Finite Group Databasebeta

← #49158093

Subgroups — #49158093

Order 37504.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#34036871C211yesmaximal, characteristic
2#34036523C211yesmaximal, characteristic, complemented
3#34036489C211yesmaximal, characteristic, complemented
4#34036488C211yesmaximal, characteristic, complemented
5#34035868C211yesmaximal, characteristic, complemented
6#34035868C211yesmaximal, characteristic, complemented
7#329×C293C211yesmaximal, characteristic, complemented
8C2×Dic1172—21no—
9C2×#17989791—21no—
10#22627624C2211yescharacteristic, complemented
11#22627613—21no—
12#22627612C2211yescharacteristic
13#22627612C2211yescharacteristic
14#22627610—21no—
15#22627610—21no—
16#22627594—21no—
17#22627594—21no—
18#22627592—21no—
19#22627549—21no—
20#22627548—21no—
21#22627546—21no—
22#22627545—21no—
23#22627535C2211yescharacteristic, complemented
24#124×C293C2211yescharacteristic
25#97×C293C2211yescharacteristic, complemented
26#97×C293C2211yescharacteristic, complemented
27C23×D293—21no—
28C2×Dic586—21no—
29C2×Dic586D411yescharacteristic
30C2×Dic586D411yescharacteristic
31C2×D1172—21no—
32C2×D1172D411yescharacteristic
33C2×D1172D411yescharacteristic
34C2×C22⋊D293—21no—
35C2×C22⋊D293—21no—
36Dic1172—42no—
37#17989791—42no—
38C2×#14556873—21no—
39C4⋊Dic293—21no—
40C4⋊Dic293—21no—
41C22⋊Dic293—21no—
42#17989779—21no—
43#17989779—21no—
44#17989779—21no—
45#17989779—21no—
46#17989779—21no—
47#17989779—21no—
48C4×Dic293—21no—
49C2×Q8×C293D411yescharacteristic
50C2×D4×C293D411yescharacteristic
51C2×C8×C293—21no—
52C2×C8×C293—21no—
53C22⋊C4×C293—21no—
54C22⋊C4×C293—21no—
55C42×C293C2311yescharacteristic
56C22×D293—21no—
57C22×D293—21no—
58C22×D293—81no—
59C22×D293—81no—
60C22×D293—81no—
61Dic586—41no—
62Dic586—41no—
63Dic586—41no—
64Dic586—41no—
65D1172—41no—
66D1172—41no—
67D1172—81no—
68C22⋊D293—81no—
69C22⋊D293—81no—
70C2×Dic293—21no—
71C2×Dic293—21no—
72C2×Dic293—41no—
73#14556873—41no—
74C23×C293—21no—
75Q8×C293—41no—
76D4×C293—41no—
77C2×C4×C293—21no—
78C2×C4×C293C2×D411yescharacteristic
79C2×C4×C293C2×D411yescharacteristic
80C2×C4×C293C2×D411yescharacteristic
81C8×C293—22no—
82C8×C293—41no—
83C22×C293—41no—
84C22×C293—41no—
85C22×C293—41no—
86C22×C293#12011yescharacteristic
87C2×D293—41no—
88C2×D293—41no—
89C2×D293—41no—
90C2×D293—41no—
91C2×D293—41no—
92C2×D293—41no—
93C2×D293—84no—
94C4×C293—21no—
95C4×C293—21no—
96C4×C293—21no—
97C4×C293—41no—
98Dic293—41no—
99Dic293—41no—
100Dic293—81no—
101C2×C293—81no—
102C2×C293#45311yescharacteristic
103C2×C293#45511yescharacteristic
104C2×C293#45511yescharacteristic
105D293—81no—
106D293—81no—
107C293#165911yescharacteristic, complemented, Sylow
108#1659—2931nomaximal, Sylow
109H(3,𝔽4)—2931no—
110#497—2931no—
111#489—2931no—
112#489—2931no—
113#329—2931no—
114#329—2931no—
115#329D29311yescharacteristic, complemented
116C2×Q16—5861no—
117C2×SD16—5861no—
118C4⋊Q8—2931no—
119#124—2931no—
120#124—2931no—
121#124—5861no—
122#124—5861no—
123#124—5861no—
124#124C2×D29311yescharacteristic
125#120—5861no—
126#120—5861no—
127#120—5861no—
128#103—5861no—
129#103—5861no—
130#102—5861no—
131#102—5861no—
132#97—2931no—
133#97C2×D29311yescharacteristic, complemented
134#97C2×D29311yescharacteristic, complemented
135C24—5861no—
136C2×Q8—2931no—
137C2×Q8—2931no—
138C2×Q8—5861no—
139C2×Q8D117211yescharacteristic
140C2×D4—2931no—
141C2×D4—2931no—
142C2×D4—5861no—
143C2×D4—5861no—
144C2×D4—5861no—
145C2×D4D117211yescharacteristic
146Q16—11722no—
147SD16—11722no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—5861no—
151C4⋊C4—5861no—
152C4⋊C4—5861no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—5861no—
156C22⋊C4—5861no—
157C22⋊C4—5861no—
158C22⋊C4—5861no—
159C22⋊C4—5861no—
160C22⋊C4—5861no—
161C22⋊C4—5861no—
162C42—5861no—
163C42C22×D29311yescharacteristic
164C23—21no—
165C23—23441no—
166C23—23441no—
167C23—23441no—
168C23—5861no—
169C23—5861no—
170Q8—41no—
171Q8—11721no—
172Q8—11721no—
173Q8—11721no—
174Q8—11721no—
175D4—41no—
176D4—23441no—
177D4—23441no—
178D4—23441no—
179D4—11721no—
180D4—11721no—
181C2×C4—21no—
182C2×C4—5861no—
183C2×C4—5861no—
184C2×C4—11721no—
185C2×C4D4×D29311yescharacteristic
186C2×C4D4×D29311yescharacteristic
187C2×C4C2×D117211yescharacteristic
188C8—22no—
189C8—41no—
190C8—11721no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—23444no—
195C22—11721no—
196C22—11721no—
197C22—11721no—
198C22—11721no—
199C22—11721no—
200C22—11721no—
201C22#2262759411yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—23441no—
207C4—11721no—
208C4—11721no—
209C2—81no—
210C2—23441no—
211C2—23441no—
212C2#3403629811yescharacteristic
213C2#3403630811yescharacteristic
214C2#3403630911yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#329×C293C2
socleC22×C293#120
prime radical#34036871C2
hypercenter#329D293
hypocenterC293#1659
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #34036523C2semidirect
3. #34036489C2semidirect
4. #34036488C2semidirect
5. #34035868C2semidirect
6. #34035868C2semidirect
7. #329×C293C2semidirect
10. #22627624C22semidirect
23. #22627535C22semidirect
25. #97×C293C22semidirect
26. #97×C293C22semidirect
107. C293#1659semidirect
115. #329D293semidirect
133. #97C2×D293semidirect
134. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340368712
#340365232
#340364892
#340364882
#340358682
#329×C2932
#1659293