Finite Group Databasebeta

← #49157951

Subgroups — #49157951

Order 37504.

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

normal subgroups only

This group has 228 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#34036794C211yesmaximal, characteristic
2#34036481C211yesmaximal, characteristic, complemented
3#34036425C211yesmaximal, characteristic, complemented
4#34036420C211yesmaximal, characteristic
5#34035859C211yesmaximal, characteristic, complemented
6#34035856C211yesmaximal, characteristic
7#332×C293C211yesmaximal, characteristic, complemented
8C2×Q8×D293—21no—
9#22627624C2211yescharacteristic
10#22627623—21no—
11#22627602—22no—
12#22627600—21no—
13C4×Dic586C2211yescharacteristic
14C4×D1172C2211yescharacteristic
15#22627586—21no—
16#22627558—21no—
17#22627556—21no—
18#22627549—21no—
19#22627547—22no—
20#22627546—21no—
21C4×#14556873C2211yescharacteristic
22C4⋊Q8×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4⋊C8×C293C2211yescharacteristic
25C2×Dic586—22no—
26C2×Dic586—21no—
27C2×Dic586D411yescharacteristic
28Q8×D293—42no—
29Q8×D293—42no—
30C2×D1172D411yescharacteristic
31C2×C4×D293—22no—
32C2×C4×D293—21no—
33C2×#14556873—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293—21no—
36C4⋊Dic293D411yescharacteristic
37C4⋊Dic293D411yescharacteristic
38#17989781—22no—
39#17989781—21no—
40#17989779—22no—
41#17989779—21no—
42C4×Dic293—21no—
43C2×Q8×C293—21no—
44C2×C8×C293—21no—
45C2×C8×C293—21no—
46C4⋊C4×C293—21no—
47C4⋊C4×C293D412yes—
48C42×C293C2311yescharacteristic
49C22×D293—21no—
50Dic586—21no—
51Dic586—44no—
52Dic586—42no—
53Dic586SD1612yes—
54D1172—21no—
55D1172Q1612yes—
56C2×Dic293—21no—
57C2×Dic293—21no—
58C2×Dic293—21no—
59C2×Dic293—41no—
60C4×D293—44no—
61C4×D293—41no—
62C4×D293—41no—
63#14556873—41no—
64Q8×C293—41no—
65Q8×C293—41no—
66C2×C4×C293—22no—
67C2×C4×C293C2×D411yescharacteristic
68C2×C4×C293C2×D411yescharacteristic
69C2×C4×C293C2×D411yescharacteristic
70C8×C293—41no—
71C8×C293—41no—
72C22×C293#12011yescharacteristic
73C2×D293—22no—
74C2×D293—41no—
75C2×D293—41no—
76C4×C293—21no—
77C4×C293—42no—
78C4×C293C2×SD1611yescharacteristic
79C4×C293C2×Q1611yescharacteristic
80C4×C293AGL(1,ℤ/8)11yescharacteristic
81C4×C293#13711yescharacteristic
82Dic293—22no—
83Dic293—41no—
84Dic293—41no—
85Dic293—81no—
86C2×C293#45011yescharacteristic
87C2×C293#45111yescharacteristic
88C2×C293#45411yescharacteristic
89D293—42no—
90C293#163711yescharacteristic, complemented, Sylow
91#1637—2931nomaximal, Sylow
92D4×Q8—2931no—
93#487—2931no—
94#477—2931no—
95#476—2931no—
96#332D29311yescharacteristic, complemented
97Q8⋊C8—2931no—
98D4⋊C8—2931no—
99C22×Q8—5861no—
100C4⋊Q8—2931no—
101C4⋊Q8—5861no—
102C4⋊Q8C2×D29311yescharacteristic
103C22⋊Q8—5861no—
104C22⋊Q8—5862no—
105C4×Q8—2931no—
106C4×D4—2931no—
107C4×D4—5861no—
108#107—5861no—
109#106—5861no—
110C4⋊C8C2×D29311yescharacteristic
111C4⋊C8C2×D29311yescharacteristic
112#103—5861no—
113#103—5862no—
114#102—5861no—
115C4×C8—2931no—
116C2×Q8—21no—
117C2×Q8—2931no—
118C2×Q8—5862no—
119C2×Q8—5861no—
120C2×Q8—11722no—
121C2×Q8—11722no—
122C2×D4—2931no—
123C22×C4—5862no—
124C22×C4—5861no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5861no—
128C4⋊C4—21no—
129C4⋊C4—2931no—
130C4⋊C4—2931no—
131C4⋊C4—5862no—
132C4⋊C4—5861no—
133C4⋊C4—5861no—
134C4⋊C4—5861no—
135C4⋊C4D117212yes—
136C22⋊C4—5862no—
137C22⋊C4—5861no—
138C42—5861no—
139C42C22×D29311yescharacteristic
140C23—5861no—
141Q8—41no—
142Q8—41no—
143Q8—2932no—
144Q8—5861no—
145Q8—11722no—
146Q8—11724no—
147D4—2932no—
148D4—5861no—
149C2×C4—22no—
150C2×C4—5861no—
151C2×C4—5861no—
152C2×C4—5861no—
153C2×C4—11724no—
154C2×C4—11721no—
155C2×C4—11721no—
156C2×C4—11721no—
157C2×C4D4×D29311yescharacteristic
158C2×C4D4×D29311yescharacteristic
159C2×C4C2×D117211yescharacteristic
160C8—41no—
161C8—41no—
162C8—11721no—
163C22—5862no—
164C22—11721no—
165C22—11721no—
166C22#2262759411yescharacteristic
167C4—21no—
168C4—42no—
169C4—23441no—
170C4—5862no—
171C4—11721no—
172C4—11721no—
173C4SD16×D29311yescharacteristic
174C4Q16×D29311yescharacteristic
175C4#2262764811yescharacteristic
176C4#2262765311yescharacteristic
177C2—11722no—
178C2#3403628111yescharacteristic
179C2#3403628611yescharacteristic
180C2#3403630411yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#332×C293C2
socleC22×C293#120
prime radicalC2×D1172D4
hypercenter#332D293
hypocenterC293#1637
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #34036481C2semidirect
3. #34036425C2semidirect
5. #34035859C2semidirect
7. #332×C293C2semidirect
90. C293#1637semidirect
96. #332D293semidirect

Maximal subgroups

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

subgroupindex
#340367942
#340364812
#340364252
#340364202
#340358592
#340358562
#332×C2932
#1637293