Finite Group Databasebeta

← #49168881

Subgroups — #49168881

Order 37504.

444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 119 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#34036681C211yesmaximal, characteristic, complemented
2C2×#22627586C211yesmaximal, characteristic
3#34036464C211yesmaximal, characteristic, complemented
4#34036408C212yesmaximal, complemented
5#34036333C212yesmaximal, complemented
6#34036282C211yesmaximal, characteristic
7#34036279C211yesmaximal, characteristic
8#34036232C212yesmaximal, complemented
9#34036228C212yesmaximal, complemented
10#34036183C211yesmaximal, characteristic, complemented
11#484×C293C211yesmaximal, characteristic, complemented
12C22×D1172C2211yescharacteristic
13C22×C4×D293—21no—
14C2×#17989791C2212yes—
15C2×#17989789C2212yes—
16#22627623C2211yescharacteristic, complemented
17#22627622C2211yescharacteristic, complemented
18#22627614—21no—
19#22627603C2211yescharacteristic
20#22627601—21no—
21Q8×Dic293C2211yescharacteristic, complemented
22#22627589—21no—
23#22627589C2211yescharacteristic, complemented
24#22627586—21no—
25#22627586—21no—
26#22627586C2212yes—
27#22627586C2212yes—
28#22627580—21no—
29C2×#17989779—21no—
30C2×C4×Dic293C2211yescharacteristic
31#22627557C2212yescomplemented
32#22627553C2212yescomplemented
33#22627547C2212yescomplemented
34#22627546C2212yes—
35#22627544C2212yes—
36C22⋊#14556873C2211yescharacteristic
37#22627534C2212yescomplemented
38C22⋊Q8×C293C2211yescharacteristic
39C2×C4⋊C4×C293C2211yescharacteristic
40#107×C293C2212yescomplemented
41#103×C293C2212yescomplemented
42C22⋊C8×C293C2211yescharacteristic
43C23×D293—21no—
44C2×Dic586—21no—
45C2×Dic586C2311yescharacteristic
46C2×D1172—24no—
47C2×D1172—21no—
48C2×D1172C2312yes—
49C22×Dic293D411yescharacteristic
50C22×Dic293D411yescharacteristic
51C2×C4×D293—22no—
52C2×C4×D293—22no—
53C2×C4×D293—44no—
54#17989791—24no—
55#17989789—24no—
56C2×#14556873C2312yes—
57C4⋊Dic293—21no—
58C4⋊Dic293C2311yescharacteristic
59#17989781—21no—
60#17989781—21no—
61#17989781—21no—
62#17989781—21no—
63#17989781—21no—
64C22⋊Dic293—21no—
65#17989779—22no—
66#17989779—22no—
67C4×Dic293—21no—
68C4×Dic293—21no—
69C4×Dic293D411yescharacteristic
70C4×Dic293D411yescharacteristic
71C4×Dic293C2311yescharacteristic
72C4×Dic293C2311yescharacteristic
73C2×Q8×C293C2311yescharacteristic
74C22×C4×C293—21no—
75C22×C4×C293C2311yescharacteristic
76C2×C8×C293C2312yes—
77C4⋊C4×C293—21no—
78C4⋊C4×C293—21no—
79C4⋊C4×C293C2312yes—
80C4⋊C4×C293C2311yescharacteristic
81C22⋊C4×C293—21no—
82C22×D293—24no—
83C22×D293—22no—
84C22×D293—42no—
85C22×D293—42no—
86Dic586—22no—
87Dic586—42no—
88D1172—24no—
89D1172—22no—
90D1172#4114yes—
91C2×Dic293—22no—
92C2×Dic293—22no—
93C2×Dic293—21no—
94C2×Dic293—21no—
95C2×Dic293C2×D411yescharacteristic
96C2×Dic293C2×D411yescharacteristic
97C2×Dic293C2×D411yescharacteristic
98C2×Dic293C2×D411yescharacteristic
99C4×D293—44no—
100C4×D293—44no—
101#14556873—22no—
102C23×C293C2×D411yescharacteristic
103Q8×C293—22no—
104C2×C4×C293—22no—
105C2×C4×C293—21no—
106C2×C4×C293—21no—
107C2×C4×C293—22no—
108C2×C4×C293—42no—
109C2×C4×C293C2×D411yescharacteristic
110C2×C4×C293C2411yescharacteristic
111C8×C293—22no—
112C22×C293—21no—
113C22×C293—21no—
114C22×C293#13712yes—
115C22×C293C22×D411yescharacteristic
116C2×D293—24no—
117C2×D293—48no—
118C2×D293—42no—
119C2×D293—42no—
120C4×C293—21no—
121C4×C293—41no—
122C4×C293—42no—
123C4×C293—41no—
124C4×C293C2×#4112yes—
125Dic293—21no—
126Dic293—21no—
127Dic293—21no—
128Dic293—41no—
129Dic293—41no—
130Dic293AGL(1,ℤ/8)12yes—
131C2×C293—22no—
132C2×C293#52511yescharacteristic
