Finite Group Databasebeta

← #17994610

Subgroups — #17994610

Order 4736.

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

normal subgroups only

This group has 292 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×#11924465C211yesmaximal, characteristic
3C2×#11924461C211yesmaximal, characteristic
4C2×#11924459C211yesmaximal, characteristic
5#14557398C211yesmaximal, characteristic
6#14557295C211yesmaximal, characteristic
7C37×#340C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C22×#64436C2211yescharacteristic
10#11924501—22no—
11#11924501C414yescomplemented
12C2×C4⋊Dic37C2211yescharacteristic
13C2×#10596936—21no—
14C2×C4×Dic37—21no—
15C2×C4×Dic37C2211yescharacteristic
16#11924465—22no—
17#11924461—22no—
18#11924459—22no—
19#11924443—21no—
20#11924443—21no—
21C22×C8×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23C2×C4⋊C4×C37C2211yescharacteristic
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×C37—21no—
40C4⋊C4×C37—21no—
41C4⋊C4×C37—21no—
42C4⋊C4×C37—21no—
43C4⋊C4×C37C2×C412yes—
44C4⋊Dic37—21no—
45C4⋊Dic37—21no—
46#10596936—24no—
47C4×Dic37—24no—
48C4×Dic37C2×C412yes—
49C4×Dic37D412yes—
50C2×#64436—21no—
51C2×#64436—21no—
52C2×#64436—21no—
53C23×C37C2×D411yescharacteristic
54C2×C4×C37—22no—
55C2×C4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37C22×C411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×Q811yescharacteristic
64C2×C4×C37#4111yescharacteristic
65C2×C4×C37#4111yescharacteristic
66C2×Dic37—22no—
67C2×Dic37—22no—
68C2×Dic37—22no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—21no—
72C2×Dic37—21no—
73C2×Dic37—41no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37C22⋊C412yes—
77C2×Dic37C22⋊C412yes—
78Dic74—22no—
79Dic74—22no—
80Dic74—22no—
81Dic74C4⋊C414yes—
82C8×C37—41no—
83#64436—41no—
84C22×C37C2×C22⋊C411yescharacteristic
85C22×C37#12111yescharacteristic
86C22×C37C22⋊Q811yescharacteristic
87C22×C37#13511yescharacteristic
88C22×C37#13511yescharacteristic
89C22×C37#13711yescharacteristic
90C22×C37#13711yescharacteristic
91C4×C37—42no—
92C4×C37—81no—
93C4×C37C2×C4⋊C411yescharacteristic
94C4×C37#11711yescharacteristic
95C4×C37#12111yescharacteristic
96C4×C37C22⋊Q811yescharacteristic
97Dic37—24no—
98Dic37—22no—
99Dic37—22no—
100Dic37—81no—
101#1805—371nomaximal, Sylow
102C2×C37#38011yescharacteristic
103C2×C37#41611yescharacteristic
104C2×C37#41911yescharacteristic
105C2×C37#46411yescharacteristic
106C2×C37#46411yescharacteristic
107C2×C37#47911yescharacteristic
108C2×C37#47911yescharacteristic
109C2×C4×Q8—371no—
110C2×C4⋊C8—371no—
111C2×#103—371no—
112C2×#103—371no—
113#382—371no—
114#340—371no—
115#340D3711yescharacteristic
116C37#180511yescharacteristic, complemented, Sylow
117C22×Q8—371no—
118C22×C8—371no—
119C22×C8C2×D3711yescharacteristic
120C4×Q8—374no—
121C4×Q8—742no—
122C2×C4⋊C4—371no—
123C2×C4⋊C4—741no—
124C2×C4⋊C4C2×D3711yescharacteristic
125C2×C4⋊C4C2×D3711yescharacteristic
126C2×C42—371no—
127C2×C42—741no—
128C4⋊C8—742no—
129#103—742no—
130#103—742no—
131#95—741no—
132#95—741no—
133C2×Q8—372no—
134C2×Q8—372no—
135C2×Q8—372no—
136C2×Q8—741no—
137C2×Q8—741no—
138C2×Q8—741no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—741no—
144C22×C4—741no—
145C22×C4C22×D3711yescharacteristic
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—741no—
150C2×C8—741no—
151C2×C8—741no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—744no—
156C4⋊C4—741no—
157C4⋊C4—741no—
158C4⋊C4C4×D3712yes—
159C42—372no—
160C42—372no—
161C42—744no—
162C23D4×D3711yescharacteristic
163Q8—374no—
164Q8—742no—
165Q8—742no—
166Q8—742no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—372no—
174C2×C4—372no—
175C2×C4—742no—
176C2×C4—742no—
177C2×C4—742no—
178C2×C4—741no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—741no—
182C2×C4—1481no—
183C2×C4—1481no—
184C2×C4—1481no—
185C2×C4C2×C4×D3711yescharacteristic
186C2×C4#1059696211yescharacteristic
187C2×C4#1059696211yescharacteristic
188C2×C4D4×D3711yescharacteristic
189C2×C4D4×D3711yescharacteristic
190C2×C4Q8×D3711yescharacteristic
191C8—41no—
192C8—1481no—
193C22C22⋊C4×D3711yescharacteristic
194C22#1192450911yescharacteristic
195C22#1192451411yescharacteristic
196C22#1192455511yescharacteristic
197C22#1192455711yescharacteristic
198C22#1192456511yescharacteristic
199C22#1192456811yescharacteristic
200C4—42no—
201C4—81no—
202C4—2961no—
203C4—742no—
204C4—742no—
205C4—744no—
206C4C4⋊C4×D3711yescharacteristic
207C4#1192449311yescharacteristic
208C4#1192450911yescharacteristic
209C4#1192451411yescharacteristic
210C2#1455739211yescharacteristic
211C2#1455752611yescharacteristic
212C2#1455754011yescharacteristic
213C2#1455775411yescharacteristic
214C2#1455775811yescharacteristic
215C2#1455783911yescharacteristic
216C2#1455784311yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#340C2
socle, prime radicalC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenter#340D37
hypocenterC37#1805
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
11. #11924501C4semidirect
116. C37#1805semidirect

Maximal subgroups

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

subgroupindex
C2×#119245012
C2×#119244652
C2×#119244612
C2×#119244592
#145573982
#145572952
C37×#3402
#180537