Finite Group Databasebeta

← #49159916

Subgroups — #49159916

Order 37504.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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#34036691C211yesmaximal, characteristic
2C2×#22627607C212yesmaximal, complemented
3C2×#22627538C212yesmaximal, complemented
4#34035896C211yesmaximal, characteristic, complemented
5#381×C293C211yesmaximal, characteristic, complemented
6C22×C22⋊D293C2212yes—
7#22627608—22no—
8#22627607—24no—
9#22627607—24no—
10#22627598—22no—
11#22627594—22no—
12C2×#17989781—22no—
13C2×C22⋊Dic293C2212yes—
14C2×#17989779—22no—
15#22627538—24no—
16C23×C4×C293C2211yescharacteristic
17C2×C22⋊C4×C293C2211yescharacteristic
18C2×C22⋊C4×C293C2211yescharacteristic
19#95×C293—22no—
20C23×D293D412yes—
21C2×D1172—22no—
22C2×C22⋊D293—22no—
23C2×C22⋊D293—22no—
24C2×C22⋊D293—22no—
25C2×C22⋊D293—22no—
26C2×C22⋊D293—22no—
27C2×C22⋊D293—22no—
28C22×Dic293—22no—
29C22×Dic293D412yes—
30C4⋊Dic293—22no—
31#17989781—28no—
32C22⋊Dic293—22no—
33C22⋊Dic293D414yescomplemented
34#17989779—24no—
35#17989779—28no—
36C24×C293C2311yescharacteristic
37C22×C4×C293—22no—
38C22×C4×C293—21no—
39C22×C4×C293—22no—
40C22×C4×C293—21no—
41C22×C4×C293—21no—
42C22×C4×C293D412yes—
43C22×C4×C293D412yescomplemented
44C22⋊C4×C293—22no—
45C22⋊C4×C293—22no—
46C22×D293—22no—
47C22×D293—22no—
48C22×D293—22no—
49C22×D293—44no—
50D1172—82no—
51C22⋊D293—42no—
52C22⋊D293—42no—
53C22⋊D293—42no—
54C22⋊D293—42no—
55C2×Dic293—24no—
56C2×Dic293—22no—
57C2×Dic293—22no—
58C2×Dic293—22no—
59C2×Dic293—44no—
60C23×C293—42no—
61C23×C293C2×D412yes—
62C23×C293C2×D412yes—
63C23×C293C2×D411yescharacteristic
64C23×C293C2×D411yescharacteristic
65C23×C293#4111yescharacteristic
66C2×C4×C293—22no—
67C2×C4×C293—24no—
68C2×C4×C293—22no—
69C2×C4×C293—41no—
70C2×C4×C293—42no—
71C2×C4×C293—41no—
72C2×C4×C293—42no—
73C2×C4×C293—42no—
74C2×C4×C293—41no—
75C22×C293—22no—
76C22×C293—24no—
77C22×C293—42no—
78C22×C293—41no—
79C22×C293—41no—
80C22×C293#12011yescharacteristic
81C22×C293#12012yes—
82C22×C293#12112yes—
83C22×C293#12111yescharacteristic
84C22×C293#12711yescharacteristic
85C2×D293—44no—
86C2×D293—42no—
87C2×D293—44no—
88C2×D293—82no—
89C4×C293—42no—
90C4×C293—42no—
91C4×C293—81no—
92Dic293—44no—
93Dic293—42no—
94C2×C293—22no—
95C2×C293—21no—
96C2×C293—22no—
97C2×C293—21no—
98C2×C293#39211yescharacteristic
99C2×C293#45812yes—
100D293—82no—
101C293#202211yescharacteristic, complemented, Sylow
102#2022—2931nomaximal, Sylow
103#534—2931no—
104C2×#123—2932no—
105C2×#99—2932no—
106#381D29311yescharacteristic, complemented
107#342—2931no—
108C22×D4—2932no—
109C23×C4C2×D29311yescharacteristic
110#123—5862no—
111#123—5864no—
112#123—5864no—
113#121—5862no—
114#120—5862no—
115C2×C4⋊C4—5862no—
116C2×C22⋊C4—2932no—
117C2×C22⋊C4—5862no—
118C2×C22⋊C4C2×D29311yescharacteristic
119C2×C22⋊C4C2×D29311yescharacteristic
120#99—5864no—
121#95—22no—
122C24—2932no—
123C24C22×D29311yescharacteristic
124C2×D4—5862no—
125C2×D4—5862no—
126C2×D4—5862no—
127C2×D4—5862no—
128C2×D4—5862no—
129C2×D4—5862no—
130C2×D4—5862no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—2932no—
137C22×C4—5862no—
138C22×C4C22⋊D29312yes—
139C22×C4D117212yescomplemented
140C4⋊C4—5868no—
141C4⋊C4—5862no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—2934no—
145C22⋊C4—5868no—
146C22⋊C4—5864no—
147C22⋊C4—5862no—
148C23—42no—
149C23—5862no—
150C23—5862no—
151C23—5862no—
152C23—11724no—
153C23D4×D29312yes—
154C23D4×D29312yes—
155C23C2×C22⋊D29311yescharacteristic
156C23C2×D117211yescharacteristic
157C23#1798980211yescharacteristic
158D4—23442no—
159D4—11722no—
160D4—11722no—
161D4—11722no—
162D4—11722no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—5862no—
173C2×C4—5864no—
174C2×C4—5862no—
175C2×C4—5862no—
176C2×C4—11724no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—23442no—
183C22—11724no—
184C22—11722no—
185C22—11724no—
186C22#2262759211yescharacteristic
187C22#2262759412yes—
188C22#2262759712yes—
189C22#2262759811yescharacteristic
190C22#2262762011yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—11724no—
195C4—11722no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—23442no—
201C2#3403603811yescharacteristic
202C2#3403631812yes—
subgroupG/H
centerC22#22627592
commutator, cosocleC24×C293C23
FrattiniC24C22×D293
Fitting#381×C293C2
socleC22×C293#120
prime radical#34036691C2
hypercenter#381D293
hypocenterC293#2022
LCSG ▷ C24×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#22627607C2semidirect
3. C2×#22627538C2semidirect
4. #34035896C2semidirect
5. #381×C293C2semidirect
33. C22⋊Dic293D4semidirect
43. C22×C4×C293D4semidirect
101. C293#2022semidirect
106. #381D293semidirect
139. C22×C4D1172semidirect

Maximal subgroups

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

subgroupindex
#340366912
C2×#226276072
C2×#226275382
#340358962
#381×C2932
#2022293