Finite Group Databasebeta

← #49169182

Subgroups — #49169182

Order 37504.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#34036678C211yesmaximal, characteristic
2#125×D293C211yesmaximal, characteristic, complemented
3#34036496C212yesmaximal, complemented
4#34036492C212yesmaximal, complemented
5#34036486C211yesmaximal, characteristic, complemented
6#34036484C211yesmaximal, characteristic, complemented
7#34036483C211yesmaximal, characteristic, complemented
8#34036129C212yesmaximal, complemented
9#34036127C212yesmaximal, complemented
10C4×#17989785C211yesmaximal, characteristic, complemented
11#488×C293C211yesmaximal, characteristic, complemented
12C2×#17989803C2211yescharacteristic
13C2×#17989801C2211yescharacteristic
14C2×#17989785C2212yes—
15#22627622C2211yescharacteristic
16#22627620C2211yescharacteristic
17#22627616C2211yescharacteristic
18#22627615C2212yes—
19#22627614—22no—
20#22627612C2211yescharacteristic
21#22627597—22no—
22#22627584—22no—
23C4⋊C4×D293—22no—
24C4⋊C4×D293C2212yes—
25C42×D293C2211yescharacteristic
26#22627549C2212yes—
27#22627548C2212yes—
28#22627547C2212yes—
29#22627546C2212yes—
30#22627545C2212yes—
31#22627544C2212yes—
32#22627534C2212yes—
33C4×#14556873C2211yescharacteristic
34#125×C293C2211yescharacteristic
35#124×C293C2211yescharacteristic
36#103×C293C2212yes—
37#102×C293C2212yes—
38C4×C8×C293C2211yescharacteristic
39#17989803—24no—
40#17989801—24no—
41C2×Dic586C2311yescharacteristic
42C2×D1172—21no—
43C2×D1172C2311yescharacteristic
44C2×C22⋊D293—21no—
45C2×C22⋊D293—22no—
46C22×Dic293—21no—
47C2×C4×D293—22no—
48C2×C4×D293—21no—
49C2×C4×D293D412yes—
50C2×C4×D293C2311yescharacteristic
51#17989785—24no—
52C2×#14556873C2312yes—
53C4⋊Dic293—22no—
54C4⋊Dic293C2312yes—
55#17989781—22no—
56#17989781—22no—
57#17989781—22no—
58#17989781—22no—
59#17989779—22no—
60C4×Dic293D412yes—
61C4×Dic293C2311yescharacteristic
62C2×Q8×C293C2311yescharacteristic
63C2×D4×C293C2311yescharacteristic
64C2×C8×C293C2312yes—
65C4⋊C4×C293—22no—
66C4⋊C4×C293C2312yes—
67C22⋊C4×C293—22no—
68C42×C293C2311yescharacteristic
69C22×D293—21no—
70C22×D293C2×D411yescharacteristic
71Dic586—22no—
72D1172—22no—
73D1172—42no—
74C22⋊D293—44no—
75C22⋊D293—42no—
76C2×Dic293—21no—
77C2×Dic293—22no—
78C2×Dic293—42no—
79C2×Dic293C2×D412yes—
80C2×Dic293C2×D411yescharacteristic
81C4×D293—42no—
82C4×D293—44no—
83C4×D293—42no—
84C4×D293#4114yes—
85#14556873—22no—
86C23×C293—21no—
87Q8×C293—22no—
88D4×C293—22no—
89C2×C4×C293—21no—
90C2×C4×C293—22no—
91C2×C4×C293C2×D412yes—
92C2×C4×C293C2411yescharacteristic
93C8×C293—22no—
94C22×C293—41no—
95C22×C293—42no—
96C22×C293C22×D411yescharacteristic
97C2×D293—22no—
98C2×D293—41no—
99C2×D293—42no—
100C2×D293#12412yes—
101C4×C293—22no—
102C4×C293—41no—
103C4×C293—42no—
104C4×C293C2×#4112yes—
105Dic293—22no—
106Dic293—41no—
107Dic293—42no—
108Dic293#12412yes—
109C2×C293—81no—
110C2×C293C2×#12411yescharacteristic
