Finite Group Databasebeta

← #18010606

Subgroups — #18010606

Order 4736.

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

normal subgroups only

This group has 386 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#14558600C211yesmaximal, characteristic
2D37⋊#99C211yesmaximal, characteristic
3#14558476C212yesmaximal, complemented
4#14558410C212yesmaximal, complemented
5#123×D37C211yesmaximal, characteristic
6D4×#3866—24no—
7#11924615—21no—
8C2×C22⋊#3866—21no—
9C2×C22⋊#3866C2212yes—
10C2×C22⋊#3866C2212yes—
11#11924595—21no—
12#11924594—21no—
13(C2×#3866)⋊C4—24no—
14C2×D4×D37C2211yescharacteristic
15C22×C4×D37C2211yescharacteristic
16#11924521—21no—
17#11924520C411yescharacteristic, complemented
18#11924519C411yescharacteristic, complemented
19#11924518—21no—
20#11924517C411yescharacteristic, complemented
21C4⋊C4×D37—21no—
22C22⋊C4×D37—21no—
23C22⋊C4×D37C2211yescharacteristic
24#123×C37C411yescharacteristic, complemented
25C23×D37D411yescharacteristic
26C23×D37C2311yescharacteristic
27C22×#3866—22no—
28C22×#3866—22no—
29C22×#3866D414yes—
30C2×D4×C37C2×C411yescharacteristic
31C22×C4×C37C2×C411yescharacteristic, complemented
32C2×C22⋊D37C2×C411yescharacteristic
33C2×C22⋊D37D411yescharacteristic
34C22×Dic37C2×C411yescharacteristic, complemented
35D4×D37—22no—
36D4×D37—22no—
37C2×D148D411yescharacteristic
38C2×C4×D37—21no—
39C2×C4×D37—21no—
40C2×C4×D37—21no—
41C2×C4×D37—22no—
42C2×C4×D37—22no—
43C2×C4×D37D411yescharacteristic
44C22⋊#3866—22no—
45C22⋊#3866—22no—
46C22⋊#3866—22no—
47C22⋊#3866—22no—
48C22⋊#3866—22no—
49C4⋊#3866—22no—
50C4×#3866—22no—
51C4⋊C4×C37—21no—
52C22⋊C4×C37—21no—
53C22⋊C4×C37C2×C411yescharacteristic, complemented
54C22⋊Dic37—21no—
55C22⋊Dic37C2×C411yescharacteristic, complemented
56#10596938—21no—
57#10596938—21no—
58#10596938—21no—
59C4⋊Dic37—21no—
60#10596936—21no—
61#10596936—21no—
62C23×C37C22⋊C411yescharacteristic
63C23×C37C22×C411yescharacteristic
64C22×D37—21no—
65C22×D37—21no—
66C22×D37—42no—
67C22×D37—42no—
68C22×D37C22⋊C411yescharacteristic
69C22×D37C2×D412yes—
70C22×D37C2×D411yescharacteristic
71C22×D37C2×D411yescharacteristic
72C22×D37#4112yes—
73C2×#3866—24no—
74C2×#3866—44no—
75C2×#3866—44no—
76C2×#3866—42no—
77C2×#3866—82no—
78D4×C37—22no—
79C2×C4×C37—21no—
80C2×C4×C37—21no—
81C2×C4×C37—22no—
82C2×C4×C37C22⋊C411yescharacteristic
83C22⋊D37—22no—
84C22⋊D37—22no—
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—22no—
88C2×Dic37C22⋊C411yescharacteristic
89D148—22no—
90C4×D37—21no—
91C4×D37—21no—
92C4×D37—42no—
93C4×D37—41no—
94C4×D37—42no—
95C4×D37—41no—
96C22×C37—21no—
97C22×C37—41no—
98C22×C37—41no—
99C22×C37C2×C22⋊C411yescharacteristic
100C22×C37C4×D412yes—
101C2×D37—22no—
102C2×D37—24no—
103C2×D37—21no—
104C2×D37—41no—
105C2×D37—42no—
106C2×D37—42no—
107C2×D37—41no—
108C2×D37—81no—
109C2×D37#12011yescharacteristic
110C2×D37#12112yes—
111C2×D37#12311yescharacteristic
112#3866—44no—
113#3866—82no—
114C4×C37—21no—
115C4×C37—41no—
116C4×C37—41no—
117Dic37—21no—
118Dic37—41no—
119Dic37—41no—
120#1890—371nomaximal, Sylow
121C2×C37—21no—
122C2×C37—22no—
123C2×C37—41no—
