Finite Group Databasebeta

← #497×D293 #49169221

Subgroups — #497×D293 #49169221

Order 37504.

564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×Q16×D293C212yesmaximal, complemented
2C2×SD16×D293C212yesmaximal
3C4⋊Q8×D293C211yesmaximal, characteristic, complemented
4#124×D293C211yesmaximal, characteristic
5#34036524C211yesmaximal, characteristic, complemented
6#34036523C211yesmaximal, characteristic, complemented
7#34036522C212yesmaximal, complemented
8#34036521C211yesmaximal, characteristic, complemented
9#34036520C212yesmaximal, complemented
10#97×D293C211yesmaximal, characteristic, complemented
11#497×C293C211yesmaximal, characteristic, complemented
12C2×Q8×D293C2211yescharacteristic
13C2×Q8×D293C2212yes—
14C2×D4×D293C2211yescharacteristic
15C2×Dic1172C2212yescomplemented
16C2×#17989792C2212yescomplemented
17C2×#17989792C2212yescomplemented
18Q16×D293—28no—
19C2×#17989791C2212yes—
20C2×#17989790C2212yes—
21C2×#17989789C2212yes—
22SD16×D293—28no—
23C2×C8×D293C2212yes—
24#22627624C2211yescharacteristic, complemented
25#22627623—22no—
26#22627622C2212yescomplemented
27#22627613C2211yescharacteristic
28#22627612C2211yescharacteristic
29#22627611C2211yescharacteristic
30#22627610—22no—
31C4⋊C4×D293—22no—
32C22⋊C4×D293—22no—
33C42×D293C2211yescharacteristic
34#22627535C2211yescharacteristic, complemented
35#22627534C2212yescomplemented
36C2×Q16×C293C2212yescomplemented
37C2×SD16×C293C2212yes—
38C4⋊Q8×C293C2211yescharacteristic, complemented
39#124×C293C2211yescharacteristic
40#97×C293C2211yescharacteristic, complemented
41C23×D293—21no—
42C2×Dic586—21no—
43C2×Dic586—22no—
44C2×Dic586C2311yescharacteristic
45C2×Dic586C2312yes—
46Q8×D293—24no—
47Q8×D293—24no—
48Q8×D293—24no—
49C2×D1172C2311yescharacteristic
50C2×C22⋊D293—21no—
51D4×D293—24no—
52C2×C4×D293—21no—
53C2×C4×D293—22no—
54C2×C4×D293D412yes—
55C2×C4×D293C2311yescharacteristic
56Dic1172—24no—
57#17989792—24no—
58#17989792—24no—
59#17989791—24no—
60#17989790—24no—
61#17989789—24no—
62C2×#14556873C2312yes—
63C8×D293D418yes—
64C4⋊Dic293—22no—
65#17989781—24no—
66C22⋊Dic293—22no—
67#17989779—22no—
68#17989779—22no—
69C4×Dic293D412yes—
70C4×Dic293C2311yescharacteristic
71C2×Q8×C293C2311yescharacteristic
72C2×Q8×C293C2312yes—
73C2×D4×C293C2311yescharacteristic
74Q16×C293—24no—
75SD16×C293—24no—
76C2×C8×C293C2312yes—
77C4⋊C4×C293—22no—
78C22⋊C4×C293—22no—
79C42×C293C2311yescharacteristic
80C22×D293—21no—
81C22×D293—42no—
82C22×D293—44no—
83C22×D293C2×D411yescharacteristic
84Dic586—22no—
85Dic586—22no—
86Dic586—22no—
87Dic586—44no—
88Dic586—42no—
89D1172—22no—
90C22⋊D293—42no—
91C2×Dic293—21no—
92C2×Dic293—22no—
93C2×Dic293C2×D412yes—
94C2×Dic293C2×D411yescharacteristic
95C4×D293—24no—
96C4×D293—42no—
97C4×D293—44no—
98C4×D293C2×D414yes—
99#14556873C2×D414yes—
100C23×C293—21no—
101Q8×C293—22no—
102Q8×C293—22no—
103Q8×C293—22no—
104D4×C293—22no—
105C2×C4×C293—21no—
106C2×C4×C293—22no—
107C2×C4×C293C2×D412yes—
108C2×C4×C293C2411yescharacteristic
109C8×C293C2×D414yes—
110C22×C293—41no—
111C22×C293—42no—
112C22×C293C22×D411yescharacteristic
113C2×D293—41no—
114C2×D293—42no—
115C2×D293—84no—
116C2×D293#12712yes—
117C2×D293#13714yes—
118C4×C293—22no—
119C4×C293—41no—
120C4×C293—42no—
121C4×C293C22×D412yes—
122Dic293—22no—
123Dic293—41no—
124Dic293—42no—
125Dic293#12712yes—
126C2×C293—81no—
127C2×C293C2×#12711yescharacteristic
128C2×C293C2×#13712yes—
129D293—81no—
130D293#49714yesdirect product factor
131C293C2×#49711yescharacteristic, complemented, Sylow
