Finite Group Databasebeta

← #17995816

Subgroups — #17995816

Order 4736.

278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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#14558109C211yesmaximal, characteristic
2#14557576C211yesmaximal, characteristic, complemented
3C2×#11924464C211yesmaximal, characteristic
4#14557535C211yesmaximal, characteristic
5C2×#11924454C211yesmaximal, characteristic, complemented
6#14557439C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10C2×#10596934C2211yescharacteristic
11#11924536—21no—
12#11924524—21no—
13#11924520—22no—
14#11924516—21no—
15#11924516—21no—
16C2×C4⋊Dic37C2211yescharacteristic
17#11924469—21no—
18#11924467—21no—
19#11924464—22no—
20#11924461—21no—
21#11924458—21no—
22#11924454—22no—
23#11924443—22no—
24C2×M16×C37C2211yescharacteristic
25#117×C37C2211yescharacteristic
26C2×C42×C37C2211yescharacteristic
27C22×C4×C37—21no—
28C22×C4×C37C2311yescharacteristic
29C2×C22⋊D37—21no—
30C22×Dic37—21no—
31C22×Dic37D412yes—
32#10596962—21no—
33#10596962—21no—
34#10596962—21no—
35#10596962—21no—
36C2×D148D411yescharacteristic
37C2×C4×D37—21no—
38C2×Dic74—21no—
39C2×Dic74—21no—
40C2×Dic74—21no—
41C2×Dic74—21no—
42C2×Dic74—21no—
43C2×Dic74—21no—
44C2×Dic74D411yescharacteristic
45M16×C37—21no—
46M16×C37—21no—
47C2×C8×C37—21no—
48C4⋊C4×C37D411yescharacteristic
49C4⋊C4×C37D411yescharacteristic
50C22⋊C4×C37—21no—
51C42×C37—21no—
52C42×C37—21no—
53C42×C37—21no—
54#10596938—22no—
55#10596938—22no—
56C4⋊Dic37—22no—
57C4⋊Dic37—22no—
58C4⋊Dic37—21no—
59C4⋊Dic37—21no—
60#10596934—21no—
61#10596934D412yes—
62C2×#64436—21no—
63C23×C37C2×D411yescharacteristic
64C22×D37—21no—
65C2×C4×C37—22no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37#4111yescharacteristic
74C2×C4×C37#4111yescharacteristic
75C2×C4×C37#4111yescharacteristic
76C22⋊D37—41no—
77C22⋊D37—41no—
78C2×Dic37—21no—
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—22no—
82C2×Dic37—42no—
83C2×Dic37—41no—
84D148—21no—
85D148—21no—
86C4×D37—41no—
87C4×D37—41no—
88Dic74—21no—
89Dic74—21no—
90Dic74—41no—
91Dic74—41no—
92Dic74—41no—
93Dic74—41no—
94C8×C37—41no—
95#64436—22no—
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—41no—
106C4×C37—41no—
107C4×C37#12111yescharacteristic
108C4×C37#12111yescharacteristic
109C4×C37#12311yescharacteristic
110C4×C37#12411yescharacteristic
111Dic37—41no—
112Dic37—42no—
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×#101—371no—
126#391—371no—
127#339D3711yescharacteristic, complemented
128C37#203811yescharacteristic, complemented, Sylow
129C2×#41—371no—
130C22×Q8—371no—
131C2×M16—371no—
132C2×M16C2×D3711yescharacteristic
133C4⋊Q8—741no—
134#124—741no—
135#123—742no—
136C22⋊Q8—741no—
137C22⋊Q8—741no—
138#117C2×D3711yescharacteristic
139C2×C4⋊C4—371no—
140C2×C42C2×D3711yescharacteristic
141#107—741no—
142#106—741no—
143#104—742no—
144#103—741no—
145#102—741no—
146#101—742no—
147#95—742no—
148#41—741no—
149#41—741no—
150#41—741no—
151#41—741no—
152C2×Q8—371no—
153C2×Q8—741no—
154C2×Q8—741no—
155C2×Q8—741no—
156C2×Q8—741no—
157C2×Q8—741no—
158C2×Q8—741no—
159C2×D4—371no—
160C2×D4—741no—
161C22×C4—21no—
162C22×C4—372no—
163C22×C4—741no—
164C22×C4—741no—
165C22×C4C22×D3711yescharacteristic
166M16—21no—
167M16—21no—
168M16—372no—
169M16—741no—
170C2×C8—21no—
171C2×C8—741no—
172C4⋊C4—742no—
173C4⋊C4—742no—
174C4⋊C4—741no—
175C4⋊C4—741no—
176C4⋊C4D14811yescharacteristic
177C4⋊C4D14811yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—742no—
180C22⋊C4—742no—
181C42—21no—
182C42—21no—
183C42—21no—
184C23—741no—
185C23D4×D3711yescharacteristic
186Q8—741no—
187Q8—741no—
188Q8—1481no—
189Q8—1481no—
190Q8—1481no—
191Q8—1481no—
192D4—741no—
193D4—741no—
194D4—1481no—
195D4—1481no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—742no—
202C2×C4—741no—
203C2×C4—742no—
204C2×C4—742no—
205C2×C4—1482no—
206C2×C4—1481no—
207C2×C4—1481no—
208C2×C4—1481no—
209C2×C4C2×D14811yescharacteristic
210C2×C4#1059696211yescharacteristic
211C2×C4#1059696211yescharacteristic
212C2×C4D4×D3711yescharacteristic
213C2×C4D4×D3711yescharacteristic
214C2×C4#1059696611yescharacteristic
215C8—41no—
216C8—742no—
217C22—21no—
218C22—21no—
219C22—1481no—
220C22—1481no—
221C22—1481no—
222C22#1192450611yescharacteristic
223C22#1192450911yescharacteristic
224C22#1192452111yescharacteristic
225C4—42no—
226C4—41no—
227C4—41no—
228C4—2961no—
229C4—1482no—
230C4—1481no—
231C4#1192450911yescharacteristic
232C4#1192451111yescharacteristic
233C4#1192452111yescharacteristic
234C4#1192452411yescharacteristic
235C2—21no—
236C2—21no—
237C2—2961no—
238C2#1455745111yescharacteristic
239C2#1455770711yescharacteristic
240C2#1455771711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37#120
prime radicalC2×#10596962C22
hypercenter#339D37
hypocenterC37#2038
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #14557576C2semidirect
5. C2×#11924454C2semidirect
6. #14557439C2semidirect
7. C37×#339C2semidirect
127. #339D37semidirect
128. C37#2038semidirect

Maximal subgroups

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

subgroupindex
#145581092
#145575762
C2×#119244642
#145575352
C2×#119244542
#145574392
C37×#3392
#203837