124C2×C37#38611yescharacteristic
125D37—22no—
126D37—21no—
127D37—41no—
128D37#45812yes—
129C2×#123—371no—
130#518—371no—
131C2×#99—371no—
132#381—372no—
133#342—372no—
134C37#189011yescharacteristic, complemented, Sylow
135C22×D4—371no—
136C23×C4—371no—
137#123—371no—
138#123—371no—
139#123—371no—
140#123—741no—
141#123—741no—
142#123#386611yescharacteristic, complemented
143C4×D4—744no—
144#117—741no—
145C2×C4⋊C4—741no—
146C2×C22⋊C4—371no—
147C2×C22⋊C4—372no—
148C2×C22⋊C4—372no—
149C2×C22⋊C4—741no—
150C2×C22⋊C4—741no—
151#99—741no—
152#99—741no—
153#95—744no—
154C24—371no—
155C24—371no—
156C2×D4—371no—
157C2×D4—371no—
158C2×D4—371no—
159C2×D4—742no—
160C2×D4—742no—
161C2×D4C2×#386611yescharacteristic
162C22×C4—371no—
163C22×C4—371no—
164C22×C4—374no—
165C22×C4—742no—
166C22×C4—741no—
167C22×C4—741no—
168C22×C4—741no—
169C22×C4—742no—
170C22×C4—742no—
171C22×C4—742no—
172C22×C4C2×#386611yescharacteristic, complemented
173C4⋊C4—21no—
174C4⋊C4—741no—
175C4⋊C4—741no—
176C4⋊C4—742no—
177C4⋊C4—741no—
178C22⋊C4—21no—
179C22⋊C4—371no—
180C22⋊C4—741no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C22⋊C4—742no—
184C22⋊C4—742no—
185C22⋊C4—742no—
186C22⋊C4—741no—
187C22⋊C4—742no—
188C22⋊C4—742no—
189C22⋊C4C2×#386611yescharacteristic, complemented
190C42—742no—
191C23—371no—
192C23—372no—
193C23—371no—
194C23—372no—
195C23—371no—
196C23—741no—
197C23—741no—
198C23—1482no—
199C23—1482no—
200C23C22⋊#386611yescharacteristic
201C23C22×#386611yescharacteristic
202D4—22no—
203D4—742no—
204D4—742no—
205D4—742no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—371no—
210C2×C4—2962no—
211C2×C4—741no—
212C2×C4—741no—
213C2×C4—744no—
214C2×C4—741no—
215C2×C4—741no—
216C2×C4—742no—
217C2×C4—1481no—
218C2×C4—1481no—
219C2×C4—1482no—
220C2×C4—1482no—
221C2×C4—1482no—
222C2×C4—1484no—
223C2×C4—1484no—
224C2×C4C22⋊#386611yescharacteristic
225C22—21no—
226C22—41no—
227C22—41no—
228C22—371no—
229C22—371no—
230C22—372no—
231C22—2961no—
232C22—744no—
233C22—742no—
234C22—741no—
235C22—1481no—
236C22—1482no—
237C22—1481no—
238C22—1482no—
239C22C2×C22⋊#386611yescharacteristic
240C22D4×#386612yes—
241C4—21no—
242C4—41no—
243C4—41no—
244C4—2962no—
245C4—741no—
246C4—1481no—
247C4—1484no—
248C4—1481no—
249C2—21no—
250C2—22no—
251C2—41no—
252C2—372no—
253C2—742no—
254C2—741no—
255C2—1481no—
256C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#123×C37C4
socleC2×C37#386
prime radicalC2×D4×D37C22
cosocleC23×D37C23
hypercenter#123#3866
hypocenterC37#1890
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #14558476C2semidirect
4. #14558410C2semidirect
17. #11924520C4semidirect
18. #11924519C4semidirect
20. #11924517C4semidirect
24. #123×C37C4semidirect
31. C22×C4×C37C2×C4semidirect
34. C22×Dic37C2×C4semidirect
53. C22⋊C4×C37C2×C4semidirect
55. C22⋊Dic37C2×C4semidirect
134. C37#1890semidirect
142. #123#3866semidirect
172. C22×C4C2×#3866semidirect
189. C22⋊C4C2×#3866semidirect

Maximal subgroups

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

subgroupindex
#145586002
D37⋊#992
#145584762
#145584102
#123×D372
#189037