Finite Group Databasebeta

← #37527242

Subgroups — #37527242

Order 22976.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19153342C211yesmaximal, characteristic, complemented
2#41×D359C211yesmaximal, characteristic, complemented
3#26040047C212yesmaximal, complemented
4#26040046C211yesmaximal, characteristic, complemented
5#26040043C211yesmaximal, characteristic, complemented
6#26040042C212yesmaximal, complemented
7#26040040C211yesmaximal, characteristic, complemented
8#26040038C212yesmaximal, complemented
9#26040036C212yesmaximal, complemented
10M16×D359C211yesmaximal, characteristic, complemented
11#137×C359C211yesmaximal, characteristic, complemented
12#19153342—21no—
13#19153342—21no—
14#19153342C2212yes—
15#19153342C2212yescomplemented
16#19153342C2211yescharacteristic, complemented
17#19153341—21no—
18#19153341C2211yescharacteristic
19#19153340—21no—
20#19153340C2211yescharacteristic, complemented
21Q8×D359C2211yescharacteristic, complemented
22C2×D1436—21no—
23C2×D1436C2211yescharacteristic, complemented
24D4×D359—21no—
25D4×D359C2211yescharacteristic, complemented
26C2×C4×D359—21no—
27C2×C4×D359—21no—
28C2×C4×D359C2211yescharacteristic
29#19153331C2212yescomplemented
30#19153330C2212yescomplemented
31#19153328C2212yescomplemented
32#19153328C2212yescomplemented
33D2872C2212yescomplemented
34#19153326C2212yescomplemented
35#19153325C2211yescharacteristic, complemented
36#19153324C2212yescomplemented
37C8×D359C2212yescomplemented
38#41×C359C2211yescharacteristic
39C2×Q8×C359C2211yescharacteristic, complemented
40Q16×C359C2212yescomplemented
41SD16×C359C2212yescomplemented
42M16×C359C2211yescharacteristic, complemented
43C22×D359—21no—
44C22×D359—21no—
45C22×D359D411yescharacteristic
46Dic718—21no—
47Dic718C2311yescharacteristic
48D1436—21no—
49D1436—22no—
50D1436—22no—
51D1436—21no—
52D1436C2312yes—
53D1436C2311yescharacteristic
54C22⋊D359—21no—
55C22⋊D359—21no—
56C22⋊D359—21no—
57C2×Dic359—21no—
58C2×Dic359D411yescharacteristic
59C4×D359—21no—
60C4×D359—21no—
61C4×D359—21no—
62C4×D359—22no—
63C4×D359—22no—
64C4×D359D411yescharacteristic
65C4×D359D411yescharacteristic
66C4×D359C2311yescharacteristic
67C4×D359C2311yescharacteristic
68C359⋊C8C2312yes—
69Q8×C359—21no—
70Q8×C359C2312yes—
71Q8×C359C2311yescharacteristic
72D4×C359—21no—
73D4×C359C2311yescharacteristic
74C2×C4×C359—21no—
75C2×C4×C359—21no—
76C2×C4×C359C2311yescharacteristic
77C8×C359C2312yes—
78C22×C359—21no—
79C22×C359C2×D411yescharacteristic
80C2×D359—21no—
81C2×D359—22no—
82C2×D359—41no—
83C2×D359—42no—
84C2×D359—42no—
85C2×D359C2×D411yescharacteristic
86C2×D359C2×D411yescharacteristic
87C4×C359—21no—
88C4×C359—22no—
89C4×C359C2×D411yescharacteristic
90C4×C359C2411yescharacteristic
91Dic359—21no—
92Dic359C2×D411yescharacteristic
93Dic359C2×D411yescharacteristic
94C2×C359—21no—
95C2×C359—41no—
96C2×C359C22×D411yescharacteristic
97D359—21no—
98D359—21no—
99D359—41no—
100D359—42no—
101C359#57511yescharacteristic, complemented, Sylow
102#575—3591nomaximal, Sylow
103C2×#41—3591no—
104C2×#41—3591no—
105#137—3591no—
106#137—3592no—
107#137D35911yescharacteristic, complemented
