Finite Group Databasebeta

← #44529691

Subgroups — #44529691

Order 31168.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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×#21441262C211yesmaximal, characteristic, complemented
2C22×D1948C211yesmaximal, characteristic, complemented
3#29510204C211yesmaximal, characteristic, complemented
4#29510200C212yesmaximal, complemented
5#29510190C211yesmaximal, characteristic, complemented
6#29510190C212yesmaximal, complemented
7#29510185C212yesmaximal, complemented
8#29510177C211yesmaximal, characteristic, complemented
9C4×C22⋊D487C211yesmaximal, characteristic, complemented
10C22⋊C4×D487C212yesmaximal, complemented
11C22⋊Q8×C487C211yesmaximal, characteristic, complemented
12C23×D487C2212yes—
13#21441262—24no—
14C2×D1948—24no—
15C2×D1948C2212yes—
16C2×D1948C2211yescharacteristic
17C2×D1948C2211yescharacteristic
18C2×D1948C2212yescomplemented
19C2×D1948C2212yescomplemented
20C2×C22⋊D487C2211yescharacteristic
21C2×C4×D487C2212yescomplemented
22C2×C4×D487C2211yescharacteristic, complemented
23C2×C4×D487C2212yescomplemented
24Dic487⋊C4C2211yescharacteristic, complemented
25C22⋊Dic487C2211yescharacteristic
26(C2×D487)⋊C4C2212yescomplemented
27(C2×D487)⋊C4C2212yescomplemented
28(C2×D487)⋊C4C2211yescharacteristic, complemented
29(C2×D487)⋊C4C2212yescomplemented
30(C2×D487)⋊C4C2212yescomplemented
31C4×Dic487C2211yescharacteristic, complemented
32C2×Q8×C487C2211yescharacteristic, complemented
33C22×C4×C487C2211yescharacteristic
34C4⋊C4×C487C2211yescharacteristic, complemented
35C4⋊C4×C487C2212yescomplemented
36C22⋊C4×C487C2212yes—
37C22×D487—24no—
38C22×D487—24no—
39C22×D487—42no—
40C22×D487C2312yes—
41C22×D487C2311yescharacteristic
42C22×D487C2312yes—
43D1948—24no—
44D1948—24no—
45D1948—22no—
46D1948—42no—
47D1948D414yescomplemented
48C22⋊D487—22no—
49C2×Dic487C2311yescharacteristic
50C2×Dic487C2311yescharacteristic
51C2×Dic487C2311yescharacteristic
52C4×D487—24no—
53C4×D487—22no—
54C4×D487—42no—
55C23×C487C2311yescharacteristic
56Q8×C487—22no—
57C2×C4×C487—22no—
58C2×C4×C487C2312yes—
59C2×C4×C487C2312yes—
60C2×C4×C487C2311yescharacteristic
61C2×C4×C487C2311yescharacteristic
62C22×C487—21no—
63C22×C487—21no—
64C22×C487#4112yescomplemented
65C22×C487C2411yescharacteristic
66C2×D487—22no—
67C2×D487—22no—
68C2×D487—21no—
69C2×D487—22no—
70C2×D487—21no—
71C2×D487—22no—
72C2×D487—21no—
73C2×D487—22no—
74C2×D487—48no—
75C2×D487C2×D414yes—
76C4×C487—21no—
77C4×C487—22no—
78C4×C487—22no—
79C4×C487C2×D412yes—
80Dic487—21no—
81Dic487—21no—
82Dic487—21no—
83C2×C487—22no—
84C2×C487C22×D411yescharacteristic
85C2×C487C2×#4111yescharacteristic
86C2×C487H(5,𝔽2)11yescharacteristic
87D487—24no—
88D487—41no—
89D487—42no—
90C487#54611yescharacteristic, complemented, Sylow
91#546—4871nomaximal, Sylow
92C2×#41—4871no—
93C22×D4—4871no—
94#124—4871no—
95#123—4872no—
96C22⋊Q8D48711yescharacteristic, complemented
97#121—4871no—
98#121—4872no—
