Finite Group Databasebeta

← #16829979

Subgroups — #16829979

Order 3712.

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×#11745311C212yesmaximal, complemented
2C22×D232C211yesmaximal, characteristic, complemented
3#14271727C212yesmaximal, complemented
4#14271549C214yesmaximal, complemented
5#14271548C212yesmaximal, complemented
6#14271538C212yesmaximal, complemented
7#14271118C211yesmaximal, characteristic, complemented
8C2×C29×#135C211yesmaximal, characteristic, complemented
9C2×#41×C29C2212yes—
10C22×D116C2212yes—
11C29×#135—24no—
12C2×Q16×C29C2211yescharacteristic, complemented
13C2×SD16×C29C2212yescomplemented
14C2×D8×C29C2211yescharacteristic, complemented
15C22×C8×C29C2211yescharacteristic
16#11745311—28no—
17#11745309C2214yescomplemented
18C2×#90784C2214yescomplemented
19#11745302C2214yescomplemented
20#11745299—24no—
21C2×#90782C2214yescomplemented
22#11745292—24no—
23#11745288C2211yescharacteristic
24C2×#90777C2211yescharacteristic
25C2×D232—24no—
26C2×D232C2212yes—
27C2×D232C2212yes—
28#11745163C2212yescomplemented
29C8×Dic29C2212yescomplemented
30C23×D29—22no—
31#41×C29—24no—
32#41×C29—24no—
33C2×Q8×C29C2312yes—
34C2×D4×C29—22no—
35C2×D4×C29C2312yes—
36C22×C4×C29—22no—
37C22×C4×C29C2311yescharacteristic
38C2×C22⋊D29—28no—
39C2×D116—24no—
40C2×D116—24no—
41C2×D116—22no—
42C2×D116C2314yes—
43Q16×C29—22no—
44SD16×C29—24no—
45D8×C29—22no—
46C2×C8×C29D414yescomplemented
47C2×C8×C29C2311yescharacteristic
48C2×C8×C29C2311yescharacteristic
49C22⋊Dic29D412yes—
50#90784—28no—
51#90782—28no—
52#90781—28no—
53C4⋊Dic29D412yes—
54C4×Dic29C2312yes—
55#90777D414yescomplemented
56C2×#6597C2312yes—
57D232—24no—
58D232—24no—
59C23×C29—22no—
60C23×C29C2×D411yescharacteristic
61C22×D29—24no—
62C22×D29—44no—
63C22×D29—84no—
64Q8×C29—22no—
65Q8×C29—22no—
66D4×C29—22no—
67D4×C29—22no—
68D4×C29—44no—
69C2×C4×C29—22no—
70C2×C4×C29—44no—
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D412yes—
73C2×C4×C29C2×D412yes—
74C2×C4×C29C2411yescharacteristic
75C22⋊D29—88no—
76C2×Dic29C2×D414yes—
77D116—24no—
78D116—24no—
79D116—44no—
80C8×C29C2×D412yes—
81C8×C29C2×D412yes—
82#6597C2×D414yes—
83#3155—291nomaximal, Sylow
84C22×C29—22no—
85C22×C29—42no—
86C22×C29—44no—
87C22×C29#12712yes—
88C22×C29C22×D411yescharacteristic
89C2×D29—44no—
90C2×D29—48no—
91C2×D29—88no—
92C4×C29—42no—
93C4×C29#12712yes—
94C4×C29C22×D411yescharacteristic
95C4×C29C22×D411yescharacteristic
96Dic29—24no—
97C2×AGL(1,ℤ/8)—292no—
98C2×#135D2911yescharacteristic, complemented
99C22×D8—291no—
100#535—292no—
101#496—294no—
102#495—292no—
103#493—292no—
104#405—291no—
105C2×C29—22no—
106C2×C29—82no—
107C2×C29C2×#12711yescharacteristic
108C2×C29#57612yes—
109D29—84no—
110C2×#41C2×D2912yes—
111C22×D4—292no—
