Finite Group Databasebeta

← #18003944

Subgroups — #18003944

Order 4736.

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

normal subgroups only

This group has 724 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
1#14558369C211yesmaximal, characteristic, complemented
2#14558331C212yesmaximal, complemented
3#14557715C212yesmaximal, complemented
4#14557710C212yesmaximal, complemented
5#14557705C212yesmaximal, complemented
6#14557700C212yesmaximal, complemented
7C2×#11924464C212yesmaximal, complemented
8#14557517C211yesmaximal, characteristic, complemented
9C37×#532C211yesmaximal, characteristic, complemented
10#11924584C2212yes—
11#11924583—22no—
12#11924582—22no—
13#11924581—22no—
14#11924581C2212yes—
15C2×#10596962—22no—
16C2×#10596962C2212yes—
17#41×D37—24no—
18#11924567C2214yescomplemented
19#11924566—22no—
20#11924562C2214yescomplemented
21#11924561—22no—
22#11924556—24no—
23C2×#10596934C2212yescomplemented
24#11924464C2214yescomplemented
25#11924464C2214yescomplemented
26#11924455C2212yescomplemented
27#11924453C2212yescomplemented
28C2×#41×C37C2211yescharacteristic
29C2×#41×C37C2211yescharacteristic, complemented
30C4⋊Q8×C37C2211yescharacteristic, complemented
31#127×C37C2211yescharacteristic, complemented
32#124×C37C2211yescharacteristic, complemented
33#124×C37C2211yescharacteristic, complemented
34#121×C37—22no—
35C4×D4×C37—22no—
36C2×C42×C37C2211yescharacteristic, complemented
37#41×C37—22no—
38#41×C37—22no—
39#41×C37—22no—
40#41×C37—22no—
41C2×Q8×C37C2311yescharacteristic
42C2×Q8×C37C2311yescharacteristic
43C2×D4×C37—22no—
44C2×D4×C37—21no—
45C2×D4×C37D412yes—
46C2×D4×C37C2311yescharacteristic
47C2×D4×C37C2311yescharacteristic
48C22×C4×C37—21no—
49C22×C4×C37—21no—
50C22×C4×C37D412yes—
51C22×C4×C37C2311yescharacteristic
52C2×C22⋊D37—24no—
53C2×C22⋊D37—22no—
54#10596966—24no—
55Q8×D37—24no—
56#10596964—28no—
57#10596964—24no—
58D4×D37—28no—
59D4×D37—24no—
60#10596962—24no—
61#10596962—24no—
62#10596962—22no—
63#10596962—24no—
64#10596962—22no—
65#10596962D414yescomplemented
66#10596962C2314yes—
67C2×D148—22no—
68C2×D148D412yescomplemented
69C2×C4×D37—24no—
70C2×C4×D37—22no—
71C2×Dic74—22no—
72C2×Dic74D412yescomplemented
73C4⋊C4×C37—22no—
74C22⋊C4×C37—22no—
75C22⋊C4×C37—22no—
76C42×C37—21no—
77C42×C37C2311yescharacteristic
78C42×C37C2311yescharacteristic
79#10596942—24no—
80#10596941—24no—
81#10596940—24no—
82#10596939—24no—
83#10596934—22no—
84#10596934C2314yes—
85C2×#64436—22no—
86C23×C37—21no—
87C23×C37C2×D412yes—
88C23×C37C2×D411yescharacteristic
89C22×D37—24no—
90C22×D37—22no—
91Q8×C37—22no—
92Q8×C37—22no—
93D4×C37—24no—
94D4×C37—22no—
95D4×C37—22no—
96D4×C37—44no—
97D4×C37—42no—
98C2×C4×C37—21no—
99C2×C4×C37—22no—
100C2×C4×C37—22no—
101C2×C4×C37—21no—
102C2×C4×C37—21no—
103C2×C4×C37—42no—
104C2×C4×C37—41no—
105C2×C4×C37—41no—
106C2×C4×C37C2×D412yes—
107C2×C4×C37C2×D412yes—
108C2×C4×C37C2×D412yes—
109C2×C4×C37C2×D411yescharacteristic
110C2×C4×C37C2411yescharacteristic
111C22⋊D37—28no—
112C22⋊D37—24no—
113C22⋊D37—24no—
114C2×Dic37—24no—
115C2×Dic37—22no—
116D148—24no—
117D148—22no—
118D148C2×D414yes—
119C4×D37—28no—
120C4×D37—24no—
121C4×D37—24no—
122Dic74—24no—
123Dic74—22no—
124Dic74C2×D414yes—
125#64436—24no—
126C22×C37—22no—
127C22×C37—41no—
128C22×C37—42no—
129C22×C37—42no—
130C22×C37—41no—
131C22×C37#12012yes—
132C22×C37C22×D411yescharacteristic
133C2×D37—24no—
134C2×D37—82no—
135C2×D37—84no—
136C4×C37—22no—
137C4×C37—22no—
138C4×C37—41no—
139C4×C37—41no—
140C4×C37#12011yescharacteristic
141C4×C37#12011yescharacteristic
142C4×C37C22×D412yes—
143Dic37—24no—
144#3018—371nomaximal, Sylow
145C2×C37—21no—
146C2×C37—22no—
147C2×C37—42no—
148C2×C37—81no—
149C2×C37C2×#12011yescharacteristic
150D37—44no—
151#585—371no—
152#575—372no—
153#532D3711yescharacteristic, complemented
154#456—372no—
155#455—372no—
156#454—372no—
157#453—372no—
