Finite Group Databasebeta

← #49174305

Subgroups — #49174305

Order 37504.

252 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 60 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#34037152C211yesmaximal, characteristic, complemented
2D293⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#34036989C212yesmaximal, complemented
4#34036987C212yesmaximal, complemented
5#34036678C211yesmaximal, characteristic
6C2×D293⋊C8—21no—
7#22627691C2212yes—
8#22627691C2212yes—
9C4⋊#14556880—21no—
10#22627681—21no—
11#22627679—21no—
12C2×#17989803C411yescharacteristic
13C2×#17989801C411yescharacteristic
14#22627622C2211yescharacteristic
15#22627620C2211yescharacteristic
16#22627612C411yescharacteristic
17#22627597—21no—
18#22627597—21no—
19#22627584—21no—
20#22627584—21no—
21C42×D293C2211yescharacteristic
22#124×C293C411yescharacteristic
23D293⋊C8—42no—
24C2×#14556880—22no—
25C2×#14556880—22no—
26#17989803—42no—
27#17989801—42no—
28C2×Dic586C2×C411yescharacteristic
29C2×D1172—21no—
30C2×D1172C2×C411yescharacteristic
31C2×C22⋊D293—21no—
32C2×C22⋊D293—21no—
33C2×C22⋊D293—21no—
34C22×Dic293—21no—
35C2×C4×D293—21no—
36C2×C4×D293C2×C411yescharacteristic
37C2×C4×D293D411yescharacteristic
38C2×C4×D293D411yescharacteristic
39#17989781—21no—
40#17989781—21no—
41#17989779—21no—
42#17989779—21no—
43C4×Dic293D411yescharacteristic
44C4×Dic293D411yescharacteristic
45C4×Dic293C2311yescharacteristic
46C2×Q8×C293C2×C411yescharacteristic
47C2×D4×C293C2×C411yescharacteristic
48C22⋊C4×C293—21no—
49C22⋊C4×C293—21no—
50C42×C293C2×C411yescharacteristic
51#14556880—42no—
52#14556880—42no—
53C22×D293—21no—
54C22×D293C22⋊C411yescharacteristic
55Dic586—41no—
56D1172—41no—
57D1172—42no—
58C22⋊D293—42no—
59C22⋊D293—42no—
60C22⋊D293—41no—
61C22⋊D293—41no—
62C2×Dic293—21no—
63C2×Dic293—42no—
64C2×Dic293C22⋊C411yescharacteristic
65C2×Dic293C2×D411yescharacteristic
66C2×Dic293C2×D411yescharacteristic
67C4×D293—22no—
68C4×D293—22no—
69C4×D293—21no—
70C4×D293—21no—
71C4×D293—42no—
72C23×C293—21no—
73Q8×C293—41no—
74D4×C293—41no—
75C2×C4×C293—21no—
76C2×C4×C293C22⋊C411yescharacteristic
77C2×C4×C293C22⋊C411yescharacteristic
78C2×C4×C293C22×C411yescharacteristic
79C22×C293—41no—
80C22×C293—41no—
81C22×C293—41no—
82C22×C293C2×C22⋊C411yescharacteristic
83C2×D293—21no—
84C2×D293—21no—
85C2×D293—41no—
86C2×D293—41no—
87C2×D293—41no—
88C2×D293#10012yes—
89C4×C293—21no—
90C4×C293—21no—
91C4×C293—21no—
92C4×C293—41no—
93Dic293—21no—
94Dic293—41no—
95Dic293#13512yes—
96Dic293AGL(1,ℤ/8)11yescharacteristic
97Dic293#13711yescharacteristic
98C2×C293—81no—
99C2×C293C2×#10011yescharacteristic
100C2×C293#41611yescharacteristic
101C2×C293#41711yescharacteristic
102D293—22no—
103D293—81no—
104C293#155111yescharacteristic, complemented, Sylow
105#1551—2931nomaximal, Sylow
106#532—2931no—
107#432—2931no—
108C2×C4⋊C8—2931no—
109#333—2932no—
110#331—2932no—
111C2×#41—2931no—
112C2×#41—2931no—
113C22×C8—5861no—
114C4⋊Q8—2931no—
115#127—2931no—
116#124—2931no—
117#124#1192407811yescharacteristic
118#121—5861no—
119#121—5861no—
120C4×D4—5861no—
121C4×D4—5861no—
122C2×C42—2931no—
123C4⋊C8—2932no—
124C4⋊C8—2932no—
125C4⋊C8—5861no—
126C22⋊C8—5861no—
127#97—5861no—
128#41—11722no—
129#41—11722no—
130C2×Q8—2931no—
131C2×Q8C2×#1192407811yescharacteristic
132C2×D4—2931no—
133C2×D4—5861no—
134C2×D4—5861no—
135C2×D4—5861no—
136C2×D4—5861no—
137C2×D4C2×#1192407811yescharacteristic
138C22×C4—2931no—
139C22×C4—2931no—
140C22×C4—2931no—
141C22×C4—5861no—
142C22×C4—5861no—
143C2×C8—5862no—
144C2×C8—5862no—
145C2×C8—11722no—
146C4⋊C4—5861no—
147C4⋊C4—5861no—
148C22⋊C4—21no—
149C22⋊C4—21no—
150C22⋊C4—5861no—
151C22⋊C4—5861no—
152C42—2931no—
153C42—2931no—
154C42—2931no—
155C42C2×#1192407811yescharacteristic
156C23—21no—
157C23—2931no—
158C23—5861no—
159Q8—41no—
160Q8—11721no—
161D4—41no—
162D4—11721no—
163D4—11722no—
164D4—11722no—
165D4—11721no—
166D4—11721no—
167D4—11722no—
168C2×C4—21no—
169C2×C4—2931no—
170C2×C4—2931no—
171C2×C4—2931no—
172C2×C4—5861no—
173C2×C4—5862no—
174C2×C4—5861no—
175C2×C4—5862no—
176C2×C4—5861no—
177C2×C4—11722no—
178C2×C4—11722no—
179C2×C4C22⋊#1192407811yescharacteristic
180C2×C4C22⋊#1192407811yescharacteristic
181C2×C4C22×#1192407811yescharacteristic
182C8—11722no—
183C8—11722no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—2932no—
188C22—5861no—
189C22—5861no—
190C22—11721no—
191C22—11721no—
192C22—11721no—
193C22C2×C22⋊#1192407811yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—41no—
198C4—2932no—
199C4—2931no—
200C4—2931no—
201C4—5861no—
202C4—11721no—
203C2—81no—
204C2—23441no—
205C2—5862no—
206C2D293⋊#10011yescharacteristic
207C2#3403711911yescharacteristic
208C2#3403712011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#124×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036678C2
cosocleC4×Dic293C23
hypercenter#124#11924078
hypocenterC293#1551
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #34037152C2semidirect
2. D293⋊(C4⋊C8)C2semidirect
3. #34036989C2semidirect
4. #34036987C2semidirect
104. C293#1551semidirect

Maximal subgroups

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

subgroupindex
#340371522
D293⋊(C4⋊C8)2
#340369892
#340369872
#340366782
#1551293