Finite Group Databasebeta

← #49160476

Subgroups — #49160476

Order 37504.

262 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 65 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#34036693C211yesmaximal, characteristic
2#34036113C211yesmaximal, characteristic, complemented
3#34035925C214yesmaximal, complemented
4#413×C293C211yesmaximal, characteristic, complemented
5C22×D1172C411yescharacteristic
6C2×#17989786—21no—
7#22627620C412yes—
8#22627613C2212yes—
9#22627598—21no—
10#22627598—21no—
11#22627592—21no—
12#22627592—21no—
13#22627583C411yescharacteristic
14#22627543C2212yescomplemented
15#22627541—21no—
16C2×#41×C293C2211yescharacteristic
17C2×M16×C293—21no—
18#101×C293C2212yescomplemented
19#100×C293—21no—
20C23×D293—21no—
21C2×D1172—21no—
22C2×D1172—41no—
23C2×D1172—41no—
24C2×D1172C2×C412yes—
25C2×C22⋊D293—22no—
26C2×C22⋊D293—22no—
27#17989786—22no—
28#17989786—41no—
29C2×#14556873—41no—
30C4⋊Dic293—21no—
31C22⋊Dic293—21no—
32#17989779—22no—
33#17989779—22no—
34C4×Dic293C2×C412yes—
35#41×C293—41no—
36#41×C293—41no—
37C2×Q8×C293C2311yescharacteristic
38C2×D4×C293C2×C411yescharacteristic
39C2×D4×C293D411yescharacteristic
40C2×D4×C293D411yescharacteristic
41C22×C4×C293C2×C411yescharacteristic
42C22×C4×C293D411yescharacteristic
43C22×C4×C293D411yescharacteristic
44M16×C293—22no—
45M16×C293—41no—
46C2×C8×C293—41no—
47C22×D293—22no—
48C22×D293—42no—
49C22×D293—82no—
50D1172—42no—
51D1172—41no—
52D1172—41no—
53C22⋊D293—82no—
54C22⋊D293—82no—
55C2×Dic293—22no—
56#14556873—42no—
57C23×C293C22⋊C411yescharacteristic
58C23×C293C22⋊C411yescharacteristic
59C23×C293C22⋊C411yescharacteristic
60Q8×C293—41no—
61D4×C293—41no—
62D4×C293—41no—
63D4×C293—41no—
64C2×C4×C293—21no—
65C2×C4×C293—21no—
66C2×C4×C293—21no—
67C2×C4×C293—21no—
68C2×C4×C293—21no—
69C2×C4×C293—21no—
70C2×C4×C293C22⋊C411yescharacteristic
71C2×C4×C293C22×C411yescharacteristic
72C2×C4×C293C2×D411yescharacteristic
73C2×C4×C293C2×D411yescharacteristic
74C8×C293—42no—
75C22×C293—21no—
76C22×C293—21no—
77C22×C293—21no—
78C22×C293—41no—
79C22×C293—41no—
80C22×C293—41no—
81C22×C293C2×C22⋊C411yescharacteristic
82C2×D293—42no—
83C2×D293—42no—
84C2×D293—42no—
85C2×D293—84no—
86C4×C293—21no—
87C4×C293—21no—
88C4×C293—21no—
89C4×C293#9911yescharacteristic
90C4×C293#9911yescharacteristic
91Dic293—42no—
92C2×C293—21no—
93C2×C293—41no—
94C2×C293—41no—
95C2×C293—41no—
96C2×C293C2×#9911yescharacteristic
97D293—82no—
98C293#213411yescharacteristic, complemented, Sylow
99#2134—2931nomaximal, Sylow
100#535—2931no—
101#413—2931no—
102#413D29311yescharacteristic, complemented
103#355—2934no—
104C2×#41C2×D29311yescharacteristic
105C22×D4—2931no—
106C2×M16—21no—
107C2×M16—5861no—
108#127—2932no—
109#124—2932no—
110#121—5861no—
111#121—5861no—
112#120—5861no—
113#120—5861no—
114#117—2931no—
115#101—2932no—
116#101C2×D29312yescomplemented
117#100—21no—
118#100—5861no—
119C24—5861no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D29311yescharacteristic
123C2×D4—2932no—
124C2×D4—5862no—
125C2×D4—5862no—
126C2×D4—5861no—
127C2×D4—11721no—
128C2×D4—11721no—
129C2×D4C4×D29311yescharacteristic
130C2×D4C22⋊D29311yescharacteristic
131C2×D4D117211yescharacteristic
132C22×C4C4×D29311yescharacteristic
133C22×C4C22⋊D29311yescharacteristic
134C22×C4D117211yescharacteristic
135M16—22no—
136M16—41no—
137M16—5862no—
138M16—11721no—
139C2×C8—41no—
140C2×C8—11721no—
141C4⋊C4—5861no—
142C22⋊C4—5861no—
143C22⋊C4—5862no—
144C22⋊C4—5862no—
145C42—2932no—
146C23—23442no—
147C23—5862no—
148C23—11722no—
149C23#1798977911yescharacteristic
150C23#1798977911yescharacteristic
151C23#1798977911yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—23442no—
157D4—23442no—
158D4—11722no—
159D4—11721no—
160D4—11721no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—5862no—
168C2×C4#1798977911yescharacteristic
169C2×C4C2×C4×D29311yescharacteristic
170C2×C4C2×C22⋊D29311yescharacteristic
171C2×C4C2×D117211yescharacteristic
172C8—42no—
173C8—11722no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—23444no—
181C22—11722no—
182C22—11722no—
183C22—11722no—
184C22C2×#1798977911yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—11722no—
189C4#2262753811yescharacteristic
190C4#2262753811yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—23442no—
196C2C2×#2262753811yescharacteristic
subgroupG/H
centerC2C2×#22627538
commutatorC2×C4×C293C22×C4
FrattiniC2×Q8C22×D293
Fitting#413×C293C2
socleC2×C293C2×#99
prime radical#34036693C2
cosocleC2×Q8×C293C23
hypercenter#413D293
hypocenterC293#2134
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #34036113C2semidirect
3. #34035925C2semidirect
4. #413×C293C2semidirect
14. #22627543C22semidirect
18. #101×C293C22semidirect
98. C293#2134semidirect
102. #413D293semidirect
116. #101C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366932
#340361132
#340359252
#413×C2932
#2134293