108AGL(1,ℤ/8)—3591no—
109AGL(1,ℤ/8)—3592no—
110AGL(1,ℤ/8)—3591no—
111#135—3592no—
112#135—3592no—
113C2×M16—3591no—
114#41—3591no—
115#41—3592no—
116#41—3592no—
117#41—3591no—
118#41—3591no—
119#41—7181no—
120#41—7181no—
121#41—7181no—
122#41—7181no—
123#41C2×D35911yescharacteristic
124C2×Q8—3591no—
125C2×Q8C2×D35911yescharacteristic, complemented
126C2×D4—3591no—
127C2×D4—3591no—
128C2×D4—7181no—
129C2×D4—7181no—
130C22×C4—3591no—
131C22×C4—7181no—
132C22×C4—7181no—
133Q16—3592no—
134Q16C2×D35912yescomplemented
135SD16—3592no—
136SD16—3592no—
137SD16—3592no—
138SD16C2×D35912yescomplemented
139D8—3592no—
140D8—3592no—
141M16—3591no—
142M16—3592no—
143M16C2×D35911yescharacteristic, complemented
144C2×C8—3592no—
145C23—3591no—
146C23—7181no—
147C23—7181no—
148Q8—21no—
149Q8—3591no—
150Q8—7181no—
151Q8C22×D35911yescharacteristic
152Q8C22×D35912yes—
153D4—21no—
154D4—3592no—
155D4—3591no—
156D4—7181no—
157D4—7182no—
158D4—7182no—
159D4—7181no—
160D4—7181no—
161D4—7181no—
162D4—7181no—
163D4C22×D35911yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—3591no—
167C2×C4—3591no—
168C2×C4—3591no—
169C2×C4—3591no—
170C2×C4—3591no—
171C2×C4—7181no—
172C2×C4—7182no—
173C2×C4—7182no—
174C2×C4—7181no—
175C2×C4—7181no—
176C2×C4—7181no—
177C2×C4C22×D35911yescharacteristic
178C8—3592no—
179C8C22×D35912yes—
180C22—21no—
181C22—3591no—
182C22—3591no—
183C22—14362no—
184C22—14361no—
185C22—14362no—
186C22—7182no—
187C22—7181no—
188C22D4×D35911yescharacteristic
189C4—21no—
190C4—22no—
191C4—3591no—
192C4—3591no—
193C4—7181no—
194C4D4×D35911yescharacteristic
195C4C23×D35911yescharacteristic
196C2—21no—
197C2—41no—
198C2—14362no—
199C2—14361no—
200C2—7181no—
201C2—7181no—
202C2C2×D4×D35911yescharacteristic
subgroupG/H
centerC2C2×D4×D359
commutator, cosocleC4×C359C24
FrattiniC4C23×D359
Fitting#137×C359C2
socleC2×C359C22×D4
hypercenter#137D359
hypocenterC359#575
LCSG ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#19153342C2semidirect
2. #41×D359C2semidirect
3. #26040047C2semidirect
4. #26040046C2semidirect
5. #26040043C2semidirect
6. #26040042C2semidirect
7. #26040040C2semidirect
8. #26040038C2semidirect
9. #26040036C2semidirect
10. M16×D359C2semidirect
11. #137×C359C2semidirect
15. #19153342C22semidirect
16. #19153342C22semidirect
20. #19153340C22semidirect
21. Q8×D359C22semidirect
23. C2×D1436C22semidirect
25. D4×D359C22semidirect
29. #19153331C22semidirect
30. #19153330C22semidirect
31. #19153328C22semidirect
32. #19153328C22semidirect
33. D2872C22semidirect
34. #19153326C22semidirect
35. #19153325C22semidirect
36. #19153324C22semidirect
37. C8×D359C22semidirect
39. C2×Q8×C359C22semidirect
40. Q16×C359C22semidirect
41. SD16×C359C22semidirect
42. M16×C359C22semidirect
101. C359#575semidirect
107. #137D359semidirect
125. C2×Q8C2×D359semidirect
134. Q16C2×D359semidirect
138. SD16C2×D359semidirect
143. M16C2×D359semidirect

Maximal subgroups

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

subgroupindex
C2×#191533422
#41×D3592
#260400472
#260400462
#260400432
#260400422
#260400402
#260400382
#260400362
M16×D3592
#137×C3592
#575359