Finite Group Databasebeta

← #49169266

Subgroups — #49169266

Order 37504.

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

normal subgroups only

This group has 596 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×#22627650C212yesmaximal, complemented
2C2×#22627646C211yesmaximal, characteristic, complemented
3#34036696C212yesmaximal, complemented
4#34036517C214yesmaximal, complemented
5#34036512C212yesmaximal, complemented
6#34036504C212yesmaximal, complemented
7#34036084C211yesmaximal, characteristic, complemented
8C22×D8×C293C211yesmaximal, characteristic, complemented
9C2×#17989802C2212yes—
10#22627650—28no—
11#22627646—24no—
12C2×Dic1172C2211yescharacteristic, complemented
13C2×#17989791C2212yescomplemented
14C2×#17989790C2214yescomplemented
15C2×D2344C2211yescharacteristic, complemented
16C2×#17989787C2214yescomplemented
17C2×#17989786C2211yescharacteristic
18#22627620C2214yescomplemented
19#22627611C2214yescomplemented
20#22627595—24no—
21#22627593—24no—
22#22627583C2211yescharacteristic
23#22627534C2212yescomplemented
24C8×Dic293C2212yescomplemented
25C22×D4×C293C2212yes—
26C2×D8×C293—24no—
27C2×D8×C293C2212yes—
28C2×D8×C293C2212yes—
29C22×C8×C293C2211yescharacteristic
30#17989802—24no—
31#17989802—24no—
32C2×Dic586C2312yes—
33C2×D1172C2312yes—
34C2×C22⋊D293—28no—
35C2×C22⋊D293—22no—
36C2×C4×D293—22no—
37Dic1172—22no—
38#17989791—24no—
39#17989790—28no—
40D2344—22no—
41#17989787—28no—
42#17989786D414yescomplemented
43C2×#14556873C2312yes—
44C4⋊Dic293D412yes—
45C22⋊Dic293—28no—
46C22⋊Dic293D412yes—
47C4×Dic293C2312yes—
48C24×C293—22no—
49C2×D4×C293—24no—
50C2×D4×C293—24no—
51C2×D4×C293—22no—
52C2×D4×C293C2314yes—
53C22×C4×C293C2311yescharacteristic
54D8×C293—24no—
55D8×C293—24no—
56C2×C8×C293D414yescomplemented
57C2×C8×C293C2311yescharacteristic
58C2×C8×C293C2311yescharacteristic
59C22×D293—22no—
60Dic586—22no—
61Dic586—22no—
62D1172—22no—
63D1172—22no—
64C22⋊D293—44no—
65C22⋊D293—88no—
66C2×Dic293—22no—
67C2×Dic293C2×D414yes—
68C4×D293—44no—
69#14556873C2×D414yes—
70C23×C293—24no—
71C23×C293—44no—
72C23×C293—84no—
73C23×C293C2×D411yescharacteristic
74D4×C293—24no—
75D4×C293—24no—
76D4×C293—44no—
77C2×C4×C293C2×D411yescharacteristic
78C2×C4×C293C2×D412yes—
79C2×C4×C293C2×D412yes—
80C2×C4×C293C2411yescharacteristic
81C8×C293C2×D412yes—
82C8×C293C2×D412yes—
83C22×C293—22no—
84C22×C293—44no—
85C22×C293—48no—
86C22×C293—88no—
87C22×C293#12712yes—
88C22×C293C22×D411yescharacteristic
89C2×D293—42no—
90C2×D293—44no—
91C4×C293#12712yes—
92C4×C293C22×D411yescharacteristic
93C4×C293C22×D411yescharacteristic
94Dic293—24no—
95Dic293—42no—
96C2×C293—22no—
97C2×C293—84no—
98C2×C293C2×#12711yescharacteristic
99C2×C293#57612yes—
100D293—82no—
101C293#315511yescharacteristic, complemented, Sylow
102#3155—2931nomaximal, Sylow
103C2×AGL(1,ℤ/8)—2932no—
