Finite Group Databasebeta

← #18005068

Subgroups — #18005068

Order 4736.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924566C211yesmaximal, characteristic, complemented
2C2×#11924562C211yesmaximal, characteristic, complemented
3C2×#11924556C211yesmaximal, characteristic, complemented
4C22×#10596940C211yesmaximal, characteristic, complemented
5#14558109C211yesmaximal, characteristic, complemented
6#14557928C212yesmaximal, complemented
7#14557920C212yesmaximal, complemented
8#14557915C212yesmaximal, complemented
9#14557905C212yesmaximal, complemented
10#14557489C211yesmaximal, characteristic, complemented
11C37×#535C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C22×Dic74C2211yescharacteristic
14#11924566—24no—
15#11924562—24no—
16#11924556—24no—
17C2×#10596942C2211yescharacteristic, complemented
18C2×#10596942C2212yescomplemented
19C2×#10596940—24no—
20C2×#10596940C2212yes—
21C2×#10596940C2212yes—
22C2×#10596940C2212yes—
23C2×#10596940C2211yescharacteristic, complemented
24C2×#10596940C2212yescomplemented
25C2×#10596941C2211yescharacteristic, complemented
26C2×#10596939C2212yes—
27C2×#10596939C2211yescharacteristic, complemented
28C2×#10596934C2211yescharacteristic
29C22×#64436C2211yescharacteristic
30#11924536C2212yescomplemented
31#11924524C2212yescomplemented
32#11924520—22no—
33#11924516—22no—
34#11924447C2212yescomplemented
35C4×#64436C2212yescomplemented
36C2×#41×C37C2211yescharacteristic
37C22×D4×C37C2211yescharacteristic
38#127×C37C2212yes—
39#124×C37C2212yes—
40#121×C37—22no—
41#120×C37—22no—
42#117×C37C2211yescharacteristic
43C24×C37—21no—
44#41×C37—22no—
45#41×C37—22no—
46C2×Q8×C37C2311yescharacteristic
47C2×D4×C37—21no—
48C2×D4×C37—22no—
49C2×D4×C37—22no—
50C2×D4×C37—21no—
51C2×D4×C37—24no—
52C2×D4×C37C2312yes—
53C2×D4×C37C2311yescharacteristic
54C22×C4×C37—21no—
55C22×C4×C37C2311yescharacteristic
56C2×C22⋊D37—21no—
57C22×Dic37—21no—
58#10596962—22no—
59#10596962—22no—
60C2×D148C2311yescharacteristic
61C2×C4×D37—21no—
62C2×Dic74—22no—
63C2×Dic74—22no—
64C2×Dic74—21no—
65C2×Dic74C2312yes—
66C2×Dic74C2311yescharacteristic
67C4⋊C4×C37D412yes—
68C22⋊C4×C37—24no—
69C22⋊C4×C37D412yes—
70C42×C37C2312yes—
71#10596942—22no—
72#10596942—24no—
73#10596941—22no—
74#10596940—24no—
75#10596940—24no—
76#10596940—24no—
77#10596940—22no—
78#10596940—24no—
79#10596939—24no—
80#10596939—22no—
81#10596938—24no—
82C4⋊Dic37—24no—
83#10596934D414yescomplemented
84C2×#64436D414yescomplemented
85C2×#64436C2311yescharacteristic
86C2×#64436C2311yescharacteristic
87C2×#64436C2312yes—
88C23×C37—22no—
89C23×C37—21no—
90C23×C37—42no—
91C23×C37—82no—
92C23×C37C2×D411yescharacteristic
93C22×D37—21no—
94Q8×C37—21no—
95Q8×C37—21no—
96D4×C37—22no—
97D4×C37—21no—
98D4×C37—22no—
99D4×C37—21no—
100D4×C37—42no—
101D4×C37—42no—
102D4×C37—84no—
103C2×C4×C37—21no—
104C2×C4×C37—42no—
105C2×C4×C37C2×D412yes—
106C2×C4×C37C2×D412yes—
107C2×C4×C37C2×D414yes—
108C2×C4×C37C2×D411yescharacteristic
109C2×C4×C37C2411yescharacteristic
110C22⋊D37—42no—
111C2×Dic37—21no—
112C2×Dic37—22no—
113C2×Dic37—42no—
114D148—21no—
115D148—21no—
116C4×D37—42no—
117Dic74—22no—
118Dic74—21no—
119Dic74—22no—
120Dic74—21no—
121Dic74—42no—
122#64436C2×D412yes—
123#64436C2×D412yes—
124#64436C2×D414yes—
125C22×C37—22no—
126C22×C37—41no—
127C22×C37—42no—
128C22×C37—42no—
129C22×C37—44no—
130C22×C37—84no—
131C22×C37#12712yes—
132C22×C37C22×D411yescharacteristic
133C2×D37—41no—
134C2×D37—42no—
135C4×C37—24no—
136C4×C37—41no—
137C4×C37#12712yes—
138C4×C37C22×D411yescharacteristic
139C4×C37C22×D411yescharacteristic
140Dic37—42no—
141Dic37—41no—
142#3154—371nomaximal, Sylow
143C2×C37—22no—
144C2×C37—81no—
145C2×C37—82no—
146C2×C37C2×#12711yescharacteristic
147C2×C37#57712yes—
