Finite Group Databasebeta

← #49158018

Subgroups — #49158018

Order 37504.

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

normal subgroups only

This group has 240 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#34036783C211yesmaximal, characteristic
2#34036532C211yesmaximal, characteristic, complemented
3#34036406C211yesmaximal, characteristic, complemented
4#34035876C211yesmaximal, characteristic, complemented
5D4⋊#14556873C211yesmaximal, characteristic, complemented
6#34035856C211yesmaximal, characteristic, complemented
7#461×C293C211yesmaximal, characteristic, complemented
8C2×#17989801—21no—
9#22627624C2211yescharacteristic
10#22627608—22no—
11#22627604—21no—
12#22627598—21no—
13C4×D1172C2211yescharacteristic
14C2×C4⋊Dic293—21no—
15#22627557—22no—
16#22627557—21no—
17C4⋊#14556873C2211yescharacteristic
18#22627544—21no—
19C4×#14556873C2211yescharacteristic
20C2×SD16×C293—21no—
21C4⋊Q8×C293C2211yescharacteristic
22C4×D4×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24#103×C293—21no—
25#17989801—42no—
26#17989801—42no—
27C2×Dic586—21no—
28C2×D1172D411yescharacteristic
29C2×C22⋊D293—22no—
30C22×Dic293—22no—
31C2×C4×D293—21no—
32C2×#14556873—21no—
33C2×#14556873—21no—
34C4⋊Dic293—22no—
35C4⋊Dic293—21no—
36C4⋊Dic293D411yescharacteristic
37C4⋊Dic293D412yes—
38#17989779—22no—
39#17989779—21no—
40C2×Q8×C293—21no—
41C2×D4×C293D411yescharacteristic
42C22×C4×C293—21no—
43SD16×C293—42no—
44C2×C8×C293—21no—
45C4⋊C4×C293—21no—
46C4⋊C4×C293—21no—
47C4⋊C4×C293D411yescharacteristic
48C22⋊C4×C293—21no—
49C42×C293C2311yescharacteristic
50C22×D293—21no—
51Dic586—41no—
52Dic586—41no—
53D1172—21no—
54D1172—21no—
55C22⋊D293—44no—
56C2×Dic293—21no—
57C2×Dic293—22no—
58C2×Dic293—44no—
59C4×D293—41no—
60C4×D293—41no—
61#14556873—22no—
62#14556873—41no—
63C23×C293—21no—
64Q8×C293—41no—
65Q8×C293—41no—
66D4×C293—21no—
67D4×C293D812yes—
68C2×C4×C293—21no—
69C2×C4×C293—41no—
70C2×C4×C293—41no—
71C2×C4×C293—41no—
72C2×C4×C293C2×D411yescharacteristic
73C2×C4×C293C2×D411yescharacteristic
74C2×C4×C293C2×D411yescharacteristic
75C8×C293—41no—
76C22×C293—22no—
77C22×C293—41no—
78C22×C293—41no—
79C22×C293#12011yescharacteristic
80C2×D293—41no—
81C2×D293—41no—
82C2×D293—41no—
83C4×C293—21no—
84C4×C293—41no—
85C4×C293—81no—
86C4×C293C2×D811yescharacteristic
87C4×C293#13511yescharacteristic
88C4×C293AGL(1,ℤ/8)11yescharacteristic
89C4×C293#13711yescharacteristic
90Dic293—41no—
91Dic293—42no—
92C2×C293—42no—
93C2×C293#44711yescharacteristic
94C2×C293#45211yescharacteristic
95C2×C293#45611yescharacteristic
96D293—81no—
97C293#164711yescharacteristic, complemented, Sylow
98#1647—2931nomaximal, Sylow
99#547—2931no—
100#500—2931no—
101#474—2931no—
102#461D29311yescharacteristic, complemented
103#332—2931no—
104D4⋊C8—2931no—
105D4⋊C8—2931no—
106C2×#41—5861no—
107C2×SD16—21no—
108C4⋊Q8—2931no—
109C4⋊Q8C2×D29311yescharacteristic
110#123—5862no—
111C22⋊Q8—5861no—
112#121—5861no—
113C4×D4—2931no—
114C4×D4C2×D29311yescharacteristic
115C2×C4⋊C4—5861no—
116#107—5861no—
117#107—5862no—
118C4⋊C8—2931no—
119C4⋊C8C2×D29311yescharacteristic
120#103—21no—
121#102—5861no—
122C4×C8—2931no—
123#41—11722no—
124#41—11722no—
125C2×Q8—21no—
126C2×Q8—5861no—
127C2×D4—2931no—
128C2×D4—5862no—
129C2×D4C22⋊D29311yescharacteristic
130C22×C4—21no—
131C22×C4—5862no—
132C22×C4—5861no—
133SD16—42no—
134C2×C8—21no—
135C2×C8—5861no—
136C2×C8—5861no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—2931no—
140C4⋊C4—2932no—
141C4⋊C4—5862no—
142C4⋊C4—5861no—
143C4⋊C4C22⋊D29311yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—5862no—
146C22⋊C4—5861no—
147C42C22×D29311yescharacteristic
148C23—21no—
149C23—5861no—
150Q8—41no—
151Q8—41no—
152Q8—11721no—
153Q8—11721no—
154D4—21no—
155D4—5861no—
156D4—5861no—
157D4—11724no—
158D4#1798978712yes—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—5861no—
164C2×C4—5862no—
165C2×C4—11724no—
166C2×C4—11721no—
167C2×C4—11721no—
168C2×C4D4×D29311yescharacteristic
169C2×C4D4×D29311yescharacteristic
170C2×C4C2×C22⋊D29311yescharacteristic
171C8—41no—
172C8—5862no—
173C8—11721no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—11721no—
178C22—11721no—
179C22—11721no—
180C22#2262759211yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—11721no—
185C4—11722no—
186C4C2×#1798978711yescharacteristic
187C4#2262764511yescharacteristic
188C4#2262764911yescharacteristic
189C4#2262765311yescharacteristic
190C2—42no—
191C2—23441no—
192C2#3403626211yescharacteristic
193C2#3403628811yescharacteristic
194C2#3403631011yescharacteristic
subgroupG/H
centerC22#22627592
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#461×C293C2
socleC22×C293#120
prime radical#34036783C2
hypercenter#461D293
hypocenterC293#1647
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #34036532C2semidirect
3. #34036406C2semidirect
4. #34035876C2semidirect
5. D4⋊#14556873C2semidirect
6. #34035856C2semidirect
7. #461×C293C2semidirect
97. C293#1647semidirect
102. #461D293semidirect

Maximal subgroups

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

subgroupindex
#340367832
#340365322
#340364062
#340358762
D4⋊#145568732
#340358562
#461×C2932
#1647293