Finite Group Databasebeta

← #18010678

Subgroups — #18010678

Order 4736.

224 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 60 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×#11924606C211yesmaximal, characteristic, complemented
2C2×#11924600C211yesmaximal, characteristic
3#14558507C211yesmaximal, characteristic
4#14558498C211yesmaximal, characteristic, complemented
5#14558403C211yesmaximal, characteristic, complemented
6(C2×#3866)⋊C8C211yesmaximal, characteristic, complemented
7#14557526C211yesmaximal, characteristic
8C2×#10596953C2211yescharacteristic
9C2×#10596953C2211yescharacteristic
10C2×D37⋊C8C2211yescharacteristic
11C2×C4×#3866C2211yescharacteristic
12#11924606—22no—
13#11924600—22no—
14C22⋊#64438—21no—
15C22⋊#64438—21no—
16#11924591—21no—
17C4×#64438—21no—
18C2×#10596964C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic
20#11924494C2211yescharacteristic
21#11924461C411yescharacteristic, complemented
22#11924459C411yescharacteristic, complemented
23#11924457C411yescharacteristic, complemented
24#102×C37C411yescharacteristic, complemented
25C22×#3866—21no—
26C2×D4×C37C2×C411yescharacteristic
27C2×C22⋊D37—21no—
28C22×Dic37—21no—
29#10596964—21no—
30#10596964—21no—
31#10596964—21no—
32#10596964—21no—
33C2×C4×D37C2311yescharacteristic
34C2×Dic74C2×C411yescharacteristic
35C2×#64438—21no—
36C2×#64438—21no—
37C2×#64438D411yescharacteristic
38C2×#64438D411yescharacteristic
39C4×#3866—21no—
40C4×#3866—21no—
41#10596953—21no—
42#10596953—21no—
43#10596953—21no—
44#10596953D412yes—
45D37⋊C8—21no—
46D37⋊C8—21no—
47C2×C8×C37C2×C411yescharacteristic
48C4⋊C4×C37C2×C411yescharacteristic
49#10596938—21no—
50C4⋊Dic37C2×C411yescharacteristic
51C4×Dic37—21no—
52C2×#64436C2×C411yescharacteristic
53C8×D37—21no—
54C8×D37—21no—
55C23×C37—21no—
56C22×D37#4111yescharacteristic
57C2×#3866—22no—
58C2×#3866—41no—
59C2×#3866—41no—
60D4×C37—21no—
61D4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37C22×C411yescharacteristic
64C22⋊D37—41no—
65C22⋊D37—41no—
66C2×Dic37—21no—
67C2×Dic37—21no—
68C2×Dic37—41no—
69C2×Dic37—41no—
70C2×Dic37C2×D411yescharacteristic
71C4×D37C2×D411yescharacteristic
72C4×D37#4111yescharacteristic
73C4×D37#4111yescharacteristic
74C4×D37#4111yescharacteristic
75Dic74—21no—
76Dic74—21no—
77#64438—22no—
78#64438—21no—
79#64438—21no—
80#64438—41no—
81C8×C37—21no—
82#64436—21no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37C4×D411yescharacteristic
87C2×D37—21no—
88C2×D37—21no—
89C2×D37#12411yescharacteristic
90C2×D37#12611yescharacteristic
91#3866—42no—
92C4×C37—41no—
93C4×C37#11711yescharacteristic
94C4×C37C4×D411yescharacteristic
95Dic37—41no—
96Dic37—41no—
97Dic37#12111yescharacteristic
98Dic37#12311yescharacteristic
99#1929—371nomaximal, Sylow
100C2×C37—81no—
101C2×C37#38811yescharacteristic
102C2×C37#44311yescharacteristic
103C2×C37#44411yescharacteristic
104D37—21no—
105D37—21no—
106C2×#108—371no—
107C2×#104—371no—
108#416—371no—
109#408—371no—
110#405—371no—
111#339—371no—
112#336—371no—
113C37#192911yescharacteristic, complemented, Sylow
114C2×#41—371no—
115C2×M16—371no—
116C2×M16—371no—
117C22×C8—371no—
118C22×C8—371no—
119#117—371no—
120C2×C42—371no—
121#108—742no—
122#104—742no—
123#103—371no—
124#103—371no—
125#102—371no—
126#102#386611yescharacteristic, complemented
127C22⋊C8—741no—
128C22⋊C8—741no—
129#97—741no—
130C4×C8—741no—
131#41—741no—
132#41—741no—
133#41—741no—
134#41—741no—
135C2×Q8—371no—
136C2×D4—741no—
137C2×D4C2×#386611yescharacteristic
138C22×C4—371no—
139C22×C4—741no—
140C22×C4—741no—
141M16—372no—
142M16—741no—
143M16—741no—
144M16—741no—
145C2×C8—371no—
146C2×C8—371no—
147C2×C8—371no—
148C2×C8—741no—
149C2×C8—741no—
150C2×C8—741no—
151C2×C8—741no—
152C2×C8—741no—
153C2×C8—741no—
154C2×C8C2×#386611yescharacteristic
155C4⋊C4—371no—
156C4⋊C4C2×#386611yescharacteristic
157C22⋊C4—741no—
158C42—741no—
159C42—741no—
160C42—741no—
161C23—21no—
162C23—371no—
163Q8—741no—
164Q8—741no—
165D4—21no—
166D4—21no—
167D4—1481no—
168D4—1481no—
169C2×C4—21no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—371no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—742no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—1481no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4C22×#386611yescharacteristic
183C8—21no—
184C8—741no—
185C8—741no—
186C8—742no—
187C8—741no—
188C8—1481no—
189C22—41no—
190C22—41no—
191C22—41no—
192C22—371no—
193C22—371no—
194C22—741no—
195C22—741no—
196C22D4×#386611yescharacteristic
197C4—41no—
198C4—371no—
199C4—371no—
200C4—1482no—
201C4—1481no—
202C4—1481no—
203C4#1192461511yescharacteristic
204C4D4×#386611yescharacteristic
205C2—81no—
206C2—741no—
207C2—741no—
208C2#1455848311yescharacteristic
209C2#1455857611yescharacteristic
210C2#1455858011yescharacteristic
subgroupG/H
centerC22D4×#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#102×C37C4
socleC22×C37C4×D4
prime radicalC2×#10596964C22
cosocleC2×C4×D37C23
hypercenter#102#3866
hypocenterC37#1929
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#11924606C2semidirect
4. #14558498C2semidirect
5. #14558403C2semidirect
6. (C2×#3866)⋊C8C2semidirect
21. #11924461C4semidirect
22. #11924459C4semidirect
23. #11924457C4semidirect
24. #102×C37C4semidirect
113. C37#1929semidirect
126. #102#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246062
C2×#119246002
#145585072
#145584982
#145584032
(C2×#3866)⋊C82
#145575262
#192937