Finite Group Databasebeta

← #49169038

Subgroups — #49169038

Order 37504.

394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#34036741C211yesmaximal, characteristic, complemented
2#34036603C211yesmaximal, characteristic
3#34036471C212yesmaximal, complemented
4#34036430C212yesmaximal, complemented
5#34036335C212yesmaximal, complemented
6#34036282C212yesmaximal
7#34036231C212yesmaximal, complemented
8C4×#17989791C212yesmaximal, complemented
9#433×C293C211yesmaximal, characteristic, complemented
10C22×D1172C2211yescharacteristic
11C2×#17989791C2212yes—
12C2×#17989791C2212yes—
13#22627624C2211yescharacteristic, complemented
14#22627617—22no—
15#22627616C2211yescharacteristic, complemented
16#22627614—22no—
17#22627603C2212yes—
18C4×Dic586C2212yescomplemented
19C4×D1172C2212yes—
20C4×D1172C2212yes—
21#22627586—22no—
22#22627583C2211yescharacteristic
23C22⋊C4×D293—22no—
24#22627558C2212yescomplemented
25#22627556C2212yescomplemented
26#22627549C2212yescomplemented
27#22627549C2212yescomplemented
28#22627546C2212yes—
29#22627546C2212yes—
30#117×C293C2211yescharacteristic
31C4⋊C8×C293C2212yescomplemented
32C22⋊C8×C293C2212yes—
33#97×C293C2211yescharacteristic, complemented
34C4×C8×C293C2211yescharacteristic, complemented
35C23×D293—21no—
36C2×Dic586C2312yes—
37C2×D1172—24no—
38C2×D1172—21no—
39C2×D1172C2312yes—
40C2×C4×D293—22no—
41C2×C4×D293—22no—
42#17989791—24no—
43#17989791—24no—
44C4⋊Dic293—22no—
45C4⋊Dic293C2312yes—
46C4⋊Dic293C2312yes—
47#17989781—22no—
48#17989781—22no—
49#17989781—22no—
50C22⋊Dic293—22no—
51C22⋊Dic293—21no—
52#17989779—22no—
53#17989779—22no—
54C4×Dic293—21no—
55C4×Dic293—22no—
56C22×C4×C293C2311yescharacteristic
57C2×C8×C293C2312yes—
58C2×C8×C293C2312yes—
59C4⋊C4×C293D412yes—
60C22⋊C4×C293D412yes—
61C42×C293C2311yescharacteristic
62C42×C293C2311yescharacteristic
63C22×D293—22no—
64C22×D293—24no—
65C22×D293—82no—
66Dic586—22no—
67Dic586—22no—
68D1172—24no—
69D1172—22no—
70D1172#4114yes—
71C2×Dic293—22no—
72C2×Dic293—22no—
73C2×Dic293—22no—
74C4×D293—82no—
75C4×D293—82no—
76C23×C293C2×D411yescharacteristic
77C2×C4×C293—22no—
78C2×C4×C293C2×D412yes—
79C2×C4×C293C2×D412yes—
80C2×C4×C293C2×D411yescharacteristic
81C2×C4×C293C2411yescharacteristic
82C8×C293—22no—
83C8×C293—22no—
84C22×C293—21no—
85C22×C293—22no—
86C22×C293C22×D411yescharacteristic
87C2×D293—24no—
88C2×D293—42no—
89C2×D293—42no—
90C2×D293—84no—
91C4×C293—21no—
92C4×C293—22no—
93C4×C293—22no—
94C4×C293C2×#4112yes—
95Dic293—42no—
96Dic293—42no—
97Dic293—42no—
98C2×C293—41no—
99C2×C293#52511yescharacteristic
100C2×C293#57712yes—
101D293—44no—
102C293#312311yescharacteristic, complemented, Sylow
103#3123—2931nomaximal, Sylow
104#541—2931no—
105#518—2931no—
106#485—2932no—
107#478—2932no—
108#461—2932no—
109#450—2932no—
110#440—2932no—
