Finite Group Databasebeta

← #49157953

Subgroups — #49157953

Order 37504.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic586C211yesmaximal, characteristic
2#34036480C211yesmaximal, characteristic, complemented
3#34036425C211yesmaximal, characteristic, complemented
4#34036419C211yesmaximal, characteristic
5#34035876C211yesmaximal, characteristic, complemented
6#34035861C211yesmaximal, characteristic, complemented
7D4⋊C8×C293C211yesmaximal, characteristic
8C22×Dic586—21no—
9#22627624C2211yescharacteristic
10#22627624C2211yescharacteristic
11#22627623—21no—
12#22627603—21no—
13#22627601—22no—
14C4×Dic586C2211yescharacteristic
15D4×Dic293—21no—
16#22627558—21no—
17#22627555—21no—
18C4⋊#14556873C2211yescharacteristic
19#22627549—21no—
20#22627549—22no—
21#22627545—21no—
22C4×D4×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4×C8×C293C2211yescharacteristic
25C2×Dic586—22no—
26C2×Dic586—21no—
27C2×Dic586—21no—
28C2×Dic586—42no—
29C2×Dic586—42no—
30C2×Dic586D411yescharacteristic
31C22×Dic293—22no—
32C2×#14556873—21no—
33C4⋊Dic293—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293—21no—
36C4⋊Dic293D411yescharacteristic
37C4⋊Dic293D412yes—
38#17989781—22no—
39#17989781—21no—
40C22⋊Dic293—22no—
41C4×Dic293—21no—
42C2×D4×C293D411yescharacteristic
43C22×C4×C293—21no—
44C2×C8×C293—21no—
45C2×C8×C293—21no—
46C4⋊C4×C293D411yescharacteristic
47C22⋊C4×C293—21no—
48C42×C293C2311yescharacteristic
49Dic586—21no—
50Dic586—44no—
51Dic586—41no—
52Dic586—41no—
53Dic586—42no—
54Dic586SD1612yes—
55C2×Dic293—21no—
56C2×Dic293—21no—
57C2×Dic293—22no—
58C2×Dic293—44no—
59C2×Dic293—41no—
60#14556873—41no—
61C23×C293—21no—
62D4×C293—21no—
63D4×C293Q1612yes—
64C2×C4×C293—21no—
65C2×C4×C293—41no—
66C2×C4×C293—41no—
67C2×C4×C293C2×D411yescharacteristic
68C2×C4×C293C2×D411yescharacteristic
69C2×C4×C293C2×D411yescharacteristic
70C8×C293—41no—
71C8×C293—41no—
72C22×C293—22no—
73C22×C293—41no—
74C22×C293—41no—
75C22×C293#12011yescharacteristic
76C4×C293—21no—
77C4×C293—41no—
78C4×C293C2×SD1611yescharacteristic
79C4×C293C2×Q1611yescharacteristic
80C4×C293AGL(1,ℤ/8)11yescharacteristic
81C4×C293#13711yescharacteristic
82Dic293—22no—
83Dic293—42no—
84Dic293—41no—
85Dic293—81no—
86C2×C293—42no—
87C2×C293#45011yescharacteristic
88C2×C293#45111yescharacteristic
89C2×C293#45411yescharacteristic
90C293#163711yescharacteristic, complemented, Sylow
91#1637—2931nomaximal, Sylow
92D4×Q8—2931no—
93#487—2931no—
94#477—2931no—
95#476—2931no—
96#332—2931no—
97Q8⋊C8—2931no—
98D4⋊C8D29311yescharacteristic
99C22×Q8—5861no—
100C4⋊Q8—2931no—
101C4⋊Q8—2931no—
102C4⋊Q8—5861no—
103C22⋊Q8—5862no—
104C22⋊Q8—5861no—
105C4×Q8—2931no—
106C4×D4—5861no—
107C4×D4C2×D29311yescharacteristic
108#107—5861no—
109#106—5861no—
110C4⋊C8—2931no—
111C4⋊C8C2×D29311yescharacteristic
112#103—5862no—
113#103—5861no—
114#102—5861no—
115C4×C8C2×D29311yescharacteristic
116C2×Q8—2931no—
117C2×Q8—5862no—
118C2×Q8—5861no—
119C2×Q8—5861no—
120C2×Q8—11722no—
121C2×Q8—11722no—
122C2×D4D117211yescharacteristic
123C22×C4—21no—
124C22×C4—5862no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5861no—
128C4⋊C4—2932no—
129C4⋊C4—2931no—
130C4⋊C4—5862no—
131C4⋊C4—5861no—
132C4⋊C4—5861no—
133C4⋊C4—5861no—
134C4⋊C4—5861no—
135C4⋊C4D117211yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5862no—
138C42—5861no—
139C42C22×D29311yescharacteristic
140C23—21no—
141Q8—2932no—
142Q8—5861no—
143Q8—11722no—
144Q8—11724no—
145Q8—11721no—
146Q8—11721no—
147D4—21no—
148D4Dic117212yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5861no—
153C2×C4—5861no—
154C2×C4—5862no—
155C2×C4—11721no—
156C2×C4—11724no—
157C2×C4D4×D29311yescharacteristic
158C2×C4D4×D29311yescharacteristic
159C2×C4C2×D117211yescharacteristic
160C8—41no—
161C8—41no—
162C8—11721no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2262759411yescharacteristic
167C4—21no—
168C4—41no—
169C4—23441no—
170C4—5862no—
171C4—11722no—
172C4—11721no—
173C4SD16×D29311yescharacteristic
174C4C2×Dic117211yescharacteristic
175C4#2262764811yescharacteristic
176C4#2262765711yescharacteristic
177C2—42no—
178C2#3403628111yescharacteristic
179C2#3403628711yescharacteristic
180C2#3403630311yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
FittingD4⋊C8×C293C2
socleC22×C293#120
prime radicalC2×D4×C293D4
hypercenterD4⋊C8D293
hypocenterC293#1637
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. #34036425C2semidirect
5. #34035876C2semidirect
6. #34035861C2semidirect
90. C293#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5862
#340364802
#340364252
#340364192
#340358762
#340358612
D4⋊C8×C2932
#1637293