Finite Group Databasebeta

← #17995648

Subgroups — #17995648

Order 4736.

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

normal subgroups only

This group has 380 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#14558331C211yesmaximal, characteristic, complemented
2C2×#11924561C211yesmaximal, characteristic, complemented
3#14558102C211yesmaximal, characteristic, complemented
4#14557551C211yesmaximal, characteristic, complemented
5#14557537C211yesmaximal, characteristic, complemented
6#14557303C211yesmaximal, characteristic, complemented
7C37×#410C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×D148C2211yescharacteristic
10#11924567—21no—
11#11924566—21no—
12#11924562—21no—
13#11924561—22no—
14#11924561—21no—
15#11924561—22no—
16#11924556—22no—
17C2×#10596941—21no—
18C2×#10596939—21no—
19C2×#10596934C2211yescharacteristic
20C2×#10596934C2211yescharacteristic
21#11924533—21no—
22#11924524—21no—
23#11924511—22no—
24#11924506—22no—
25#11924464—22no—
26#11924456—22no—
27C2×#41×C37C2211yescharacteristic
28#117×C37C2211yescharacteristic
29#117×C37C2211yescharacteristic
30#99×C37—22no—
31C23×D37—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×C37D411yescharacteristic, complemented
39C22×C4×C37—21no—
40C22×C4×C37C2311yescharacteristic
41C2×C22⋊D37—21no—
42#10596962—21no—
43#10596962—21no—
44#10596962—21no—
45#10596962—21no—
46C2×D148—21no—
47C2×D148—21no—
48C2×D148—21no—
49C2×D148—21no—
50C2×D148—21no—
51C2×D148—24no—
52C2×D148D412yes—
53C2×D148D411yescharacteristic
54C2×C4×D37—21no—
55C2×Dic74D411yescharacteristic
56C4⋊C4×C37—21no—
57C4⋊C4×C37—21no—
58C22⋊C4×C37—21no—
59C22⋊C4×C37D412yes—
60C42×C37—21no—
61C42×C37—21no—
62#10596942—22no—
63#10596941—24no—
64#10596941—22no—
65#10596940—22no—
66#10596939—24no—
67#10596939—22no—
68#10596938—24no—
69#10596934—21no—
70#10596934—21no—
71#10596934—21no—
72#10596934D412yescomplemented
73C2×#64436—21no—
74C2×#64436D412yescomplemented
75C23×C37—21no—
76C23×C37C2×D411yescharacteristic
77C22×D37—22no—
78C22×D37—21no—
79C22×D37—41no—
80C22×D37—41no—
81C22×D37—82no—
82Q8×C37—21no—
83Q8×C37—21no—
84D4×C37—21no—
85D4×C37—21no—
86D4×C37—41no—
87D4×C37—41no—
88C2×C4×C37—22no—
89C2×C4×C37—21no—
90C2×C4×C37—41no—
91C2×C4×C37—41no—
92C2×C4×C37—41no—
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2×D411yescharacteristic
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37#4111yescharacteristic
99C22⋊D37—41no—
100C22⋊D37—41no—
101C2×Dic37—21no—
102D148—22no—
103D148—21no—
104D148—22no—
105D148—21no—
106D148—41no—
107D148—41no—
108D148—84no—
109C4×D37—41no—
110C4×D37—41no—
111Dic74—21no—
112Dic74—21no—
113#64436—22no—
114#64436—22no—
115C22×C37—41no—
116C22×C37—41no—
117C22×C37—81no—
118C22×C37#12011yescharacteristic
119C22×C37#12111yescharacteristic
120C22×C37#12711yescharacteristic
121C2×D37—42no—
122C2×D37—44no—
123C2×D37—41no—
124C2×D37—42no—
125C2×D37—82no—
126C2×D37—82no—
127C4×C37—42no—
128C4×C37—41no—
129C4×C37—81no—
130C4×C37#12011yescharacteristic
131C4×C37#12011yescharacteristic
132C4×C37#12111yescharacteristic
133C4×C37#12111yescharacteristic
134Dic37—41no—
135#2008—371nomaximal, Sylow
136C2×C37—21no—
137C2×C37—21no—
138C2×C37—21no—
139C2×C37—81no—
140C2×C37#39211yescharacteristic
141D37—81no—
142D37—82no—
