Finite Group Databasebeta

← #49169251

Subgroups — #49169251

Order 37504.

572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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×#22627657C212yesmaximal, complemented
2C2×#22627652C212yesmaximal, complemented
3#34036679C211yesmaximal, characteristic, complemented
4C2×#22627612C211yesmaximal, characteristic, complemented
5#34036523C212yesmaximal, complemented
6#34036518C212yesmaximal, complemented
7#34036513C214yesmaximal, complemented
8C4×M16×C293C211yesmaximal, characteristic, complemented
9C2×#17989802C2212yes—
10C22×Dic586C2211yescharacteristic
11C22×D1172C2211yescharacteristic
12#22627657—28no—
13#22627652—28no—
14C2×Dic1172C2214yescomplemented
15C2×#17989791C2214yes—
16C2×#17989791C2214yescomplemented
17C2×D2344C2214yes—
18#22627624C2211yescharacteristic, complemented
19#22627621C2211yescharacteristic, complemented
20#22627612—22no—
21#22627612C2212yes—
22#22627612C2212yes—
23#22627612C2212yescomplemented
24#22627598—22no—
25C4×D1172—22no—
26C2×#17989779—22no—
27C2×M16×C293C2212yes—
28C2×C42×C293C2211yescharacteristic
29#97×C293C2212yescomplemented
30C4×C8×C293C2212yescomplemented
31C23×D293—21no—
32#17989802—24no—
33#17989802—24no—
34C2×Dic586—21no—
35C2×Dic586—24no—
36C2×Dic586C2312yes—
37C2×Dic586C2312yes—
38C2×D1172—24no—
39C2×D1172—22no—
40C2×D1172—21no—
41C2×D1172C2312yes—
42C2×D1172C2312yes—
43C2×C22⋊D293—22no—
44C22×Dic293—21no—
45C2×C4×D293—22no—
46Dic1172—28no—
47#17989791—28no—
48#17989791—28no—
49D2344—28no—
50C4⋊Dic293—22no—
51#17989779—24no—
52#17989779—24no—
53#17989779—24no—
54C22×C4×C293D412yes—
55C22×C4×C293C2311yescharacteristic
56M16×C293D418yescomplemented
57C2×C8×C293C2314yes—
58C42×C293D412yes—
59C42×C293C2311yescharacteristic
60C42×C293C2311yescharacteristic
61C22×D293—22no—
62C22×D293—22no—
63C22×D293—44no—
64C22×D293—42no—
65Dic586—22no—
66Dic586—24no—
67Dic586—22no—
68Dic586—42no—
69D1172—22no—
70D1172—24no—
71D1172—22no—
72D1172—44no—
73D1172—42no—
74C22⋊D293—44no—
75C2×Dic293—22no—
76C2×Dic293—22no—
77C2×Dic293—42no—
78C4×D293—44no—
79C23×C293C2×D411yescharacteristic
80C2×C4×C293—42no—
81C2×C4×C293C2×D412yes—
82C2×C4×C293C2×D412yes—
83C2×C4×C293C2×D411yescharacteristic
84C2×C4×C293C2×D414yes—
85C2×C4×C293C2411yescharacteristic
86C8×C293C2×D418yes—
87C22×C293—22no—
88C22×C293#12712yes—
89C22×C293C22×D411yescharacteristic
90C2×D293—42no—
91C2×D293—42no—
92C2×D293—44no—
93C2×D293—44no—
94C2×D293—84no—
95C4×C293—22no—
96C4×C293—22no—
97C4×C293#12712yes—
98C4×C293C22×D412yes—
99Dic293—42no—
100Dic293—42no—
101C2×C293—22no—
102C2×C293C2×#12711yescharacteristic
103C2×C293#57512yes—
104D293—82no—
105D293—82no—
106C293#315311yescharacteristic, complemented, Sylow
107#3153—2931nomaximal, Sylow
108C2×#137—2932no—
109C2×AGL(1,ℤ/8)—2932no—
110#532—2931no—
111C2×#124—2931no—
112#497—2932no—
113#496—2932no—
