Finite Group Databasebeta

← #17995112

Subgroups — #17995112

Order 4736.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#11924569C211yesmaximal, characteristic
2C2×#11924544C211yesmaximal, characteristic
3#14557532C211yesmaximal, characteristic
4C2×#11924459C211yesmaximal, characteristic, complemented
5C2×#11924454C211yesmaximal, characteristic, complemented
6#14557297C211yesmaximal, characteristic, complemented
7C37×#343C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924569—22no—
11#11924569C414yescomplemented
12C2×Dic148—21no—
13C2×#10596930—21no—
14#11924544—22no—
15#11924544—22no—
16C2×#10596934C2211yescharacteristic
17C2×#10596929—21no—
18C22×#64436C2211yescharacteristic
19C2×C8×D37—21no—
20#11924459—21no—
21#11924459—21no—
22#11924459—21no—
23#11924456—21no—
24#11924454—22no—
25C2×M16×C37C2211yescharacteristic
26C2×M16×C37C2211yescharacteristic
27C2×C4⋊C4×C37C2211yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32#10596962—21no—
33#10596962—21no—
34#10596962C2×C412yes—
35#10596962D412yes—
36C2×D148D411yescharacteristic
37C2×C4×D37—21no—
38C2×Dic74—21no—
39C2×Dic74—21no—
40C2×Dic74—21no—
41C2×Dic74—21no—
42C2×Dic74—21no—
43C2×Dic74C2×C412yes—
44C2×Dic74D411yescharacteristic
45M16×C37—21no—
46M16×C37—21no—
47M16×C37C2×C412yes—
48M16×C37D412yes—
49C2×C8×C37—21no—
50C2×C8×C37—21no—
51C4⋊C4×C37—21no—
52C4⋊C4×C37—21no—
53#10596934—21no—
54#10596934—21no—
55C2×#64436—21no—
56C2×#64436—21no—
57C2×#64436—21no—
58C2×#64436D411yescharacteristic
59C2×#64436D411yescharacteristic
60Dic148—24no—
61#10596930—24no—
62#10596929—24no—
63C8×D37—24no—
64C23×C37#4111yescharacteristic
65C22×D37—21no—
66C2×C4×C37—41no—
67C2×C4×C37—81no—
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37#4111yescharacteristic
74C22⋊D37—22no—
75C22⋊D37—22no—
76C2×Dic37—21no—
77C2×Dic37—22no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80D148—21no—
81D148C22⋊C412yes—
82C4×D37—22no—
83C4×D37—22no—
84Dic74—21no—
85Dic74—22no—
86Dic74—22no—
87Dic74—41no—
88Dic74—41no—
89Dic74C22⋊C412yes—
90C8×C37—22no—
91C8×C37—22no—
92#64436—21no—
93#64436—21no—
94#64436—41no—
95C22×C37—21no—
96C22×C37—21no—
97C22×C37C4×D411yescharacteristic
98C22×C37#12111yescharacteristic
99C22×C37#12311yescharacteristic
100C2×D37—22no—
101C2×D37—41no—
102C2×D37—41no—
103C4×C37—81no—
104C4×C37C2×C22⋊C411yescharacteristic
105C4×C37C4×D411yescharacteristic
106C4×C37#12011yescharacteristic
107C4×C37#12111yescharacteristic
108Dic37—22no—
109Dic37—42no—
110#1908—371nomaximal, Sylow
111C2×C37—21no—
112C2×C37—21no—
113C2×C37#38611yescharacteristic
114C2×C37#47111yescharacteristic
115C2×C37#47311yescharacteristic
116D37—42no—
117C2×#137—371no—
118C2×#131—371no—
119#417—371no—
120C2×#103—371no—
121C2×#101—371no—
122#343D3711yescharacteristic, complemented
123#341—371no—
124C37#190811yescharacteristic, complemented, Sylow
125C2×#41—371no—
126C22×Q8—371no—
127#137—374no—
128#137—742no—
129C2×Q16—741no—
130C2×SD16—741no—
131#131—742no—
132#131—742no—
133C2×M16—371no—
134C2×M16—741no—
135C2×M16C2×D3711yescharacteristic
136C2×M16C2×D3711yescharacteristic
137C22×C8—371no—
138C22×C8—741no—
139C2×C4⋊C4C2×D3711yescharacteristic
140#103—741no—
141#103—741no—
142#103—741no—
143#102—741no—
144#101—742no—
145#41—372no—
146#41—372no—
147#41—741no—
148#41—741no—
149C2×Q8—372no—
150C2×Q8—371no—
151C2×Q8—741no—
152C2×Q8—741no—
153C2×Q8—741no—
154C2×Q8—741no—
155C2×Q8—741no—
156C2×D4—371no—
157C2×D4—741no—
158C22×C4—21no—
159C22×C4—741no—
160C22×C4—741no—
161C22×C4C22×D3711yescharacteristic
162Q16—744no—
163SD16—744no—
164M16—21no—
165M16—21no—
166M16—744no—
167M16—741no—
168M16—741no—
169M16C4×D3712yes—
170M16D14812yes—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—371no—
174C2×C8—371no—
175C2×C8—744no—
176C2×C8—741no—
177C2×C8—741no—
178C2×C8—741no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C23—741no—
182C23#1059696211yescharacteristic
183Q8—372no—
184Q8—741no—
185Q8—742no—
186Q8—742no—
187Q8—1481no—
188Q8—1481no—
189D4—372no—
190D4—742no—
191D4—742no—
192D4—741no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—741no—
196C2×C4—742no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4—1481no—
200C2×C4—1481no—
201C2×C4C2×C4×D3711yescharacteristic
202C2×C4C2×D14811yescharacteristic
203C2×C4D4×D3711yescharacteristic
204C2×C4D4×D3711yescharacteristic
205C2×C4D4×D3711yescharacteristic
206C2×C4#1059696611yescharacteristic
207C8—22no—
208C8—22no—
209C8—741no—
210C8—741no—
211C8—1481no—
212C22—21no—
213C22—21no—
214C22—742no—
215C22—1481no—
216C22—1481no—
217C22C4×D14811yescharacteristic
218C22#1192450911yescharacteristic
219C22#1192452111yescharacteristic
220C4—81no—
221C4—742no—
222C4—1482no—
223C4C22⋊C4×D3711yescharacteristic
224C4#1192449811yescharacteristic
225C4#1192450611yescharacteristic
226C4#1192451111yescharacteristic
227C2—21no—
228C2—21no—
229C2—1482no—
230C2#1455741111yescharacteristic
231C2#1455779511yescharacteristic
232C2#1455780711yescharacteristic
subgroupG/H
centerC22#11924509
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37#121
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenter#343D37
hypocenterC37#1908
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
4. C2×#11924459C2semidirect
5. C2×#11924454C2semidirect
6. #14557297C2semidirect
7. C37×#343C2semidirect
11. #11924569C4semidirect
122. #343D37semidirect
124. C37#1908semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
C2×#119245442
#145575322
C2×#119244592
C2×#119244542
#145572972
C37×#3432
#190837