Finite Group Databasebeta

← #18010467

Subgroups — #18010467

Order 4736.

292 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D37⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×#11924599C212yesmaximal
3#14558477C211yesmaximal, characteristic
4#14558406C212yesmaximal
5C4×Q8×D37C211yesmaximal, characteristic
6C2×D37⋊C8C2212yes—
7C2×C4⋊#3866C2212yes—
8#11924603—21no—
9C4⋊#64438—21no—
10#11924599—24no—
11(C2×#3866)⋊C4—21no—
12(C2×#3866)⋊C4—21no—
13C2×Q8×D37C2211yescharacteristic
14Q8×Dic37C411yescharacteristic, complemented
15C4×Dic74—21no—
16C4×Dic74C411yescharacteristic, complemented
17#11924501—21no—
18#11924501C411yescharacteristic, complemented
19C4⋊C4×D37—21no—
20C4⋊C4×D37C2211yescharacteristic
21C42×D37—21no—
22C42×D37C2211yescharacteristic
23C4×Q8×C37C411yescharacteristic, complemented
24C22×#3866—22no—
25C2×Q8×C37C2×C411yescharacteristic
26Q8×D37—21no—
27Q8×D37—21no—
28Q8×D37D412yes—
29Q8×D37Q812yes—
30C2×C4×D37—21no—
31C2×C4×D37—21no—
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37C2311yescharacteristic
35C2×Dic74—21no—
36C2×Dic74C2×C411yescharacteristic
37C2×#64438—22no—
38C4⋊#3866—22no—
39C4⋊#3866—22no—
40D37⋊C8—22no—
41D37⋊C8—22no—
42C4⋊C4×C37—21no—
43C4⋊C4×C37C2×C411yescharacteristic
44C42×C37—21no—
45C42×C37C2×C411yescharacteristic
46C4⋊Dic37—21no—
47C4⋊Dic37C2×C411yescharacteristic
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51C4×Dic37—21no—
52C4×Dic37—21no—
53C4×Dic37—21no—
54C4×Dic37C2×C411yescharacteristic
55C4×Dic37D411yescharacteristic
56C4×Dic37D411yescharacteristic
57C22×D37C2×D411yescharacteristic
58C2×#3866—42no—
59C2×#3866—42no—
60C2×#3866—42no—
61Q8×C37—21no—
62Q8×C37C4⋊C412yes—
63C2×C4×C37—21no—
64C2×C4×C37—21no—
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22⋊C411yescharacteristic
67C2×C4×C37C22×C411yescharacteristic
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37C22⋊C411yescharacteristic
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C2×D411yescharacteristic
73C4×D37—22no—
74C4×D37—22no—
75C4×D37—22no—
76C4×D37—22no—
77C4×D37—42no—
78C4×D37C2×D411yescharacteristic
79C4×D37C2×Q811yescharacteristic
80C4×D37#4111yescharacteristic
81C4×D37#4111yescharacteristic
82Dic74—21no—
83Dic74—22no—
84Dic74—22no—
85Dic74C4⋊C412yes—
86#64438—42no—
87C22×C37C2×C22⋊C411yescharacteristic
88C2×D37#12111yescharacteristic
89C2×D37C22⋊Q811yescharacteristic
90C2×D37#13512yes—
91C2×D37#13712yes—
92#3866—82no—
93C4×C37—22no—
94C4×C37—21no—
95C4×C37—21no—
96C4×C37—41no—
97C4×C37C2×C4⋊C411yescharacteristic
98C4×C37#11711yescharacteristic
99Dic37—22no—
100Dic37—21no—
101Dic37—21no—
102Dic37—41no—
103Dic37#12111yescharacteristic
104Dic37C22⋊Q811yescharacteristic
105#1805—371nomaximal, Sylow
106C2×C37#38011yescharacteristic
107C2×C37#41611yescharacteristic
108C2×C37#41911yescharacteristic
109D37#46412yes—
110D37#47912yes—
111C2×C4×Q8—371no—
112C2×C4⋊C8—371no—
113C2×#103—372no—
114#382—371no—
115#340—372no—
116C37#180511yescharacteristic, complemented, Sylow
117C22×Q8—371no—
118C22×C8—372no—
119C4×Q8—371no—
120C4×Q8—371no—
121C4×Q8—371no—
122C4×Q8—741no—
123C4×Q8—741no—
124C4×Q8#386611yescharacteristic, complemented
125C2×C4⋊C4—371no—
126C2×C4⋊C4—372no—
127C2×C4⋊C4—741no—
128C2×C42—371no—
129C2×C42—741no—
130C4⋊C8—741no—
131C4⋊C8—741no—
132#103—744no—
133#95—741no—
134#95—741no—
135C2×Q8—372no—
136C2×Q8—372no—
137C2×Q8—371no—
138C2×Q8—741no—
139C2×Q8—741no—
140C2×Q8—741no—
141C2×Q8C2×#386611yescharacteristic
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—741no—
146C22×C4—741no—
147C22×C4—742no—
148C2×C8—742no—
149C2×C8—742no—
150C2×C8—742no—
151C4⋊C4—21no—
152C4⋊C4—371no—
153C4⋊C4—741no—
154C4⋊C4—741no—
155C4⋊C4—741no—
156C4⋊C4—742no—
157C4⋊C4—742no—
158C4⋊C4—741no—
159C4⋊C4C2×#386611yescharacteristic
160C42—21no—
161C42—371no—
162C42—371no—
163C42—371no—
164C42—741no—
165C42—741no—
166C42—741no—
167C42C2×#386611yescharacteristic
168C23—371no—
169Q8—21no—
170Q8—372no—
171Q8—742no—
172Q8—742no—
173Q8—741no—
174Q8C4⋊#386612yes—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—371no—
178C2×C4—371no—
179C2×C4—371no—
180C2×C4—371no—
181C2×C4—371no—
182C2×C4—371no—
183C2×C4—371no—
184C2×C4—742no—
185C2×C4—742no—
186C2×C4—742no—
187C2×C4—742no—
188C2×C4—741no—
189C2×C4—741no—
190C2×C4—1482no—
191C2×C4—1482no—
192C2×C4—1482no—
193C2×C4—1482no—
194C2×C4C22⋊#386611yescharacteristic
195C2×C4C22⋊#386611yescharacteristic
196C2×C4C22×#386611yescharacteristic
197C8—1482no—
198C22—371no—
199C22—371no—
200C22—372no—
201C22—372no—
202C22C2×C22⋊#386611yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—371no—
208C4—371no—
209C4—2962no—
210C4—742no—
211C4—741no—
212C4—741no—
213C4—1481no—
214C4C2×C4⋊#386611yescharacteristic
215C4#1192461511yescharacteristic
216C2—372no—
217C2—372no—
218C2#1455847511yescharacteristic
219C2#1455852311yescharacteristic
220C2#1455852611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenterC4×Q8#3866
hypocenterC37#1805
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic37C4semidirect
16. C4×Dic74C4semidirect
18. #11924501C4semidirect
23. C4×Q8×C37C4semidirect
116. C37#1805semidirect
124. C4×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊(C4⋊C8)2
C2×#119245992
#145584772
#145584062
C4×Q8×D372
#180537