Finite Group Databasebeta

← #49169327

Subgroups — #49169327

Order 37504.

380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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#34036686C211yesmaximal, characteristic
2#34036535C214yesmaximal, complemented
3#34036532C212yesmaximal, complemented
4#34036525C212yesmaximal, complemented
5#34036169C214yesmaximal
6C4×#17989786C211yesmaximal, characteristic
7C2×C4⋊Q8×C293C211yesmaximal, characteristic
8C2×#17989786C2212yes—
9#22627624C2211yescharacteristic
10#22627624C2211yescharacteristic
11#22627616C2212yes—
12#22627603—21no—
13#22627603—21no—
14C4×Dic586—21no—
15C4×Dic586—21no—
16#22627583C2212yes—
17#22627557C2218yes—
18#22627555C2218yes—
19#22627535C2212yes—
20C4×#14556873C2212yes—
21C22×Q8×C293—21no—
22C4⋊Q8×C293—21no—
23C4⋊Q8×C293—21no—
24C4⋊Q8×C293C2212yes—
25C4⋊Q8×C293C2212yes—
26C2×C4⋊C4×C293—21no—
27C2×C4⋊C4×C293C2212yes—
28C2×C42×C293C2211yescharacteristic
29C2×Dic586—21no—
30C2×Dic586—21no—
31#17989786Q818yescomplemented
32C2×#14556873C2314yes—
33C4⋊Dic293—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293C2312yes—
36C4⋊Dic293C2312yes—
37#17989781—22no—
38#17989781—22no—
39C22⋊Dic293—22no—
40C4×Dic293—22no—
41C2×Q8×C293—22no—
42C2×Q8×C293—22no—
43C2×Q8×C293—44no—
44C22×C4×C293—22no—
45C22×C4×C293D411yescharacteristic
46C22×C4×C293D411yescharacteristic
47C22×C4×C293C2311yescharacteristic
48C4⋊C4×C293—22no—
49C4⋊C4×C293—22no—
50C4⋊C4×C293—22no—
51C4⋊C4×C293C2314yes—
52C42×C293D411yescharacteristic
53C42×C293D411yescharacteristic
54C42×C293C2311yescharacteristic
55C42×C293C2311yescharacteristic
56Dic586—42no—
57Dic586—42no—
58C2×Dic293—22no—
59C2×Dic293—22no—
60#14556873C2×Q818yescomplemented
61C23×C293C2×D411yescharacteristic
62Q8×C293—44no—
63Q8×C293—44no—
64C2×C4×C293—22no—
65C2×C4×C293—22no—
66C2×C4×C293—24no—
67C2×C4×C293—44no—
68C2×C4×C293C2×D411yescharacteristic
69C2×C4×C293C2×D411yescharacteristic
70C2×C4×C293C2×D411yescharacteristic
71C2×C4×C293C2×D411yescharacteristic
72C2×C4×C293C2×D411yescharacteristic
73C2×C4×C293C2×Q814yes—
74C2×C4×C293C2411yescharacteristic
75C22×C293—21no—
76C22×C293—21no—
77C22×C293C4⋊Q812yes—
78C22×C293C22×D411yescharacteristic
79C4×C293—21no—
80C4×C293—21no—
81C4×C293—44no—
82C4×C293C4⋊Q812yes—
83C4×C293AGL(1,ℤ/8)12yes—
84C4×C293#13712yes—
85C4×C293C22×Q812yes—
86Dic293—42no—
87Dic293—42no—
88C2×C293—22no—
89C2×C293C2×C4⋊Q811yescharacteristic
90C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
91C2×C293C2×#13711yescharacteristic
92C293#316511yescharacteristic, complemented, Sylow
93#3165—2931nomaximal, Sylow
94#533—2931no—
95C2×C4⋊Q8D29311yescharacteristic
96#501—2934no—
97#500—2932no—
98#498—2932no—
99#428—2934no—
100C4×M16—2931no—
101C22×Q8—21no—
102C2×M16—2932no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—2931no—
106C4⋊Q8—2931no—
107C4⋊Q8C2×D29312yes—
108C4⋊Q8C2×D29312yes—
109#125—2932no—
110C22⋊Q8—5861no—
111C22⋊Q8—5861no—
112C4×Q8—5861no—
113C4×Q8—5861no—
114#117—2932no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4C2×D29312yes—
117C2×C42C2×D29311yescharacteristic
118#107—2938no—
119#106—2938no—
120#97—2932no—
121C4×C8—2932no—
122C2×Q8—22no—
123C2×Q8—22no—
124C2×Q8—44no—
125C2×Q8—5861no—
126C2×Q8—5861no—
127C22×C4—22no—
128C22×C4C22⋊D29311yescharacteristic
129C22×C4C22⋊D29311yescharacteristic
130C22×C4C22×D29311yescharacteristic
131M16—2938no—
132C2×C8—2934no—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—2932no—
137C4⋊C4—2932no—
138C4⋊C4—5862no—
139C4⋊C4—5862no—
140C4⋊C4—5861no—
141C4⋊C4—5861no—
142C4⋊C4C22×D29314yes—
143C22⋊C4—5862no—
144C42—5862no—
145C42C22⋊D29311yescharacteristic
146C42C22⋊D29311yescharacteristic
147C42C22×D29311yescharacteristic
148C42C22×D29311yescharacteristic
149C23C2×C22⋊D29311yescharacteristic
150Q8—44no—
151Q8—44no—
152Q8—11722no—
153Q8—11722no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—44no—
158C2×C4—5862no—
159C2×C4—5862no—
160C2×C4C2×C22⋊D29311yescharacteristic
161C2×C4C2×C22⋊D29311yescharacteristic
162C2×C4C2×C22⋊D29311yescharacteristic
163C2×C4C2×C22⋊D29311yescharacteristic
164C2×C4C2×C22⋊D29311yescharacteristic
165C2×C4Q8×D29314yes—
166C2×C4C23×D29311yescharacteristic
167C8—2938no—
168C22—21no—
169C22—21no—
170C22#2262762212yes—
171C22C22×C22⋊D29311yescharacteristic
172C4—21no—
173C4—21no—
174C4—44no—
175C4—11722no—
176C4—11722no—
177C4#2262762212yes—
178C4#2262765012yes—
179C4#2262765512yes—
180C4C2×Q8×D29312yes—
181C2—22no—
182C2C2×#2262762211yescharacteristic
183C2C2×#2262765011yescharacteristic
184C2C2×#2262765511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×C4⋊Q8×C293C2
socleC22×C293C22×D4
prime radicalC23×C293C2×D4
hypercenterC2×C4⋊Q8D293
hypocenterC293#3165
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #34036535C2semidirect
3. #34036532C2semidirect
4. #34036525C2semidirect
31. #17989786Q8semidirect
60. #14556873C2×Q8semidirect
92. C293#3165semidirect

Maximal subgroups

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

subgroupindex
#340366862
#340365352
#340365322
#340365252
#340361692
C4×#179897862
C2×C4⋊Q8×C2932
#3165293