Finite Group Databasebeta

← #49168710

Subgroups — #49168710

Order 37504.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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#34036640C211yesmaximal, characteristic
2C22×C4⋊Dic293C211yesmaximal, characteristic, complemented
3#34036465C212yesmaximal, complemented
4#34036460C212yesmaximal, complemented
5#34036448C212yesmaximal, complemented
6#34036443C212yesmaximal, complemented
7#34036171C212yesmaximal, complemented
8#34036131C212yesmaximal, complemented
9#407×C293C211yesmaximal, characteristic, complemented
10C2×#17989802C2211yescharacteristic
11C23×Dic293—21no—
12#22627607—21no—
13#22627603C2211yescharacteristic
14#22627603C2211yescharacteristic
15#22627598C2211yescharacteristic
16#22627598C2211yescharacteristic
17#22627593—21no—
18C4×C22⋊D293—21no—
19C4×C22⋊D293—21no—
20#22627583C2211yescharacteristic
21C2×C4⋊Dic293—21no—
22C2×C4⋊Dic293—21no—
23C2×C4⋊Dic293—21no—
24C2×C4⋊Dic293C2212yes—
25C2×C4⋊Dic293C2212yes—
26C2×C4⋊Dic293C2212yes—
27#22627558C2214yescomplemented
28#22627556C2214yescomplemented
29#22627549C2214yescomplemented
30#22627546C2214yescomplemented
31C23×C4×C293C2211yescharacteristic
32C2×M16×C293C2212yes—
33C22⋊C8×C293C2212yes—
34C22⋊C8×C293C2212yes—
35#17989802—24no—
36C2×Dic586C2311yescharacteristic
37C2×D1172C2311yescharacteristic
38C2×C22⋊D293—21no—
39C2×C22⋊D293—21no—
40C2×C22⋊D293—21no—
41C22×Dic293—22no—
42C22×Dic293—22no—
43C22×Dic293—22no—
44C22×Dic293—44no—
45C2×C4×D293—21no—
46C4⋊Dic293—22no—
47C4⋊Dic293—22no—
48C4⋊Dic293—22no—
49C4⋊Dic293C2311yescharacteristic
50C4⋊Dic293C2311yescharacteristic
51C4⋊Dic293C2314yes—
52#17989781—21no—
53#17989781—21no—
54C22⋊Dic293—21no—
55C22⋊Dic293—21no—
56C22⋊Dic293—21no—
57#17989779—21no—
58#17989779—21no—
59C4×Dic293—21no—
60C24×C293D411yescharacteristic
61C22×C4×C293—24no—
62C22×C4×C293D411yescharacteristic
63C22×C4×C293D411yescharacteristic
64C22×C4×C293D411yescharacteristic
65C22×C4×C293C2311yescharacteristic
66C22×C4×C293C2311yescharacteristic
67C22×C4×C293C2311yescharacteristic
68M16×C293—24no—
69C2×C8×C293C2314yes—
70C22×D293—21no—
71Dic586—22no—
72D1172—22no—
73C22⋊D293—42no—
74C22⋊D293—42no—
75C22⋊D293—42no—
76C2×Dic293—21no—
77C2×Dic293—21no—
78C2×Dic293—21no—
79C2×Dic293—24no—
80C2×Dic293—44no—
81C2×Dic293—44no—
82C2×Dic293—44no—
83C4×D293—42no—
84C23×C293—22no—
85C23×C293—22no—
86C23×C293—22no—
87C23×C293C2×D411yescharacteristic
88C23×C293C2×D411yescharacteristic
89C23×C293C2×D411yescharacteristic
90C2×C4×C293—22no—
91C2×C4×C293—22no—
92C2×C4×C293—22no—
93C2×C4×C293—22no—
94C2×C4×C293—22no—
95C2×C4×C293C2×D411yescharacteristic
96C2×C4×C293C2×D411yescharacteristic
97C2×C4×C293C2×D411yescharacteristic
98C2×C4×C293#4114yes—
99C2×C4×C293C2411yescharacteristic
100C8×C293—24no—
101C22×C293—28no—
102C22×C293—21no—
103C22×C293—21no—
104C22×C293—21no—
105C22×C293—21no—
106C22×C293—21no—
107C22×C293—21no—
108C22×C293#12312yes—
109C22×C293AGL(1,ℤ/8)12yes—
110C22×C293#13712yes—
111C22×C293C22×D411yescharacteristic
112C2×D293—41no—
113C2×D293—41no—
114C2×D293—41no—
115C4×C293—21no—
116C4×C293—21no—
117C4×C293#12312yes—
118C4×C293C2×#4112yes—
119Dic293—41no—
120Dic293—44no—
121Dic293—41no—
122Dic293—41no—
123C2×C293—22no—
124C2×C293—22no—
125C2×C293—22no—
126C2×C293C2×#12311yescharacteristic
127C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C293C2×#13711yescharacteristic
