Finite Group Databasebeta

← #18010604

Subgroups — #18010604

Order 4736.

344 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 68 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
1#14558601C211yesmaximal, characteristic, complemented
2#14558525C212yesmaximal
3D37⋊#101C211yesmaximal, characteristic, complemented
4#14558404C212yesmaximal, complemented
5#124×D37C211yesmaximal, characteristic
6D37⋊M16C2212yes—
7Q8×#3866—24no—
8#11924615—22no—
9#11924615C2212yes—
10#11924598—24no—
11#11924597—22no—
12C2×Q8×D37C2211yescharacteristic
13C2×D4×D37C2211yescharacteristic
14#11924525C411yescharacteristic, complemented
15#11924524C411yescharacteristic, complemented
16#11924523C411yescharacteristic, complemented
17#11924522—22no—
18C22⋊C4×D37—22no—
19C42×D37C2211yescharacteristic
20#124×C37C411yescharacteristic, complemented
21C23×D37—21no—
22C2×Q8×C37C2×C411yescharacteristic
23C2×D4×C37C2×C411yescharacteristic
24C2×C22⋊D37—21no—
25Q8×D37—22no—
26Q8×D37—22no—
27D4×D37—22no—
28D4×D37—22no—
29C2×D148C2×C411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37D412yes—
32C2×C4×D37C2311yescharacteristic
33C2×Dic74C2×C411yescharacteristic
34C2×Dic74D412yes—
35C22⋊#3866—22no—
36#10596957—22no—
37C4⋊#3866—24no—
38C4⋊#3866D414yes—
39C4×#3866—24no—
40C4×#3866—22no—
41#10596953—22no—
42D37⋊C8—22no—
43C22⋊C4×C37—22no—
44C42×C37C2×C411yescharacteristic
45C22⋊Dic37—22no—
46#10596938—22no—
47#10596938—22no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C23×C37—21no—
51C22×D37—21no—
52C22×D37—44no—
53C22×D37—41no—
54C22×D37—41no—
55C22×D37C2×D411yescharacteristic
56C2×#3866—24no—
57Q8×C37—22no—
58D4×C37—22no—
59C2×C4×C37—21no—
60C2×C4×C37C22⋊C412yes—
61C2×C4×C37C22×C411yescharacteristic
62C22⋊D37—42no—
63C2×Dic37—21no—
64C2×Dic37C22⋊C412yes—
65C2×Dic37C2×D411yescharacteristic
66D148—22no—
67C4×D37—22no—
68C4×D37—22no—
69C4×D37—42no—
70C4×D37C2×D412yes—
71C4×D37#4112yes—
72Dic74—22no—
73Dic74—24no—
74#64438—42no—
75C22×C37—42no—
76C22×C37—41no—
77C22×C37C2×C22⋊C411yescharacteristic
78C2×D37—22no—
79C2×D37—42no—
80C2×D37—41no—
81C2×D37—82no—
82C2×D37—82no—
83C2×D37#12011yescharacteristic
84C2×D37#12311yescharacteristic
85#3866—44no—
86C4×C37—22no—
87C4×C37—41no—
88C4×C37C4×D412yes—
89Dic37—22no—
90Dic37—41no—
91Dic37#12112yes—
92#1888—371nomaximal, Sylow
93C2×C37—21no—
94C2×C37—81no—
95C2×C37#38611yescharacteristic
96D37—21no—
97D37—81no—
98D37#45412yes—
99C2×#124—371no—
100#519—371no—
101#418—372no—
102C2×#101—371no—
103#339—372no—
104C37#188811yescharacteristic, complemented, Sylow
105C22×Q8—371no—
106C22×D4—371no—
107C2×M16—372no—
108#124—371no—
109#124—371no—
110#124—371no—
111#124—742no—
112#124#386611yescharacteristic, complemented
113C4×Q8—744no—
114#117—372no—
115#117—742no—
116C2×C22⋊C4—742no—
117C2×C42—371no—
118#102—744no—
119#101—742no—
120C24—741no—
121C2×Q8—372no—
122C2×Q8—371no—
123C2×Q8—742no—
124C2×Q8—742no—
125C2×Q8C2×#386611yescharacteristic
126C2×D4—371no—
127C2×D4—742no—
128C2×D4—742no—
129C2×D4—741no—
130C2×D4C2×#386611yescharacteristic
131C22×C4—371no—
132C22×C4—372no—
133C22×C4—741no—
134M16—742no—
135M16—742no—
136C2×C8—742no—
137C4⋊C4—374no—
138C4⋊C4—744no—
139C22⋊C4—22no—
140C22⋊C4—742no—
141C22⋊C4—742no—
142C22⋊C4—742no—
143C22⋊C4—742no—
144C42—371no—
145C42—741no—
146C42—742no—
147C42—744no—
148C42C2×#386611yescharacteristic
149C23—21no—
150C23—371no—
151C23—741no—
152C23—1481no—
153C23—1481no—
154C23—1484no—
155Q8—22no—
156Q8—744no—
157Q8—742no—
158D4—22no—
159D4—742no—
160D4—1482no—
161C2×C4—21no—
162C2×C4—371no—
163C2×C4—372no—
164C2×C4—372no—
165C2×C4—372no—
166C2×C4—742no—
167C2×C4—742no—
168C2×C4—744no—
169C2×C4—741no—
170C2×C4—1482no—
171C2×C4C22⋊#386612yes—
172C2×C4C22×#386611yescharacteristic
173C8—1482no—
174C22—42no—
175C22—41no—
176C22—371no—
177C22—371no—
178C22—2962no—
179C22—2962no—
180C22—742no—
181C22—1482no—
182C22—1481no—
183C22C2×C22⋊#386611yescharacteristic
184C4—22no—
185C4—41no—
186C4—372no—
187C4—742no—
188C4—1481no—
189C4—1484no—
190C4D4×#386612yes—
191C2—21no—
192C2—81no—
193C2—372no—
194C2—2961no—
195C2—741no—
196C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC2×C37#386
prime radicalC2×D4×D37C22
cosocleC2×C4×D37C23
hypercenter#124#3866
hypocenterC37#1888
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14558601C2semidirect
3. D37⋊#101C2semidirect
4. #14558404C2semidirect
14. #11924525C4semidirect
15. #11924524C4semidirect
16. #11924523C4semidirect
20. #124×C37C4semidirect
104. C37#1888semidirect
112. #124#3866semidirect

Maximal subgroups

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

subgroupindex
#145586012
#145585252
D37⋊#1012
#145584042
#124×D372
#188837