Finite Group Databasebeta

← #17994938

Subgroups — #17994938

Order 4736.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×Dic148C211yesmaximal, characteristic
2C2×#11924501C211yesmaximal, characteristic
3C2×#11924459C211yesmaximal, characteristic
4C2×#11924459C211yesmaximal, characteristic
5#14557438C211yesmaximal, characteristic
6#14557287C211yesmaximal, characteristic
7C37×#340C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10C2×Dic148—22no—
11C2×Dic148—22no—
12C2×Dic148C414yescomplemented
13C22×#64436C2211yescharacteristic
14#11924501—22no—
15#11924501—22no—
16C2×#10596936—21no—
17C2×C4×Dic37—21no—
18C2×C4×Dic37C2211yescharacteristic
19#11924459—22no—
20#11924459—22no—
21#11924443—21no—
22#11924443—21no—
23C22×C8×C37C2211yescharacteristic
24C2×C4⋊C4×C37C2211yescharacteristic
25C2×C4⋊C4×C37C2211yescharacteristic
26C22×C4×C37—21no—
27C22×C4×C37—21no—
28C22×C4×C37C2311yescharacteristic
29C22×Dic37—21no—
30C22×Dic37—21no—
31C22×Dic37D411yescharacteristic
32C22×Dic37D411yescharacteristic
33C2×Dic74—21no—
34C2×Dic74—21no—
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74—21no—
39C2×Dic74—21no—
40C2×Dic74—21no—
41C2×Dic74C2×C412yes—
42C2×Dic74C2×C412yes—
43C2×Dic74D412yes—
44C2×Dic74D412yes—
45C2×C8×C37—21no—
46C2×C8×C37—21no—
47C2×C8×C37C2×C412yes—
48C4⋊C4×C37—21no—
49C4⋊C4×C37—21no—
50C4⋊C4×C37—21no—
51C4⋊C4×C37D412yes—
52#10596936—24no—
53C4×Dic37—24no—
54C4×Dic37—21no—
55C4×Dic37—21no—
56C2×#64436—21no—
57C2×#64436—21no—
58C2×#64436—21no—
59Dic148—28no—
60C23×C37C2×D411yescharacteristic
61C2×C4×C37—22no—
62C2×C4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37C22×C411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37#4111yescharacteristic
72C2×C4×C37#4111yescharacteristic
73C2×Dic37—22no—
74C2×Dic37—21no—
75C2×Dic37—22no—
76C2×Dic37—22no—
77C2×Dic37—21no—
78C2×Dic37—22no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81C2×Dic37—21no—
82C2×Dic37—41no—
83C2×Dic37—41no—
84C2×Dic37Q1612yescomplemented
85Dic74—22no—
86Dic74—22no—
87Dic74—22no—
88Dic74—22no—
89Dic74—22no—
90Dic74—41no—
91Dic74—41no—
92Dic74C22⋊C414yes—
93C8×C37—22no—
94#64436—41no—
95C22×C37C4×D411yescharacteristic
96C22×C37#12011yescharacteristic
97C22×C37#12111yescharacteristic
98C22×C37C2×Q1611yescharacteristic
99C22×C37#13511yescharacteristic
100C22×C37#13711yescharacteristic
101C22×C37#13711yescharacteristic
102C4×C37—42no—
103C4×C37—81no—
104C4×C37C2×C22⋊C411yescharacteristic
105C4×C37C4×D411yescharacteristic
106C4×C37#12111yescharacteristic
107C4×C37#12311yescharacteristic
108Dic37—24no—
109Dic37—22no—
110Dic37—42no—
111Dic37—41no—
112#1878—371nomaximal, Sylow
113C2×C37#38611yescharacteristic
114C2×C37C4×Q1611yescharacteristic
115C2×C37#44111yescharacteristic
116C2×C37#45111yescharacteristic
117C2×C37#45211yescharacteristic
118C2×C37#46211yescharacteristic
119C2×C37#46411yescharacteristic
120C22×Q16—371no—
121C2×C4×Q8—371no—
122C2×#103—371no—
123C2×#103—371no—
124#391—371no—
125#340D3711yescharacteristic
126#336—371no—
127C37#187811yescharacteristic, complemented, Sylow
128C22×Q8—371no—
129C22×Q8—371no—
130C2×Q16—374no—
131C2×Q16—742no—
132C2×Q16—742no—
133C22×C8—371no—
134C22×C8C2×D3711yescharacteristic
135C4×Q8—742no—
136C4×Q8—742no—
137C2×C4⋊C4—741no—
138C2×C4⋊C4C2×D3711yescharacteristic
139C2×C4⋊C4C2×D3711yescharacteristic
140C2×C42—371no—
141C2×C42—741no—
142#103—742no—
143#103—742no—
144#95—741no—
145#95—741no—
146C2×Q8—372no—
147C2×Q8—372no—
148C2×Q8—372no—
149C2×Q8—372no—
150C2×Q8—741no—
151C2×Q8—741no—
152C2×Q8—741no—
153C2×Q8—741no—
154C2×Q8—741no—
155C2×Q8—741no—
156C2×Q8—741no—
157C2×Q8—741no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—741no—
163C22×C4—741no—
164C22×C4C22×D3711yescharacteristic
165Q16—748no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—741no—
169C2×C8—741no—
170C2×C8—741no—
171C2×C8C4×D3712yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—744no—
176C4⋊C4D14812yes—
177C42—744no—
178C42—741no—
179C42—741no—
180C23D4×D3711yescharacteristic
181Q8—374no—
182Q8—742no—
183Q8—742no—
184Q8—742no—
185Q8—742no—
186Q8—742no—
187Q8—1481no—
188Q8—1481no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—372no—
196C2×C4—742no—
197C2×C4—741no—
198C2×C4—742no—
199C2×C4—742no—
200C2×C4—741no—
201C2×C4—742no—
202C2×C4—741no—
203C2×C4—741no—
204C2×C4—741no—
205C2×C4—1481no—
206C2×C4—1481no—
207C2×C4C2×C4×D3711yescharacteristic
208C2×C4C2×D14811yescharacteristic
209C2×C4#1059696211yescharacteristic
210C2×C4D4×D3711yescharacteristic
211C2×C4D4×D3711yescharacteristic
212C2×C4#1059696611yescharacteristic
213C8—22no—
214C8—1481no—
215C22#1192449811yescharacteristic
216C22#1192450611yescharacteristic
217C22#1192450911yescharacteristic
218C22Q16×D3711yescharacteristic
219C22#1192455511yescharacteristic
220C22#1192456511yescharacteristic
221C22#1192456511yescharacteristic
222C4—42no—
223C4—81no—
224C4—744no—
225C4—742no—
226C4—1481no—
227C4—1482no—
228C4C22⋊C4×D3711yescharacteristic
229C4C4×D14811yescharacteristic
230C4#1192451111yescharacteristic
231C4#1192452111yescharacteristic
232C2#1455741111yescharacteristic
233C2#1455762711yescharacteristic
234C2#1455763911yescharacteristic
235C2#1455769011yescharacteristic
236C2#1455769611yescharacteristic
237C2#1455774211yescharacteristic
238C2#1455775411yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#340C2
socle, prime radicalC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenter#340D37
hypocenterC37#1878
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
12. C2×Dic148C4semidirect
84. C2×Dic37Q16semidirect
127. C37#1878semidirect

Maximal subgroups

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

subgroupindex
C22×Dic1482
C2×#119245012
C2×#119244592
#145574382
#145572872
C37×#3402
#187837