133C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C293C2×#13711yescharacteristic
135D293—44no—
136C293#311011yescharacteristic, complemented, Sylow
137#3110—2931nomaximal, Sylow
138#533—2931no—
139C2×C4×D4—2931no—
140#484—2931no—
141#484D29311yescharacteristic, complemented
142#474—2932no—
143#461—2932no—
144#450—2931no—
145#450—2931no—
146#440—2932no—
147#440—2932no—
148#432—2931no—
149C22×D4—2931no—
150C23×C4—5861no—
151C2×SD16—2932no—
152C2×SD16—2932no—
153C4⋊Q8—2931no—
154C4⋊Q8—2931no—
155#125—5861no—
156C22⋊Q8—2931no—
157C22⋊Q8—5861no—
158C22⋊Q8C2×D29311yescharacteristic
159C4×Q8—2931no—
160C4×Q8—2931no—
161C4×Q8—5861no—
162C4×D4—2932no—
163C4×D4—2932no—
164C4×D4—5861no—
165C4×D4—5861no—
166#117—5861no—
167C2×C4⋊C4C2×D29311yescharacteristic
168C2×C22⋊C4—5861no—
169C2×C42—2931no—
170#107—2932no—
171#107C2×D29312yescomplemented
172C4⋊C8—2932no—
173#103—2932no—
174#103C2×D29312yescomplemented
175#102—2932no—
176#102—2932no—
177C22⋊C8—2931no—
178C22⋊C8C2×D29311yescharacteristic
179#97—2932no—
180C24—5861no—
181C2×Q8—2931no—
182C2×Q8—5861no—
183C2×Q8C22×D29311yescharacteristic
184C2×D4—2932no—
185C2×D4—5864no—
186C2×D4—5861no—
187C22×C4—21no—
188C22×C4—2931no—
189C22×C4—2931no—
190C22×C4—5862no—
191C22×C4—5862no—
192C22×C4—11724no—
193C22×C4C22×D29311yescharacteristic
194SD16—5864no—
195SD16—5864no—
196C2×C8—2932no—
197C2×C8C22×D29312yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—2931no—
201C4⋊C4—5861no—
202C4⋊C4—5861no—
203C4⋊C4—5861no—
204C4⋊C4—5861no—
205C4⋊C4—5861no—
206C4⋊C4—5861no—
207C4⋊C4C22×D29311yescharacteristic
208C4⋊C4C22×D29312yes—
209C22⋊C4—21no—
210C22⋊C4—5862no—
211C22⋊C4—5862no—
212C22⋊C4—5861no—
213C42—2931no—
214C42—2931no—
215C42—2931no—
216C42—2931no—
217C42—5861no—
218C42—5861no—
219C23—5864no—
220C23—5862no—
221C23—11722no—
222C23—11722no—
223C23D4×D29311yescharacteristic
224Q8—22no—
225Q8—5862no—
226Q8—11722no—
227D4—2934no—
228D4—5864no—
229D4—5862no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—2931no—
236C2×C4—2931no—
237C2×C4—2931no—
238C2×C4—2931no—
239C2×C4—5862no—
240C2×C4—5862no—
241C2×C4—5861no—
242C2×C4—5861no—
243C2×C4—11724no—
244C2×C4—11724no—
245C2×C4D4×D29311yescharacteristic
246C2×C4C23×D29311yescharacteristic
247C8—22no—
248C8—5862no—
249C22—21no—
250C22—21no—
251C22—5864no—
252C22—11728no—
253C22—11722no—
254C22—11722no—
255C22#2262765612yes—
256C22C2×D4×D29311yescharacteristic
257C4—21no—
258C4—41no—
259C4—42no—
260C4—41no—
261C4—2932no—
262C4—5861no—
263C4—5861no—
264C4—5861no—
265C4—11721no—
266C4—11721no—
267C4#41×D29312yes—
268C2—22no—
269C2—11724no—
270C2#3403663711yescharacteristic
271C2AGL(1,ℤ/8)×D29311yescharacteristic
272C2C2×#2262765611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#484×C293C2
socleC22×C293C22×D4
prime radicalC22×D1172C22
hypercenter#484D293
hypocenterC293#3110
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #34036681C2semidirect
3. #34036464C2semidirect
4. #34036408C2semidirect
5. #34036333C2semidirect
8. #34036232C2semidirect
9. #34036228C2semidirect
10. #34036183C2semidirect
11. #484×C293C2semidirect
16. #22627623C22semidirect
17. #22627622C22semidirect
21. Q8×Dic293C22semidirect
23. #22627589C22semidirect
31. #22627557C22semidirect
32. #22627553C22semidirect
33. #22627547C22semidirect
37. #22627534C22semidirect
40. #107×C293C22semidirect
41. #103×C293C22semidirect
136. C293#3110semidirect
141. #484D293semidirect
171. #107C2×D293semidirect
174. #103C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366812
C2×#226275862
#340364642
#340364082
#340363332
#340362822
#340362792
#340362322
#340362282
#340361832
#484×C2932
#3110293