Finite Group Databasebeta

← #18005044

Subgroups — #18005044

Order 4736.

656 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11924564C211yesmaximal, characteristic, complemented
2C2×#11924562C211yesmaximal, characteristic, complemented
3C2×#11924561C211yesmaximal, characteristic, complemented
4#14558079C211yesmaximal, characteristic, complemented
5C2×#11924532C211yesmaximal, characteristic, complemented
6#14557921C212yesmaximal, complemented
7#14557919C212yesmaximal, complemented
8#14557908C212yesmaximal, complemented
9#14557904C212yesmaximal, complemented
10M16×Dic37C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C22×D148C2211yescharacteristic
14C22×C22⋊D37—22no—
15#11924564—24no—
16#11924562—24no—
17#11924561—24no—
18C2×#10596930C2212yescomplemented
19C2×#10596940C2212yescomplemented
20C2×#10596941C2212yescomplemented
21C2×D296C2212yescomplemented
22C2×#10596939C2212yescomplemented
23C2×#10596939C2212yescomplemented
24C2×#10596934C2211yescharacteristic
25#11924534C2211yescharacteristic, complemented
26#11924532—22no—
27#11924532C2212yes—
28#11924532C2212yes—
29#11924532C2211yescharacteristic, complemented
30#11924525C2211yescharacteristic, complemented
31#11924523C2211yescharacteristic, complemented
32#11924508—22no—
33C4×C22⋊D37—22no—
34C2×C4×Dic37C2211yescharacteristic
35#11924446C2212yescomplemented
36C8×Dic37C2212yescomplemented
37C2×#41×C37C2211yescharacteristic
38C22×D4×C37C2211yescharacteristic
39AGL(1,ℤ/8)×C37—24no—
40C2×SD16×C37C2212yescomplemented
41C2×D8×C37C2212yescomplemented
42C2×M16×C37C2211yescharacteristic
43C24×C37—21no—
44C23×D37—21no—
45#41×C37—22no—
46#41×C37—22no—
47C2×Q8×C37C2311yescharacteristic
48C2×D4×C37—21no—
49C2×D4×C37—22no—
50C2×D4×C37—22no—
51C2×D4×C37—21no—
52C2×D4×C37C2311yescharacteristic
53C2×D4×C37C2312yes—
54C22×C4×C37—21no—
55C22×C4×C37C2311yescharacteristic
56C2×C22⋊D37—21no—
57C2×C22⋊D37—22no—
58C2×C22⋊D37—24no—
59C2×C22⋊D37—24no—
60C2×C22⋊D37—48no—
61C22×Dic37D412yes—
62#10596962—22no—
63#10596962—22no—
64C2×D148—22no—
65C2×D148—22no—
66C2×D148—21no—
67C2×D148C2311yescharacteristic
68C2×D148C2312yes—
69C2×C4×D37—21no—
70C2×Dic74C2311yescharacteristic
71SD16×C37—24no—
72D8×C37—24no—
73M16×C37D414yescomplemented
74C2×C8×C37C2312yes—
75C22⋊Dic37—22no—
76#10596941—24no—
77#10596940—24no—
78#10596939—24no—
79#10596939—24no—
80#10596938—22no—
81#10596936—22no—
82C4×Dic37D412yes—
83C4×Dic37C2311yescharacteristic
84C4×Dic37C2311yescharacteristic
85#10596934D414yescomplemented
86C2×#64436C2312yes—
87D296—24no—
88#10596930—24no—
89C23×C37—21no—
90C23×C37—22no—
91C23×C37—44no—
92C23×C37—42no—
93C23×C37C2×D411yescharacteristic
94C22×D37—21no—
95C22×D37—22no—
96C22×D37—44no—
97C22×D37—42no—