158C2×#104—372no—
159#413—371no—
160C37#301811yescharacteristic, complemented, Sylow
1612−1+4—372no—
1622−1+4—742no—
163H(5,𝔽2)—372no—
164H(5,𝔽2)—742no—
165H(5,𝔽2)—742no—
166C2×#41—372no—
167C2×#41—744no—
168C2×#41—742no—
169C2×#41C2×D3711yescharacteristic
170C2×#41C2×D3711yescharacteristic, complemented
171#137—374no—
172#137—742no—
173AGL(1,ℤ/8)—374no—
174AGL(1,ℤ/8)—742no—
175#135—744no—
176C2×M16—372no—
177C4⋊Q8C2×D3711yescharacteristic, complemented
178#127C2×D3711yescharacteristic, complemented
179#124C2×D3711yescharacteristic, complemented
180#124C2×D3711yescharacteristic, complemented
181#121—22no—
182C4×D4—22no—
183C2×C42C2×D3711yescharacteristic, complemented
184#104—374no—
185#104—374no—
186#101—372no—
187#100—372no—
188#41—22no—
189#41—22no—
190#41—22no—
191#41—22no—
192#41—374no—
193#41—374no—
194#41—744no—
195#41—744no—
196#41—744no—
197#41—748no—
198#41—744no—
199#41—742no—
200#41—742no—
201#41—744no—
202C2×Q8—372no—
203C2×Q8—742no—
204C2×Q8—744no—
205C2×Q8C22×D3711yescharacteristic
206C2×Q8C22×D3711yescharacteristic
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—372no—
210C2×D4—742no—
211C2×D4—744no—
212C2×D4—748no—
213C2×D4—742no—
214C2×D4—744no—
215C2×D4C22⋊D3712yes—
216C2×D4C22×D3711yescharacteristic
217C2×D4C22×D3711yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—744no—
221C22×C4—742no—
222C22×C4C22⋊D3712yes—
223C22×C4C22×D3711yescharacteristic
224Q16—744no—
225SD16—744no—
226SD16—744no—
227D8—744no—
228M16—374no—
229M16—742no—
230C2×C8—742no—
231C4⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C42—21no—
235C42C22×D3711yescharacteristic
236C42C22×D3711yescharacteristic
237C23—21no—
238C23—744no—
239C23—742no—
240C23C2×C22⋊D3712yes—
241C23C2×C22⋊D3711yescharacteristic
242Q8—22no—
243Q8—22no—
244Q8—374no—
245Q8—744no—
246Q8—742no—
247D4—24no—
248D4—22no—
249D4—22no—
250D4—44no—
251D4—42no—
252D4—374no—
253D4—744no—
254D4—748no—
255D4—744no—
256D4—744no—
257D4—742no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—748no—
267C2×C4—744no—
268C2×C4—742no—
269C2×C4—744no—
270C2×C4—744no—
271C2×C4D4×D3712yes—
272C2×C4D4×D3712yes—
273C2×C4C2×C22⋊D3712yes—
274C2×C4C2×C22⋊D3711yescharacteristic
275C2×C4C23×D3711yescharacteristic
276C8—744no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—2962no—
283C22—2964no—
284C22—744no—
285C22#1192450412yes—
286C22C22×C22⋊D3711yescharacteristic
287C4—22no—
288C4—22no—
289C4—41no—
290C4—41no—
291C4—744no—
292C4#1192450411yescharacteristic
293C4#1192450411yescharacteristic
294C4C2×D4×D3712yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—81no—
299C2—1484no—
300C2C2×#1192450411yescharacteristic
subgroupG/H
centerC4#11924504
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#532C2
socleC2×C37C2×#120
hypercenter#532D37
hypocenterC37#3018
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14558369C2semidirect
2. #14558331C2semidirect
3. #14557715C2semidirect
4. #14557710C2semidirect
5. #14557705C2semidirect
6. #14557700C2semidirect
7. C2×#11924464C2semidirect
8. #14557517C2semidirect
9. C37×#532C2semidirect
18. #11924567C22semidirect
20. #11924562C22semidirect
23. C2×#10596934C22semidirect
24. #11924464C22semidirect
25. #11924464C22semidirect
26. #11924455C22semidirect
27. #11924453C22semidirect
29. C2×#41×C37C22semidirect
30. C4⋊Q8×C37C22semidirect
31. #127×C37C22semidirect
32. #124×C37C22semidirect
33. #124×C37C22semidirect
36. C2×C42×C37C22semidirect
65. #10596962D4semidirect
68. C2×D148D4semidirect
72. C2×Dic74D4semidirect
153. #532D37semidirect
160. C37#3018semidirect
170. C2×#41C2×D37semidirect
177. C4⋊Q8C2×D37semidirect
178. #127C2×D37semidirect
179. #124C2×D37semidirect
180. #124C2×D37semidirect
183. C2×C42C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583692
#145583312
#145577152
#145577102
#145577052
#145577002
C2×#119244642
#145575172
C37×#5322
#301837