Finite Group Databasebeta

← #18010681

Subgroups — #18010681

Order 4736.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558544C211yesmaximal, characteristic
2#14558526C211yesmaximal, characteristic
3C2×#11924599C211yesmaximal, characteristic
4#14558499C211yesmaximal, characteristic
5#14558412C211yesmaximal, characteristic
6#14558408C211yesmaximal, characteristic
7#101×D37C211yesmaximal, characteristic
8D37⋊M16C2211yescharacteristic
9C2×D37⋊C8C2211yescharacteristic
10#11924615C2211yescharacteristic
11C2×C4⋊#3866C2211yescharacteristic
12#11924605—21no—
13#11924604—21no—
14#11924599—21no—
15#11924599—21no—
16#11924599—21no—
17#11924599—21no—
18#11924590—21no—
19C8×#3866—21no—
20C2×Q8×D37C2211yescharacteristic
21M16×D37C2211yescharacteristic
22M16×D37C2211yescharacteristic
23#11924455C411yescharacteristic, complemented
24#11924454C411yescharacteristic, complemented
25#11924454C411yescharacteristic, complemented
26#101×C37C411yescharacteristic, complemented
27C22×#3866—21no—
28C2×Q8×C37C2×C411yescharacteristic
29Q8×D37—21no—
30Q8×D37—21no—
31Q8×D37—21no—
32Q8×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37C2311yescharacteristic
35C2×Dic74—21no—
36C2×Dic74C2×C411yescharacteristic
37C22⋊#3866—21no—
38#10596957—21no—
39C2×#64438—21no—
40C4⋊#3866—21no—
41C4⋊#3866—21no—
42C4⋊#3866D411yescharacteristic
43C4⋊#3866D411yescharacteristic
44C4×#3866—21no—
45#10596953—21no—
46D37⋊C8—21no—
47D37⋊C8—21no—
48D37⋊C8D411yescharacteristic
49D37⋊C8D411yescharacteristic
50M16×C37C2×C411yescharacteristic
51M16×C37C2×C411yescharacteristic
52#10596934C2×C411yescharacteristic
53#10596934C2×C411yescharacteristic
54#10596929—21no—
55#10596929—21no—
56C8×D37—21no—
57C8×D37—21no—
58C22×D37#4111yescharacteristic
59C2×#3866—21no—
60C2×#3866—21no—
61C2×#3866—41no—
62C2×#3866—81no—
63Q8×C37—21no—
64Q8×C37—21no—
65C2×C4×C37—21no—
66C2×C4×C37C22×C411yescharacteristic
67C2×Dic37—21no—
68C2×Dic37#4111yescharacteristic
69C4×D37—41no—
70C4×D37—41no—
71C4×D37C2×D411yescharacteristic
72C4×D37C2×D411yescharacteristic
73C4×D37#4111yescharacteristic
74C4×D37#4111yescharacteristic
75Dic74—21no—
76Dic74—21no—
77Dic74—41no—
78Dic74—41no—
79#64438—21no—
80#64438—21no—
81#64438—41no—
82C8×C37—21no—
83C8×C37—21no—
84#64436—21no—
85#64436—21no—
86C22×C37#11711yescharacteristic
87C2×D37—21no—
88C2×D37—21no—
89C2×D37#12111yescharacteristic
90C2×D37#12611yescharacteristic
91#3866—41no—
92#3866—41no—
93#3866—81no—
94C4×C37—41no—
95C4×C37C4×D411yescharacteristic
96C4×C37C4×D411yescharacteristic
97Dic37—41no—
98Dic37#12311yescharacteristic
99Dic37#12411yescharacteristic
100#1930—371nomaximal, Sylow
101C2×C37—21no—
102C2×C37#38811yescharacteristic
103D37—21no—
104D37#47111yescharacteristic
105D37#47311yescharacteristic
106#428—371no—
107#419—371no—
108C2×#103—371no—
109C2×#101—371no—
110#405—371no—
111#343—371no—
112#341—371no—
113C37#193011yescharacteristic, complemented, Sylow
114C22×Q8—371no—
115C2×M16—371no—
116C2×M16—371no—
117C2×M16—371no—
118C22×C8—371no—
119#117—371no—
120C2×C4⋊C4—371no—
121#107—741no—
122#106—741no—
123#103—741no—
124#103—741no—
125#103—741no—
126#103—741no—
127#101—371no—
128#101—371no—
129#101—371no—
130#101#386611yescharacteristic, complemented
131#97—741no—
132C4×C8—741no—
133C2×Q8—371no—
134C2×Q8—741no—
135C2×Q8—741no—
136C2×Q8—741no—
137C2×Q8—741no—
138C2×Q8—741no—
139C2×Q8C2×#386611yescharacteristic
140C22×C4—371no—
141C22×C4—741no—
142C22×C4—741no—
143M16—371no—
144M16—371no—
145M16—741no—
146M16—741no—
147M16—741no—
148M16—741no—
149M16C2×#386611yescharacteristic
150M16C2×#386611yescharacteristic
151C2×C8—371no—
152C2×C8—371no—
153C2×C8—741no—
154C2×C8—741no—
155C2×C8—741no—
156C2×C8—741no—
157C2×C8—741no—
158C4⋊C4—371no—
159C4⋊C4—371no—
160C4⋊C4—741no—
161C4⋊C4—741no—
162C22⋊C4—741no—
163C42—741no—
164C23—371no—
165Q8—21no—
166Q8—21no—
167Q8—741no—
168Q8—741no—
169Q8—1481no—
170Q8—1481no—
171C2×C4—21no—
172C2×C4—371no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—371no—
176C2×C4—371no—
177C2×C4—2961no—
178C2×C4—741no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—1481no—
182C2×C4—1481no—
183C2×C4—1481no—
184C2×C4C22×#386611yescharacteristic
185C8—21no—
186C8—21no—
187C8—741no—
188C8—741no—
189C8—741no—
190C8—741no—
191C8—1481no—
192C22—371no—
193C22—371no—
194C22—741no—
195C22—741no—
196C22#1192461511yescharacteristic
197C4—41no—
198C4—371no—
199C4—371no—
200C4—2961no—
201C4—1481no—
202C4—1481no—
203C4—1481no—
204C4D4×#386611yescharacteristic
205C4D4×#386611yescharacteristic
206C2—21no—
207C2—371no—
208C2—371no—
209C2—741no—
210C2#1455848311yescharacteristic
subgroupG/H
centerC2#14558483
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#101×C37C4
socleC2×C37#388
prime radicalC22×D37#41
cosocleC2×C4×D37C23
hypercenter#101#3866
hypocenterC37#1930
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
23. #11924455C4semidirect
24. #11924454C4semidirect
25. #11924454C4semidirect
26. #101×C37C4semidirect
113. C37#1930semidirect
130. #101#3866semidirect

Maximal subgroups

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

subgroupindex
#145585442
#145585262
C2×#119245992
#145584992
#145584122
#145584082
#101×D372
#193037