Finite Group Databasebeta

← #17995611

Subgroups — #17995611

Order 4736.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#11924562C211yesmaximal, characteristic, complemented
2#14558100C211yesmaximal, characteristic, complemented
3C2×#11924464C211yesmaximal, characteristic, complemented
4#14557538C211yesmaximal, characteristic, complemented
5C2×#11924453C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C2×#127×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924562—22no—
10#11924562—22no—
11C2×#10596940—21no—
12C2×#10596939—21no—
13C2×#10596934C2211yescharacteristic
14C2×#10596934C2211yescharacteristic
15#11924532—21no—
16#11924523—21no—
17#11924507—22no—
18#11924505—22no—
19#11924495C2211yescharacteristic
20#11924464—22no—
21#11924457—22no—
22#11924453—22no—
23C22×D4×C37—22no—
24C22×D4×C37C2211yescharacteristic
25C22×D4×C37C2211yescharacteristic
26#127×C37—22no—
27#127×C37—22no—
28C2×C42×C37C2211yescharacteristic
29C24×C37—21no—
30C24×C37D412yes—
31C2×D4×C37—28no—
32C2×D4×C37—21no—
33C2×D4×C37—21no—
34C2×D4×C37—21no—
35C2×D4×C37—21no—
36C2×D4×C37—21no—
37C2×D4×C37—21no—
38C2×D4×C37—21no—
39C2×D4×C37—21no—
40C2×D4×C37—21no—
41C2×D4×C37—21no—
42C2×D4×C37—21no—
43C2×D4×C37—48no—
44C2×D4×C37D412yescomplemented
45C22×C4×C37—21no—
46C22×C4×C37C2311yescharacteristic
47C2×C22⋊D37—21no—
48C2×C22⋊D37—24no—
49#10596962—21no—
50#10596962—21no—
51#10596962—21no—
52#10596962—21no—
53C2×D148D411yescharacteristic, complemented
54C2×C4×D37—21no—
55C2×Dic74D411yescharacteristic, complemented
56C42×C37—21no—
57C42×C37D412yescomplemented
58C22⋊Dic37—24no—
59C22⋊Dic37—21no—
60#10596940—24no—
61#10596939—24no—
62C4⋊Dic37D412yescomplemented
63C4×Dic37—21no—
64#10596934—21no—
65#10596934—21no—
66#10596934—21no—
67#10596934D412yescomplemented
68C2×#64436—21no—
69C2×#64436—21no—
70C23×C37—22no—
71C23×C37—22no—
72C23×C37—22no—
73C23×C37—22no—
74C23×C37—44no—
75C23×C37—44no—
76C23×C37—41no—
77C23×C37—41no—
78C23×C37C2×D411yescharacteristic
79C22×D37—21no—
80D4×C37—22no—
81D4×C37—22no—
82D4×C37—416no—
83D4×C37—41no—
84D4×C37—41no—
85D4×C37—41no—
86D4×C37—41no—
87D4×C37—41no—
88D4×C37—41no—
89C2×C4×C37—24no—
90C2×C4×C37—22no—
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37#4111yescharacteristic
97C22⋊D37—41no—
98C22⋊D37—41no—
99C22⋊D37—84no—
100C2×Dic37—22no—
101C2×Dic37—21no—
102D148—21no—
103D148—21no—
104C4×D37—41no—
105C4×D37—41no—
106Dic74—21no—
107Dic74—21no—
108#64436—22no—
109#64436—41no—
110C22×C37—22no—
111C22×C37—44no—
112C22×C37—44no—
113C22×C37—42no—
114C22×C37—42no—
115C22×C37—44no—
116C22×C37—82no—
117C22×C37—82no—
118C22×C37—82no—
119C22×C37#12011yescharacteristic
120C22×C37#12011yescharacteristic
121C22×C37#12111yescharacteristic
122C2×D37—41no—
123C2×D37—42no—
124C4×C37—24no—
125C4×C37#12011yescharacteristic
126C4×C37#12111yescharacteristic
127C4×C37#12111yescharacteristic
128C4×C37#12711yescharacteristic
129Dic37—41no—
130Dic37—42no—
131#2002—371nomaximal, Sylow
132C2×C37—21no—
133C2×C37—21no—
134C2×C37—82no—
135C2×C37—82no—
136C2×C37#39211yescharacteristic
137C2×C37#45312yes—