99#120—4872no—
100C4×D4—4871no—
101C4×D4—4871no—
102C2×C22⋊C4—4872no—
103C24—4872no—
104#41—9744no—
105C2×Q8C2×D48711yescharacteristic, complemented
106C2×D4—9744no—
107C2×D4—4871no—
108C2×D4—4872no—
109C2×D4—4872no—
110C2×D4—4872no—
111C2×D4—4871no—
112C2×D4—4871no—
113C22×C4—4872no—
114C22×C4—4872no—
115C22×C4—4871no—
116C22×C4C2×D48711yescharacteristic
117C4⋊C4—4871no—
118C4⋊C4C2×D48711yescharacteristic, complemented
119C4⋊C4C2×D48712yescomplemented
120C22⋊C4—4871no—
121C22⋊C4—4872no—
122C22⋊C4—4872no—
123C22⋊C4—4872no—
124C22⋊C4—4871no—
125C22⋊C4—4872no—
126C22⋊C4C2×D48712yes—
127C42—4871no—
128C23—19482no—
129C23—9744no—
130C23—9744no—
131C23—4872no—
132C23—4871no—
133C23—4872no—
134C23C22×D48711yescharacteristic
135Q8—22no—
136D4—19482no—
137D4—9744no—
138D4—9744no—
139D4—9742no—
140D4—9742no—
141D4—4874no—
142C2×C4—22no—
143C2×C4—19482no—
144C2×C4—9744no—
145C2×C4—9742no—
146C2×C4—4871no—
147C2×C4—4871no—
148C2×C4—4871no—
149C2×C4C22×D48712yes—
150C2×C4C22×D48712yes—
151C2×C4C22×D48711yescharacteristic
152C2×C4C22×D48711yescharacteristic
153C22—21no—
154C22—21no—
155C22—19488no—
156C22—9741no—
157C22—9742no—
158C22—9741no—
159C22—9742no—
160C22—9741no—
161C22—9742no—
162C22—9742no—
163C22—9742no—
164C22—4874no—
165C22#2144126212yescomplemented
166C22C23×D48711yescharacteristic
167C4—21no—
168C4—22no—
169C4—22no—
170C4—9741no—
171C4—9741no—
172C4—9741no—
173C4D4×D48712yes—
174C2—22no—
175C2—19482no—
176C2—19481no—
177C2—9744no—
178C2C2×D4×D48711yescharacteristic
179C2C2×#2144126211yescharacteristic
180C2#2951026111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D487
commutator, socle, cosocleC22×C487C24
FittingC22⋊Q8×C487C2
hypercenterC22⋊Q8D487
hypocenterC487#546
LCSG ▷ C22×C487 ▷ C487
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#21441262C2semidirect
2. C22×D1948C2semidirect
3. #29510204C2semidirect
4. #29510200C2semidirect
5. #29510190C2semidirect
6. #29510190C2semidirect
7. #29510185C2semidirect
8. #29510177C2semidirect
9. C4×C22⋊D487C2semidirect
10. C22⋊C4×D487C2semidirect
11. C22⋊Q8×C487C2semidirect
18. C2×D1948C22semidirect
19. C2×D1948C22semidirect
21. C2×C4×D487C22semidirect
22. C2×C4×D487C22semidirect
23. C2×C4×D487C22semidirect
24. Dic487⋊C4C22semidirect
26. (C2×D487)⋊C4C22semidirect
27. (C2×D487)⋊C4C22semidirect
28. (C2×D487)⋊C4C22semidirect
29. (C2×D487)⋊C4C22semidirect
30. (C2×D487)⋊C4C22semidirect
31. C4×Dic487C22semidirect
32. C2×Q8×C487C22semidirect
34. C4⋊C4×C487C22semidirect
35. C4⋊C4×C487C22semidirect
47. D1948D4semidirect
64. C22×C487#41semidirect
90. C487#546semidirect
96. C22⋊Q8D487semidirect
105. C2×Q8C2×D487semidirect
118. C4⋊C4C2×D487semidirect
119. C4⋊C4C2×D487semidirect
165. C22#21441262semidirect

Maximal subgroups

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

subgroupindex
C2×#214412622
C22×D19482
#295102042
#295102002
#295101902
#295101852
#295101772
C4×C22⋊D4872
C22⋊C4×D4872
C22⋊Q8×C4872
#546487