Finite Group Databasebeta

← #17995814

Subgroups — #17995814

Order 4736.

278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558107C211yesmaximal, characteristic
2#14557575C211yesmaximal, characteristic, complemented
3C2×#11924462C211yesmaximal, characteristic
4#14557535C211yesmaximal, characteristic
5#14557440C211yesmaximal, characteristic, complemented
6#14557294C211yesmaximal, characteristic, complemented
7C2×#101×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924534—21no—
10#11924525—21no—
11#11924519—22no—
12#11924512—21no—
13#11924512—21no—
14#11924495C2211yescharacteristic
15C2×C4⋊Dic37C2211yescharacteristic
16C2×C4×Dic37C2211yescharacteristic
17#11924470—21no—
18#11924468—21no—
19#11924462—22no—
20#11924461—21no—
21#11924458—21no—
22#11924443—22no—
23C22×Q8×C37C2211yescharacteristic
24C2×M16×C37C2211yescharacteristic
25C2×M16×C37C2211yescharacteristic
26#101×C37—22no—
27C2×Q8×C37—21no—
28C2×Q8×C37—21no—
29C2×Q8×C37—21no—
30C2×Q8×C37—21no—
31C2×Q8×C37—21no—
32C2×Q8×C37—21no—
33C22×C4×C37D412yes—
34C22×C4×C37C2311yescharacteristic
35C2×C22⋊D37—21no—
36C22×Dic37—21no—
37C22×Dic37—21no—
38#10596962—21no—
39#10596962—21no—
40#10596962—21no—
41#10596962—21no—
42C2×D148D411yescharacteristic
43C2×C4×D37—21no—
44C2×Dic74D411yescharacteristic
45M16×C37—21no—
46M16×C37—21no—
47M16×C37—21no—
48M16×C37D412yes—
49C2×C8×C37—21no—
50C2×C8×C37—21no—
51C22⋊Dic37—21no—
52#10596938—22no—
53#10596938—22no—
54C4⋊Dic37—21no—
55C4⋊Dic37—21no—
56C4⋊Dic37D411yescharacteristic
57C4⋊Dic37D411yescharacteristic
58#10596936—22no—
59#10596936—22no—
60C4×Dic37—21no—
61C4×Dic37—21no—
62C4×Dic37—21no—
63C23×C37C2×D411yescharacteristic
64C22×D37—21no—
65Q8×C37—41no—
66Q8×C37—41no—
67Q8×C37—41no—
68Q8×C37—41no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37#4111yescharacteristic
76C2×C4×C37#4111yescharacteristic
77C2×C4×C37#4111yescharacteristic
78C22⋊D37—41no—
79C22⋊D37—41no—
80C2×Dic37—22no—
81C2×Dic37—21no—
82C2×Dic37—21no—
83C2×Dic37—21no—
84C2×Dic37—41no—
85C2×Dic37—41no—
86C2×Dic37—42no—
87C2×Dic37—41no—
88D148—21no—
89D148—21no—
90C4×D37—41no—
91C4×D37—41no—
92Dic74—21no—
93Dic74—21no—
94C8×C37—22no—
95C8×C37—41no—
96C22×C37—21no—
97C22×C37—21no—
98C22×C37#12011yescharacteristic
99C22×C37#12111yescharacteristic
100C22×C37#12311yescharacteristic
101C2×D37—41no—
102C2×D37—41no—
103C2×D37—41no—
104C4×C37—42no—
105C4×C37#12111yescharacteristic
106C4×C37#12111yescharacteristic
107C4×C37#12311yescharacteristic
108C4×C37#12411yescharacteristic
109Dic37—42no—
110Dic37—41no—
111Dic37—41no—
112Dic37—41no—
113Dic37—81no—
114#2038—371nomaximal, Sylow
115C2×C37—21no—
116C2×C37—21no—
117C2×C37#39411yescharacteristic
118C2×C37#45411yescharacteristic
119C2×C37#45611yescharacteristic
120D37—81no—
121#536—371no—
122#428—371no—
123C2×#104—371no—
124#417—371no—
125C2×#101D3711yescharacteristic, complemented
126#391—371no—
127#339—371no—
128C37#203811yescharacteristic, complemented, Sylow
129C2×#41—371no—
130C22×Q8C2×D3711yescharacteristic
131C2×M16C2×D3711yescharacteristic
132C2×M16C2×D3711yescharacteristic
133C4⋊Q8—741no—
134#124—741no—
135#123—742no—
136C22⋊Q8—741no—
137C22⋊Q8—741no—
138#117—371no—
139C2×C4⋊C4—371no—
140C2×C42—371no—
141#107—741no—
142#106—741no—
143#104—742no—
144#103—741no—
145#102—741no—
146#101—22no—
147#95—742no—
148#41—741no—
149#41—741no—
150#41—741no—
151#41—741no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—371no—
159C2×D4—371no—
160C2×D4—741no—
161C22×C4—741no—
162C22×C4—741no—
163C22×C4—741no—
164C22×C4D14812yes—
165C22×C4C22×D3711yescharacteristic
166M16—21no—
167M16—21no—
168M16—21no—
169M16C22⋊D3712yes—
170C2×C8—21no—
171C2×C8—21no—
172C4⋊C4—371no—
173C4⋊C4—371no—
174C4⋊C4—742no—
175C4⋊C4—742no—
176C4⋊C4—741no—
177C4⋊C4—741no—
178C22⋊C4—742no—
179C22⋊C4—742no—
180C22⋊C4—741no—
181C42—741no—
182C42—741no—
183C42—741no—
184C23—741no—
185C23C2×D14811yescharacteristic
186Q8—41no—
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—741no—
191Q8—741no—
192D4—741no—
193D4—741no—
194D4—1481no—
195D4—1481no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—742no—
200C2×C4—741no—
201C2×C4—741no—
202C2×C4—741no—
203C2×C4—1482no—
204C2×C4—1481no—
205C2×C4—1481no—
206C2×C4—1481no—
207C2×C4—1481no—
208C2×C4—1481no—
209C2×C4#1059696211yescharacteristic
210C2×C4D4×D3711yescharacteristic
211C2×C4D4×D3711yescharacteristic
212C2×C4#1059696411yescharacteristic
213C2×C4#1059696411yescharacteristic
214C2×C4C2×C22⋊D3711yescharacteristic
215C8—22no—
216C8—41no—
217C22—21no—
218C22—21no—
219C22—1481no—
220C22—1481no—
221C22—1481no—
222C22#1192450611yescharacteristic
223C22#1192451011yescharacteristic
224C22#1192452011yescharacteristic
225C4—42no—
226C4—2961no—
227C4—1482no—
228C4—1481no—
229C4—1481no—
230C4—1481no—
231C4#1192450711yescharacteristic
232C4#1192450811yescharacteristic
233C4#1192451811yescharacteristic
234C4#1192452211yescharacteristic
235C2—21no—
236C2—21no—
237C2—2961no—
238C2#1455744911yescharacteristic
239C2#1455770811yescharacteristic
240C2#1455771811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#101×C37C2
socleC22×C37#120
prime radicalC2×#10596962C22
hypercenterC2×#101D37
hypocenterC37#2038
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #14557575C2semidirect
5. #14557440C2semidirect
6. #14557294C2semidirect
7. C2×#101×C37C2semidirect
125. C2×#101D37semidirect
128. C37#2038semidirect

Maximal subgroups

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

subgroupindex
#145581072
#145575752
C2×#119244622
#145575352
#145574402
#145572942
C2×#101×C372
#203837