Finite Group Databasebeta

← #49174217

Subgroups — #49174217

Order 37504.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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
2#34037073C211yesmaximal, characteristic
3#34036982C214yesmaximal
4#34036684C211yesmaximal, characteristic
5C2×C4⋊#11924078—21no—
6#22627691—21no—
7#22627681C2212yes—
8C4×#14556880—21no—
9(C2×#11924078)⋊C4—21no—
10(C2×#11924078)⋊C4C2212yes—
11#22627624C411yescharacteristic, complemented
12#22627615—21no—
13#22627604C2212yes—
14#22627600—21no—
15Q8×Dic293—21no—
16#22627589C412yescomplemented
17#22627582—21no—
18C42×D293C2211yescharacteristic
19C4⋊Q8×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21C2×#14556880—22no—
22C4⋊#11924078—42no—
23C2×Dic586C2×C412yes—
24C2×C4×D293D411yescharacteristic
25C2×C4×D293D411yescharacteristic
26C2×C4×D293C2311yescharacteristic
27C4⋊Dic293—22no—
28C4⋊Dic293—21no—
29C4⋊Dic293—21no—
30#17989781—22no—
31#17989779—22no—
32C4×Dic293—22no—
33C4×Dic293C2×C411yescharacteristic
34C4×Dic293D411yescharacteristic
35C4×Dic293D411yescharacteristic
36C2×Q8×C293—21no—
37C4⋊C4×C293—21no—
38C4⋊C4×C293C2×C412yes—
39C42×C293C2×C411yescharacteristic
40C2×#11924078—42no—
41C2×#11924078—42no—
42C2×#11924078—42no—
43#14556880—42no—
44C22×D293C2×D411yescharacteristic
45Dic586—42no—
46C2×Dic293—22no—
47C2×Dic293C22⋊C411yescharacteristic
48C2×Dic293C22⋊C411yescharacteristic
49C2×Dic293C2×D411yescharacteristic
50C4×D293—41no—
51C4×D293—41no—
52C4×D293SD1612yes—
53C4×D293Q1612yes—
54Q8×C293—42no—
55C2×C4×C293—22no—
56C2×C4×C293C22⋊C411yescharacteristic
57C2×C4×C293C22⋊C411yescharacteristic
58C2×C4×C293C22×C411yescharacteristic
59C22×C293C2×C22⋊C411yescharacteristic
60C2×D293—21no—
61C2×D293—21no—
62C2×D293C2×SD1611yescharacteristic
63C2×D293C2×Q1611yescharacteristic
64#11924078—82no—
65C4×C293—21no—
66C4×C293—21no—
67C4×C293—42no—
68C4×C293#10312yes—
69Dic293—21no—
70Dic293—21no—
71Dic293—42no—
72Dic293#10312yes—
73C2×C293#41011yescharacteristic
74C2×C293C2×#10311yescharacteristic
75C2×C293#42111yescharacteristic
76D293—21no—
77D293—21no—
78C293#151811yescharacteristic, complemented, Sylow
79#1518—2931nomaximal, Sylow
80#533—2931no—
81#431—2931no—
82#382—2931no—
83#328—2934no—
84C4⋊Q8—2931no—
85C4⋊Q8#1192407811yescharacteristic, complemented
86#125—5861no—
87C22⋊Q8—2932no—
88C22⋊Q8—5861no—
89C4×Q8—2932no—
90C4×Q8—5861no—
91#117—5861no—
92C2×C4⋊C4—5861no—
93C2×C42—2931no—
94C4⋊C8—5861no—
95C22⋊C8—2932no—
96C4×C8—5861no—
97#95—2932no—
98#95—5861no—
99C2×Q8—21no—
100C2×Q8—2932no—
101C22×C4—2931no—
102C22×C4—2931no—
103C22×C4—2931no—
104C22×C4—5862no—
105C2×C8—5862no—
106C4⋊C4—21no—
107C4⋊C4—5862no—
108C4⋊C4—5862no—
109C4⋊C4—5861no—
110C4⋊C4—5861no—
111C4⋊C4—11722no—
112C4⋊C4C2×#1192407812yes—
113C22⋊C4—5862no—
114C42—2931no—
115C42—2931no—
116C42—2931no—
117C42—5862no—
118C42C2×#1192407811yescharacteristic
119C23—2931no—
120Q8—42no—
121Q8—11722no—
122C2×C4—22no—
123C2×C4—2931no—
124C2×C4—2932no—
125C2×C4—2932no—
126C2×C4—2931no—
127C2×C4—2931no—
128C2×C4—5862no—
129C2×C4—11721no—
130C2×C4—11721no—
131C2×C4—11722no—
132C2×C4—11722no—
133C2×C4—11722no—
134C2×C4C22⋊#1192407811yescharacteristic
135C2×C4C22⋊#1192407811yescharacteristic
136C2×C4C22×#1192407811yescharacteristic
137C8—11722no—
138C22—2931no—
139C22—2931no—
140C22—5861no—
141C22—5861no—
142C22C2×C22⋊#1192407811yescharacteristic
143C4—21no—
144C4—21no—
145C4—42no—
146C4—2932no—
147C4—23442no—
148C4—5861no—
149C4—5861no—
150C4—11722no—
151C4#2262768712yes—
152C2—5861no—
153C2—5861no—
154C2#3403711011yescharacteristic
155C2C2×#2262768711yescharacteristic
156C2#3403712711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#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#1518
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #22627624C4semidirect
16. #22627589C4semidirect
19. C4⋊Q8×C293C4semidirect
78. C293#1518semidirect
85. C4⋊Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371472
#340370732
#340369822
#340366842
#1518293