129D293—81no—
130C293#309211yescharacteristic, complemented, Sylow
131#3092—2931nomaximal, Sylow
132#525—2931no—
133C22×C4⋊C4—2931no—
134#484—2932no—
135#483—2932no—
136#481—2932no—
137#480—2932no—
138#428—2932no—
139#417—2932no—
140#407D29311yescharacteristic, complemented
141C2×#41—2931no—
142C23×C4—5861no—
143C23×C4C2×D29311yescharacteristic
144C2×M16C2×D29312yes—
145#123—5861no—
146C22⋊Q8—2931no—
147C22⋊Q8—2931no—
148#121—2931no—
149#121—2931no—
150#120—5861no—
151C4×D4—5861no—
152C4×D4—5861no—
153#117—2931no—
154C2×C4⋊C4—2932no—
155C2×C4⋊C4—2932no—
156C2×C4⋊C4—2932no—
157C2×C4⋊C4—5861no—
158C2×C4⋊C4—5861no—
159C2×C4⋊C4—5861no—
160#107—2934no—
161#106—2934no—
162#103—2934no—
163#102—2934no—
164C22⋊C8C2×D29312yes—
165C22⋊C8C2×D29312yes—
166C24D117211yescharacteristic
167#41—5864no—
168C2×Q8—2931no—
169C2×D4—2931no—
170C2×D4—5861no—
171C2×D4—5861no—
172C2×D4—5861no—
173C22×C4—24no—
174C22×C4—5862no—
175C22×C4—5862no—
176C22×C4—5862no—
177C22×C4—5861no—
178C22×C4—11724no—
179C22×C4D117211yescharacteristic
180C22×C4D117211yescharacteristic
181C22×C4D117211yescharacteristic
182C22×C4C22×D29311yescharacteristic
183C22×C4C22×D29311yescharacteristic
184C22×C4C22×D29311yescharacteristic
185M16—24no—
186C2×C8C22×D29314yes—
187C4⋊C4—2934no—
188C4⋊C4—2931no—
189C4⋊C4—2931no—
190C4⋊C4—5862no—
191C4⋊C4—5862no—
192C4⋊C4—5862no—
193C4⋊C4—5861no—
194C4⋊C4—5861no—
195C22⋊C4—5861no—
196C22⋊C4—5861no—
197C22⋊C4—5861no—
198C22⋊C4—5861no—
199C22⋊C4—5861no—
200C42—5861no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—5861no—
205C23C2×D117211yescharacteristic
206C23C2×D117211yescharacteristic
207C23C2×D117211yescharacteristic
208Q8—5862no—
209D4—5862no—
210D4—11722no—
211D4—11722no—
212D4—11722no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—5861no—
219C2×C4—5861no—
220C2×C4—5861no—
221C2×C4—5864no—
222C2×C4—11724no—
223C2×C4—11724no—
224C2×C4—11724no—
225C2×C4—11722no—
226C2×C4C2×D117211yescharacteristic
227C2×C4C2×D117211yescharacteristic
228C2×C4C2×D117211yescharacteristic
229C2×C4#1798980114yes—
230C2×C4C23×D29311yescharacteristic
231C8—24no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—11721no—
240C22—11721no—
241C22—11721no—
242C22#2262760812yes—
243C22#2262765212yes—
244C22#2262765712yes—
245C22C22×D117211yescharacteristic
246C4—21no—
247C4—21no—
248C4—11721no—
249C4—11724no—
250C4—11721no—
251C4—11721no—
252C4#2262760812yes—
253C4C2×#1798980112yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—23441no—
258C2C2×#2262760811yescharacteristic
259C2C2×#2262765211yescharacteristic
260C2C2×#2262765711yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#407×C293C2
socleC22×C293C22×D4
prime radical#34036640C2
hypercenter#407D293
hypocenterC293#3092
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic293C2semidirect
3. #34036465C2semidirect
4. #34036460C2semidirect
5. #34036448C2semidirect
6. #34036443C2semidirect
7. #34036171C2semidirect
8. #34036131C2semidirect
9. #407×C293C2semidirect
27. #22627558C22semidirect
28. #22627556C22semidirect
29. #22627549C22semidirect
30. #22627546C22semidirect
130. C293#3092semidirect
140. #407D293semidirect

Maximal subgroups

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

subgroupindex
#340366402
C22×C4⋊Dic2932
#340364652
#340364602
#340364482
#340364432
#340361712
#340361312
#407×C2932
#3092293