98Q8×C37—21no—
99Q8×C37—21no—
100D4×C37—21no—
101D4×C37—22no—
102D4×C37—21no—
103D4×C37—22no—
104D4×C37—42no—
105D4×C37—42no—
106C2×C4×C37—21no—
107C2×C4×C37—42no—
108C2×C4×C37C2×D411yescharacteristic
109C2×C4×C37C2×D412yes—
110C2×C4×C37C2×D412yes—
111C2×C4×C37C2411yescharacteristic
112C22⋊D37—48no—
113C22⋊D37—42no—
114C22⋊D37—44no—
115C22⋊D37—48no—
116C2×Dic37—24no—
117C2×Dic37—21no—
118C2×Dic37C2×D412yes—
119C2×Dic37C2×D412yes—
120D148—22no—
121D148—21no—
122D148—21no—
123D148—22no—
124D148—42no—
125C4×D37—42no—
126Dic74—21no—
127Dic74—21no—
128C8×C37C2×D414yescomplemented
129#64436C2×D414yescomplemented
130C22×C37—22no—
131C22×C37—41no—
132C22×C37—42no—
133C22×C37—44no—
134C22×C37—42no—
135C22×C37—84no—
136C22×C37#12712yes—
137C22×C37C22×D411yescharacteristic
138C2×D37—41no—
139C2×D37—42no—
140C2×D37—44no—
141C2×D37—42no—
142C2×D37—84no—
143C4×C37—41no—
144C4×C37#12712yes—
145C4×C37C22×D411yescharacteristic
146C4×C37C22×D411yescharacteristic
147Dic37—22no—
148Dic37—41no—
149Dic37AGL(1,ℤ/8)14yescomplemented
150#3151—371nomaximal, Sylow
151C2×C37—22no—
152C2×C37—81no—
153C2×C37—82no—
154C2×C37C2×#12711yescharacteristic
155C2×C37C2×AGL(1,ℤ/8)12yes—
156D37—81no—
157D37—82no—
158C2×AGL(1,ℤ/8)—371no—
159C2×AGL(1,ℤ/8)—371no—
160C2×AGL(1,ℤ/8)—371no—
161C2×AGL(1,ℤ/8)D3711yescharacteristic, complemented
162#532—371no—
163C2×#127—371no—
164#496—372no—
165#496—372no—
166#493—372no—
167#492—372no—
168C4×M16—371no—
169C37#315111yescharacteristic, complemented, Sylow
170C2×#41—371no—
171C2×#41C2×D3711yescharacteristic
172C22×D4—371no—
173C22×D4—742no—
174C22×D4C2×D3711yescharacteristic
175AGL(1,ℤ/8)—24no—
176AGL(1,ℤ/8)—744no—
177AGL(1,ℤ/8)—744no—
178AGL(1,ℤ/8)—744no—
179C2×SD16—372no—
180C2×SD16—372no—
181C2×SD16—372no—
182C2×SD16C2×D3712yescomplemented
183C2×D8—372no—
184C2×D8—372no—
185C2×D8—372no—
186C2×D8C2×D3712yescomplemented
187C2×M16—371no—
188C2×M16C2×D3711yescharacteristic
189C4⋊Q8—371no—
190#127—372no—
191#127—372no—
192#127—371no—
193#127—742no—
194#124—371no—
195#124—371no—
196#121—742no—
197C4×D4—742no—
198C2×C42—371no—
199#97—372no—
200C4×C8—372no—
201C24—21no—
202C24—741no—
203#41—22no—
204#41—22no—
205#41—742no—
206#41—742no—
207C2×Q8—371no—
208C2×Q8C22×D3711yescharacteristic
209C2×D4—21no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—22no—
213C2×D4—371no—
214C2×D4—372no—
215C2×D4—742no—
216C2×D4—744no—
217C2×D4—744no—
218C2×D4—741no—
219C2×D4—742no—
220C2×D4—741no—
221C2×D4—742no—
222C2×D4—1488no—
223C2×D4C22×D3711yescharacteristic
224C2×D4C22×D3712yes—
225C22×C4—21no—
226C22×C4—372no—
227C22×C4—741no—
228C22×C4C22×D3711yescharacteristic
229SD16—24no—
230SD16—744no—
231SD16—744no—
232SD16—744no—
233D8—24no—
234D8—744no—