104C2×#135—2931no—
105C22×D8D29311yescharacteristic, complemented
106#535—2932no—
107#496—2934no—
108#495—2932no—
109#493—2932no—
110#405—2931no—
111C2×#41—2932no—
112C22×D4C2×D29312yes—
113AGL(1,ℤ/8)—5868no—
114#135—5864no—
115C2×Q16—2931no—
116C2×SD16—2934no—
117C2×SD16—2932no—
118C2×D8—24no—
119C2×D8—2934no—
120C2×D8—2931no—
121C2×D8C2×D29312yes—
122C2×D8C2×D29312yes—
123C2×M16—2931no—
124C22×C8C2×D29311yescharacteristic
125#127—2934no—
126#124—2934no—
127#121—5864no—
128#120—5864no—
129#117—2931no—
130#97—2932no—
131C4×C8—2932no—
132C24—22no—
133#41—5864no—
134#41—5864no—
135C2×Q8—2932no—
136C2×D4—24no—
137C2×D4—22no—
138C2×D4—24no—
139C2×D4—2932no—
140C2×D4—5868no—
141C2×D4—5862no—
142C2×D4C22×D29314yes—
143C22×C4—5862no—
144C22×C4C22×D29311yescharacteristic
145Q16—5862no—
146SD16—5868no—
147SD16—5864no—
148D8—24no—
149D8—24no—
150D8—5868no—
151D8—5862no—
152M16—2934no—
153C2×C8—2932no—
154C2×C8C22⋊D29314yescomplemented
155C2×C8C22×D29311yescharacteristic
156C2×C8C22×D29311yescharacteristic
157C4⋊C4—2932no—
158C22⋊C4—2932no—
159C22⋊C4—5868no—
160C42—2932no—
161C23—24no—
162C23—44no—
163C23—84no—
164C23—5862no—
165C23D4×D29311yescharacteristic
166Q8—5862no—
167Q8—5862no—
168D4—24no—
169D4—24no—
170D4—44no—
171D4—23448no—
172D4—5862no—
173D4—5862no—
174D4—11724no—
175C2×C4—2934no—
176C2×C4—5862no—
177C2×C4—11724no—
178C2×C4D4×D29311yescharacteristic
179C2×C4D4×D29312yes—
180C2×C4C2×C22⋊D29312yes—
181C2×C4C23×D29311yescharacteristic
182C8—2934no—
183C8C2×C22⋊D29312yes—
184C8C2×C22⋊D29312yes—
185C22—22no—
186C22—44no—
187C22—48no—
188C22—88no—
189C22—11722no—
190C22—11724no—
191C22#2262762012yes—
192C22C2×D4×D29311yescharacteristic
193C4—5864no—
194C4—11722no—
195C4#2262762012yes—
196C4C2×D4×D29311yescharacteristic
197C4C22×C22⋊D29311yescharacteristic
198C2—22no—
199C2—84no—
200C2—23442no—
201C2C2×#2262762011yescharacteristic
202C2#3403693012yes—
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC22×D8×C293C2
socleC22×C293C22×D4
hypercenterC22×D8D293
hypocenterC293#3155
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#22627650C2semidirect
2. C2×#22627646C2semidirect
3. #34036696C2semidirect
4. #34036517C2semidirect
5. #34036512C2semidirect
6. #34036504C2semidirect
7. #34036084C2semidirect
8. C22×D8×C293C2semidirect
12. C2×Dic1172C22semidirect
13. C2×#17989791C22semidirect
14. C2×#17989790C22semidirect
15. C2×D2344C22semidirect
16. C2×#17989787C22semidirect
18. #22627620C22semidirect
19. #22627611C22semidirect
23. #22627534C22semidirect
24. C8×Dic293C22semidirect
42. #17989786D4semidirect
56. C2×C8×C293D4semidirect
101. C293#3155semidirect
105. C22×D8D293semidirect
154. C2×C8C22⋊D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276502
C2×#226276462
#340366962
#340365172
#340365122
#340365042
#340360842
C22×D8×C2932
#3155293