Finite Group Databasebeta

← #49160733

Subgroups — #49160733

Order 37504.

226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 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#34036929C211yesmaximal, characteristic, complemented
2#34036567C212yesmaximal, complemented
3#34036382C211yesmaximal, characteristic, complemented
4#34035940C212yesmaximal, complemented
5#349×C293C211yesmaximal, characteristic, complemented
6C2×#17989802—21no—
7#22627657—22no—
8#22627652—22no—
9#22627646—21no—
10#22627646C2212yes—
11C2×D2344C2211yescharacteristic, complemented
12#22627598—21no—
13#22627569—22no—
14D4688—22no—
15#22627556C2211yescharacteristic, complemented
16#22627546—21no—
17C2×M16×C293C2211yescharacteristic
18M32×C293C2212yescomplemented
19#17989802—22no—
20#17989802—22no—
21#17989802—41no—
22#17989802—41no—
23C2×Dic586—21no—
24C2×D1172—21no—
25C2×D1172—21no—
26C2×C22⋊D293—41no—
27C2×C22⋊D293—41no—
28C2×C4×D293—41no—
29Dic1172—21no—
30Dic1172D412yescomplemented
31#17989791—22no—
32#17989791—22no—
33D2344—21no—
34D2344—22no—
35D2344D412yescomplemented
36C4⋊Dic293—21no—
37#17989779—41no—
38C22×C4×C293D411yescharacteristic
39M16×C293—22no—
40C2×C8×C293D411yescharacteristic
41C2×C8×C293C2311yescharacteristic
42C16×C293—22no—
43C22×D293—41no—
44C22×D293—41no—
45Dic586—22no—
46Dic586—41no—
47D1172—22no—
48D1172—41no—
49D1172—41no—
50D1172—41no—
51C22⋊D293—42no—
52C22⋊D293—42no—
53C22⋊D293—82no—
54C2×Dic293—41no—
55C2×Dic293—41no—
56C4×D293—42no—
57C4×D293—42no—
58C23×C293D811yescharacteristic
59C2×C4×C293—21no—
60C2×C4×C293—21no—
61C2×C4×C293D811yescharacteristic
62C2×C4×C293C2×D411yescharacteristic
63C8×C293—21no—
64C8×C293C2×D412yes—
65C22×C293—21no—
66C22×C293—41no—
67C22×C293C2×D811yescharacteristic
68C2×D293—42no—
69C2×D293—82no—
70C2×D293—81no—
71C2×D293—81no—
72C2×D293—81no—
73C4×C293—21no—
74C4×C293#12011yescharacteristic
75C4×C293AGL(1,ℤ/8)11yescharacteristic
76Dic293—42no—
77Dic293—81no—
78C2×C293—21no—
79C2×C293—41no—
80C2×C293#44711yescharacteristic
81D293—82no—
82D293—161no—
83C293#219011yescharacteristic, complemented, Sylow
84#2190—2931nomaximal, Sylow
85#575—2931no—
86#509—2932no—
87#469—2931no—
88#360—2932no—
89#349D29311yescharacteristic, complemented
90C2×#41—5861no—
91#137—5862no—
92AGL(1,ℤ/8)—5862no—
93#135—2932no—
94#135—5861no—
95C2×D8—2931no—
96C2×M16C2×D29311yescharacteristic
97#121—5861no—
98SD32—5862no—
99D16—5862no—
100M32C2×D29312yescomplemented
101#106—2931no—
102#102—5861no—
103#41—5862no—
104#41—5862no—
105#41—11721no—
106#41—11721no—
107C2×Q8—5861no—
108C2×D4—5861no—
109C2×D4—5861no—
110C2×D4—11721no—
111C2×D4—11721no—
112C22×C4—11721no—
113C22×C4D117211yescharacteristic
114Q16—2932no—
115Q16—5861no—
116SD16—5862no—
117SD16—5862no—
118D8—2932no—
119D8—5861no—
120D8—5862no—
121M16—22no—
122C2×C8D117211yescharacteristic
123C2×C8C22×D29311yescharacteristic
124C4⋊C4—5861no—
125C22⋊C4—11721no—
126C16—22no—
127C23—11721no—
128C23—11721no—
129C23D234411yescharacteristic
130Q8—5862no—
131Q8—11721no—
132D4—23442no—
133D4—5862no—
134D4—11721no—
135D4—11722no—
136D4—11722no—
137D4—11721no—
138D4—11721no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—11722no—
142C2×C4—11721no—
143C2×C4—11721no—
144C2×C4—11722no—
145C2×C4D234411yescharacteristic
146C2×C4C2×D117211yescharacteristic
147C8—21no—
148C8D4×D29312yes—
149C22—21no—
150C22—41no—
151C22—23441no—
152C22—23441no—
153C22—23442no—
154C22—23441no—
155C22—11722no—
156C22C2×D234411yescharacteristic
157C4—21no—
158C4—23441no—
159C4—11722no—
160C4#2262759411yescharacteristic
161C4#2262765211yescharacteristic
162C2—21no—
163C2—41no—
164C2—23442no—
165C2—46881no—
166C2#3403626511yescharacteristic
subgroupG/H
centerC2#34036265
commutator, cosocleC2×C8×C293C23
FrattiniC2×C8C22×D293
Fitting#349×C293C2
socleC2×C293#447
hypercenter#349D293
hypocenterC293#2190
LCSG ▷ C2×C8×C293 ▷ C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
1. #34036929C2semidirect
2. #34036567C2semidirect
3. #34036382C2semidirect
4. #34035940C2semidirect
5. #349×C293C2semidirect
11. C2×D2344C22semidirect
15. #22627556C22semidirect
18. M32×C293C22semidirect
30. Dic1172D4semidirect
35. D2344D4semidirect
83. C293#2190semidirect
89. #349D293semidirect
100. M32C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340369292
#340365672
#340363822
#340359402
#349×C2932
#2190293