Finite Group Databasebeta

← #49174294

Subgroups — #49174294

Order 37504.

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

normal subgroups only

This group has 240 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
1#34037146C211yesmaximal, characteristic
2#34037132C211yesmaximal, characteristic
3#34036988C214yesmaximal, complemented
4C2×#22627623C211yesmaximal, characteristic
5C2×#17989811—21no—
6#22627691C2212yes—
7#22627691C2212yes—
8C4⋊#14556880—21no—
9C22⋊#14556880—21no—
10C4×#14556880—21no—
11C22×Dic586—21no—
12#22627623—21no—
13#22627623—21no—
14#22627623C412yes—
15#22627623C2212yes—
16C2×C4⋊Dic293C411yescharacteristic
17C2×#17989781—21no—
18C2×C4×Dic293C2211yescharacteristic
19C2×C4⋊C4×C293C411yescharacteristic
20#17989811—42no—
21C2×#14556880—22no—
22C2×#14556880—22no—
23C2×Dic586—22no—
24C2×Dic586—22no—
25C2×Dic586—42no—
26C2×Dic586—42no—
27C22×Dic293—21no—
28C22×Dic293D411yescharacteristic
29C22×Dic293D411yescharacteristic
30C4⋊Dic293—21no—
31C4⋊Dic293C2×C412yes—
32#17989781—22no—
33#17989781—22no—
34C4×Dic293C2×C411yescharacteristic
35C4×Dic293D411yescharacteristic
36C4×Dic293D411yescharacteristic
37C4×Dic293C2311yescharacteristic
38C22×C4×C293—21no—
39C22×C4×C293C2×C411yescharacteristic
40C4⋊C4×C293—21no—
41C4⋊C4×C293C2×C412yes—
42#14556880—42no—
43#14556880—42no—
44Dic586—44no—
45Dic586—42no—
46Dic586—42no—
47C2×Dic293—22no—
48C2×Dic293—22no—
49C2×Dic293—42no—
50C2×Dic293C22⋊C411yescharacteristic
51C2×Dic293C22⋊C411yescharacteristic
52C2×Dic293D812yes—
53C2×Dic293SD1612yes—
54C2×Dic293C2×D411yescharacteristic
55C2×Dic293C2×D411yescharacteristic
56C23×C293C22⋊C411yescharacteristic
57C2×C4×C293—22no—
58C2×C4×C293—22no—
59C2×C4×C293—42no—
60C2×C4×C293C22⋊C411yescharacteristic
61C2×C4×C293C22×C411yescharacteristic
62C22×C293—21no—
63C22×C293—21no—
64C22×C293#10212yes—
65C22×C293C2×C22⋊C411yescharacteristic
66C4×C293—21no—
67C4×C293—42no—
68C4×C293#10112yes—
69Dic293—21no—
70Dic293—42no—
71Dic293#10212yes—
72Dic293C2×D811yescharacteristic
73Dic293C2×SD1611yescharacteristic
74Dic293#13712yes—
75C2×C293—22no—
76C2×C293C2×#10111yescharacteristic
77C2×C293C2×#10211yescharacteristic
78C2×C293#41911yescharacteristic
79C293#154611yescharacteristic, complemented, Sylow
80#1546—2931nomaximal, Sylow
81C2×C4⋊Q8—2931no—
82#431—2931no—
83#423—2931no—
84#332—2934no—
85C22×Q8—5861no—
86C2×M16—5861no—
87C4⋊Q8—2932no—
88C4⋊Q8—2932no—
89C4⋊Q8—5861no—
90C4⋊Q8—5861no—
91C2×C4⋊C4—2931no—
92C2×C4⋊C4—5861no—
93C2×C4⋊C4#1192407811yescharacteristic
94C2×C42—2931no—
95C4⋊C8—2932no—
96C4⋊C8—2932no—
97C4⋊C8—5861no—
98C22⋊C8—5861no—
99C4×C8—5861no—
100C2×Q8—5862no—
101C2×Q8—5862no—
102C2×Q8—11722no—
103C2×Q8—11722no—
104C22×C4—21no—
105C22×C4—2931no—
106C22×C4—2931no—
107C22×C4—5861no—
108C22×C4C2×#1192407811yescharacteristic
109M16—11722no—
110C2×C8—5862no—
111C2×C8—5862no—
112C4⋊C4—21no—
113C4⋊C4—2932no—
114C4⋊C4—5862no—
115C4⋊C4—5862no—
116C4⋊C4—5861no—
117C4⋊C4C2×#1192407812yes—
118C42—2931no—
119C42—2931no—
120C42—2931no—
121C42—2931no—
122C23C22⋊#1192407811yescharacteristic
123Q8—11722no—
124Q8—11724no—
125Q8—11722no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—42no—
129C2×C4—2932no—
130C2×C4—2932no—
131C2×C4—2931no—
132C2×C4—2931no—
133C2×C4—2931no—
134C2×C4—2931no—
135C2×C4—5862no—
136C2×C4—5862no—
137C2×C4—11722no—
138C2×C4C22⋊#1192407811yescharacteristic
139C2×C4C22×#1192407811yescharacteristic
140C8—11722no—
141C8—11722no—
142C22—21no—
143C22—21no—
144C22#2262768612yes—
145C22C2×C22⋊#1192407811yescharacteristic
146C4—21no—
147C4—42no—
148C4—2931no—
149C4—2932no—
150C4—2931no—
151C4—2932no—
152C4—5861no—
153C4—11722no—
154C4#2262768512yes—
155C2—22no—
156C2C2×#2262768511yescharacteristic
157C2C2×#2262768611yescharacteristic
158C2#3403712211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC2×C4⋊C4×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC23×C293C22⋊C4
cosocleC4×Dic293C23
hypercenterC2×C4⋊C4#11924078
hypocenterC293#1546
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #34036988C2semidirect
79. C293#1546semidirect

Maximal subgroups

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

subgroupindex
#340371462
#340371322
#340369882
C2×#226276232
#1546293