111C2×C293#57512yes—
112D293—22no—
113D293—81no—
114C293#314211yescharacteristic, complemented, Sylow
115#3142—2931nomaximal, Sylow
116#532—2931no—
117C2×#125—2931no—
118#491—2932no—
119#490—2932no—
120#488—2931no—
121#488—2931no—
122#488—2931no—
123#488D29311yescharacteristic, complemented
124#417—2932no—
125#417—2932no—
126C4×M16—2931no—
127C2×#41—2931no—
128C2×#41—2931no—
129C2×M16—2932no—
130C4⋊Q8—2931no—
131#127—2931no—
132#125—2932no—
133#125—2931no—
134#125—5862no—
135#125C2×D29311yescharacteristic
136#124—2931no—
137#124C2×D29311yescharacteristic
138#121—5862no—
139C4×D4—5862no—
140C2×C4⋊C4—2932no—
141C2×C4⋊C4—5862no—
142C2×C42—2931no—
143#103—2932no—
144#103—2932no—
145#103—2932no—
146#103C2×D29312yes—
147#102—2932no—
148#102—2932no—
149#102—2932no—
150#102C2×D29312yes—
151#97—2932no—
152C4×C8—2931no—
153C4×C8C2×D29311yescharacteristic
154#41—5864no—
155#41—5864no—
156C2×Q8—2931no—
157C2×Q8C22×D29311yescharacteristic
158C2×D4—2931no—
159C2×D4—5861no—
160C2×D4—5862no—
161C2×D4—5861no—
162C2×D4C22×D29311yescharacteristic
163C22×C4—2931no—
164C22×C4—2932no—
165C22×C4—5861no—
166C22×C4—5862no—
167C22×C4—5861no—
168M16—5864no—
169C2×C8—2932no—
170C2×C8C22×D29312yes—
171C4⋊C4—22no—
172C4⋊C4—2932no—
173C4⋊C4—5862no—
174C4⋊C4—5862no—
175C4⋊C4—5862no—
176C4⋊C4—5862no—
177C4⋊C4—5862no—
178C4⋊C4C22×D29312yes—
179C22⋊C4—22no—
180C22⋊C4—5862no—
181C42—2932no—
182C42—2931no—
183C42C22×D29311yescharacteristic
184C23—21no—
185C23—2931no—
186C23—5861no—
187Q8—22no—
188Q8—5862no—
189D4—22no—
190D4—5862no—
191D4—11722no—
192D4—11724no—
193D4—11722no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—2931no—
197C2×C4—2934no—
198C2×C4—2932no—
199C2×C4—5861no—
200C2×C4—5862no—
201C2×C4—11722no—
202C2×C4—11722no—
203C2×C4—11724no—
204C2×C4—11722no—
205C2×C4D4×D29312yes—
206C2×C4C23×D29311yescharacteristic
207C8—22no—
208C8—5862no—
209C22—41no—
210C22—42no—
211C22—2932no—
212C22—5862no—
213C22—11721no—
214C22—11722no—
215C22C2×D4×D29311yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—2932no—
220C4—5862no—
221C4—11721no—
222C4—11722no—
223C4#41×D29312yes—
224C2—81no—
225C2—23441no—
226C2—5862no—
227C2#124×D29311yescharacteristic
228C2#3403692612yes—
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#488×C293C2
socleC22×C293C22×D4
prime radical#34036678C2
hypercenter#488D293
hypocenterC293#3142
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D293C2semidirect
3. #34036496C2semidirect
4. #34036492C2semidirect
5. #34036486C2semidirect
6. #34036484C2semidirect
7. #34036483C2semidirect
8. #34036129C2semidirect
9. #34036127C2semidirect
10. C4×#17989785C2semidirect
11. #488×C293C2semidirect
114. C293#3142semidirect
123. #488D293semidirect

Maximal subgroups

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

subgroupindex
#340366782
#125×D2932
#340364962
#340364922
#340364862
#340364842
#340364832
#340361292
#340361272
C4×#179897852
#488×C2932
#3142293