Finite Group Databasebeta

← #49157889

Subgroups — #49157889

Order 37504.

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

normal subgroups only

This group has 250 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, complemented
2#34036477C211yesmaximal, characteristic, complemented
3#34036330C211yesmaximal, characteristic, complemented
4#34036325C211yesmaximal, characteristic
5#34035859C211yesmaximal, characteristic, complemented
6#34035856C211yesmaximal, characteristic, complemented
7#332×C293C211yesmaximal, characteristic, complemented
8C2×Q8×D293—21no—
9C2×#17989791—21no—
10C2×D2344—21no—
11#22627623—21no—
12#22627621C2211yescharacteristic
13#22627602—22no—
14#22627600—21no—
15C4×Dic586C2211yescharacteristic
16C4×D1172C2211yescharacteristic
17#22627586—21no—
18#22627546—21no—
19#22627546—21no—
20#22627544—22no—
21C4×#14556873C2211yescharacteristic
22C4⋊Q8×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4⋊C8×C293C2211yescharacteristic
25C2×Dic586—22no—
26C2×Dic586D411yescharacteristic
27Q8×D293—42no—
28Q8×D293—42no—
29C2×D1172—21no—
30C2×D1172—21no—
31C2×D1172—21no—
32C2×D1172D411yescharacteristic
33C2×C4×D293—22no—
34C2×C4×D293—21no—
35#17989791—42no—
36D2344—42no—
37C2×#14556873—21no—
38C4⋊Dic293D411yescharacteristic
39C4⋊Dic293D411yescharacteristic
40#17989781—22no—
41#17989781—21no—
42#17989779—22no—
43#17989779—21no—
44C4×Dic293—21no—
45C2×Q8×C293—21no—
46C2×C8×C293—21no—
47C2×C8×C293—21no—
48C4⋊C4×C293—21no—
49C4⋊C4×C293D412yes—
50C42×C293C2311yescharacteristic
51C22×D293—21no—
52C22×D293—41no—
53Dic586—21no—
54Dic586—44no—
55Dic586D812yescomplemented
56D1172—21no—
57D1172—42no—
58D1172—41no—
59D1172—41no—
60D1172—41no—
61D1172—41no—
62D1172SD1612yescomplemented
63C2×Dic293—21no—
64C2×Dic293—21no—
65C2×Dic293—21no—
66C4×D293—44no—
67C4×D293—41no—
68C4×D293—41no—
69#14556873—41no—
70Q8×C293—41no—
71Q8×C293—41no—
72C2×C4×C293—22no—
73C2×C4×C293C2×D411yescharacteristic
74C2×C4×C293C2×D411yescharacteristic
75C2×C4×C293C2×D411yescharacteristic
76C8×C293—41no—
77C8×C293—41no—
78C22×C293#12011yescharacteristic
79C2×D293—22no—
80C2×D293—41no—
81C2×D293—41no—
82C2×D293—81no—
83C2×D293—81no—
84C2×D293—81no—
85C4×C293—21no—
86C4×C293—42no—
87C4×C293C2×D811yescharacteristic
88C4×C293C2×SD1611yescharacteristic
89C4×C293AGL(1,ℤ/8)11yescharacteristic
90C4×C293#13711yescharacteristic
91Dic293—22no—
92Dic293—41no—
93Dic293—41no—
94C2×C293#44711yescharacteristic
95C2×C293#44811yescharacteristic
96C2×C293#45411yescharacteristic
97D293—42no—
98D293—161no—
99C293#162711yescharacteristic, complemented, Sylow
100#1627—2931nomaximal, Sylow
101D4×Q8—2931no—
102#486—2931no—
103#460—2931no—
104#459—2931no—
105#332D29311yescharacteristic, complemented
106Q8⋊C8—2931no—
107D4⋊C8—2931no—
108C22×Q8—5861no—
109C2×SD16—5861no—
110C2×D8—5861no—
111C4⋊Q8—5861no—
112C4⋊Q8C2×D29311yescharacteristic
113#127—2931no—
114C22⋊Q8—5861no—
115C22⋊Q8—5862no—
116C4×Q8—2931no—
117C4×D4—2931no—
118C4×D4—5861no—
119C4⋊C8C2×D29311yescharacteristic
120C4⋊C8C2×D29311yescharacteristic
121#102—5861no—
122#102—5861no—
123#102—5862no—
124C4×C8—2931no—
125C2×Q8—21no—
126C2×Q8—2931no—
127C2×Q8—5862no—
128C2×Q8—11722no—
129C2×Q8—11722no—
130C2×D4—2931no—
131C2×D4—5861no—
132C2×D4—5861no—
133C2×D4—5861no—
134C22×C4—5862no—
135C22×C4—5861no—
136SD16—11722no—
137D8—11722no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5861no—
141C4⋊C4—21no—
142C4⋊C4—2931no—
143C4⋊C4—2931no—
144C4⋊C4—5862no—
145C4⋊C4—5861no—
146C4⋊C4D117212yes—
147C22⋊C4—5862no—
148C22⋊C4—5861no—
149C42—5861no—
150C42C22×D29311yescharacteristic
151C23—5861no—
152C23—11721no—
153Q8—41no—
154Q8—41no—
155Q8—2932no—
156Q8—5861no—
157Q8—11724no—
158D4—2932no—
159D4—5861no—
160D4—11722no—
161D4—11721no—
162D4—11721no—
163D4—11721no—
164D4—11721no—
165C2×C4—22no—
166C2×C4—5861no—
167C2×C4—5861no—
168C2×C4—5861no—
169C2×C4—11724no—
170C2×C4—11721no—
171C2×C4—11721no—
172C2×C4D4×D29311yescharacteristic
173C2×C4D4×D29311yescharacteristic
174C2×C4C2×D117211yescharacteristic
175C8—41no—
176C8—41no—
177C8—11721no—
178C22—23441no—
179C22—23441no—
180C22—23441no—
181C22—5862no—
182C22—11721no—
183C22—11721no—
184C22#2262759411yescharacteristic
185C4—21no—
186C4—42no—
187C4—5862no—
188C4—11721no—
189C4—11721no—
190C4D8×D29311yescharacteristic
191C4SD16×D29311yescharacteristic
192C4#2262765111yescharacteristic
193C4#2262765611yescharacteristic
194C2—46881no—
195C2—11722no—
196C2#3403626411yescharacteristic
197C2#3403626911yescharacteristic
198C2#3403630411yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#332×C293C2
socleC22×C293#120
prime radical#34036325C2
hypercenter#332D293
hypocenterC293#1627
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #34036794C2semidirect
2. #34036477C2semidirect
3. #34036330C2semidirect
5. #34035859C2semidirect
6. #34035856C2semidirect
7. #332×C293C2semidirect
55. Dic586D8semidirect
62. D1172SD16semidirect
99. C293#1627semidirect
105. #332D293semidirect

Maximal subgroups

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

subgroupindex
#340367942
#340364772
#340363302
#340363252
#340358592
#340358562
#332×C2932
#1627293