138D37—81no—
139C2×AGL(1,ℤ/8)—371no—
140#535—371no—
141C2×#127D3711yescharacteristic, complemented
142C2×#104—371no—
143#418—371no—
144C2×#100—371no—
145#339—371no—
146C37#200211yescharacteristic, complemented, Sylow
147C2×#41—371no—
148C22×D4—22no—
149C22×D4C2×D3711yescharacteristic
150C22×D4C2×D3711yescharacteristic
151AGL(1,ℤ/8)—742no—
152AGL(1,ℤ/8)—742no—
153C2×SD16—741no—
154C2×D8—741no—
155C2×M16—371no—
156C2×M16—371no—
157#127—22no—
158#127—22no—
159#127—741no—
160#124—741no—
161#121—742no—
162#120—742no—
163#117—371no—
164C2×C42C2×D3711yescharacteristic
165#104—742no—
166#102—742no—
167#100—742no—
168C24—21no—
169C24C22⋊D3712yes—
170#41—741no—
171#41—741no—
172#41—741no—
173#41—741no—
174C2×Q8—371no—
175C2×D4—28no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—48no—
188C2×D4—371no—
189C2×D4—744no—
190C2×D4—741no—
191C2×D4C22⋊D3712yescomplemented
192C22×C4—21no—
193C22×C4—741no—
194C22×C4C22×D3711yescharacteristic
195SD16—744no—
196D8—744no—
197M16—372no—
198M16—741no—
199M16—741no—
200M16—741no—
201C2×C8—741no—
202C2×C8—741no—
203C4⋊C4—372no—
204C22⋊C4—744no—
205C22⋊C4—741no—
206C42—21no—
207C42—741no—
208C42C22⋊D3712yescomplemented
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—44no—
214C23—44no—
215C23—41no—
216C23—41no—
217C23—741no—
218C23C2×C22⋊D3711yescharacteristic
219Q8—741no—
220Q8—741no—
221D4—22no—
222D4—22no—
223D4—416no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—41no—
230D4—2964no—
231D4—741no—
232D4—741no—
233D4—1481no—
234D4—1481no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—742no—
238C2×C4—741no—
239C2×C4—1481no—
240C2×C4—1481no—
241C2×C4D4×D3711yescharacteristic
242C2×C4D4×D3711yescharacteristic
243C2×C4D4×D3711yescharacteristic
244C2×C4#1059696411yescharacteristic
245C2×C4C2×C22⋊D3711yescharacteristic
246C2×C4C2×C22⋊D3711yescharacteristic
247C8—742no—
248C8—1481no—
249C22—22no—
250C22—44no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—1481no—
259C22—1482no—
260C22#1192450411yescharacteristic
261C22#1192450511yescharacteristic
262C22#1192450811yescharacteristic
263C4—24no—
264C4—1481no—
265C4—1482no—
266C4#1192450411yescharacteristic
267C4#1192450711yescharacteristic
268C4#1192450811yescharacteristic
269C4#1192453211yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—82no—
274C2—2961no—
275C2#1455744111yescharacteristic
276C2#1455770012yes—
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#127×C37C2
socleC22×C37#120
hypercenterC2×#127D37
hypocenterC37#2002
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. #14558100C2semidirect
3. C2×#11924464C2semidirect
4. #14557538C2semidirect
5. C2×#11924453C2semidirect
6. #14557293C2semidirect
7. C2×#127×C37C2semidirect
44. C2×D4×C37D4semidirect
53. C2×D148D4semidirect
55. C2×Dic74D4semidirect
57. C42×C37D4semidirect
62. C4⋊Dic37D4semidirect
67. #10596934D4semidirect
141. C2×#127D37semidirect
146. C37#2002semidirect
191. C2×D4C22⋊D37semidirect
208. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
#145581002
C2×#119244642
#145575382
C2×#119244532
#145572932
C2×#127×C372
#200237