111C4×SD16—2932no—
112#433D29311yescharacteristic, complemented
113C22×D4—2931no—
114C2×SD16—2932no—
115C2×SD16—2932no—
116C4⋊Q8—2931no—
117#126—5862no—
118#125—2931no—
119#125—5862no—
120C22⋊Q8—2932no—
121C4×Q8—2932no—
122C4×D4—2932no—
123C4×D4—2932no—
124C4×D4—5862no—
125#117—2931no—
126#117C2×D29311yescharacteristic
127C2×C22⋊C4—5862no—
128#107—2932no—
129#106—2932no—
130C4⋊C8C2×D29312yescomplemented
131#103—2932no—
132#103—2932no—
133#102—2932no—
134#102—2932no—
135C22⋊C8C2×D29312yes—
136#97C2×D29311yescharacteristic, complemented
137C4×C8C2×D29311yescharacteristic, complemented
138C24—5861no—
139C2×Q8—2932no—
140C2×D4—2932no—
141C2×D4—5864no—
142C2×D4—5861no—
143C22×C4—5862no—
144C22×C4—5862no—
145C22×C4C22×D29311yescharacteristic
146SD16—5864no—
147SD16—5864no—
148C2×C8C22×D29312yes—
149C2×C8C22×D29312yes—
150C4⋊C4—2932no—
151C4⋊C4—2932no—
152C4⋊C4—5862no—
153C4⋊C4—5862no—
154C4⋊C4—5862no—
155C4⋊C4—5862no—
156C4⋊C4D117212yes—
157C22⋊C4—5861no—
158C22⋊C4—5862no—
159C22⋊C4—5862no—
160C22⋊C4—5862no—
161C22⋊C4D117212yes—
162C42—5861no—
163C42—5862no—
164C42C22×D29311yescharacteristic
165C42C22×D29311yescharacteristic
166C23—23442no—
167C23—5864no—
168C23—5862no—
169C23C2×D117211yescharacteristic
170Q8—5862no—
171Q8—5862no—
172D4—2934no—
173D4—5864no—
174D4—5862no—
175C2×C4—22no—
176C2×C4—23442no—
177C2×C4—23442no—
178C2×C4—5862no—
179C2×C4—5862no—
180C2×C4—5862no—
181C2×C4C2×D117212yes—
182C2×C4C2×D117211yescharacteristic
183C2×C4C2×D117212yes—
184C2×C4C23×D29311yescharacteristic
185C8—22no—
186C8—22no—
187C22—21no—
188C22—22no—
189C22—23444no—
190C22—5864no—
191C22—11722no—
192C22—11722no—
193C22C22×D117211yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—11722no—
198C4—11722no—
199C4—11722no—
200C4#41×D29312yes—
201C2—41no—
202C2—11724no—
203C2#3403664111yescharacteristic
204C2#3403694112yes—
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#433×C293C2
socleC22×C293C22×D4
prime radicalC22×D1172C22
hypercenter#433D293
hypocenterC293#3123
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #34036741C2semidirect
3. #34036471C2semidirect
4. #34036430C2semidirect
5. #34036335C2semidirect
7. #34036231C2semidirect
8. C4×#17989791C2semidirect
9. #433×C293C2semidirect
13. #22627624C22semidirect
15. #22627616C22semidirect
18. C4×Dic586C22semidirect
24. #22627558C22semidirect
25. #22627556C22semidirect
26. #22627549C22semidirect
27. #22627549C22semidirect
31. C4⋊C8×C293C22semidirect
33. #97×C293C22semidirect
34. C4×C8×C293C22semidirect
102. C293#3123semidirect
112. #433D293semidirect
130. C4⋊C8C2×D293semidirect
136. #97C2×D293semidirect
137. C4×C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340367412
#340366032
#340364712
#340364302
#340363352
#340362822
#340362312
C4×#179897912
#433×C2932
#3123293