Finite Group Databasebeta

← #49157331

Subgroups — #49157331

Order 37504.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#34036679C211yesmaximal, characteristic
2#34036186C211yesmaximal, characteristic, complemented
3#34035862C214yesmaximal, complemented
4#383×C293C211yesmaximal, characteristic, complemented
5C2×#17989802—21no—
6#22627624C411yescharacteristic, complemented
7#22627621C411yescharacteristic, complemented
8#22627612—21no—
9#22627598—21no—
10#22627598C2212yes—
11C4×D1172—21no—
12C4×D1172C412yescomplemented
13C4⋊#14556873—21no—
14C22⋊#14556873C2212yes—
15#22627535—21no—
16C2×C42×C293C2211yescharacteristic
17#95×C293—21no—
18#95×C293—21no—
19#95×C293C2212yes—
20#17989802—44no—
21C2×Dic586—21no—
22C2×D1172—21no—
23C2×D1172—21no—
24C2×D1172C2×C412yes—
25C2×C22⋊D293—22no—
26C2×C4×D293—22no—
27C2×#14556873—22no—
28C4⋊Dic293—21no—
29C4⋊Dic293C2×C412yes—
30#17989779—22no—
31#17989779—22no—
32C22×C4×C293—22no—
33C22×C4×C293D411yescharacteristic
34C22×C4×C293D411yescharacteristic
35C22×C4×C293C2311yescharacteristic
36C42×C293C2×C411yescharacteristic
37C42×C293C2×C411yescharacteristic
38C42×C293D411yescharacteristic
39C42×C293D411yescharacteristic
40C22×D293—22no—
41Dic586—42no—
42D1172—42no—
43D1172—42no—
44D1172—42no—
45C22⋊D293—44no—
46C2×Dic293—22no—
47C4×D293—44no—
48#14556873—42no—
49C23×C293C2×D411yescharacteristic
50C2×C4×C293—22no—
51C2×C4×C293—41no—
52C2×C4×C293—41no—
53C2×C4×C293—42no—
54C2×C4×C293—42no—
55C2×C4×C293—42no—
56C2×C4×C293C22⋊C411yescharacteristic
57C2×C4×C293C22⋊C411yescharacteristic
58C2×C4×C293C22⋊C411yescharacteristic
59C2×C4×C293C22⋊C411yescharacteristic
60C2×C4×C293C22×C411yescharacteristic
61C2×C4×C293C2×D411yescharacteristic
62C22×C293—21no—
63C22×C293—21no—
64C22×C293C2×C22⋊C411yescharacteristic
65C22×C293AGL(1,ℤ/8)12yes—
66C2×D293—42no—
67C2×D293—42no—
68C2×D293—42no—
69C4×C293—21no—
70C4×C293—21no—
71C4×C293—21no—
72C4×C293—21no—
73C4×C293—21no—
74C4×C293—21no—
75C4×C293—82no—
76Dic293—42no—
77C2×C293—22no—
78C2×C293#41011yescharacteristic
79C2×C293#41811yescharacteristic
80C2×C293#42111yescharacteristic
81D293—82no—
82C293#151411yescharacteristic, complemented, Sylow
83#1514—2931nomaximal, Sylow
84#532—2931no—
85#432—2931no—
86#383D29311yescharacteristic, complemented
87#327—2934no—
88C2×#41—5861no—
89C4⋊Q8—2931no—
90#127—2931no—
91#124—5861no—
92#121—2932no—
93#121—5861no—
94C4×D4—2932no—
95C4×D4—5861no—
96C2×C42C2×D29311yescharacteristic
97C4⋊C8—5861no—
98C22⋊C8—2932no—
99#97—5861no—
100#95—21no—
101#95—21no—
102#95C2×D29312yes—
103#41—11724no—
104C2×Q8—5861no—
105C2×D4—2932no—
106C2×D4—5862no—
107C2×D4—5861no—
108C2×D4—5861no—
109C22×C4—22no—
110C22×C4—5862no—
111C22×C4C22⋊D29311yescharacteristic
112C22×C4C22⋊D29311yescharacteristic
113C22×C4C22×D29311yescharacteristic
114C2×C8—5862no—
115C4⋊C4—2932no—
116C4⋊C4—5861no—
117C22⋊C4—5862no—
118C22⋊C4—5862no—
119C42C4×D29311yescharacteristic
120C42C4×D29311yescharacteristic
121C42D117211yescharacteristic
122C42D117211yescharacteristic
123C23—5862no—
124C23C2×C22⋊D29311yescharacteristic
125Q8—11722no—
126D4—11722no—
127D4—11722no—
128D4—11722no—
129D4—11724no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—42no—
135C2×C4—42no—
136C2×C4—5862no—
137C2×C4—11724no—
138C2×C4#1798977911yescharacteristic
139C2×C4#1798977911yescharacteristic
140C2×C4#1798977911yescharacteristic
141C2×C4#1798977911yescharacteristic
142C2×C4C2×C4×D29311yescharacteristic
143C2×C4C2×D117211yescharacteristic
144C8—11722no—
145C22—21no—
146C22—21no—
147C22—11722no—
148C22—11722no—
149C22—11722no—
150C22C2×#1798977911yescharacteristic
151C22#2262764912yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—82no—
159C4—11722no—
160C2—22no—
161C2—23442no—
162C2#3403610211yescharacteristic
163C2#3403613311yescharacteristic
164C2#3403614711yescharacteristic
subgroupG/H
centerC22C2×#17989779
commutatorC2×C4×C293C22×C4
FrattiniC22×C4C22×D293
Fitting#383×C293C2
socleC22×C293C2×C22⋊C4
prime radical#34036679C2
cosocleC22×C4×C293C23
hypercenter#383D293
hypocenterC293#1514
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #34036186C2semidirect
3. #34035862C2semidirect
4. #383×C293C2semidirect
6. #22627624C4semidirect
7. #22627621C4semidirect
12. C4×D1172C4semidirect
82. C293#1514semidirect
86. #383D293semidirect

Maximal subgroups

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

subgroupindex
#340366792
#340361862
#340358622
#383×C2932
#1514293