Finite Group Databasebeta

← #49169394

Subgroups — #49169394

Order 37504.

364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 115 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#34036684C211yesmaximal, characteristic, complemented
2#34036658C211yesmaximal, characteristic
3#34036535C211yesmaximal, characteristic, complemented
4#34036524C211yesmaximal, characteristic, complemented
5#34036498C211yesmaximal, characteristic, complemented
6#34036386C212yesmaximal, complemented
7#34036374C212yesmaximal
8#34036221C212yesmaximal, complemented
9#34036220C212yesmaximal, complemented
10#34036081C211yesmaximal, characteristic, complemented
11#489×C293C211yesmaximal, characteristic, complemented
12C2×#17989792C2212yes—
13C2×#17989790C2212yes—
14C2×#17989785C2212yes—
15#22627624C2211yescharacteristic
16#22627617—21no—
17#22627616C2211yescharacteristic
18#22627615—21no—
19#22627606—21no—
20#22627604C2212yes—
21#22627600—21no—
22#22627600C2211yescharacteristic
23#22627595C2211yescharacteristic
24Q8×Dic293—21no—
25Q8×Dic293C2211yescharacteristic
26#22627589C2212yes—
27D4×Dic293C2211yescharacteristic
28#22627584—21no—
29#22627582—21no—
30#22627580—21no—
31C42×D293C2211yescharacteristic
32#22627557C2212yes—
33#22627555C2212yes—
34#22627549C2212yes—
35#22627549C2212yes—
36#22627535C2211yescharacteristic
37C8×Dic293C2212yes—
38C4⋊Q8×C293C2211yescharacteristic
39#124×C293C2211yescharacteristic
40#103×C293C2212yes—
41#102×C293C2212yes—
42#97×C293C2211yescharacteristic
43C2×Dic586C2312yes—
44C2×C22⋊D293—21no—
45C22×Dic293—21no—
46C2×C4×D293D411yescharacteristic
47C2×C4×D293D411yescharacteristic
48C2×C4×D293C2311yescharacteristic
49#17989792—24no—
50#17989790—24no—
51#17989785—24no—
52C2×#14556873C2312yes—
53C4⋊Dic293—22no—
54C4⋊Dic293—21no—
55C4⋊Dic293—21no—
56C4⋊Dic293—21no—
57C4⋊Dic293C2311yescharacteristic
58C4⋊Dic293C2311yescharacteristic
59#17989781—22no—
60#17989781—21no—
61#17989781—21no—
62#17989781—21no—
63C22⋊Dic293—21no—
64C22⋊Dic293—21no—
65#17989779—21no—
66#17989779—22no—
67C4×Dic293—21no—
68C4×Dic293—22no—
69C4×Dic293D411yescharacteristic
70C4×Dic293D411yescharacteristic
71C4×Dic293C2311yescharacteristic
72C2×Q8×C293—21no—
73C2×Q8×C293C2311yescharacteristic
74C2×D4×C293C2311yescharacteristic
75C2×C8×C293C2312yes—
76C4⋊C4×C293—21no—
77C4⋊C4×C293C2312yes—
78C22⋊C4×C293—21no—
79C22⋊C4×C293—21no—
80C42×C293C2311yescharacteristic
81C22×D293C2×D411yescharacteristic
82Dic586—22no—
83Dic586—22no—
84C22⋊D293—42no—
85C2×Dic293—22no—
86C2×Dic293—21no—
87C2×Dic293—21no—
88C2×Dic293—42no—
89C2×Dic293C2×D411yescharacteristic
90C2×Dic293C2×D411yescharacteristic
91C2×Dic293C2×D411yescharacteristic
92C4×D293—22no—
93C4×D293—22no—
94C4×D293—41no—
95#14556873#4114yes—
96C23×C293—21no—
97Q8×C293—22no—
98Q8×C293—42no—
99D4×C293—22no—
100C2×C4×C293—21no—
101C2×C4×C293—22no—
102C2×C4×C293C2×D411yescharacteristic
103C2×C4×C293C2×D411yescharacteristic
104C2×C4×C293C2411yescharacteristic
105C8×C293—22no—
106C22×C293—41no—
107C22×C293—41no—
108C22×C293—41no—
109C22×C293C22×D411yescharacteristic
110C2×D293—21no—
111C2×D293—21no—
112C2×D293—21no—
113C4×C293—21no—
114C4×C293—21no—
115C4×C293—41no—
116C4×C293—42no—
117C4×C293C2×#4112yes—
118Dic293—21no—
119Dic293—21no—
120Dic293—42no—
121Dic293—41no—
122Dic293—41no—
123Dic293#13712yes—
