Finite Group Databasebeta

← #49169385

Subgroups — #49169385

Order 37504.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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#34036663C211yesmaximal, characteristic
2#34036535C211yesmaximal, characteristic, complemented
3#34036521C211yesmaximal, characteristic, complemented
4#34036497C211yesmaximal, characteristic, complemented
5#34036491C211yesmaximal, characteristic, complemented
6#34036385C212yesmaximal, complemented
7#34036377C212yesmaximal
8C4×#17989792C212yesmaximal, complemented
9C4×#17989789C212yesmaximal, complemented
10C4×#17989786C211yesmaximal, characteristic, complemented
11#533×C293C211yesmaximal, characteristic, complemented
12C2×#17989792C2212yes—
13C2×#17989789C2212yes—
14C2×#17989786C2212yes—
15#22627618—21no—
16#22627616C2211yescharacteristic
17#22627612C2211yescharacteristic
18#22627607—21no—
19#22627603C2211yescharacteristic
20#22627598C2211yescharacteristic
21C4×Dic586C2211yescharacteristic
22C4×D1172C2211yescharacteristic
23C4×C22⋊D293—21no—
24#22627581—21no—
25#22627557C2212yes—
26#22627555C2212yes—
27#22627548C2212yes—
28#22627548C2212yes—
29#22627547C2212yes—
30#22627544C2212yes—
31#22627535C2211yescharacteristic
32#22627535C2211yescharacteristic
33C4×#14556873C2212yes—
34C4⋊Q8×C293C2211yescharacteristic
35C4⋊Q8×C293C2211yescharacteristic
36#125×C293—21no—
37C22⋊Q8×C293—21no—
38C22⋊Q8×C293C2212yes—
39C4×Q8×C293—21no—
40C4×Q8×C293C2212yes—
41#117×C293—21no—
42C2×C42×C293C2211yescharacteristic
43C2×Dic586C2311yescharacteristic
44C2×D1172C2311yescharacteristic
45C2×C22⋊D293—21no—
46C2×C4×D293—21no—
47#17989792—24no—
48#17989789—24no—
49#17989786—24no—
50C2×#14556873C2312yes—
51C2×#14556873C2312yes—
52C4⋊Dic293C2311yescharacteristic
53C4⋊Dic293C2311yescharacteristic
54#17989781—21no—
55#17989781—21no—
56#17989781—21no—
57#17989781—21no—
58C22⋊Dic293—21no—
59#17989779—21no—
60#17989779—21no—
61#17989779—21no—
62#17989779—21no—
63C4×Dic293—21no—
64C2×Q8×C293—21no—
65C2×Q8×C293C2312yes—
66C22×C4×C293D411yescharacteristic
67C22×C4×C293D411yescharacteristic
68C22×C4×C293C2311yescharacteristic
69C4⋊C4×C293—21no—
70C4⋊C4×C293—21no—
71C4⋊C4×C293—21no—
72C4⋊C4×C293—22no—
73C4⋊C4×C293—22no—
74C4⋊C4×C293C2312yes—
75C22⋊C4×C293—22no—
76C42×C293—22no—
77C42×C293D411yescharacteristic
78C42×C293D411yescharacteristic
79C42×C293C2311yescharacteristic
80C42×C293C2311yescharacteristic
81C22×D293—21no—
82Dic586—22no—
83D1172—22no—
84C22⋊D293—42no—
85C2×Dic293—21no—
86C2×Dic293—21no—
87C2×Dic293—21no—
88C4×D293—42no—
89#14556873—22no—
90#14556873#4114yes—
91C23×C293C2×D411yescharacteristic
92Q8×C293—22no—
93Q8×C293—22no—
94Q8×C293—42no—
95C2×C4×C293—22no—
96C2×C4×C293—22no—
97C2×C4×C293—22no—
98C2×C4×C293—22no—
99C2×C4×C293—41no—
100C2×C4×C293C2×D411yescharacteristic
101C2×C4×C293C2×D411yescharacteristic
102C2×C4×C293C2×D411yescharacteristic
103C2×C4×C293C2×D411yescharacteristic
104C2×C4×C293C2×D411yescharacteristic
105C2×C4×C293C2411yescharacteristic
106C22×C293—21no—
107C22×C293—21no—
108C22×C293—21no—
109C22×C293C22×D411yescharacteristic
110C2×D293—41no—
111C2×D293—41no—
112C2×D293—41no—
113C4×C293—21no—
114C4×C293—21no—
115C4×C293—21no—
116C4×C293—21no—
117C4×C293—42no—
118C4×C293—42no—
119C4×C293#13712yes—
120C4×C293C2×#4112yes—
121Dic293—41no—
