Finite Group Databasebeta

← #18010658

Subgroups — #18010658

Order 4736.

230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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#14558484C211yesmaximal, characteristic
2C4⋊C4×#3866C211yesmaximal, characteristic
3#14558407C211yesmaximal, characteristic
4#14558406C211yesmaximal, characteristic
5#14558406C211yesmaximal, characteristic
6(C2×#3866)⋊C8C211yesmaximal, characteristic
7#106×D37C211yesmaximal, characteristic
8C2×D37⋊C8C2211yescharacteristic
9C2×C4⋊#3866—21no—
10C2×C4⋊#3866C2211yescharacteristic
11C2×C4⋊#3866C2211yescharacteristic
12C2×C4×#3866—21no—
13C2×C4×#3866C2211yescharacteristic
14(C2×#3866)⋊C4—21no—
15(C2×#3866)⋊C4—21no—
16C2×C8×D37C2211yescharacteristic
17C4⋊C4×D37C2211yescharacteristic
18C4⋊C4×D37C2211yescharacteristic
19#11924468C411yescharacteristic, complemented
20#11924467C411yescharacteristic, complemented
21#11924467C411yescharacteristic, complemented
22#106×C37C411yescharacteristic, complemented
23C22×#3866—21no—
24C22×#3866—21no—
25C22×#3866D411yescharacteristic
26C22×#3866D411yescharacteristic
27C2×C4×D37—21no—
28C2×C4×D37—21no—
29C2×C4×D37C2311yescharacteristic
30C2×#64438—21no—
31C4⋊#3866—21no—
32C4⋊#3866—21no—
33C4⋊#3866—21no—
34C4⋊#3866—42no—
35C4⋊#3866Q812yes—
36C4×#3866—21no—
37C4×#3866—21no—
38C4×#3866—42no—
39D37⋊C8—21no—
40D37⋊C8—21no—
41C2×C8×C37C2×C411yescharacteristic
42C4⋊C4×C37C2×C411yescharacteristic
43C4⋊C4×C37C2×C411yescharacteristic
44C4⋊Dic37C2×C411yescharacteristic
45C4⋊Dic37C2×C411yescharacteristic
46#10596936—21no—
47#10596936—21no—
48C2×#64436C2×C411yescharacteristic
49C8×D37—21no—
50C8×D37—21no—
51C22×D37C2×D411yescharacteristic
52C2×#3866—21no—
53C2×#3866—21no—
54C2×#3866—22no—
55C2×#3866—21no—
56C2×#3866—21no—
57C2×#3866—21no—
58C2×#3866—41no—
59C2×#3866—41no—
60C2×#3866—41no—
61C2×#3866—41no—
62C2×#3866—41no—
63C2×#3866SD1612yes—
64C2×C4×C37—21no—
65C2×C4×C37—21no—
66C2×C4×C37C22×C411yescharacteristic
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37#4111yescharacteristic
70C4×D37—41no—
71C4×D37—41no—
72C4×D37—41no—
73C4×D37—41no—
74C4×D37C2×Q811yescharacteristic
75C4×D37#4111yescharacteristic
76C4×D37#4111yescharacteristic
77C4×D37#4111yescharacteristic
78#64438—41no—
79C8×C37—21no—
80#64436—21no—
81C22×C37C4×D411yescharacteristic
82C2×D37C22⋊Q811yescharacteristic
83C2×D37#12311yescharacteristic
84C2×D37C2×SD1611yescharacteristic
85C2×D37#13511yescharacteristic
86C2×D37AGL(1,ℤ/8)11yescharacteristic
87C2×D37#13711yescharacteristic
88#3866—22no—
89#3866—42no—
90#3866—41no—
91#3866—81no—
92C4×C37—41no—
93C4×C37—41no—
94C4×C37#11711yescharacteristic
95C4×C37C4×Q811yescharacteristic
96Dic37—41no—
97Dic37—41no—
98Dic37#12511yescharacteristic
99Dic37#12611yescharacteristic
100#1919—371nomaximal, Sylow
101C2×C37#38711yescharacteristic
102C2×C37C4×SD1611yescharacteristic
103C2×C37#44011yescharacteristic
104D37#47511yescharacteristic
105D37#47811yescharacteristic
106D37#48111yescharacteristic
107D37#48511yescharacteristic
108C2×#106—371no—
109#389—371no—
110C4×C4⋊C4—371no—
111#340—371no—
112#340—371no—
113#340—371no—
114#336—371no—
115C37#191911yescharacteristic, complemented, Sylow
116C22×C8—371no—
117C22×C8—371no—
118C2×C4⋊C4—371no—
119C2×C4⋊C4—371no—
120C2×C4⋊C4—371no—
121C2×C4⋊C4—371no—
122C2×C4⋊C4—741no—
123C2×C42—371no—
124C2×C42—741no—
125#106—371no—
126#106—371no—
127#106—371no—
128#106#386611yescharacteristic, complemented
129#95—741no—
130#95—741no—
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—371no—
134C22×C4—741no—
135C22×C4—741no—
136C22×C4—741no—
137C22×C4—741no—
138C2×C8—371no—
139C2×C8—741no—
140C2×C8—741no—
141C2×C8—741no—
142C2×C8—741no—
143C2×C8—741no—
144C2×C8C2×#386611yescharacteristic
145C4⋊C4—372no—
146C4⋊C4—371no—
147C4⋊C4—371no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4—741no—
153C4⋊C4—1482no—
154C4⋊C4C2×#386611yescharacteristic
155C4⋊C4C2×#386611yescharacteristic
156C42—741no—
157C42—741no—
158C42—1482no—
159C23—371no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—371no—
165C2×C4—371no—
166C2×C4—371no—
167C2×C4—372no—
168C2×C4—741no—
169C2×C4—741no—
170C2×C4—741no—
171C2×C4—742no—
172C2×C4—741no—
173C2×C4—741no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—1481no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4—1481no—
183C2×C4—1481no—
184C2×C4—1481no—
185C2×C4C22×#386611yescharacteristic
186C8—21no—
187C8—741no—
188C8—1481no—
189C22—371no—
190C22—371no—
191C22—371no—
192C22—371no—
193C22—371no—
194C22—371no—
195C22D4×#386611yescharacteristic
196C4—41no—
197C4—41no—
198C4—371no—
199C4—371no—
200C4—2961no—
201C4—742no—
202C4—1481no—
203C4—1482no—
204C4—1481no—
205C4—1481no—
206C4#1192461511yescharacteristic
207C4Q8×#386611yescharacteristic
208C2—371no—
209C2—371no—
210C2—371no—
211C2—371no—
212C2#1455848211yescharacteristic
213C2SD16×#386611yescharacteristic
214C2#1455857211yescharacteristic
subgroupG/H
centerC22D4×#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#106×C37C4
socleC22×C37C4×D4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenter#106#3866
hypocenterC37#1919
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
19. #11924468C4semidirect
20. #11924467C4semidirect
21. #11924467C4semidirect
22. #106×C37C4semidirect
115. C37#1919semidirect
128. #106#3866semidirect

Maximal subgroups

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

subgroupindex
#145584842
C4⋊C4×#38662
#145584072
#145584062
(C2×#3866)⋊C82
#106×D372
#191937