114#495—2934no—
115C4×M16D29311yescharacteristic, complemented
116C2×#41—2932no—
117C22×Q8—2931no—
118C22×D4—2931no—
119#137—5868no—
120AGL(1,ℤ/8)—5868no—
121C2×Q16—2934no—
122C2×SD16—2934no—
123C2×SD16—2934no—
124C2×D8—2934no—
125C2×M16C2×D29312yes—
126C4⋊Q8—2931no—
127#127—2931no—
128#124—2932no—
129#124—2932no—
130#124—2932no—
131#124—5862no—
132#121—5862no—
133C4×D4—5862no—
134C2×C22⋊C4—5862no—
135C2×C42C2×D29311yescharacteristic
136#97C2×D29312yescomplemented
137C4×C8C2×D29312yescomplemented
138C24—5861no—
139#41—5864no—
140#41—5864no—
141C2×Q8—2932no—
142C2×Q8—2932no—
143C2×Q8—5861no—
144C2×Q8—5864no—
145C2×D4—2932no—
146C2×D4—2932no—
147C2×D4—5862no—
148C2×D4—5864no—
149C2×D4—5862no—
150C2×D4—5861no—
151C22×C4—5861no—
152C22×C4—5862no—
153C22×C4D117212yes—
154C22×C4C22×D29311yescharacteristic
155Q16—5868no—
156SD16—5868no—
157SD16—5868no—
158D8—5868no—
159M16D117218yescomplemented
160C2×C8C22×D29314yes—
161C4⋊C4—5862no—
162C22⋊C4—5864no—
163C22⋊C4—5864no—
164C22⋊C4—5864no—
165C42D117212yes—
166C42C22×D29311yescharacteristic
167C42C22×D29311yescharacteristic
168C23—5862no—
169C23—5862no—
170C23—11724no—
171C23—11722no—
172C23C2×D117211yescharacteristic
173Q8—5862no—
174Q8—5864no—
175Q8—5862no—
176Q8—11722no—
177D4—5862no—
178D4—5864no—
179D4—5862no—
180D4—11724no—
181D4—11724no—
182D4—11722no—
183C2×C4—42no—
184C2×C4—5862no—
185C2×C4—5862no—
186C2×C4—11722no—
187C2×C4—11724no—
188C2×C4C2×D117212yes—
189C2×C4C2×D117212yes—
190C2×C4C2×D117211yescharacteristic
191C2×C4C2×D117214yes—
192C2×C4C23×D29311yescharacteristic
193C8C2×D117218yes—
194C22—22no—
195C22—23444no—
196C22—11722no—
197C22—11722no—
198C22—11724no—
199C22—11724no—
200C22#2262762112yes—
201C22C22×D117211yescharacteristic
202C4—22no—
203C4—22no—
204C4—11722no—
205C4—11722no—
206C4#2262762112yes—
207C4C22×D117212yes—
208C2—22no—
209C2—23442no—
210C2—23442no—
211C2C2×#2262762111yescharacteristic
212C2#3403692912yes—
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×M16×C293C2
socleC22×C293C22×D4
hypercenterC4×M16D293
hypocenterC293#3153
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#22627657C2semidirect
2. C2×#22627652C2semidirect
3. #34036679C2semidirect
4. C2×#22627612C2semidirect
5. #34036523C2semidirect
6. #34036518C2semidirect
7. #34036513C2semidirect
8. C4×M16×C293C2semidirect
14. C2×Dic1172C22semidirect
16. C2×#17989791C22semidirect
18. #22627624C22semidirect
19. #22627621C22semidirect
23. #22627612C22semidirect
29. #97×C293C22semidirect
30. C4×C8×C293C22semidirect
56. M16×C293D4semidirect
106. C293#3153semidirect
115. C4×M16D293semidirect
136. #97C2×D293semidirect
137. C4×C8C2×D293semidirect
159. M16D1172semidirect

Maximal subgroups

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

subgroupindex
C2×#226276572
C2×#226276522
#340366792
C2×#226276122
#340365232
#340365182
#340365132
C4×M16×C2932
#3153293