122Dic293—41no—
123Dic293—41no—
124C2×C293—41no—
125C2×C293#53211yescharacteristic
126C2×C293C2×#13711yescharacteristic
127C2×C293#57511yescharacteristic
128D293—81no—
129C293#317211yescharacteristic, complemented, Sylow
130#3172—2931nomaximal, Sylow
131#533D29311yescharacteristic, complemented
132#529—2931no—
133#501—2931no—
134#497—2931no—
135#491—2931no—
136#489—2931no—
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⋊Q8C2×D29311yescharacteristic
146C4⋊Q8C2×D29311yescharacteristic
147#126—5861no—
148#125—21no—
149#125—2931no—
150#124—2931no—
151#123—5861no—
152C22⋊Q8—21no—
153C22⋊Q8—2931no—
154C22⋊Q8C2×D29312yes—
155#121—2931no—
156C4×Q8—21no—
157C4×Q8—2931no—
158C4×Q8C2×D29312yes—
159C4×D4—2931no—
160C4×D4—5861no—
161#117—21no—
162#117—5861no—
163C2×C42C2×D29311yescharacteristic
164#107—2932no—
165#106—2932no—
166#103—2932no—
167#103—2932no—
168#103—2932no—
169#102—2932no—
170#97—2931no—
171#97—2931no—
172C4×C8—2932no—
173C2×Q8—21no—
174C2×Q8—2931no—
175C2×Q8C22×D29312yes—
176C2×D4—2931no—
177C2×D4—5861no—
178C22×C4—5861no—
179C22×C4C22⋊D29311yescharacteristic
180C22×C4C22⋊D29311yescharacteristic
181C22×C4C22×D29311yescharacteristic
182Q16—5864no—
183SD16—5864no—
184M16—5864no—
185C2×C8—2932no—
186C2×C8—2932no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—2931no—
193C4⋊C4—2931no—
194C4⋊C4—5861no—
195C4⋊C4—5861no—
196C4⋊C4—5861no—
197C4⋊C4—5861no—
198C4⋊C4C22×D29312yes—
199C22⋊C4—22no—
200C22⋊C4—5861no—
201C22⋊C4—5861no—
202C22⋊C4—5861no—
203C22⋊C4—5861no—
204C22⋊C4—5861no—
205C42—22no—
206C42—5861no—
207C42C22⋊D29311yescharacteristic
208C42C22⋊D29311yescharacteristic
209C42C22×D29311yescharacteristic
210C42C22×D29311yescharacteristic
211C23—5861no—
212C23C2×C22⋊D29311yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—5862no—
217D4—5862no—
218D4—11722no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—5861no—
225C2×C4—5861no—
226C2×C4—5861no—
227C2×C4—11722no—
228C2×C4C2×C22⋊D29311yescharacteristic
229C2×C4C2×C22⋊D29311yescharacteristic
230C2×C4C2×C22⋊D29311yescharacteristic
231C2×C4C2×C22⋊D29311yescharacteristic
232C2×C4C2×C22⋊D29311yescharacteristic
233C2×C4C23×D29311yescharacteristic
234C8—2934no—
235C8—5862no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—11721no—
240C22—11721no—
241C22—11721no—
242C22C22×C22⋊D29311yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—11721no—
250C4—11721no—
251C4—11721no—
252C4#2262765512yes—
253C4#41×D29312yes—
254C2—41no—
255C2—23441no—
256C2#3403667511yescharacteristic
257C2C2×#2262765511yescharacteristic
258C2#3403692711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#533×C293C2
socleC22×C293C22×D4
prime radical#22627598C22
hypercenter#533D293
hypocenterC293#3172
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #34036535C2semidirect
3. #34036521C2semidirect
4. #34036497C2semidirect
5. #34036491C2semidirect
6. #34036385C2semidirect
8. C4×#17989792C2semidirect
9. C4×#17989789C2semidirect
10. C4×#17989786C2semidirect
11. #533×C293C2semidirect
129. C293#3172semidirect
131. #533D293semidirect

Maximal subgroups

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

subgroupindex
#340366632
#340365352
#340365212
#340364972
#340364912
#340363852
#340363772
C4×#179897922
C4×#179897892
C4×#179897862
#533×C2932
#3172293