Finite Group Databasebeta

← #17995647

Subgroups — #17995647

Order 4736.

380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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#14558331C211yesmaximal, characteristic, complemented
2#14558100C211yesmaximal, characteristic, complemented
3#14557549C211yesmaximal, characteristic, complemented
4#14557538C211yesmaximal, characteristic, complemented
5#14557507C211yesmaximal, characteristic, complemented
6#14557305C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567—21no—
10#11924566—21no—
11#11924562—21no—
12#11924561—21no—
13#11924556—22no—
14C2×#10596934C2211yescharacteristic
15#11924532—21no—
16#11924523—21no—
17#11924507—22no—
18#11924505—22no—
19#11924495C2211yescharacteristic
20#11924495C2211yescharacteristic
21#11924462—22no—
22#11924457—22no—
23#11924451—22no—
24C2×#41×C37C2211yescharacteristic
25C22×D4×C37C2211yescharacteristic
26AGL(1,ℤ/8)×C37—22no—
27AGL(1,ℤ/8)×C37—22no—
28C2×SD16×C37—21no—
29C2×D8×C37—21no—
30C2×M16×C37C2211yescharacteristic
31C24×C37—21no—
32#41×C37—21no—
33#41×C37—21no—
34#41×C37—21no—
35#41×C37—21no—
36C2×Q8×C37D411yescharacteristic, complemented
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×C37D412yes—
44C2×D4×C37D411yescharacteristic, complemented
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
54C2×C4×D37—21no—
55C2×Dic74D411yescharacteristic
56SD16×C37—24no—
57D8×C37—24no—
58M16×C37—21no—
59M16×C37D412yescomplemented
60C2×C8×C37—21no—
61C22⋊Dic37—24no—
62C22⋊Dic37—21no—
63C22⋊Dic37D412yes—
64#10596942—22no—
65#10596941—22no—
66#10596940—22no—
67#10596939—22no—
68C4⋊Dic37—21no—
69C4⋊Dic37—21no—
70C4×Dic37—21no—
71C4×Dic37—21no—
72#10596934—21no—
73#10596934—21no—
74C2×#64436D412yescomplemented
75C23×C37—22no—
76C23×C37—21no—
77C23×C37—41no—
78C23×C37—41no—
79C23×C37—82no—
80C23×C37C2×D411yescharacteristic
81C22×D37—21no—
82Q8×C37—21no—
83Q8×C37—21no—
84D4×C37—21no—
85D4×C37—21no—
86D4×C37—22no—
87D4×C37—22no—
88D4×C37—41no—
89D4×C37—41no—
90D4×C37—41no—
91D4×C37—41no—
92C2×C4×C37—21no—
93C2×C4×C37—41no—
94C2×C4×C37—41no—
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2×D411yescharacteristic
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37#4111yescharacteristic
101C22⋊D37—41no—
102C22⋊D37—41no—
103C22⋊D37—84no—
104C2×Dic37—22no—
105C2×Dic37—21no—
106C2×Dic37—41no—
107D148—21no—
108D148—21no—
109C4×D37—41no—
110C4×D37—41no—
111Dic74—21no—
112Dic74—21no—
113C8×C37—22no—
114#64436—22no—
115C22×C37—41no—
116C22×C37—44no—
117C22×C37—41no—
118C22×C37—42no—
119C22×C37—81no—
120C22×C37—82no—
121C22×C37—82no—
122C22×C37#12011yescharacteristic
123C22×C37#12111yescharacteristic
124C22×C37#12711yescharacteristic
125C2×D37—42no—
126C2×D37—41no—
127C4×C37—41no—
128C4×C37#12011yescharacteristic
129C4×C37#12011yescharacteristic
130C4×C37#12111yescharacteristic
131C4×C37#12111yescharacteristic
132Dic37—42no—
133Dic37—41no—
134Dic37—81no—
135#2008—371nomaximal, Sylow
136C2×C37—21no—
137C2×C37—21no—
138C2×C37—21no—
139C2×C37—82no—
140C2×C37—81no—
141C2×C37#39211yescharacteristic
142D37—81no—
143#575—371no—
144C2×AGL(1,ℤ/8)D3711yescharacteristic, complemented
145#535—371no—
146#421—371no—
147#418—371no—
148#410—371no—
