Finite Group Databasebeta

← #49157993

Subgroups — #49157993

Order 37504.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#34036840C211yesmaximal, characteristic
2#34036479C211yesmaximal, characteristic, complemented
3#34036415C211yesmaximal, characteristic, complemented
4#34036335C211yesmaximal, characteristic
5#34035859C211yesmaximal, characteristic, complemented
6#34035856C211yesmaximal, characteristic
7#333×C293C211yesmaximal, characteristic, complemented
8C2×#17989791—21no—
9#22627624C2211yescharacteristic
10#22627615—21no—
11#22627604—21no—
12#22627600—22no—
13C4×Dic586C2211yescharacteristic
14C4×D1172C2211yescharacteristic
15#22627586—21no—
16C4⋊C4×D293—21no—
17#22627556—21no—
18#22627549—21no—
19#22627549—21no—
20#22627548—22no—
21C4×#14556873C2211yescharacteristic
22C4⋊Q8×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4⋊C8×C293C2211yescharacteristic
25C2×Dic586—21no—
26C2×Dic586D411yescharacteristic
27C2×D1172D411yescharacteristic
28C2×C4×D293—22no—
29C2×C4×D293—21no—
30#17989791—42no—
31C2×#14556873—21no—
32C4⋊Dic293—22no—
33C4⋊Dic293—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293D411yescharacteristic
36C4⋊Dic293D411yescharacteristic
37#17989781—22no—
38#17989781—21no—
39#17989779—22no—
40#17989779—21no—
41C4×Dic293—21no—
42C2×Q8×C293D412yes—
43C2×C8×C293—21no—
44C2×C8×C293—21no—
45C4⋊C4×C293—21no—
46C4⋊C4×C293—21no—
47C42×C293C2311yescharacteristic
48C22×D293—21no—
49Dic586—21no—
50Dic586—21no—
51Dic586—41no—
52Dic586—41no—
53D1172—21no—
54D1172SD1612yes—
55C2×Dic293—21no—
56C2×Dic293—21no—
57C2×Dic293—21no—
58C2×Dic293—41no—
59C4×D293—41no—
60C4×D293—41no—
61C4×D293—82no—
62#14556873—41no—
63Q8×C293—42no—
64C2×C4×C293—22no—
65C2×C4×C293C2×D411yescharacteristic
66C2×C4×C293C2×D411yescharacteristic
67C2×C4×C293C2×D411yescharacteristic
68C8×C293—41no—
69C8×C293—41no—
70C22×C293#12011yescharacteristic
71C2×D293—22no—
72C2×D293—41no—
73C2×D293—41no—
74C4×C293—21no—
75C4×C293—42no—
76C4×C293C2×SD1611yescharacteristic
77C4×C293#13511yescharacteristic
78C4×C293#13711yescharacteristic
79C4×C293#13711yescharacteristic
80Dic293—41no—
81Dic293—41no—
82Dic293—41no—
83Dic293—81no—
84C2×C293#44811yescharacteristic
85C2×C293#45211yescharacteristic
86C2×C293#45511yescharacteristic
87D293—42no—
88C293#164311yescharacteristic, complemented, Sylow
89#1643—2931nomaximal, Sylow
90#554—2931no—
91#487—2931no—
92#475—2931no—
93#461—2931no—
94#333D29311yescharacteristic, complemented
95Q8⋊C8—2931no—
96D4⋊C8—2931no—
97C2×SD16—5861no—
98C4⋊Q8—2931no—
99C4⋊Q8C2×D29311yescharacteristic
100#125—5861no—
101C22⋊Q8—5861no—
102C22⋊Q8—5862no—
103C4×Q8—2931no—
104C4×D4—2931no—
105C4×D4—5861no—
106C2×C4⋊C4—5861no—
107#106—5861no—
108C4⋊C8C2×D29311yescharacteristic
109C4⋊C8C2×D29311yescharacteristic
110#103—5861no—
111#103—5861no—
112#103—5862no—
113C4×C8—2931no—
114C2×Q8—2931no—
115C2×Q8—5861no—
116C2×Q8D117212yes—
117C2×D4—2931no—
118C22×C4—5862no—
119C22×C4—5861no—
120SD16—11722no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—5861no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2931no—
127C4⋊C4—2931no—
128C4⋊C4—5862no—
129C4⋊C4—5862no—
130C4⋊C4—5861no—
131C4⋊C4—5861no—
132C4⋊C4—5861no—
133C22⋊C4—5862no—
134C22⋊C4—5861no—
135C42—5861no—
136C42C22×D29311yescharacteristic
137C23—5861no—
138Q8—42no—
139Q8—5861no—
140Q8—5861no—
141Q8—11721no—
142Q8—11721no—
143D4—2932no—
144D4—5861no—
145C2×C4—22no—
146C2×C4—23442no—
147C2×C4—5861no—
148C2×C4—5861no—
149C2×C4—5861no—
150C2×C4—11721no—
151C2×C4—11721no—
152C2×C4—11721no—
153C2×C4D4×D29311yescharacteristic
154C2×C4D4×D29311yescharacteristic
155C2×C4C2×D117211yescharacteristic
156C8—41no—
157C8—41no—
158C8—11721no—
159C22—5862no—
160C22—11721no—
161C22—11721no—
162C22#2262759411yescharacteristic
163C4—21no—
164C4—42no—
165C4—23441no—
166C4—11721no—
167C4—11721no—
168C4—11721no—
169C4SD16×D29311yescharacteristic
170C4#2262764511yescharacteristic
171C4#2262765611yescharacteristic
172C4#2262765611yescharacteristic
173C2—11722no—
174C2#3403626911yescharacteristic
175C2#3403629411yescharacteristic
176C2#3403630911yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#333×C293C2
socleC22×C293#120
prime radicalC2×D1172D4
hypercenter#333D293
hypocenterC293#1643
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #34036479C2semidirect
3. #34036415C2semidirect
5. #34035859C2semidirect
7. #333×C293C2semidirect
88. C293#1643semidirect
94. #333D293semidirect

Maximal subgroups

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

subgroupindex
#340368402
#340364792
#340364152
#340363352
#340358592
#340358562
#333×C2932
#1643293