Finite Group Databasebeta

← #17994861

Subgroups — #17994861

Order 4736.

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

normal subgroups only

This group has 298 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
1C2×#11924501C211yesmaximal, characteristic
2C2×#11924461C211yesmaximal, characteristic
3C2×#11924459C211yesmaximal, characteristic
4#14557429C211yesmaximal, characteristic
5#14557295C211yesmaximal, characteristic
6#14557287C211yesmaximal, characteristic
7C2×#106×C37C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C22×#64436C2211yescharacteristic
10#11924501—22no—
11#11924501—22no—
12C2×C4⋊Dic37C2211yescharacteristic
13C2×#10596936—21no—
14C2×#10596936—21no—
15C2×C4×Dic37—21no—
16C2×C4×Dic37C2211yescharacteristic
17#11924461C414yescomplemented
18#11924459—22no—
19#11924443—21no—
20C22×C8×C37C2211yescharacteristic
21C2×C4⋊C4×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23#106×C37—22no—
24C22×C4×C37—21no—
25C22×C4×C37—21no—
26C22×C4×C37C2311yescharacteristic
27C22×Dic37—21no—
28C22×Dic37—21no—
29C22×Dic37D411yescharacteristic
30C22×Dic37D411yescharacteristic
31C2×Dic74—21no—
32C2×Dic74—21no—
33C2×Dic74—21no—
34C2×Dic74C2×C412yes—
35C2×Dic74D412yes—
36C2×Dic74Q812yes—
37C2×C8×C37—21no—
38C2×C8×C37—21no—
39C2×C8×C37C2×C412yes—
40C4⋊C4×C37—21no—
41C4⋊C4×C37—21no—
42C4⋊C4×C37—21no—
43C4⋊C4×C37D412yes—
44C4⋊Dic37—21no—
45C4⋊Dic37C2×C412yes—
46#10596936—24no—
47#10596936—42no—
48C4×Dic37—24no—
49C4×Dic37—21no—
50C4×Dic37—21no—
51C2×#64436—21no—
52C2×#64436—21no—
53C2×#64436—21no—
54C23×C37C2×D411yescharacteristic
55C2×C4×C37—22no—
56C2×C4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37C22×C411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×Q811yescharacteristic
65C2×C4×C37#4111yescharacteristic
66C2×C4×C37#4111yescharacteristic
67C2×Dic37—22no—
68C2×Dic37—21no—
69C2×Dic37—22no—
70C2×Dic37—22no—
71C2×Dic37—21no—
72C2×Dic37—22no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—41no—
77C2×Dic37—41no—
78C2×Dic37SD1612yes—
79Dic74—22no—
80Dic74—22no—
81Dic74—22no—
82Dic74C4⋊C414yescomplemented
83C8×C37—22no—
84#64436—41no—
85C22×C37C4×D411yescharacteristic
86C22×C37#12011yescharacteristic
87C22×C37C22⋊Q811yescharacteristic
88C22×C37C2×SD1611yescharacteristic
89C22×C37#13511yescharacteristic
90C22×C37#13711yescharacteristic
91C22×C37#13711yescharacteristic
92C4×C37—42no—
93C4×C37—81no—
94C4×C37C2×C4⋊C411yescharacteristic
95C4×C37C4×D411yescharacteristic
96C4×C37C22⋊Q811yescharacteristic
97C4×C37#12311yescharacteristic
98Dic37—24no—
99Dic37—22no—
100Dic37—42no—
101Dic37—41no—
102#1865—371nomaximal, Sylow
103C2×C37#38511yescharacteristic
104C2×C37C4×SD1611yescharacteristic
105C2×C37#44111yescharacteristic
106C2×C37#44811yescharacteristic
107C2×C37#45211yescharacteristic
108C2×C37#47511yescharacteristic
109C2×C37#47911yescharacteristic
110C2×C4×Q8—371no—
111C2×#106D3711yescharacteristic
112C2×#103—371no—
113C2×#103—371no—
114#389—371no—
115#340—371no—
116#336—371no—
117C37#186511yescharacteristic, complemented, Sylow
118C22×Q8—371no—
119C22×C8—371no—
120C22×C8C2×D3711yescharacteristic
121C4×Q8—742no—
122C4×Q8—742no—
123C2×C4⋊C4—371no—
124C2×C4⋊C4—741no—
125C2×C4⋊C4—741no—
126C2×C4⋊C4C2×D3711yescharacteristic
127C2×C4⋊C4C2×D3711yescharacteristic
128C2×C42—371no—
129C2×C42—741no—
130#106—22no—
131#103—374no—
132#103—742no—
133#95—741no—
134C2×Q8—372no—
135C2×Q8—372no—
136C2×Q8—372no—
137C2×Q8—741no—
138C2×Q8—741no—
139C2×Q8—741no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—741no—
145C22×C4—741no—
146C22×C4C22×D3711yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—741no—
150C2×C8—741no—
151C2×C8—741no—
152C2×C8C4×D3712yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—372no—
157C4⋊C4—744no—
158C4⋊C4—741no—
159C4⋊C4—1482no—
160C4⋊C4C22⋊D3712yes—
161C42—744no—
162C42—741no—
163C42—741no—
164C23D4×D3711yescharacteristic
165Q8—374no—
166Q8—742no—
167Q8—742no—
168Q8—742no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—372no—
176C2×C4—742no—
177C2×C4—741no—
178C2×C4—742no—
179C2×C4—742no—
180C2×C4—741no—
181C2×C4—742no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—1481no—
186C2×C4—1481no—
187C2×C4C2×C4×D3711yescharacteristic
188C2×C4#1059696211yescharacteristic
189C2×C4D4×D3711yescharacteristic
190C2×C4Q8×D3711yescharacteristic
191C2×C4#1059696611yescharacteristic
192C2×C4C2×C22⋊D3711yescharacteristic
193C8—22no—
194C8—1481no—
195C22#1192449811yescharacteristic
196C22#1192450411yescharacteristic
197C22#1192451411yescharacteristic
198C22SD16×D3711yescharacteristic
199C22#1192455711yescharacteristic
200C22#1192456511yescharacteristic
201C22#1192456511yescharacteristic
202C4—42no—
203C4—81no—
204C4—744no—
205C4—742no—
206C4—1482no—
207C4—1481no—
208C4C4⋊C4×D3711yescharacteristic
209C4C4×C22⋊D3711yescharacteristic
210C4#1192451211yescharacteristic
211C4#1192452111yescharacteristic
212C2#1455740411yescharacteristic
213C2#1455762011yescharacteristic
214C2#1455763911yescharacteristic
215C2#1455767011yescharacteristic
216C2#1455769211yescharacteristic
217C2#1455781711yescharacteristic
218C2#1455784311yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#106×C37C2
socle, prime radicalC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenterC2×#106D37
hypocenterC37#1865
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
17. #11924461C4semidirect
82. Dic74C4⋊C4semidirect
117. C37#1865semidirect

Maximal subgroups

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

subgroupindex
C2×#119245012
C2×#119244612
C2×#119244592
#145574292
#145572952
#145572872
C2×#106×C372
#186537