143#575—371no—
144C2×AGL(1,ℤ/8)—371no—
145#535—371no—
146#421—371no—
147#418—371no—
148#410D3711yescharacteristic, complemented
149#344—371no—
150C37#200811yescharacteristic, complemented, Sylow
151C2×#41—371no—
152C2×#41C2×D3711yescharacteristic
153C22×D4—371no—
154#137—741no—
155#137—741no—
156AGL(1,ℤ/8)—742no—
157AGL(1,ℤ/8)—742no—
158AGL(1,ℤ/8)—741no—
159AGL(1,ℤ/8)—741no—
160#135—742no—
161C2×SD16—741no—
162C2×D8—741no—
163C2×M16—371no—
164C2×M16—371no—
165#127—741no—
166#124—741no—
167#121—742no—
168#120—742no—
169#117C2×D3711yescharacteristic
170#117C2×D3711yescharacteristic
171#104—742no—
172#102—742no—
173#99—22no—
174C24—741no—
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×Q8D14811yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—372no—
187C2×D4—371no—
188C2×D4—744no—
189C2×D4—741no—
190C2×D4—741no—
191C2×D4—741no—
192C2×D4—741no—
193C2×D4—741no—
194C2×D4—741no—
195C2×D4D14811yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—741no—
198C22×C4C22×D3711yescharacteristic
199Q16—742no—
200SD16—742no—
201SD16—744no—
202SD16—742no—
203D8—744no—
204D8—742no—
205M16—372no—
206M16—741no—
207M16—741no—
208M16—741no—
209C2×C8—372no—
210C2×C8—741no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—744no—
215C22⋊C4C22⋊D3712yes—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—2962no—
220C23—742no—
221C23—741no—
222C23—1481no—
223C23—1481no—
224C23C2×C22⋊D3711yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—741no—
228Q8—741no—
229D4—21no—
230D4—21no—
231D4—41no—
232D4—41no—
233D4—2964no—
234D4—742no—
235D4—741no—
236D4—742no—
237D4—741no—
238D4—1481no—
239D4—1481no—
240D4—1481no—
241D4—1481no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—741no—
248C2×C4—1481no—
249C2×C4—1481no—
250C2×C4C2×D14811yescharacteristic
251C2×C4#1059696211yescharacteristic
252C2×C4D4×D3711yescharacteristic
253C2×C4D4×D3711yescharacteristic
254C2×C4D4×D3711yescharacteristic
255C2×C4D4×D3711yescharacteristic
256C8—742no—
257C8—742no—
258C22—41no—
259C22—41no—
260C22—81no—
261C22—2962no—
262C22—2962no—
263C22—1482no—
264C22—1484no—
265C22—1481no—
266C22—1482no—
267C22#1192450411yescharacteristic
268C22#1192451011yescharacteristic
269C22#1192453211yescharacteristic
270C4—42no—
271C4—41no—
272C4—81no—
273C4—1481no—
274C4#1192450611yescharacteristic
275C4#1192450611yescharacteristic
276C4#1192450911yescharacteristic
277C4#1192450911yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2—2962no—
283C2—2961no—
284C2#1455744211yescharacteristic
subgroupG/H
centerC2#14557442
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#410C2
socleC2×C37#392
hypercenter#410D37
hypocenterC37#2008
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14558331C2semidirect
2. C2×#11924561C2semidirect
3. #14558102C2semidirect
4. #14557551C2semidirect
5. #14557537C2semidirect
6. #14557303C2semidirect
7. C37×#410C2semidirect
36. C2×Q8×C37D4semidirect
38. C2×D4×C37D4semidirect
72. #10596934D4semidirect
74. C2×#64436D4semidirect
148. #410D37semidirect
150. C37#2008semidirect
184. C2×Q8D148semidirect
195. C2×D4D148semidirect

Maximal subgroups

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

subgroupindex
#145583312
C2×#119245612
#145581022
#145575512
#145575372
#145573032
C37×#4102
#200837