Finite Group Databasebeta

← #18003952

Subgroups — #18003952

Order 4736.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11924581C211yesmaximal, characteristic, complemented
2#14558331C212yesmaximal, complemented
3#14557710C214yesmaximal, complemented
4#14557700C214yesmaximal, complemented
5#14557551C212yesmaximal, complemented
6C2×#11924453C211yesmaximal, characteristic, complemented
7C37×#535C211yesmaximal, characteristic, complemented
8#11924581—22no—
9#11924581—24no—
10#11924581C2214yes—
11C2×#10596962C2212yes—
12C2×#10596964—22no—
13C22×C22⋊D37—22no—
14C2×D4×D37—22no—
15#11924567C2214yescomplemented
16#11924566—22no—
17#11924562C2214yescomplemented
18#11924561—22no—
19#11924556—24no—
20C2×#10596934C2212yescomplemented
21#11924464C2218yescomplemented
22#11924453C2214yescomplemented
23C2×#41×C37C2211yescharacteristic, complemented
24C22×D4×C37C2211yescharacteristic
25#127×C37C2212yescomplemented
26#124×C37C2212yescomplemented
27#121×C37—22no—
28#120×C37—22no—
29#117×C37C2211yescharacteristic, complemented
30C24×C37D412yes—
31C23×D37—22no—
32#41×C37—22no—
33#41×C37—22no—
34C2×Q8×C37C2311yescharacteristic, complemented
35C2×D4×C37—21no—
36C2×D4×C37—24no—
37C2×D4×C37—22no—
38C2×D4×C37—22no—
39C2×D4×C37D412yes—
40C2×D4×C37C2312yes—
41C2×D4×C37C2311yescharacteristic, complemented
42C22×C4×C37—21no—
43C22×C4×C37C2311yescharacteristic
44C2×C22⋊D37—24no—
45C2×C22⋊D37—28no—
46C2×C22⋊D37—22no—
47C2×C22⋊D37—28no—
48C22×Dic37—22no—
49#10596964—28no—
50#10596964—28no—
51D4×D37—28no—
52D4×D37—28no—
53#10596962—22no—
54#10596962—22no—
55#10596962D414yescomplemented
56#10596962C2314yes—
57C2×D148D412yescomplemented
58C2×C4×D37—22no—
59C2×Dic74D412yescomplemented
60C4⋊C4×C37—21no—
61C22⋊C4×C37—21no—
62C22⋊C4×C37—24no—
63C42×C37C2312yescomplemented
64#10596942—24no—
65#10596941—24no—
66#10596940—24no—
67#10596939—24no—
68#10596934—22no—
69#10596934C2314yescomplemented
70C2×#64436—22no—
71C23×C37—22no—
72C23×C37—22no—
73C23×C37—21no—
74C23×C37—82no—
75C23×C37C2×D414yes—
76C23×C37C2×D411yescharacteristic
77C22×D37—22no—
78C22×D37—28no—
79C22×D37—84no—
80Q8×C37—22no—
81D4×C37—24no—
82D4×C37—24no—
83D4×C37—22no—
84D4×C37—41no—
85D4×C37—41no—
86D4×C37—84no—
87C2×C4×C37—22no—
88C2×C4×C37—21no—
89C2×C4×C37—42no—
90C2×C4×C37C2×D412yes—
91C2×C4×C37C2×D412yes—
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2411yescharacteristic
94C22⋊D37—216no—
95C22⋊D37—24no—
96C22⋊D37—24no—
97C2×Dic37—28no—
98C2×Dic37—22no—
99D148—22no—
100D148C2×D414yes—
101C4×D37—24no—
102C4×D37—24no—
103Dic74—22no—
104Dic74C2×D414yes—
105#64436—24no—
106C22×C37—24no—
107C22×C37—41no—
108C22×C37—44no—
109C22×C37—44no—
110C22×C37—42no—
111C22×C37—41no—
112C22×C37—82no—
113C22×C37#12011yescharacteristic
114C22×C37#12011yescharacteristic
115C22×C37C22×D411yescharacteristic
116C2×D37—24no—
117C2×D37—44no—
118C2×D37—88no—
119C4×C37—42no—
120C4×C37—41no—
121C4×C37#12012yes—
122C4×C37C22×D412yes—
123Dic37—24no—
124#3019—371nomaximal, Sylow
125C2×C37—21no—
126C2×C37—21no—
127C2×C37—21no—
128C2×C37—44no—
129C2×C37—81no—
130C2×C37C2×#12011yescharacteristic
131D37—44no—
132C2×H(5,𝔽2)—371no—
133#575—372no—
134#535D3711yescharacteristic, complemented
135#455—374no—
136#453—374no—
137#421—372no—
138C2×#100—371no—
139C37#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—374no—
141H(5,𝔽2)—744no—
142H(5,𝔽2)—742no—
