Finite Group Databasebeta

← #49174167

Subgroups — #49174167

Order 37504.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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#34037147C211yesmaximal, characteristic
2C4×C4⋊#11924078C211yesmaximal, characteristic
3#34036983C212yesmaximal
4#34036982C212yesmaximal
5#34036683C211yesmaximal, characteristic
6C2×C4⋊#11924078—21no—
7C2×C4×#11924078—21no—
8#22627691—21no—
9#22627681C2212yes—
10C4×#14556880—21no—
11(C2×#11924078)⋊C4C2212yes—
12#22627623C411yescharacteristic, complemented
13#22627622C411yescharacteristic, complemented
14#22627614—21no—
15#22627604C2211yescharacteristic
16#22627602—21no—
17#22627600C2211yescharacteristic
18C4×Dic586—21no—
19C4×Dic586C411yescharacteristic, complemented
20#22627581—21no—
21C42×D293C2211yescharacteristic
22C4×Q8×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24C2×#14556880—22no—
25C4⋊#11924078—24no—
26C4×#11924078—42no—
27C2×Dic586—21no—
28C2×Dic586C2×C411yescharacteristic
29C2×C4×D293D411yescharacteristic
30C2×C4×D293D411yescharacteristic
31C2×C4×D293C2311yescharacteristic
32C4⋊Dic293—21no—
33C4⋊Dic293C2×C411yescharacteristic
34#17989781—21no—
35#17989781—21no—
36#17989781—21no—
37#17989781—21no—
38#17989781—21no—
39#17989779—21no—
40#17989779—21no—
41C4×Dic293—21no—
42C4×Dic293C2×C411yescharacteristic
43C4×Dic293D411yescharacteristic
44C4×Dic293D411yescharacteristic
45C2×Q8×C293C2×C411yescharacteristic
46C4⋊C4×C293—21no—
47C4⋊C4×C293C2×C411yescharacteristic
48C42×C293—21no—
49C42×C293C2×C411yescharacteristic
50C2×#11924078—24no—
51C2×#11924078—42no—
52C2×#11924078—42no—
53#14556880—42no—
54C22×D293C2×D411yescharacteristic
55Dic586—42no—
56Dic586—41no—
57C2×Dic293—21no—
58C2×Dic293—21no—
59C2×Dic293C22⋊C411yescharacteristic
60C2×Dic293C22⋊C411yescharacteristic
61C2×Dic293C2×D411yescharacteristic
62C4×D293—22no—
63C4×D293—41no—
64C4×D293SD1612yes—
65C4×D293Q1612yes—
66Q8×C293—41no—
67C2×C4×C293—21no—
68C2×C4×C293—21no—
69C2×C4×C293C22⋊C411yescharacteristic
70C2×C4×C293C22⋊C411yescharacteristic
71C2×C4×C293C22×C411yescharacteristic
72C22×C293C2×C22⋊C411yescharacteristic
73C2×D293—21no—
74C2×D293—21no—
75C2×D293C2×SD1611yescharacteristic
76C2×D293C2×Q1611yescharacteristic
77#11924078—44no—
78C4×C293—21no—
79C4×C293—21no—
80C4×C293—41no—
81C4×C293—41no—
82C4×C293#10312yes—
83Dic293—21no—
84Dic293—41no—
85Dic293—41no—
86Dic293#10312yes—
87Dic293#10412yes—
88C2×C293#41011yescharacteristic
89C2×C293C2×#10311yescharacteristic
90C2×C293C2×#10411yescharacteristic
91D293—21no—
92D293—21no—
93C293#150311yescharacteristic, complemented, Sylow
94#1503—2931nomaximal, Sylow
95#533—2931no—
96#431—2931no—
97C4×C4⋊C4—2931no—
98#328—2932no—
99#328—2932no—
100C4⋊Q8—2931no—
101C4⋊Q8—2931no—
102#125—5861no—
103C22⋊Q8—2931no—
104C22⋊Q8—2931no—
105C22⋊Q8—5861no—
106C4×Q8—2931no—
107C4×Q8—5861no—
108C4×Q8#1192407811yescharacteristic, complemented
109#117—5861no—
110C2×C4⋊C4—5861no—
111C2×C42—2931no—
112C2×C42—5861no—
113C4⋊C8—5861no—
114C22⋊C8—2932no—
115C4×C8—5861no—
116#95—2932no—
117C2×Q8—2931no—
118C2×Q8—5861no—
119C2×Q8C2×#1192407811yescharacteristic
120C22×C4—2931no—
121C22×C4—2931no—
122C22×C4—2931no—
123C22×C4—5862no—
124C2×C8—5862no—
125C4⋊C4—21no—
126C4⋊C4—2931no—
127C4⋊C4—5861no—
128C4⋊C4—5861no—
129C4⋊C4—5861no—
130C4⋊C4—5861no—
131C4⋊C4—5861no—
132C4⋊C4—5864no—
133C4⋊C4—5861no—
134C4⋊C4C2×#1192407811yescharacteristic
135C22⋊C4—5861no—
136C22⋊C4—5861no—
137C42—21no—
138C42—2931no—
139C42—2931no—
140C42—2931no—
141C42—5861no—
142C42—11722no—
143C42C2×#1192407811yescharacteristic
144C23—2931no—
145Q8—41no—
146Q8—11721no—
147Q8—11722no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—2931no—
151C2×C4—2931no—
152C2×C4—2932no—
153C2×C4—2932no—
154C2×C4—2931no—
155C2×C4—5862no—
156C2×C4—5864no—
157C2×C4—5861no—
158C2×C4—5861no—
159C2×C4—11721no—
160C2×C4—11722no—
161C2×C4—11722no—
162C2×C4C22⋊#1192407811yescharacteristic
163C2×C4C22⋊#1192407811yescharacteristic
164C2×C4C22×#1192407811yescharacteristic
165C8—11722no—
166C22—2931no—
167C22—2931no—
168C22—5861no—
169C22—5861no—
170C22C2×C22⋊#1192407811yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—2932no—
176C4—2932no—
177C4—5861no—
178C4—11724no—
179C4—11721no—
180C4—11721no—
181C4#2262768712yes—
182C2—5861no—
183C2—5861no—
184C2#3403710811yescharacteristic
185C2C2×#2262768711yescharacteristic
186C2D293⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4×Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC22×D293C2×D4
cosocleC2×C4×D293C23
hypercenterC4×Q8#11924078
hypocenterC293#1503
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #22627623C4semidirect
13. #22627622C4semidirect
19. C4×Dic586C4semidirect
22. C4×Q8×C293C4semidirect
93. C293#1503semidirect
108. C4×Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371472
C4×C4⋊#119240782
#340369832
#340369822
#340366832
#1503293