Finite Group Databasebeta

← #49174962

Subgroups — #49174962

Order 37504.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#17989812C211yesmaximal, characteristic
2C4×C4⋊#11924078C211yesmaximal, characteristic
3#34036999C212yesmaximal
4#34036999C212yesmaximal
5#34036685C211yesmaximal, characteristic
6C2×#17989812C2212yes—
7C2×C4⋊#11924078—21no—
8C2×C4×#11924078C2212yes—
9#22627679—21no—
10C4×#14556880—21no—
11(C2×#11924078)⋊C4—21no—
12#22627623C411yescharacteristic, complemented
13#22627623C411yescharacteristic, complemented
14#22627616C411yescharacteristic, complemented
15#22627602—21no—
16#22627602—21no—
17#22627589—21no—
18#22627589—21no—
19#22627582C2211yescharacteristic
20#22627582C2211yescharacteristic
21C42×D293C2211yescharacteristic
22#125×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24#17989812—22no—
25#17989812Q814yescomplemented
26C2×#14556880—22no—
27C4⋊#11924078—24no—
28C4×#11924078—24no—
29C2×Dic586—21no—
30C2×Dic586—21no—
31C2×C4×D293D411yescharacteristic
32C2×C4×D293D411yescharacteristic
33C2×C4×D293C2311yescharacteristic
34C4⋊Dic293C2×C411yescharacteristic
35C4⋊Dic293C2×C411yescharacteristic
36#17989781—21no—
37#17989781—21no—
38#17989781—21no—
39#17989781—21no—
40#17989779—21no—
41#17989779—21no—
42C4×Dic293—21no—
43C4×Dic293—21no—
44C4×Dic293C2×C411yescharacteristic
45C4×Dic293D411yescharacteristic
46C4×Dic293D411yescharacteristic
47C4⋊C4×C293—21no—
48C4⋊C4×C293—21no—
49C4⋊C4×C293C2×C411yescharacteristic
50C4⋊C4×C293C2×C411yescharacteristic
51C42×C293C2×C411yescharacteristic
52C2×#11924078—24no—
53C2×#11924078—42no—
54C2×#11924078—42no—
55#14556880—24no—
56C22×D293C2×D411yescharacteristic
57Dic586—42no—
58Dic586—42no—
59C2×Dic293—21no—
60C2×Dic293—21no—
61C2×Dic293C22⋊C411yescharacteristic
62C2×Dic293C22⋊C411yescharacteristic
63C2×Dic293C2×D411yescharacteristic
64C4×D293—22no—
65C4×D293—41no—
66C4×D293C2×Q812yes—
67C4×D293#4112yes—
68C2×C4×C293—21no—
69C2×C4×C293—21no—
70C2×C4×C293C22⋊C411yescharacteristic
71C2×C4×C293C22⋊C411yescharacteristic
72C2×C4×C293C22×C411yescharacteristic
73C22×C293C2×C22⋊C411yescharacteristic
74C2×D293—21no—
75C2×D293—21no—
76C2×D293#12411yescharacteristic
77C2×D293C4⋊Q811yescharacteristic
78#11924078—44no—
79C4×C293—21no—
80C4×C293—21no—
81C4×C293—41no—
82C4×C293—41no—
83C4×C293C4×Q812yes—
84Dic293—21no—
85Dic293—41no—
86Dic293—41no—
87Dic293#10412yes—
88Dic293C22⋊Q812yes—
89C2×C293#39111yescharacteristic
90C2×C293C2×#10411yescharacteristic
91C2×C293#42111yescharacteristic
92D293—21no—
93D293—21no—
94C293#198611yescharacteristic, complemented, Sylow
95#1986—2931nomaximal, Sylow
96#533—2931no—
97C4×M16—2931no—
98C4×C4⋊C4—2931no—
99#339—2932no—
100#339—2932no—
101C2×M16—2932no—
102C4⋊Q8—2931no—
103C4⋊Q8—2931no—
104#125—2931no—
105#125#1192407811yescharacteristic, complemented
106C22⋊Q8—5861no—
107C22⋊Q8—5861no—
108C4×Q8—5861no—
109C4×Q8—5861no—
110#117—2931no—
111#117—2931no—
112C2×C4⋊C4—5861no—
113C2×C42—2931no—
114C2×C42—2932no—
115#97—5861no—
116C4×C8—5861no—
117#95—5861no—
118C2×Q8—5861no—
119C2×Q8—5861no—
120C22×C4—2931no—
121C22×C4—2931no—
122C22×C4—2931no—
123C22×C4—5862no—
124M16—2934no—
125M16—5862no—
126C2×C8—5862no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2931no—
130C4⋊C4—2931no—
131C4⋊C4—5861no—
132C4⋊C4—5861no—
133C4⋊C4—5864no—
134C4⋊C4—5861no—
135C4⋊C4—5861no—
136C4⋊C4C2×#1192407811yescharacteristic
137C4⋊C4C2×#1192407811yescharacteristic
138C22⋊C4—5861no—
139C22⋊C4—5861no—
140C42—2931no—
141C42—2931no—
142C42—2931no—
143C42—5861no—
144C42—5861no—
145C42—5864no—
146C42C2×#1192407811yescharacteristic
147C23—2931no—
148Q8—11722no—
149Q8—11722no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2931no—
153C2×C4—2931no—
154C2×C4—2932no—
155C2×C4—2932no—
156C2×C4—2931no—
157C2×C4—5862no—
158C2×C4—5864no—
159C2×C4—5861no—
160C2×C4—5861no—
161C2×C4—11721no—
162C2×C4—11722no—
163C2×C4—11722no—
164C2×C4C22⋊#1192407811yescharacteristic
165C2×C4C22⋊#1192407811yescharacteristic
166C2×C4C22×#1192407811yescharacteristic
167C8—5864no—
168C22—2931no—
169C22—2931no—
170C22—5861no—
171C22—5861no—
172C22C2×C22⋊#1192407811yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—2932no—
178C4—2932no—
179C4—5861no—
180C4—11724no—
181C4—11721no—
182C4—11721no—
183C4Q8×#1192407812yes—
184C2—5861no—
185C2—5861no—
186C2(C2×#11924078)⋊Q811yescharacteristic
187C2D293⋊#10411yescharacteristic
188C2#3403712611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#125×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC22×D293C2×D4
cosocleC2×C4×D293C23
hypercenter#125#11924078
hypocenterC293#1986
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #22627623C4semidirect
13. #22627623C4semidirect
14. #22627616C4semidirect
22. #125×C293C4semidirect
25. #17989812Q8semidirect
94. C293#1986semidirect
105. #125#11924078semidirect

Maximal subgroups

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

subgroupindex
C4×#179898122
C4×C4⋊#119240782
#340369992
#340366852
#1986293