235D8—744no—
236D8—744no—
237M16—374no—
238M16C22⋊D3714yescomplemented
239C2×C8—372no—
240C2×C8C22×D3712yes—
241C4⋊C4—742no—
242C22⋊C4—742no—
243C22⋊C4—742no—
244C42—372no—
245C42—371no—
246C42—371no—
247C23—21no—
248C23—22no—
249C23—44no—
250C23—42no—
251C23—741no—
252C23—742no—
253C23—1484no—
254C23—1482no—
255C23D4×D3711yescharacteristic
256Q8—21no—
257Q8—21no—
258Q8—741no—
259Q8—741no—
260D4—21no—
261D4—22no—
262D4—21no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—741no—
267D4—742no—
268D4—741no—
269D4—742no—
270D4—1488no—
271D4—1484no—
272D4—1488no—
273D4—1482no—
274D4—1482no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—372no—
278C2×C4—372no—
279C2×C4—744no—
280C2×C4—741no—
281C2×C4—1482no—
282C2×C4D4×D3711yescharacteristic
283C2×C4D4×D3712yes—
284C2×C4C2×C22⋊D3712yes—
285C2×C4C23×D3711yescharacteristic
286C8—374no—
287C8C2×C22⋊D3714yescomplemented
288C22—22no—
289C22—44no—
290C22—42no—
291C22—41no—
292C22—42no—
293C22—84no—
294C22—2964no—
295C22—1484no—
296C22—1482no—
297C22—1481no—
298C22—1482no—
299C22#1192453212yes—
300C22C2×D4×D3711yescharacteristic
301C4—41no—
302C4—374no—
303C4—742no—
304C4—1481no—
305C4#1192453212yes—
306C4C2×D4×D3711yescharacteristic
307C4C22×C22⋊D3711yescharacteristic
308C2—22no—
309C2—82no—
310C2—81no—
311C2—2962no—
312C2—2961no—
313C2C2×#1192453211yescharacteristic
314C2AGL(1,ℤ/8)×D3712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×AGL(1,ℤ/8)×C37C2
socleC22×C37C22×D4
hypercenterC2×AGL(1,ℤ/8)D37
hypocenterC37#3151
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. C2×#11924562C2semidirect
3. C2×#11924561C2semidirect
4. #14558079C2semidirect
5. C2×#11924532C2semidirect
6. #14557921C2semidirect
7. #14557919C2semidirect
8. #14557908C2semidirect
9. #14557904C2semidirect
10. M16×Dic37C2semidirect
11. C2×AGL(1,ℤ/8)×C37C2semidirect
18. C2×#10596930C22semidirect
19. C2×#10596940C22semidirect
20. C2×#10596941C22semidirect
21. C2×D296C22semidirect
22. C2×#10596939C22semidirect
23. C2×#10596939C22semidirect
25. #11924534C22semidirect
29. #11924532C22semidirect
30. #11924525C22semidirect
31. #11924523C22semidirect
35. #11924446C22semidirect
36. C8×Dic37C22semidirect
40. C2×SD16×C37C22semidirect
41. C2×D8×C37C22semidirect
73. M16×C37D4semidirect
85. #10596934D4semidirect
128. C8×C37C2×D4semidirect
129. #64436C2×D4semidirect
149. Dic37AGL(1,ℤ/8)semidirect
161. C2×AGL(1,ℤ/8)D37semidirect
169. C37#3151semidirect
182. C2×SD16C2×D37semidirect
186. C2×D8C2×D37semidirect
238. M16C22⋊D37semidirect
287. C8C2×C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
C2×#119245622
C2×#119245612
#145580792
C2×#119245322
#145579212
#145579192
#145579082
#145579042
M16×Dic372
C2×AGL(1,ℤ/8)×C372
#315137