Finite Group Databasebeta

← #49159949

Subgroups — #49159949

Order 37504.

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

normal subgroups only

This group has 466 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#34036755C211yesmaximal, characteristic, complemented
2#34035985C212yesmaximal
3#34035896C211yesmaximal, characteristic, complemented
4#34035895C212yesmaximal, complemented
5#379×C293C211yesmaximal, characteristic
6#22627603—22no—
7#22627601—24no—
8C2×C22⋊Dic293—24no—
9C2×C22⋊Dic293C2212yes—
10C2×C22⋊Dic293C2212yes—
11C25×C293C2211yescharacteristic
12C2×C22⋊C4×C293—22no—
13C2×C22⋊C4×C293C2211yescharacteristic
14C2×C22⋊C4×C293C2211yescharacteristic
15C2×Dic586—22no—
16C22×Dic293—22no—
17C22×Dic293D414yes—
18C4⋊Dic293—22no—
19#17989781—24no—
20C22⋊Dic293—22no—
21C22⋊Dic293—22no—
22C22⋊Dic293—22no—
23C22⋊Dic293—22no—
24C22⋊Dic293—48no—
25C24×C293—21no—
26C24×C293—22no—
27C24×C293—22no—
28C24×C293—21no—
29C24×C293—44no—
30C24×C293Q812yescomplemented
31C24×C293C2311yescharacteristic
32C22×C4×C293—21no—
33C22×C4×C293D412yes—
34C22⋊C4×C293—22no—
35C22⋊C4×C293—22no—
36C22⋊C4×C293—44no—
37Dic586—82no—
38C2×Dic293—24no—
39C2×Dic293—44no—
40C2×Dic293—44no—
41C2×Dic293—42no—
42C23×C293—24no—
43C23×C293—28no—
44C23×C293—24no—
45C23×C293—22no—
46C23×C293—44no—
47C23×C293—42no—
48C23×C293—42no—
49C23×C293—44no—
50C23×C293—48no—
51C23×C293—44no—
52C23×C293—41no—
53C23×C293—42no—
54C23×C293—41no—
55C23×C293C2×D412yes—
56C23×C293C2×D411yescharacteristic
57C23×C293C2×Q811yescharacteristic
58C23×C293#4112yes—
59C23×C293#4111yescharacteristic
60C2×C4×C293—22no—
61C2×C4×C293—42no—
62C2×C4×C293—42no—
63C2×C4×C293—41no—
64C22×C293—22no—
65C22×C293—24no—
66C22×C293—24no—
67C22×C293—28no—
68C22×C293—41no—
69C22×C293—42no—
70C22×C293—41no—
71C22×C293—48no—
72C22×C293—44no—
73C22×C293—44no—
74C22×C293—42no—
75C22×C293—42no—
76C22×C293—44no—
77C22×C293#12011yescharacteristic
78C22×C293C22⋊Q812yes—
79C22×C293C22⋊Q811yescharacteristic
80C22×C293#12412yes—
81C22×C293#12411yescharacteristic
82C4×C293—42no—
83C4×C293—81no—
84Dic293—44no—
85Dic293—82no—
86C2×C293—22no—
87C2×C293—21no—
88C2×C293—22no—
89C2×C293—21no—
90C2×C293—44no—
91C2×C293#39311yescharacteristic
92C2×C293B(4,𝔽2)12yes—
93C293#202911yescharacteristic, complemented, Sylow
94#2029—2931nomaximal, Sylow
95#543—2931no—
96#379—2932no—
97#379D29311yescharacteristic
98#342—2932no—
99#342—2931no—
100C25C2×D29311yescharacteristic
101C22⋊Q8—5864no—
102C22⋊Q8—5862no—
103C2×C22⋊C4—22no—
104C2×C22⋊C4—2932no—
105C2×C22⋊C4—2932no—
106C2×C22⋊C4—5864no—
107C2×C22⋊C4C2×D29311yescharacteristic
108C2×C22⋊C4C2×D29311yescharacteristic
109C24—22no—
110C24—21no—
111C24—22no—
112C24—21no—
113C24—44no—
114C24Dic58612yescomplemented
115C24C22×D29311yescharacteristic
116C2×Q8—5862no—
117C22×C4—21no—
118C22×C4—2934no—
119C22×C4—5862no—
120C22×C4C22⋊D29312yes—
121C4⋊C4—5864no—
122C4⋊C4—5862no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—5862no—
127C22⋊C4—5862no—
128C22⋊C4—5862no—
129C22⋊C4—5862no—
130C22⋊C4—11728no—
131C23—24no—
132C23—28no—
133C23—24no—
134C23—22no—
135C23—44no—
136C23—42no—
137C23—42no—
138C23—44no—
139C23—48no—
140C23—44no—
141C23—41no—
142C23—42no—
143C23—41no—
144C23D4×D29312yes—
145C23C2×C22⋊D29311yescharacteristic
146C23C2×Dic58611yescharacteristic
147C23#1798980112yes—
148C23#1798980211yescharacteristic
149Q8—23442no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—5864no—
155C2×C4—11724no—
156C2×C4—11722no—
157C2×C4—11724no—
158C22—22no—
159C22—24no—
160C22—28no—
161C22—24no—
162C22—41no—
163C22—42no—
164C22—41no—
165C22—44no—
166C22—48no—
167C22—44no—
168C22—42no—
169C22—42no—
170C22—44no—
171C22#2262759211yescharacteristic
172C22#2262760112yes—
173C22#2262760311yescharacteristic
174C22#2262761012yes—
175C22#2262761111yescharacteristic
176C4—42no—
177C4—81no—
178C4—23442no—
179C4—11724no—
180C2—21no—
181C2—22no—
182C2—22no—
183C2—21no—
184C2—44no—
185C2#3403604111yescharacteristic
186C2#3403631512yes—
subgroupG/H
centerC22#22627592
commutator, cosocleC24×C293C23
FrattiniC24C22×D293
Fitting#379×C293C2
socleC22×C293#120
prime radicalC25×C293C22
hypercenter#379D293
hypocenterC293#2029
LCSG ▷ C24×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #34036755C2semidirect
3. #34035896C2semidirect
4. #34035895C2semidirect
30. C24×C293Q8semidirect
93. C293#2029semidirect
114. C24Dic586semidirect

Maximal subgroups

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

subgroupindex
#340367552
#340359852
#340358962
#340358952
#379×C2932
#2029293