Finite Group Databasebeta

← #18004081

Subgroups — #18004081

Order 4736.

480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11924566C211yesmaximal, characteristic
2C2×#11924534C211yesmaximal, characteristic, complemented
3#41×Dic37C211yesmaximal, characteristic
4#14557741C214yesmaximal, complemented
5#14557736C214yesmaximal, complemented
6#14557556C211yesmaximal, characteristic, complemented
7#14557543C211yesmaximal, characteristic, complemented
8#14557542C211yesmaximal, characteristic, complemented
9C2×#137×C37C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11#11924566—24no—
12C2×#10596942C2212yes—
13C2×#10596940C2212yes—
14C2×#10596934C2211yescharacteristic
15#11924534—21no—
16#11924534—21no—
17#11924534C2214yes—
18Q8×Dic37C2212yes—
19D4×Dic37—22no—
20D4×Dic37C2212yes—
21#11924495—21no—
22#11924495C2211yescharacteristic
23C2×#10596936—22no—
24C2×C4×Dic37—21no—
25C2×C4×Dic37C2211yescharacteristic
26#11924465C2214yes—
27#11924461C2214yes—
28#11924460C2214yes—
29C2×#41×C37C2211yescharacteristic
30C22×Q8×C37C2211yescharacteristic
31#137×C37—24no—
32C2×Q16×C37C2212yes—
33C2×SD16×C37C2212yes—
34C2×M16×C37C2211yescharacteristic
35#41×C37—22no—
36#41×C37D414yes—
37C2×Q8×C37—21no—
38C2×Q8×C37—22no—
39C2×Q8×C37—22no—
40C2×Q8×C37C2312yes—
41C2×Q8×C37C2311yescharacteristic
42C2×D4×C37—21no—
43C2×D4×C37C2311yescharacteristic
44C22×C4×C37—21no—
45C22×C4×C37—21no—
46C22×C4×C37C2311yescharacteristic
47C22×Dic37—21no—
48C22×Dic37—22no—
49C22×Dic37D412yes—
50C2×Dic74—22no—
51C2×Dic74—22no—
52C2×Dic74—21no—
53C2×Dic74C2312yes—
54Q16×C37—24no—
55SD16×C37—24no—
56M16×C37—22no—
57C2×C8×C37C2312yes—
58C22⋊Dic37—21no—
59C22⋊Dic37—22no—
60#10596942—24no—
61#10596940—24no—
62C4⋊Dic37—22no—
63C4⋊Dic37C2312yes—
64#10596936—24no—
65#10596936—24no—
66C4×Dic37—21no—
67C4×Dic37—22no—
68C4×Dic37D411yescharacteristic
69C4×Dic37D411yescharacteristic
70C4×Dic37C2312yes—
71#10596934—22no—
72C2×#64436C2312yes—
73C23×C37—21no—
74C23×C37C2×D411yescharacteristic
75Q8×C37—21no—
76Q8×C37—22no—
77Q8×C37—22no—
78Q8×C37—42no—
79Q8×C37C2×D412yes—
80D4×C37—24no—
81D4×C37—21no—
82D4×C37C2×D412yes—
83C2×C4×C37—21no—
84C2×C4×C37—24no—
85C2×C4×C37—22no—
86C2×C4×C37—42no—
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D412yes—
89C2×C4×C37#4112yes—
90C2×C4×C37C2411yescharacteristic
91C2×Dic37—24no—
92C2×Dic37—22no—
93C2×Dic37—22no—
94C2×Dic37—42no—
95C2×Dic37—44no—
96C2×Dic37C2×D412yes—
97C2×Dic37C2×D412yes—
98Dic74—22no—
99Dic74—22no—
100Dic74—42no—
101C8×C37—22no—
102#64436—22no—
103C22×C37—22no—
104C22×C37—22no—
105C22×C37—42no—
106C22×C37#12112yes—
107C22×C37C22×D411yescharacteristic
108C4×C37—22no—
109C4×C37—42no—
110C4×C37#12112yes—
111C4×C37C22×D411yescharacteristic
112C4×C37C2×#4111yescharacteristic
113Dic37—22no—
114Dic37—42no—
115Dic37—42no—
116Dic37#13714yescomplemented
117#3039—371nomaximal, Sylow
118C2×C37—22no—
119C2×C37—42no—