148D37—81no—
149C2×#137—371no—
150C2×AGL(1,ℤ/8)—371no—
151C2×#135—371no—
152C22×SD16—371no—
153#536—371no—
154#535D3711yescharacteristic, complemented
155#497—372no—
156#496—372no—
157#495—372no—
158#492—372no—
159#405—371no—
160C37#315411yescharacteristic, complemented, Sylow
161C2×#41—371no—
162C2×#41C2×D3711yescharacteristic
163C22×Q8—371no—
164C22×D4C2×D3711yescharacteristic
165#137—744no—
166AGL(1,ℤ/8)—744no—
167#135—744no—
168C2×Q16—371no—
169C2×Q16—372no—
170C2×SD16—371no—
171C2×SD16—372no—
172C2×SD16—372no—
173C2×SD16—371no—
174C2×SD16—372no—
175C2×SD16—372no—
176C2×SD16—744no—
177C2×D8—371no—
178C2×D8—372no—
179C2×M16—371no—
180C22×C8—371no—
181C4⋊Q8—372no—
182#127C2×D3712yes—
183#124—372no—
184#124C2×D3712yes—
185#123—742no—
186C22⋊Q8—742no—
187#121—22no—
188#120—22no—
189#117C2×D3711yescharacteristic
190#97—372no—
191C4×C8—372no—
192C24—21no—
193#41—22no—
194#41—22no—
195#41—742no—
196#41—742no—
197C2×Q8—372no—
198C2×Q8—371no—
199C2×Q8—741no—
200C2×Q8—742no—
201C2×Q8—742no—
202C2×Q8C22×D3711yescharacteristic
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—24no—
208C2×D4—371no—
209C2×D4—741no—
210C2×D4C22×D3712yes—
211C2×D4C22×D3711yescharacteristic
212C22×C4—21no—
213C22×C4—741no—
214C22×C4—741no—
215C22×C4C22×D3711yescharacteristic
216Q16—742no—
217Q16—744no—
218SD16—744no—
219SD16—744no—
220SD16—742no—
221SD16—744no—
222SD16—744no—
223SD16—742no—
224D8—742no—
225D8—744no—
226M16—374no—
227C2×C8—374no—
228C2×C8—371no—
229C2×C8—372no—
230C2×C8—371no—
231C4⋊C4—744no—
232C4⋊C4C22⋊D3712yes—
233C22⋊C4—24no—
234C22⋊C4—744no—
235C22⋊C4C22⋊D3712yes—
236C42C22×D3712yes—
237C23—22no—
238C23—21no—
239C23—42no—
240C23—82no—
241C23—741no—
242C23C2×C22⋊D3711yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—742no—
246Q8—741no—
247Q8—742no—
248Q8—741no—
249Q8—1482no—
250D4—22no—
251D4—21no—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—84no—
257D4—741no—
258D4—741no—
259D4—1482no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—742no—
263C2×C4—741no—
264C2×C4—1482no—
265C2×C4—1482no—
266C2×C4D4×D3712yes—
267C2×C4D4×D3712yes—
268C2×C4C2×C22⋊D3714yes—
269C2×C4C2×C22⋊D3711yescharacteristic
270C2×C4C23×D3711yescharacteristic
271C8—372no—
272C8—372no—
273C8—374no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—44no—
279C22—84no—
280C22—1481no—
281C22—1482no—
282C22#1192453212yes—
283C22C22×C22⋊D3711yescharacteristic
284C4—24no—
285C4—41no—
286C4—1481no—
287C4—1482no—
288C4#1192453212yes—
289C4C2×D4×D3711yescharacteristic
290C4C2×D4×D3711yescharacteristic
291C2—22no—
292C2—82no—
293C2—81no—
294C2—2961no—
295C2C2×#1192453211yescharacteristic
296C2#1455834412yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#535C2
socleC22×C37C22×D4
hypercenter#535D37
hypocenterC37#3154
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#11924566C2semidirect
2. C2×#11924562C2semidirect
3. C2×#11924556C2semidirect
4. C22×#10596940C2semidirect
5. #14558109C2semidirect
6. #14557928C2semidirect
7. #14557920C2semidirect
8. #14557915C2semidirect
9. #14557905C2semidirect
10. #14557489C2semidirect
11. C37×#535C2semidirect
17. C2×#10596942C22semidirect
18. C2×#10596942C22semidirect
23. C2×#10596940C22semidirect
24. C2×#10596940C22semidirect
25. C2×#10596941C22semidirect
27. C2×#10596939C22semidirect
30. #11924536C22semidirect
31. #11924524C22semidirect
34. #11924447C22semidirect
35. C4×#64436C22semidirect
83. #10596934D4semidirect
84. C2×#64436D4semidirect
154. #535D37semidirect
160. C37#3154semidirect

Maximal subgroups

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

subgroupindex
C2×#119245662
C2×#119245622
C2×#119245562
C22×#105969402
#145581092
#145579282
#145579202
#145579152
#145579052
#145574892
C37×#5352
#315437