149#344—371no—
150C37#200811yescharacteristic, complemented, Sylow
151C2×#41—371no—
152C2×#41C2×D3711yescharacteristic
153C22×D4C2×D3711yescharacteristic
154#137—741no—
155#137—741no—
156AGL(1,ℤ/8)—22no—
157AGL(1,ℤ/8)—22no—
158AGL(1,ℤ/8)—741no—
159AGL(1,ℤ/8)—741no—
160#135—742no—
161C2×SD16—21no—
162C2×D8—21no—
163C2×M16—371no—
164C2×M16C2×D3711yescharacteristic
165#127—741no—
166#124—741no—
167#121—742no—
168#120—742no—
169#117—371no—
170#117—371no—
171#104—742no—
172#102—742no—
173#99—742no—
174C24—21no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—741no—
180#41—741no—
181#41—741no—
182#41—741no—
183C2×Q8—371no—
184C2×Q8C22⋊D3711yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—371no—
192C2×D4—744no—
193C2×D4—741no—
194C2×D4C22⋊D3712yes—
195C2×D4C22⋊D3711yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—741no—
198C22×C4C22×D3711yescharacteristic
199Q16—742no—
200SD16—24no—
201SD16—742no—
202SD16—742no—
203D8—24no—
204D8—742no—
205M16—21no—
206M16—741no—
207M16—741no—
208M16C22⋊D3712yescomplemented
209C2×C8—21no—
210C2×C8—372no—
211C4⋊C4—741no—
212C4⋊C4—741no—
213C22⋊C4—372no—
214C22⋊C4—744no—
215C22⋊C4—741no—
216C42—741no—
217C42—741no—
218C23—22no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23—82no—
223C23—741no—
224C23D4×D3711yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—741no—
228Q8—741no—
229D4—21no—
230D4—21no—
231D4—22no—
232D4—22no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—2964no—
238D4—741no—
239D4—741no—
240D4—1481no—
241D4—1481no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—742no—
246C2×C4—741no—
247C2×C4—1481no—
248C2×C4—1481no—
249C2×C4—1481no—
250C2×C4D4×D3711yescharacteristic
251C2×C4D4×D3711yescharacteristic
252C2×C4#1059696411yescharacteristic
253C2×C4C2×C22⋊D3711yescharacteristic
254C2×C4C2×C22⋊D3711yescharacteristic
255C2×C4C2×C22⋊D3711yescharacteristic
256C8—22no—
257C8—742no—
258C22—41no—
259C22—44no—
260C22—41no—
261C22—42no—
262C22—81no—
263C22—82no—
264C22—82no—
265C22—1482no—
266C22—1481no—
267C22#1192450411yescharacteristic
268C22#1192450811yescharacteristic
269C22#1192453211yescharacteristic
270C4—41no—
271C4—2961no—
272C4—1482no—
273C4—1481no—
274C4#1192450411yescharacteristic
275C4#1192450511yescharacteristic
276C4#1192450711yescharacteristic
277C4#1192450811yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—82no—
282C2—81no—
283C2—2961no—
284C2#1455744111yescharacteristic
subgroupG/H
centerC2#14557441
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×AGL(1,ℤ/8)×C37C2
socleC2×C37#392
hypercenterC2×AGL(1,ℤ/8)D37
hypocenterC37#2008
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #14558331C2semidirect
2. #14558100C2semidirect
3. #14557549C2semidirect
4. #14557538C2semidirect
5. #14557507C2semidirect
6. #14557305C2semidirect
7. C2×AGL(1,ℤ/8)×C37C2semidirect
36. C2×Q8×C37D4semidirect
44. C2×D4×C37D4semidirect
59. M16×C37D4semidirect
74. C2×#64436D4semidirect
144. C2×AGL(1,ℤ/8)D37semidirect
150. C37#2008semidirect
184. C2×Q8C22⋊D37semidirect
195. C2×D4C22⋊D37semidirect
208. M16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583312
#145581002
#145575492
#145575382
#145575072
#145573052
C2×AGL(1,ℤ/8)×C372
#200837