Finite Group Databasebeta

← #49159946

Subgroups — #49159946

Order 37504.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#34036760C211yesmaximal, characteristic
2#34036138C212yesmaximal
3#34035898C211yesmaximal, characteristic
4#34035889C212yesmaximal
5#391×C293C211yesmaximal, characteristic
6C2×#17989786C2212yes—
7#22627623—22no—
8#22627615—22no—
9#22627603—22no—
10#22627583C2212yes—
11#22627548—22no—
12#22627548—22no—
13C22×Q8×C293C2211yescharacteristic
14C2×C4⋊C4×C293C2211yescharacteristic
15C2×C42×C293C2211yescharacteristic
16#95×C293—22no—
17C2×Dic586—22no—
18#17989786—22no—
19#17989786—22no—
20C2×#14556873—22no—
21C4⋊Dic293—22no—
22C4⋊Dic293D412yes—
23C4⋊Dic293D412yes—
24#17989781—24no—
25C22⋊Dic293—22no—
26C4×Dic293—22no—
27C2×Q8×C293—21no—
28C2×Q8×C293—22no—
29C2×Q8×C293—22no—
30C2×Q8×C293Q812yescomplemented
31C22×C4×C293—21no—
32C22×C4×C293—21no—
33C22×C4×C293D412yes—
34C22×C4×C293C2311yescharacteristic
35C4⋊C4×C293—22no—
36C42×C293—22no—
37Dic586—82no—
38C2×Dic293—22no—
39C2×Dic293—22no—
40#14556873—42no—
41C23×C293C2×D411yescharacteristic
42Q8×C293—24no—
43Q8×C293—42no—
44C2×C4×C293—22no—
45C2×C4×C293—22no—
46C2×C4×C293—22no—
47C2×C4×C293—41no—
48C2×C4×C293—41no—
49C2×C4×C293—41no—
50C2×C4×C293—41no—
51C2×C4×C293—42no—
52C2×C4×C293C2×D412yes—
53C2×C4×C293C2×Q811yescharacteristic
54C2×C4×C293#4112yes—
55C2×C4×C293#4111yescharacteristic
56C22×C293—21no—
57C22×C293—21no—
58C22×C293#12011yescharacteristic
59C22×C293C22⋊Q811yescharacteristic
60C22×C293#12411yescharacteristic
61C4×C293—42no—
62C4×C293—42no—
63C4×C293—42no—
64C4×C293C22⋊Q812yes—
65C4×C293#12412yes—
66Dic293—42no—
67Dic293—42no—
68C2×C293—21no—
69C2×C293—21no—
70C2×C293#39311yescharacteristic
71C2×C293#45511yescharacteristic
72C2×C293#45611yescharacteristic
73C293#202811yescharacteristic, complemented, Sylow
74#2028—2931nomaximal, Sylow
75#544—2931no—
76#419—2932no—
77#391D29311yescharacteristic
78#343—2931no—
79#339—2932no—
80C22×Q8C2×D29311yescharacteristic
81C2×M16—2932no—
82C4⋊Q8—5862no—
83#125—5862no—
84C22⋊Q8—5862no—
85#117—2932no—
86C2×C4⋊C4C2×D29311yescharacteristic
87C2×C42C2×D29311yescharacteristic
88#103—5862no—
89#103—5862no—
90#95—22no—
91C2×Q8—21no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8—5862no—
95C2×Q8Dic58612yescomplemented
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D29312yes—
99C22×C4C22×D29311yescharacteristic
100M16—5862no—
101M16—5862no—
102C2×C8—5862no—
103C4⋊C4—22no—
104C4⋊C4—2932no—
105C4⋊C4—2932no—
106C4⋊C4—5862no—
107C4⋊C4—5864no—
108C22⋊C4—5862no—
109C42—22no—
110C42—5862no—
111C23C2×C22⋊D29311yescharacteristic
112Q8—24no—
113Q8—42no—
114Q8—23442no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—5862no—
124C2×C4—5862no—
125C2×C4D4×D29312yes—
126C2×C4C2×Dic58611yescharacteristic
127C2×C4#1798980112yes—
128C2×C4#1798980211yescharacteristic
129C8—11722no—
130C22—21no—
131C22—21no—
132C22#2262759211yescharacteristic
133C22#2262760311yescharacteristic
134C22#2262761111yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—11722no—
139C4—11722no—
140C4#2262760112yes—
141C4#2262761012yes—
142C2—21no—
143C2—21no—
144C2#3403604111yescharacteristic
145C2#3403630611yescharacteristic
146C2#3403631111yescharacteristic
subgroupG/H
centerC22#22627592
commutator, cosocleC22×C4×C293C23
FrattiniC22×C4C22×D293
Fitting#391×C293C2
socleC22×C293#120
prime radicalC23×C293C2×D4
hypercenter#391D293
hypocenterC293#2028
LCSG ▷ C22×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C293Q8semidirect
73. C293#2028semidirect
95. C2×Q8Dic586semidirect

Maximal subgroups

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

subgroupindex
#340367602
#340361382
#340358982
#340358892
#391×C2932
#2028293