Finite Group Databasebeta

← #49174309

Subgroups — #49174309

Order 37504.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#34037149C211yesmaximal, characteristic, complemented
2#34037146C211yesmaximal, characteristic, complemented
3#34036988C212yesmaximal, complemented
4#34036987C212yesmaximal, complemented
5#34036674C211yesmaximal, characteristic
6#22627691C2212yes—
7#22627691C2212yes—
8C22⋊#14556880—21no—
9C22⋊#14556880—21no—
10#22627679—21no—
11C4×#14556880—21no—
12C2×#17989801—21no—
13#22627623C2211yescharacteristic
14#22627620C2211yescharacteristic
15#22627610—21no—
16#22627598C411yescharacteristic
17#22627596—21no—
18D4×Dic293C411yescharacteristic
19#22627586C411yescharacteristic
20#22627584—21no—
21C2×C4×Dic293C2211yescharacteristic
22#121×C293C411yescharacteristic
23C2×#14556880—22no—
24C2×#14556880—22no—
25#17989801—44no—
26C2×Dic586—21no—
27C2×D1172C2×C411yescharacteristic
28C2×C22⋊D293—21no—
29C2×C22⋊D293—21no—
30C2×C22⋊D293—21no—
31C22×Dic293—21no—
32C22×Dic293D411yescharacteristic
33C22×Dic293D411yescharacteristic
34C2×C4×D293—21no—
35C4⋊Dic293C2×C411yescharacteristic
36#17989781—21no—
37C22⋊Dic293—21no—
38#17989779—21no—
39#17989779—21no—
40C4×Dic293C2×C411yescharacteristic
41C4×Dic293D411yescharacteristic
42C4×Dic293D411yescharacteristic
43C4×Dic293C2311yescharacteristic
44C2×D4×C293—21no—
45C2×D4×C293C2×C411yescharacteristic
46C22×C4×C293C2×C411yescharacteristic
47C4⋊C4×C293C2×C411yescharacteristic
48C22⋊C4×C293—21no—
49#14556880—42no—
50#14556880—42no—
51C22×D293—21no—
52Dic586—42no—
53D1172—41no—
54C22⋊D293—42no—
55C22⋊D293—42no—
56C22⋊D293—42no—
57C2×Dic293—22no—
58C2×Dic293—22no—
59C2×Dic293—21no—
60C2×Dic293—42no—
61C2×Dic293C22⋊C411yescharacteristic
62C2×Dic293C22⋊C411yescharacteristic
63C2×Dic293C2×D411yescharacteristic
64C2×Dic293C2×D411yescharacteristic
65C4×D293—42no—
66C23×C293—21no—
67C23×C293C22⋊C411yescharacteristic
68D4×C293—41no—
69D4×C293—42no—
70C2×C4×C293—21no—
71C2×C4×C293—41no—
72C2×C4×C293C22⋊C411yescharacteristic
73C2×C4×C293C22×C411yescharacteristic
74C22×C293—21no—
75C22×C293—21no—
76C22×C293—21no—
77C22×C293—41no—
78C22×C293—41no—
79C22×C293—41no—
80C22×C293C2×C22⋊C411yescharacteristic
81C2×D293—41no—
82C2×D293—41no—
83C2×D293—41no—
84C4×C293—21no—
85C4×C293—21no—
86C4×C293—41no—
87Dic293—21no—
88Dic293—21no—
89Dic293—41no—
90Dic293#13512yes—
91Dic293AGL(1,ℤ/8)12yes—
92C2×C293—41no—
93C2×C293—81no—
94C2×C293#41311yescharacteristic
95C2×C293#41611yescharacteristic
96C2×C293#41811yescharacteristic
97D293—81no—
98C293#155311yescharacteristic, complemented, Sylow
99#1553—2931nomaximal, Sylow
100#532—2931no—
101#432—2931no—
102#431—2931no—
103#332—2932no—
104#331—2932no—
105C2×#41—5861no—
106C4⋊Q8—2931no—
107#127—2931no—
108#124—5861no—
109#121—2931no—
110#121—5861no—
111#121#1192407811yescharacteristic
112C4×D4—2931no—
113C4×D4—2931no—
114C4×D4—5861no—
115C2×C42—2931no—
116C4⋊C8—2932no—
117C4⋊C8—2932no—
118C22⋊C8—5861no—
119C22⋊C8—5861no—
120#97—5861no—
121C4×C8—5861no—
122#41—11724no—
123C2×Q8—5861no—
124C2×D4—21no—
125C2×D4—2931no—
126C2×D4—5861no—
127C2×D4—5861no—
128C2×D4—5861no—
129C2×D4C2×#1192407811yescharacteristic
130C22×C4—2931no—
131C22×C4—2931no—
132C22×C4—5861no—
133C22×C4—5861no—
134C22×C4C2×#1192407811yescharacteristic
135C2×C8—5862no—
136C2×C8—5862no—
137C4⋊C4—2931no—
138C4⋊C4—5861no—
139C4⋊C4C2×#1192407811yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—5861no—
142C22⋊C4—5861no—
143C22⋊C4—5861no—
144C42—2931no—
145C42—2931no—
146C42—2931no—
147C42—2931no—
148C23—21no—
149C23—5861no—
150C23C22⋊#1192407811yescharacteristic
151Q8—11722no—
152D4—41no—
153D4—42no—
154D4—11721no—
155D4—11722no—
156D4—11722no—
157D4—11722no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—2931no—
161C2×C4—2931no—
162C2×C4—2931no—
163C2×C4—2931no—
164C2×C4—5862no—
165C2×C4—5862no—
166C2×C4—5861no—
167C2×C4—11722no—
168C2×C4—11722no—
169C2×C4C22⋊#1192407811yescharacteristic
170C2×C4C22×#1192407811yescharacteristic
171C8—11722no—
172C8—11722no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—11721no—
180C22—11721no—
181C22—11721no—
182C22C2×C22⋊#1192407811yescharacteristic
183C4—21no—
184C4—21no—
185C4—41no—
186C4—2932no—
187C4—2932no—
188C4—5861no—
189C4—5861no—
190C4—11721no—
191C2—41no—
192C2—81no—
193C2—23441no—
194C2#3403711611yescharacteristic
195C2#3403711911yescharacteristic
196C2#3403712111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#121×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036674C2
cosocleC4×Dic293C23
hypercenter#121#11924078
hypocenterC293#1553
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #34037149C2semidirect
2. #34037146C2semidirect
3. #34036988C2semidirect
4. #34036987C2semidirect
98. C293#1553semidirect

Maximal subgroups

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

subgroupindex
#340371492
#340371462
#340369882
#340369872
#340366742
#1553293