120C2×C37C2×#12111yescharacteristic
121C2×C37C2×#13712yes—
122C2×#137—371no—
123C2×#137D3711yescharacteristic
124C2×C4⋊Q8—371no—
125C4×#41—371no—
126#462—374no—
127#461—374no—
128#423—371no—
129#419—371no—
130#419—371no—
131C37#303911yescharacteristic, complemented, Sylow
132C2×#41C2×D3711yescharacteristic
133C22×Q8—371no—
134C22×Q8C2×D3711yescharacteristic
135#137—24no—
136#137—744no—
137C2×Q16—372no—
138C2×Q16C2×D3712yes—
139C2×SD16—372no—
140C2×SD16C2×D3712yes—
141C2×M16—371no—
142C2×M16C2×D3711yescharacteristic
143C4⋊Q8—374no—
144C4⋊Q8—741no—
145C4⋊Q8—741no—
146C4×Q8—372no—
147C4×D4—372no—
148C4×D4—742no—
149#117—371no—
150#117—741no—
151C2×C4⋊C4—742no—
152C2×C42—371no—
153C2×C42—741no—
154C4⋊C8—374no—
155#103—374no—
156#103—374no—
157#41—22no—
158#41C22⋊D3714yes—
159C2×Q8—21no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—372no—
163C2×Q8—741no—
164C2×Q8—742no—
165C2×Q8—742no—
166C2×Q8C22×D3712yes—
167C2×Q8C22×D3711yescharacteristic
168C2×D4—21no—
169C2×D4C22×D3711yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—372no—
173C22×C4—742no—
174C22×C4—741no—
175C22×C4C22×D3711yescharacteristic
176Q16—24no—
177Q16—744no—
178SD16—24no—
179SD16—744no—
180M16—22no—
181M16—742no—
182C2×C8—372no—
183C2×C8C22×D3712yes—
184C4⋊C4—372no—
185C4⋊C4—744no—
186C4⋊C4—744no—
187C4⋊C4—742no—
188C22⋊C4—742no—
189C22⋊C4—741no—
190C42—371no—
191C42—371no—
192C42—372no—
193C42—742no—
194C42—741no—
195C23—21no—
196C23D4×D3711yescharacteristic
197Q8—21no—
198Q8—22no—
199Q8—22no—
200Q8—42no—
201Q8—742no—
202Q8—742no—
203Q8—1482no—
204Q8C2×C22⋊D3712yes—
205D4—24no—
206D4—21no—
207D4C2×C22⋊D3712yes—
208C2×C4—21no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—372no—
213C2×C4—372no—
214C2×C4—744no—
215C2×C4—742no—
216C2×C4—742no—
217C2×C4—1484no—
218C2×C4—1482no—
219C2×C4D4×D3711yescharacteristic
220C2×C4#1059696412yes—
221C2×C4C2×C22⋊D3712yes—
222C2×C4C23×D3711yescharacteristic
223C8—22no—
224C8—742no—
225C22—22no—
226C22—22no—
227C22—42no—
228C22#1192450812yes—
229C22C2×D4×D3711yescharacteristic
230C4—22no—
231C4—42no—
232C4—374no—
233C4—742no—
234C4—1482no—
235C4—1482no—
236C4#1192450812yes—
237C4C22×C22⋊D3711yescharacteristic
238C4C2×#1059696411yescharacteristic
239C2—22no—
240C2—42no—
241C2C2×#1192450811yescharacteristic
242C2#137×D3712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#137×C37C2
socleC22×C37C22×D4
prime radicalC2×#41×C37C22
hypercenterC2×#137D37
hypocenterC37#3039
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#11924534C2semidirect
4. #14557741C2semidirect
5. #14557736C2semidirect
6. #14557556C2semidirect
7. #14557543C2semidirect
8. #14557542C2semidirect
116. Dic37#137semidirect
131. C37#3039semidirect

Maximal subgroups

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

subgroupindex
C2×#119245662
C2×#119245342
#41×Dic372
#145577412
#145577362
#145575562
#145575432
#145575422
C2×#137×C372
#303937