×C37—21no—
114C2×C37—21no—
115C2×C37—21no—
116C2×C37#38611yescharacteristic
117D37—42no—
118D37—81no—
119#575—371no—
120#568—371no—
121#421—371no—
122#416—371no—
123#408—371no—
124#344D3711yescharacteristic, complemented
125#341—371no—
126C37#188111yescharacteristic, complemented, Sylow
127C2×#41—371no—
128C2×#41—371no—
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—742no—
138C2×M16C2×D3711yescharacteristic
139C2×M16C2×D3711yescharacteristic
140C22×C8—371no—
141#117C2×D3711yescharacteristic
142#104—742no—
143#103—741no—
144#102—741no—
145C22⋊C8—742no—
146#41—372no—
147#41—372no—
148#41—741no—
149#41—741no—
150#41—741no—
151#41—741no—
152#41—741no—
153#41—741no—
154C2×Q8—371no—
155C2×Q8—371no—
156C2×D4—371no—
157C2×D4—371no—
158C2×D4—741no—
159C2×D4—741no—
160C22×C4—741no—
161C22×C4—741no—
162C22×C4C22×D3711yescharacteristic
163Q16—742no—
164SD16—742no—
165SD16—742no—
166D8—742no—
167M16—21no—
168M16—21no—
169M16—21no—
170M16—372no—
171M16—744no—
172M16—741no—
173M16C4×D3712yes—
174C2×C8—21no—
175C2×C8—744no—
176C2×C8—741no—
177C2×C8—741no—
178C2×C8—741no—
179C2×C8—741no—
180C2×C8D14812yes—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42—21no—
184C23—741no—
185C23—741no—
186C23#1059696211yescharacteristic
187Q8—372no—
188Q8—741no—
189Q8—741no—
190Q8—741no—
191D4—372no—
192D4—742no—
193D4—742no—
194D4—741no—
195D4—741no—
196D4—741no—
197D4—1481no—
198D4—1481no—
199C2×C4—41no—
200C2×C4—741no—
201C2×C4—742no—
202C2×C4—742no—
203C2×C4—741no—
204C2×C4—1481no—
205C2×C4—1481no—
206C2×C4C2×C4×D3711yescharacteristic
207C2×C4C2×D14811yescharacteristic
208C2×C4D4×D3711yescharacteristic
209C2×C4D4×D3711yescharacteristic
210C2×C4D4×D3711yescharacteristic
211C2×C4#1059696611yescharacteristic
212C8—22no—
213C8—22no—
214C8—742no—
215C8—1481no—
216C22—41no—
217C22—2961no—
218C22—742no—
219C22—1482no—
220C22—1481no—
221C22C4×D14811yescharacteristic
222C22#1192450911yescharacteristic
223C22#1192452111yescharacteristic
224C4—81no—
225C4—742no—
226C4—1481no—
227C4C22⋊C4×D3711yescharacteristic
228C4#1192449811yescharacteristic
229C4#1192450611yescharacteristic
230C4#1192451111yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—2961no—
235C2—1482no—
236C2#1455741111yescharacteristic
subgroupG/H
centerC4#11924506
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#344C2
socleC2×C37#386
prime radical#14558333C2
cosocleC22×C4×C37C23
hypercenter#344D37
hypocenterC37#1881
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #14558299C2semidirect
3. #14557551C2semidirect
4. #14557527C2semidirect
5. #14557501C2semidirect
6. #14557297C2semidirect
7. C37×#344C2semidirect
11. #11924569C4semidirect
13. #11924564C4semidirect
124. #344D37semidirect
126. C37#1881semidirect

Maximal subgroups

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

subgroupindex
#145583332
#145582992
#145575512
#145575272
#145575012
#145572972
C37×#3442
#188137