143C2×#41—372no—
144C2×#41—742no—
145C2×#41C2×D3711yescharacteristic, complemented
146C22×D4—742no—
147C22×D4—742no—
148C22×D4C2×D3711yescharacteristic
149#137—374no—
150#137—742no—
151AGL(1,ℤ/8)—374no—
152AGL(1,ℤ/8)—742no—
153#135—744no—
154C2×M16—372no—
155#127C2×D3712yescomplemented
156#124C2×D3712yescomplemented
157#121—22no—
158#120—22no—
159#117C2×D3711yescharacteristic, complemented
160#104—378no—
161#100—374no—
162C24—742no—
163C24C22⋊D3712yes—
164#41—22no—
165#41—22no—
166#41—374no—
167#41—374no—
168#41—748no—
169#41—748no—
170#41—742no—
171#41—742no—
172C2×Q8—372no—
173C2×Q8C22×D3711yescharacteristic, complemented
174C2×D4—21no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—372no—
179C2×D4—748no—
180C2×D4—748no—
181C2×D4—744no—
182C2×D4—748no—
183C2×D4—742no—
184C2×D4—748no—
185C2×D4C22⋊D3712yes—
186C2×D4C22×D3712yes—
187C2×D4C22×D3711yescharacteristic, complemented
188C22×C4—21no—
189C22×C4—742no—
190C22×C4—742no—
191C22×C4C22×D3711yescharacteristic
192Q16—744no—
193SD16—744no—
194SD16—744no—
195D8—744no—
196M16—374no—
197M16—742no—
198C2×C8—742no—
199C4⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—24no—
202C42C22×D3712yescomplemented
203C23—22no—
204C23—22no—
205C23—21no—
206C23—82no—
207C23—2964no—
208C23—748no—
209C23—742no—
210C23C2×C22⋊D3714yes—
211C23C2×C22⋊D3711yescharacteristic
212Q8—22no—
213Q8—374no—
214Q8—742no—
215D4—24no—
216D4—24no—
217D4—22no—
218D4—41no—
219D4—41no—
220D4—84no—
221D4—374no—
222D4—7416no—
223D4—744no—
224D4—744no—
225D4—742no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—748no—
230C2×C4—742no—
231C2×C4—744no—
232C2×C4—744no—
233C2×C4D4×D3712yes—
234C2×C4D4×D3712yes—
235C2×C4C2×C22⋊D3711yescharacteristic
236C2×C4C23×D3711yescharacteristic
237C8—744no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—41no—
244C22—82no—
245C22—2968no—
246C22—744no—
247C22—1484no—
248C22#1192450411yescharacteristic
249C22#1192450411yescharacteristic
250C22C22×C22⋊D3711yescharacteristic
251C4—42no—
252C4—41no—
253C4—744no—
254C4#1192450412yes—
255C4C2×D4×D3712yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—81no—
261C2—1484no—
262C2C2×#1192450411yescharacteristic
subgroupG/H
centerC2C2×#11924504
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#535C2
socleC2×C37C2×#120
hypercenter#535D37
hypocenterC37#3019
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#11924581C2semidirect
2. #14558331C2semidirect
3. #14557710C2semidirect
4. #14557700C2semidirect
5. #14557551C2semidirect
6. C2×#11924453C2semidirect
7. C37×#535C2semidirect
15. #11924567C22semidirect
17. #11924562C22semidirect
20. C2×#10596934C22semidirect
21. #11924464C22semidirect
22. #11924453C22semidirect
23. C2×#41×C37C22semidirect
25. #127×C37C22semidirect
26. #124×C37C22semidirect
29. #117×C37C22semidirect
34. C2×Q8×C37C23semidirect
41. C2×D4×C37C23semidirect
55. #10596962D4semidirect
57. C2×D148D4semidirect
59. C2×Dic74D4semidirect
63. C42×C37C23semidirect
69. #10596934C23semidirect
134. #535D37semidirect
139. C37#3019semidirect
145. C2×#41C2×D37semidirect
155. #127C2×D37semidirect
156. #124C2×D37semidirect
159. #117C2×D37semidirect
173. C2×Q8C22×D37semidirect
187. C2×D4C22×D37semidirect
202. C42C22×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245812
#145583312
#145577102
#145577002
#145575512
C2×#119244532
C37×#5352
#301937