Finite Group Databasebeta

← #49157994

Subgroups — #49157994

Order 37504.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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#34036836C211yesmaximal, characteristic
2#34036480C211yesmaximal, characteristic, complemented
3#34036415C211yesmaximal, characteristic, complemented
4#34036334C211yesmaximal, characteristic
5#34035877C211yesmaximal, characteristic, complemented
6#34035861C211yesmaximal, characteristic, complemented
7D4⋊C8×C293C211yesmaximal, characteristic
8C2×#17989790—21no—
9#22627624C2211yescharacteristic
10#22627624C2211yescharacteristic
11#22627615—21no—
12#22627603—21no—
13#22627601—22no—
14C4×Dic586C2211yescharacteristic
15D4×Dic293—21no—
16C2×C4⋊Dic293—21no—
17#22627556—21no—
18C4⋊#14556873C2211yescharacteristic
19#22627549—22no—
20#22627549—21no—
21#22627547—21no—
22C4×D4×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4×C8×C293C2211yescharacteristic
25C2×Dic586—21no—
26C2×Dic586D411yescharacteristic
27C2×Dic586D412yes—
28C22×Dic293—22no—
29#17989790—42no—
30C2×#14556873—21no—
31C4⋊Dic293—22no—
32C4⋊Dic293—21no—
33C4⋊Dic293—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293—21no—
36C4⋊Dic293D411yescharacteristic
37#17989781—22no—
38#17989781—21no—
39C22⋊Dic293—22no—
40C4×Dic293—21no—
41C2×D4×C293D411yescharacteristic
42C22×C4×C293—21no—
43C2×C8×C293—21no—
44C2×C8×C293—21no—
45C4⋊C4×C293D411yescharacteristic
46C22⋊C4×C293—21no—
47C42×C293C2311yescharacteristic
48Dic586—21no—
49Dic586—21no—
50Dic586—42no—
51Dic586—41no—
52Dic586—41no—
53C2×Dic293—21no—
54C2×Dic293—21no—
55C2×Dic293—22no—
56C2×Dic293—41no—
57C2×Dic293—82no—
58#14556873—41no—
59C23×C293—21no—
60D4×C293—21no—
61D4×C293SD1612yes—
62C2×C4×C293—21no—
63C2×C4×C293—41no—
64C2×C4×C293—41no—
65C2×C4×C293C2×D411yescharacteristic
66C2×C4×C293C2×D411yescharacteristic
67C2×C4×C293C2×D411yescharacteristic
68C8×C293—41no—
69C8×C293—41no—
70C22×C293—22no—
71C22×C293—41no—
72C22×C293—41no—
73C22×C293#12011yescharacteristic
74C4×C293—21no—
75C4×C293—41no—
76C4×C293C2×SD1611yescharacteristic
77C4×C293#13511yescharacteristic
78C4×C293#13711yescharacteristic
79C4×C293#13711yescharacteristic
80Dic293—41no—
81Dic293—41no—
82Dic293—42no—
83Dic293—81no—
84C2×C293—42no—
85C2×C293#44811yescharacteristic
86C2×C293#45211yescharacteristic
87C2×C293#45511yescharacteristic
88C293#164311yescharacteristic, complemented, Sylow
89#1643—2931nomaximal, Sylow
90#554—2931no—
91#487—2931no—
92#475—2931no—
93#461—2931no—
94#333—2931no—
95Q8⋊C8—2931no—
96D4⋊C8D29311yescharacteristic
97C2×SD16—5861no—
98C4⋊Q8—2931no—
99C4⋊Q8—2931no—
100#125—5861no—
101C22⋊Q8—5862no—
102C22⋊Q8—5861no—
103C4×Q8—2931no—
104C4×D4—5861no—
105C4×D4C2×D29311yescharacteristic
106C2×C4⋊C4—5861no—
107#106—5861no—
108C4⋊C8—2931no—
109C4⋊C8C2×D29311yescharacteristic
110#103—5861no—
111#103—5862no—
112#103—5861no—
113C4×C8C2×D29311yescharacteristic
114C2×Q8—2931no—
115C2×Q8—2932no—
116C2×Q8—5861no—
117C2×D4D117211yescharacteristic
118C22×C4—21no—
119C22×C4—5862no—
120SD16—11722no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—5861no—
124C4⋊C4—2931no—
125C4⋊C4—5862no—
126C4⋊C4—5862no—
127C4⋊C4—5861no—
128C4⋊C4—5861no—
129C4⋊C4—5861no—
130C4⋊C4—5861no—
131C4⋊C4—5861no—
132C4⋊C4D117211yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—5862no—
135C42—5861no—
136C42C22×D29311yescharacteristic
137C23—21no—
138Q8—5861no—
139Q8—5861no—
140Q8—11722no—
141Q8—11721no—
142Q8—11721no—
143D4—21no—
144D4#1798979112yes—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—23442no—
149C2×C4—5861no—
150C2×C4—5861no—
151C2×C4—5862no—
152C2×C4—11721no—
153C2×C4D4×D29311yescharacteristic
154C2×C4D4×D29311yescharacteristic
155C2×C4C2×D117211yescharacteristic
156C8—41no—
157C8—41no—
158C8—11721no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#2262759411yescharacteristic
163C4—21no—
164C4—41no—
165C4—23441no—
166C4—11721no—
167C4—11721no—
168C4—11722no—
169C4C2×#1798979111yescharacteristic
170C4#2262764311yescharacteristic
171C4#2262765311yescharacteristic
172C4#2262765711yescharacteristic
173C2—42no—
174C2#3403627011yescharacteristic
175C2#3403629211yescharacteristic
176C2#3403630811yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
FittingD4⋊C8×C293C2
socleC22×C293#120
prime radicalC2×D4×C293D4
hypercenterD4⋊C8D293
hypocenterC293#1643
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #34036480C2semidirect
3. #34036415C2semidirect
5. #34035877C2semidirect
6. #34035861C2semidirect
88. C293#1643semidirect

Maximal subgroups

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

subgroupindex
#340368362
#340364802
#340364152
#340363342
#340358772
#340358612
D4⋊C8×C2932
#1643293