Finite Group Databasebeta

← #49169249

Subgroups — #49169249

Order 37504.

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

normal subgroups only

This group has 572 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×#22627655C212yesmaximal, complemented
2C2×#22627650C212yesmaximal, complemented
3#34036679C211yesmaximal, characteristic, complemented
4#34036524C212yesmaximal, complemented
5#34036519C212yesmaximal, complemented
6#34036511C214yesmaximal, complemented
7C4×#17989786C211yesmaximal, characteristic, complemented
8C2×#124×C293C211yesmaximal, characteristic, complemented
9C2×#17989802C2212yes—
10#22627655—28no—
11#22627650—28no—
12C2×#17989792C2214yescomplemented
13C2×#17989790C2214yes—
14C2×#17989789C2214yescomplemented
15C2×#17989787C2214yes—
16C2×#17989786C2212yes—
17#22627624C2211yescharacteristic, complemented
18#22627621C2211yescharacteristic, complemented
19#22627612C2212yescomplemented
20#22627598—22no—
21C4×D1172—22no—
22#22627535C2212yescomplemented
23C4×#14556873C2212yescomplemented
24C22×Q8×C293C2211yescharacteristic
25C22×D4×C293C2211yescharacteristic
26#124×C293—22no—
27#124×C293C2212yes—
28#124×C293C2212yes—
29C2×C22⋊C4×C293—22no—
30C2×C42×C293C2211yescharacteristic
31#17989802—24no—
32#17989802—24no—
33C2×Dic586C2312yes—
34C2×D1172—22no—
35C2×D1172C2312yes—
36C2×C22⋊D293—22no—
37C2×C4×D293—22no—
38#17989792—28no—
39#17989790—28no—
40#17989789—28no—
41#17989787—28no—
42#17989786D418yescomplemented
43C2×#14556873C2314yes—
44C4⋊Dic293—22no—
45#17989779—24no—
46C24×C293—21no—
47C2×Q8×C293—21no—
48C2×Q8×C293—24no—
49C2×Q8×C293C2312yes—
50C2×D4×C293—24no—
51C2×D4×C293—21no—
52C2×D4×C293C2312yes—
53C22×C4×C293—21no—
54C22×C4×C293D412yes—
55C22×C4×C293C2311yescharacteristic
56C22⋊C4×C293—24no—
57C22⋊C4×C293—24no—
58C42×C293D412yes—
59C42×C293C2311yescharacteristic
60C42×C293C2311yescharacteristic
61C22×D293—22no—
62Dic586—22no—
63Dic586—22no—
64D1172—22no—
65D1172—22no—
66D1172—44no—
67C22⋊D293—44no—
68C2×Dic293—22no—
69C4×D293—44no—
70#14556873C2×D418yes—
71C23×C293—22no—
72C23×C293—44no—
73C23×C293—42no—
74C23×C293C2×D411yescharacteristic
75Q8×C293—24no—
76Q8×C293—42no—
77D4×C293—24no—
78D4×C293—42no—
79C2×C4×C293—22no—
80C2×C4×C293—42no—
81C2×C4×C293—42no—
82C2×C4×C293C2×D414yes—
83C2×C4×C293C2×D412yes—
84C2×C4×C293C2×D412yes—
85C2×C4×C293C2×D411yescharacteristic
86C2×C4×C293C2411yescharacteristic
87C22×C293—22no—
88C22×C293—42no—
89C22×C293—44no—
90C22×C293—84no—
91C22×C293#12712yes—
92C22×C293C22×D411yescharacteristic
93C2×D293—42no—
94C2×D293—44no—
95C4×C293—22no—
96C4×C293—22no—
97C4×C293—42no—
98C4×C293#12712yes—
99C4×C293C22×D412yes—
100Dic293—42no—
101C2×C293—22no—
102C2×C293—82no—
103C2×C293C2×#12711yescharacteristic
104C2×C293#57512yes—
105D293—82no—
106C293#315311yescharacteristic, complemented, Sylow
107#3153—2931nomaximal, Sylow
108C2×#137—2932no—
109C2×AGL(1,ℤ/8)—2932no—
110#532—2931no—
111C2×#124D29311yescharacteristic, complemented
112#497—2932no—
113#496—2932no—
114#495—2934no—
115C4×M16—2931no—
116C2×#41—2932no—
117C22×Q8C2×D29311yescharacteristic
118C22×D4C2×D29311yescharacteristic
119#137—5868no—
120AGL(1,ℤ/8)—5868no—
121C2×Q16—2934no—
122C2×SD16—2934no—
123C2×SD16—2934no—
124C2×D8—2934no—
125C2×M16—2932no—
126C4⋊Q8—2931no—
127#127—2931no—
128#124—22no—
129#124—2932no—
130#124C2×D29312yes—
131#124C2×D29312yes—
132#121—5862no—
133C4×D4—5862no—
134C2×C22⋊C4—22no—
135C2×C42C2×D29311yescharacteristic
136#97—2932no—
137C4×C8—2932no—
138C24—21no—
139#41—5864no—
140#41—5864no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—2932no—
144C2×Q8C22×D29312yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—2932no—
148C2×D4—5862no—
149C2×D4—5862no—
150C2×D4C22×D29312yes—
151C22×C4—21no—
152C22×C4—5862no—
153C22×C4C22⋊D29312yes—
154C22×C4C22×D29311yescharacteristic
155Q16—5868no—
156SD16—5868no—
157SD16—5868no—
158D8—5868no—
159M16—2938no—
160C2×C8—2934no—
161C4⋊C4—5862no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—5864no—
165C42C22⋊D29312yes—
166C42C22×D29311yescharacteristic
167C42C22×D29311yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—5862no—
172C23C2×C22⋊D29311yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—5862no—
176Q8—5862no—
177D4—24no—
178D4—42no—
179D4—5862no—
180D4—5862no—
181D4—11724no—
182D4—11724no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—5862no—
187C2×C4—11724no—
188C2×C4D4×D29314yes—
189C2×C4C2×C22⋊D29312yes—
190C2×C4C2×C22⋊D29312yes—
191C2×C4C2×C22⋊D29311yescharacteristic
192C2×C4C23×D29311yescharacteristic
193C8—2938no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—11722no—
199C22—11724no—
200C22#2262762012yes—
201C22C22×C22⋊D29311yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—11722no—
206C4#2262762012yes—
207C4C2×D4×D29312yes—
208C2—22no—
209C2—82no—
210C2—23442no—
211C2C2×#2262762011yescharacteristic
212C2#3403692712yes—
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×#124×C293C2
socleC22×C293C22×D4
hypercenterC2×#124D293
hypocenterC293#3153
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#22627655C2semidirect
2. C2×#22627650C2semidirect
3. #34036679C2semidirect
4. #34036524C2semidirect
5. #34036519C2semidirect
6. #34036511C2semidirect
7. C4×#17989786C2semidirect
8. C2×#124×C293C2semidirect
12. C2×#17989792C22semidirect
14. C2×#17989789C22semidirect
17. #22627624C22semidirect
18. #22627621C22semidirect
19. #22627612C22semidirect
22. #22627535C22semidirect
23. C4×#14556873C22semidirect
42. #17989786D4semidirect
106. C293#3153semidirect
111. C2×#124D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276552
C2×#226276502
#340366792
#340365242
#340365192
#340365112
C4×#179897862
C2×#124×C2932
#3153293