132C2×#497—2931nomaximal, Sylow
133C22×Q16—2932no—
134C22×SD16—2932no—
135C2×C4⋊Q8—2931no—
136C2×#124—2931no—
137#497—2932no—
138#497—2932no—
139#497—2931no—
140#497—2931no—
141#497—2931no—
142#497D29311yescharacteristic, direct product factor
143C2×#97—2931no—
144C22×Q8—2931no—
145C22×Q8—2932no—
146C22×D4—2931no—
147C2×Q16—2932no—
148C2×Q16—2932no—
149C2×Q16—2932no—
150C2×Q16—5868no—
151C2×Q16C2×D29312yescomplemented
152C2×SD16—2932no—
153C2×SD16—2932no—
154C2×SD16—2932no—
155C2×SD16—5868no—
156C2×SD16C2×D29312yes—
157C22×C8—2932no—
158C4⋊Q8—2932no—
159C4⋊Q8—2931no—
160C4⋊Q8—5862no—
161C4⋊Q8C2×D29311yescharacteristic, complemented
162#124—2931no—
163#124—2931no—
164#124—2931no—
165#124—5862no—
166#124C2×D29311yescharacteristic
167C2×C4⋊C4—5862no—
168C2×C22⋊C4—5862no—
169C2×C42—2931no—
170#97—2932no—
171#97—2931no—
172#97C2×D29311yescharacteristic, complemented
173C24—5861no—
174C2×Q8—2931no—
175C2×Q8—2932no—
176C2×Q8—5861no—
177C2×Q8—5862no—
178C2×Q8—5864no—
179C2×Q8—5864no—
180C2×Q8—5864no—
181C2×Q8C22×D29311yescharacteristic
182C2×Q8C22×D29312yes—
183C2×D4—2931no—
184C2×D4—5864no—
185C2×D4—5861no—
186C2×D4C22×D29311yescharacteristic
187C22×C4—2931no—
188C22×C4—2932no—
189C22×C4—5861no—
190C22×C4—5862no—
191Q16—24no—
192Q16—5864no—
193Q16—5864no—
194Q16—5864no—
195SD16—24no—
196SD16—5864no—
197SD16—5864no—
198SD16—5864no—
199C2×C8—2932no—
200C2×C8—2938no—
201C2×C8C22×D29312yes—
202C4⋊C4—22no—
203C4⋊C4—5864no—
204C4⋊C4—5862no—
205C22⋊C4—22no—
206C22⋊C4—5862no—
207C22⋊C4—5862no—
208C22⋊C4—5862no—
209C42—2932no—
210C42—2931no—
211C42C22×D29311yescharacteristic
212C23—21no—
213C23—2931no—
214C23—5861no—
215C23—11722no—
216C23—11724no—
217Q8—22no—
218Q8—22no—
219Q8—22no—
220Q8—5862no—
221Q8—5862no—
222Q8—5862no—
223Q8—11722no—
224Q8—11724no—
225D4—22no—
226D4—5862no—
227D4—11722no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—2931no—
231C2×C4—2934no—
232C2×C4—2932no—
233C2×C4—5864no—
234C2×C4—5861no—
235C2×C4—5862no—
236C2×C4—11722no—
237C2×C4—11724no—
238C2×C4D4×D29312yes—
239C2×C4C23×D29311yescharacteristic
240C8—2934no—
241C8D4×D29314yes—
242C22—42no—
243C22—41no—
244C22—2934no—
245C22—2932no—
246C22—23444no—
247C22—11722no—
248C22—11721no—
249C22C2×D4×D29311yescharacteristic
250C4—22no—
251C4—41no—
252C4—42no—
253C4—2932no—
254C4—5862no—
255C4—11721no—
256C4—11722no—
257C4C2×D4×D29312yes—
258C2—81no—
259C2—2934no—
260C2—23441no—
261C2#127×D29311yescharacteristic
262C2#137×D29312yes—
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#497×C293C2
socleC22×C293C22×D4
prime radicalC2×D4×D293C22
hypercenter#497D293
hypocenterC293C2×#497
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D293C2semidirect
3. C4⋊Q8×D293C2semidirect
5. #34036524C2semidirect
6. #34036523C2semidirect
7. #34036522C2semidirect
8. #34036521C2semidirect
9. #34036520C2semidirect
10. #97×D293C2semidirect
11. #497×C293C2semidirect
15. C2×Dic1172C22semidirect
16. C2×#17989792C22semidirect
17. C2×#17989792C22semidirect
24. #22627624C22semidirect
26. #22627622C22semidirect
34. #22627535C22semidirect
35. #22627534C22semidirect
36. C2×Q16×C293C22semidirect
38. C4⋊Q8×C293C22semidirect
40. #97×C293C22semidirect
130. D293#497direct (N × H)
131. C293C2×#497semidirect
142. #497D293direct (N × H)
151. C2×Q16C2×D293semidirect
161. C4⋊Q8C2×D293semidirect
172. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D2932
C2×SD16×D2932
C4⋊Q8×D2932
#124×D2932
#340365242
#340365232
#340365222
#340365212
#340365202
#97×D2932
#497×C2932
C2×#497293