124C2×C293—81no—
125C2×C293#53211yescharacteristic
126C2×C293C2×#13711yescharacteristic
127C2×C293#57511yescharacteristic
128D293—41no—
129C293#317211yescharacteristic, complemented, Sylow
130#3172—2931nomaximal, Sylow
131#533—2931no—
132#529—2931no—
133#501—2931no—
134#497—2931no—
135#491—2931no—
136#489D29311yescharacteristic, complemented
137#470—2932no—
138#468—2932no—
139C4×Q16—2932no—
140C4×SD16—2932no—
141C4×M16—2931no—
142C2×Q16—2932no—
143C2×SD16—2932no—
144C2×M16—2932no—
145C4⋊Q8—2931no—
146C4⋊Q8C2×D29311yescharacteristic
147#126—5861no—
148#125—2931no—
149#125—5861no—
150#124C2×D29311yescharacteristic
151#123—5861no—
152C22⋊Q8—2931no—
153C22⋊Q8—2932no—
154C22⋊Q8—5861no—
155#121—2931no—
156C4×Q8—2931no—
157C4×Q8—2932no—
158C4×Q8—5861no—
159C4×D4—2931no—
160C4×D4—5861no—
161#117—5861no—
162#117—5861no—
163C2×C42—2931no—
164#107—2932no—
165#106—2932no—
166#103—2932no—
167#103—2932no—
168#103C2×D29312yes—
169#102C2×D29312yes—
170#97—2931no—
171#97C2×D29311yescharacteristic
172C4×C8—2932no—
173C2×Q8—21no—
174C2×Q8—2932no—
175C2×Q8C22×D29311yescharacteristic
176C2×D4—5861no—
177C2×D4C22×D29311yescharacteristic
178C22×C4—2931no—
179C22×C4—2931no—
180C22×C4—2931no—
181C22×C4—5861no—
182Q16—5864no—
183SD16—5864no—
184M16—5864no—
185C2×C8—2932no—
186C2×C8C22×D29312yes—
187C4⋊C4—21no—
188C4⋊C4—2931no—
189C4⋊C4—2931no—
190C4⋊C4—5861no—
191C4⋊C4—5862no—
192C4⋊C4—5861no—
193C4⋊C4—5862no—
194C4⋊C4—5861no—
195C4⋊C4—5861no—
196C4⋊C4—5861no—
197C4⋊C4—5861no—
198C4⋊C4C22×D29312yes—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—5862no—
202C22⋊C4—5861no—
203C22⋊C4—5861no—
204C22⋊C4—5861no—
205C42—2931no—
206C42—2931no—
207C42—2931no—
208C42—5861no—
209C42—5862no—
210C42C22×D29311yescharacteristic
211C23—21no—
212C23—2931no—
213Q8—22no—
214Q8—42no—
215Q8—5862no—
216Q8—5862no—
217D4—22no—
218D4—11722no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—2931no—
222C2×C4—2931no—
223C2×C4—2931no—
224C2×C4—5862no—
225C2×C4—5862no—
226C2×C4—5861no—
227C2×C4—5862no—
228C2×C4—5861no—
229C2×C4—11721no—
230C2×C4—11722no—
231C2×C4D4×D29311yescharacteristic
232C2×C4D4×D29311yescharacteristic
233C2×C4C23×D29311yescharacteristic
234C8—22no—
235C8—2934no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—5861no—
240C22—5861no—
241C22—5861no—
242C22C2×D4×D29311yescharacteristic
243C4—21no—
244C4—21no—
245C4—42no—
246C4—41no—
247C4—2932no—
248C4—5861no—
249C4—5861no—
250C4—11721no—
251C4—11721no—
252C4—11722no—
253C4#41×D29312yes—
254C2—81no—
255C2—11721no—
256C2#3403667811yescharacteristic
257C2#137×D29311yescharacteristic
258C2#3403692511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#489×C293C2
socleC22×C293C22×D4
prime radical#22627595C22
hypercenter#489D293
hypocenterC293#3172
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #34036684C2semidirect
3. #34036535C2semidirect
4. #34036524C2semidirect
5. #34036498C2semidirect
6. #34036386C2semidirect
8. #34036221C2semidirect
9. #34036220C2semidirect
10. #34036081C2semidirect
11. #489×C293C2semidirect
129. C293#3172semidirect
136. #489D293semidirect

Maximal subgroups

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

subgroupindex
#340366842
#340366582
#340365352
#340365242
#340364982
#340363862
#340363742
#340362212
#340362202
#340360812
#489×C2932
#3172293