112AGL(1,ℤ/8)—588no—
113#135—24no—
114C2×Q16C2×D2911yescharacteristic, complemented
115C2×SD16—294no—
116C2×SD16C2×D2912yescomplemented
117C2×D8—294no—
118C2×D8—292no—
119C2×D8—292no—
120C2×D8—584no—
121C2×D8C2×D2911yescharacteristic, complemented
122C2×M16—291no—
123C22×C8C2×D2911yescharacteristic
124#127—294no—
125#124—294no—
126#121—584no—
127#120—584no—
128#117—291no—
129#97—292no—
130C4×C8—292no—
131C29#315511yescharacteristic, complemented, Sylow
132C24—582no—
133#41—24no—
134#41—24no—
135C2×Q8C22×D2912yes—
136C2×D4—22no—
137C2×D4—294no—
138C2×D4—588no—
139C2×D4—584no—
140C2×D4—582no—
141C2×D4—584no—
142C2×D4C22×D2912yes—
143C22×C4—22no—
144C22×C4C22×D2911yescharacteristic
145Q16—22no—
146SD16—24no—
147SD16—588no—
148D8—22no—
149D8—588no—
150D8—584no—
151D8—584no—
152M16—294no—
153C2×C8—292no—
154C2×C8C22⋊D2914yescomplemented
155C2×C8C22×D2911yescharacteristic
156C2×C8C22×D2911yescharacteristic
157C4⋊C4—292no—
158C22⋊C4—292no—
159C22⋊C4—588no—
160C42—292no—
161C23—22no—
162C23—584no—
163C23—1164no—
164C23—2324no—
165C23D4×D2911yescharacteristic
166Q8—22no—
167Q8—22no—
168D4—22no—
169D4—22no—
170D4—44no—
171D4—584no—
172D4—584no—
173D4—1164no—
174D4—2328no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—294no—
178C2×C4D4×D2911yescharacteristic
179C2×C4D4×D2912yes—
180C2×C4C2×C22⋊D2912yes—
181C2×C4C23×D2911yescharacteristic
182C8—294no—
183C8C2×C22⋊D2912yes—
184C8C2×C22⋊D2912yes—
185C22—22no—
186C22—42no—
187C22—44no—
188C22—1164no—
189C22—1168no—
190C22—2328no—
191C22#1174530212yes—
192C22C2×D4×D2911yescharacteristic
193C4—42no—
194C4—584no—
195C4#1174530212yes—
196C4C2×D4×D2911yescharacteristic
197C4C22×C22⋊D2911yescharacteristic
198C2—22no—
199C2—82no—
200C2—2324no—
201C2C2×#1174530211yescharacteristic
202C2#1427196512yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#135C2
socleC22×C29C22×D4
hypercenterC2×#135D29
hypocenterC29#3155
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#11745311C2semidirect
2. C22×D232C2semidirect
3. #14271727C2semidirect
4. #14271549C2semidirect
5. #14271548C2semidirect
6. #14271538C2semidirect
7. #14271118C2semidirect
8. C2×C29×#135C2semidirect
12. C2×Q16×C29C22semidirect
13. C2×SD16×C29C22semidirect
14. C2×D8×C29C22semidirect
17. #11745309C22semidirect
18. C2×#90784C22semidirect
19. #11745302C22semidirect
21. C2×#90782C22semidirect
28. #11745163C22semidirect
29. C8×Dic29C22semidirect
46. C2×C8×C29D4semidirect
55. #90777D4semidirect
98. C2×#135D29semidirect
114. C2×Q16C2×D29semidirect
116. C2×SD16C2×D29semidirect
121. C2×D8C2×D29semidirect
131. C29#3155semidirect
154. C2×C8C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117453112
C22×D2322
#142717272
#142715492
#142715482
#142715382
#142711182
C2×C29×#1352
#315529