Finite Group Databasebeta

← #49174175

Subgroups — #49174175

Order 37504.

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

normal subgroups only

This group has 272 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#34037152C211yesmaximal, characteristic, complemented
2#34037065C211yesmaximal, characteristic, complemented
3#34036981C212yesmaximal, complemented
4#34036980C212yesmaximal, complemented
5#34036676C211yesmaximal, characteristic
6C2×C4×#11924078—21no—
7#22627691—21no—
8#22627681C2212yes—
9#22627679—21no—
10(C2×#11924078)⋊C4—21no—
11(C2×#11924078)⋊C4C2212yes—
12C2×#17989802—21no—
13#22627623C411yescharacteristic, complemented
14#22627620C411yescharacteristic, complemented
15#22627610—21no—
16#22627599C2211yescharacteristic
17#22627597—21no—
18#22627595C2211yescharacteristic
19C4×D1172C411yescharacteristic, complemented
20C4×C22⋊D293—21no—
21C42×D293C2211yescharacteristic
22C4×D4×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24C2×#14556880—22no—
25C4×#11924078—24no—
26#17989802—44no—
27C2×Dic586—21no—
28C2×D1172—21no—
29C2×D1172C2×C411yescharacteristic
30C2×C22⋊D293—21no—
31C2×C22⋊D293—21no—
32C2×C22⋊D293—21no—
33C2×C4×D293—21no—
34C2×C4×D293D411yescharacteristic
35C2×C4×D293D411yescharacteristic
36C2×C4×D293C2311yescharacteristic
37C4⋊Dic293C2×C411yescharacteristic
38#17989781—21no—
39C22⋊Dic293—21no—
40#17989779—21no—
41#17989779—21no—
42C4×Dic293C2×C411yescharacteristic
43C4×Dic293D411yescharacteristic
44C4×Dic293D411yescharacteristic
45C2×D4×C293C2×C411yescharacteristic
46C22×C4×C293—21no—
47C4⋊C4×C293C2×C411yescharacteristic
48C22⋊C4×C293—21no—
49C42×C293C2×C411yescharacteristic
50C2×#11924078—24no—
51C2×#11924078—42no—
52C2×#11924078—42no—
53#14556880—42no—
54C22×D293—21no—
55C22×D293C2×D411yescharacteristic
56Dic586—42no—
57D1172—41no—
58D1172—42no—
59C22⋊D293—42no—
60C22⋊D293—42no—
61C22⋊D293—42no—
62C2×Dic293—21no—
63C2×Dic293C22⋊C411yescharacteristic
64C2×Dic293C22⋊C411yescharacteristic
65C2×Dic293C2×D411yescharacteristic
66C4×D293—22no—
67C4×D293—22no—
68C4×D293—41no—
69C4×D293—42no—
70C23×C293—21no—
71D4×C293—41no—
72C2×C4×C293—21no—
73C2×C4×C293—42no—
74C2×C4×C293C22⋊C411yescharacteristic
75C2×C4×C293C22⋊C411yescharacteristic
76C2×C4×C293C22×C411yescharacteristic
77C22×C293—41no—
78C22×C293—41no—
79C22×C293—41no—
80C22×C293C2×C22⋊C411yescharacteristic
81C2×D293—21no—
82C2×D293—21no—
83C2×D293—41no—
84C2×D293—41no—
85C2×D293—41no—
86C2×D293AGL(1,ℤ/8)12yes—
87#11924078—44no—
88C4×C293—21no—
89C4×C293—21no—
90C4×C293—21no—
91C4×C293—41no—
92Dic293—21no—
93Dic293—21no—
94Dic293—41no—
95Dic293#10412yes—
96C2×C293—81no—
97C2×C293#41011yescharacteristic
98C2×C293#41811yescharacteristic
99C2×C293C2×#10411yescharacteristic
100D293—22no—
101D293—81no—
102C293#150511yescharacteristic, complemented, Sylow
103#1505—2931nomaximal, Sylow
104#532—2931no—
105#432—2931no—
106#376—2931no—
107#327—2932no—
108#327—2932no—
109C2×#41—5861no—
110C4⋊Q8—2931no—
111#127—2931no—
112#124—5861no—
113#121—2931no—
114#121—2931no—
115#121—5861no—
116C4×D4—2931no—
117C4×D4—5861no—
118C4×D4#1192407811yescharacteristic, complemented
119C2×C42—2931no—
120C2×C42—5861no—
121C4⋊C8—5861no—
122C22⋊C8—2932no—
123#97—5861no—
124#95—2932no—
125#95—5861no—
126#41—11724no—
127C2×Q8—5861no—
128C2×D4—2931no—
129C2×D4—5861no—
130C2×D4—5861no—
131C2×D4—5861no—
132C2×D4—5861no—
133C2×D4C2×#1192407811yescharacteristic
134C22×C4—21no—
135C22×C4—2931no—
136C22×C4—2931no—
137C22×C4—2931no—
138C22×C4—5862no—
139C22×C4—5861no—
140C2×C8—5862no—
141C4⋊C4—2931no—
142C4⋊C4—5861no—
143C4⋊C4C2×#1192407811yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—5861no—
146C22⋊C4—5861no—
147C22⋊C4—5861no—
148C42—2931no—
149C42—2931no—
150C42—2931no—
151C42—5864no—
152C42C2×#1192407811yescharacteristic
153C23—21no—
154C23—2931no—
155C23—5861no—
156Q8—11722no—
157D4—41no—
158D4—11721no—
159D4—11722no—
160D4—11722no—
161D4—11722no—
162D4—11722no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—2931no—
166C2×C4—2931no—
167C2×C4—2931no—
168C2×C4—5862no—
169C2×C4—5862no—
170C2×C4—5864no—
171C2×C4—5861no—
172C2×C4—11721no—
173C2×C4—11722no—
174C2×C4—11722no—
175C2×C4—11722no—
176C2×C4C22⋊#1192407811yescharacteristic
177C2×C4C22⋊#1192407811yescharacteristic
178C2×C4C22×#1192407811yescharacteristic
179C8—11722no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—2932no—
184C22—5861no—
185C22—5861no—
186C22—11721no—
187C22—11721no—
188C22—11721no—
189C22C2×C22⋊#1192407811yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—2932no—
195C4—5861no—
196C4—5861no—
197C4—11724no—
198C4—11721no—
199C2—81no—
200C2—23441no—
201C2—5862no—
202C2#3403710811yescharacteristic
203C2#3403712111yescharacteristic
204C2D293⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4×D4×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036676C2
cosocleC2×C4×D293C23
hypercenterC4×D4#11924078
hypocenterC293#1505
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #34037152C2semidirect
2. #34037065C2semidirect
3. #34036981C2semidirect
4. #34036980C2semidirect
13. #22627623C4semidirect
14. #22627620C4semidirect
19. C4×D1172C4semidirect
22. C4×D4×C293C4semidirect
102. C293#1505semidirect
118. C4×D4#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371522
#340370652
#340369812
#340369802
#340366762
#1505293