Finite Group Databasebeta

← #49157751

Subgroups — #49157751

Order 37504.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#34036728C211yesmaximal, characteristic
2#34036284C211yesmaximal, characteristic, complemented
3#34036270C211yesmaximal, characteristic
4#34036050C211yesmaximal, characteristic, complemented
5#34035862C211yesmaximal, characteristic
6#34035854C211yesmaximal, characteristic, complemented
7#328×C293C211yesmaximal, characteristic, complemented
8C22×Dic586C2211yescharacteristic
9C2×#17989792—21no—
10C2×#17989791—21no—
11#22627619—21no—
12#22627615—21no—
13#22627609—21no—
14#22627608—21no—
15#22627600—21no—
16#22627598C2211yescharacteristic
17#22627584—21no—
18C2×C4⋊Dic293—21no—
19C2×#17989781C2211yescharacteristic
20#22627549—21no—
21#22627547—21no—
22C22⋊#14556873C2211yescharacteristic
23#22627531—21no—
24C22⋊Q8×C293C2211yescharacteristic
25C22⋊C8×C293C2211yescharacteristic
26#95×C293C2211yescharacteristic
27C2×Dic586—21no—
28C2×Dic586—21no—
29C2×Dic586—42no—
30C2×D1172D411yescharacteristic
31C2×C22⋊D293—21no—
32C22×Dic293—21no—
33C22×Dic293D411yescharacteristic
34C22×Dic293D411yescharacteristic
35C2×C4×D293—21no—
36#17989792—42no—
37#17989791—42no—
38C2×#14556873—21no—
39C4⋊Dic293—21no—
40C4⋊Dic293—21no—
41C4⋊Dic293—42no—
42C4⋊Dic293D411yescharacteristic
43#17989781—21no—
44#17989781—21no—
45#17989781—21no—
46#17989779—21no—
47#17989779—21no—
48#17989779—21no—
49#17989779—21no—
50C4×Dic293—21no—
51C2×Q8×C293D411yescharacteristic
52C22×C4×C293—21no—
53C22×C4×C293C2311yescharacteristic
54C2×C8×C293—21no—
55C4⋊C4×C293—21no—
56C4⋊C4×C293D411yescharacteristic
57C22⋊C4×C293—21no—
58C22×D293—21no—
59Dic586—22no—
60Dic586—22no—
61Dic586—41no—
62Dic586—41no—
63D1172—41no—
64C22⋊D293—41no—
65C22⋊D293—41no—
66C2×Dic293—22no—
67C2×Dic293—21no—
68C2×Dic293—21no—
69C2×Dic293—21no—
70C2×Dic293—21no—
71C2×Dic293—21no—
72C2×Dic293—41no—
73C2×Dic293—41no—
74C2×Dic293—41no—
75C4×D293—81no—
76#14556873—41no—
77C23×C293C2×D411yescharacteristic
78Q8×C293—41no—
79C2×C4×C293—22no—
80C2×C4×C293—21no—
81C2×C4×C293—21no—
82C2×C4×C293—41no—
83C2×C4×C293—41no—
84C2×C4×C293—41no—
85C2×C4×C293C2×D411yescharacteristic
86C2×C4×C293C2×D411yescharacteristic
87C8×C293—41no—
88C22×C293—21no—
89C22×C293—21no—
90C22×C293#12011yescharacteristic
91C22×C293#13511yescharacteristic
92C22×C293#13711yescharacteristic
93C2×D293—41no—
94C2×D293—41no—
95C2×D293—41no—
96C4×C293—21no—
97C4×C293—21no—
98C4×C293—42no—
99C4×C293—41no—
100C4×C293—41no—
101Dic293—41no—
102Dic293—41no—
103Dic293—41no—
104Dic293—42no—
105C2×C293—21no—
106C2×C293—21no—
107C2×C293#45211yescharacteristic
108C2×C293#45611yescharacteristic
109C2×C293B(4,𝔽2)11yescharacteristic
110D293—81no—
111C293#160311yescharacteristic, complemented, Sylow
112#1603—2931nomaximal, Sylow
113#539—2931no—
114#451—2931no—
115#448—2931no—
116#395—2931no—
117#328D29311yescharacteristic, complemented
118#327—2931no—
119#324—2931no—
120C22×Q8—2931no—
121C2×Q16—5861no—
122C2×SD16—5861no—
123#126—5861no—
124#125—5861no—
125#123—5861no—
126#123—5861no—
127C22⋊Q8—5861no—
128C22⋊Q8C2×D29311yescharacteristic
129#121—2931no—
130C4×D4—5861no—
131C2×C4⋊C4—2931no—
132C2×C4⋊C4—5861no—
133#103—5861no—
134#103—5861no—
135C22⋊C8—2931no—
136C22⋊C8C2×D29311yescharacteristic
137#95—5861no—
138#95C2×D29311yescharacteristic
139C2×Q8—5861no—
140C2×Q8—5861no—
141C2×Q8—11722no—
142C2×Q8D117211yescharacteristic
143C2×D4—2931no—
144C2×D4—5861no—
145C22×C4—21no—
146C22×C4—2931no—
147C22×C4—2931no—
148C22×C4—5861no—
149C22×C4—5861no—
150C22×C4C22×D29311yescharacteristic
151Q16—11722no—
152SD16—11722no—
153C2×C8—21no—
154C2×C8—5861no—
155C4⋊C4—21no—
156C4⋊C4—2931no—
157C4⋊C4—5861no—
158C4⋊C4—5861no—
159C4⋊C4—5861no—
160C4⋊C4—5861no—
161C4⋊C4—5861no—
162C4⋊C4—11722no—
163C4⋊C4D117211yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—5861no—
166C22⋊C4—5861no—
167C22⋊C4—5861no—
168C22⋊C4—5861no—
169C42—5861no—
170C23—5861no—
171C23D4×D29311yescharacteristic
172Q8—41no—
173Q8—5862no—
174Q8—5862no—
175Q8—11721no—
176Q8—11721no—
177D4—11721no—
178D4—11721no—
179D4—11721no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—23441no—
187C2×C4—5862no—
188C2×C4—5861no—
189C2×C4—5861no—
190C2×C4—5861no—
191C2×C4—5861no—
192C2×C4—5861no—
193C2×C4—11721no—
194C2×C4—11721no—
195C2×C4—11721no—
196C2×C4D4×D29311yescharacteristic
197C2×C4C2×D117211yescharacteristic
198C8—41no—
199C8—11721no—
200C22—21no—
201C22—21no—
202C22—11721no—
203C22—11721no—
204C22—11721no—
205C22#2262759411yescharacteristic
206C22#2262764511yescharacteristic
207C22#2262765611yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—11721no—
214C4—11721no—
215C4—11721no—
216C4—11722no—
217C2—21no—
218C2—21no—
219C2—23441no—
220C2#3403629411yescharacteristic
221C2#3403631311yescharacteristic
222C2#3403631711yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC22×C4×C293C23
FrattiniC22×C4C22×D293
Fitting#328×C293C2
socleC22×C293#120
prime radical#22627598C22
hypercenter#328D293
hypocenterC293#1603
LCSG ▷ C22×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #34036284C2semidirect
4. #34036050C2semidirect
6. #34035854C2semidirect
7. #328×C293C2semidirect
111. C293#1603semidirect
117. #328D293semidirect

Maximal subgroups

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

subgroupindex
#340367282
#340362842
#340362702
#340360502
#340358622
#340358542
#328×C2932
#1603293