Finite Group Databasebeta

← #49157288

Subgroups — #49157288

Order 37504.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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#34036642C211yesmaximal, characteristic
2#34036091C211yesmaximal, characteristic, complemented
3#95×D293C211yesmaximal, characteristic, complemented
4#34035866C211yesmaximal, characteristic, complemented
5#34035864C211yesmaximal, characteristic, complemented
6#34035862C211yesmaximal, characteristic, complemented
7#328×C293C211yesmaximal, characteristic, complemented
8C2×#17989803C411yescharacteristic, complemented
9C22×C4×D293—21no—
10C22×C4×D293C2211yescharacteristic
11C2×#17989785—21no—
12#22627609—21no—
13#22627600C411yescharacteristic, complemented
14#22627599C411yescharacteristic, complemented
15#22627598C2211yescharacteristic
16#22627594—21no—
17#22627586—21no—
18#22627584—21no—
19#22627582C411yescharacteristic, complemented
20C22⋊#14556873C2211yescharacteristic
21#22627536—21no—
22#22627531—21no—
23#22627531C2211yescharacteristic
24C22⋊Q8×C293C2211yescharacteristic
25C22⋊C8×C293C2211yescharacteristic
26#95×C293C2211yescharacteristic
27C23×D293D411yescharacteristic
28#17989803—42no—
29C2×D1172—21no—
30C2×D1172—21no—
31C2×D1172C2×C411yescharacteristic, complemented
32C2×C22⋊D293—21no—
33C22×Dic293—21no—
34C22×Dic293D411yescharacteristic
35C2×C4×D293—24no—
36C2×C4×D293—21no—
37C2×C4×D293—42no—
38C2×C4×D293—42no—
39C2×C4×D293—42no—
40C2×C4×D293C2×C411yescharacteristic
41C2×C4×D293C2×C411yescharacteristic
42C2×C4×D293D411yescharacteristic
43C2×C4×D293D411yescharacteristic
44#17989785—42no—
45C2×#14556873—21no—
46C4⋊Dic293C2×C411yescharacteristic, complemented
47#17989781—21no—
48#17989779—21no—
49#17989779—21no—
50#17989779—21no—
51#17989779—21no—
52C4×Dic293—21no—
53C2×Q8×C293C2×C411yescharacteristic, complemented
54C22×C4×C293—21no—
55C22×C4×C293C2311yescharacteristic
56C2×C8×C293—21no—
57C4⋊C4×C293—21no—
58C4⋊C4×C293C2×C411yescharacteristic, complemented
59C22⋊C4×C293—21no—
60C22×D293—21no—
61C22×D293—21no—
62C22×D293—22no—
63C22×D293—22no—
64C22×D293—21no—
65C22×D293C22⋊C411yescharacteristic
66C22×D293C22⋊C411yescharacteristic
67D1172—41no—
68D1172—42no—
69D1172—42no—
70C22⋊D293—41no—
71C22⋊D293—41no—
72C2×Dic293—22no—
73C2×Dic293—21no—
74C2×Dic293—41no—
75C2×Dic293—41no—
76C2×Dic293—41no—
77C2×Dic293C22⋊C411yescharacteristic
78C2×Dic293C22⋊C411yescharacteristic
79C4×D293—22no—
80C4×D293—22no—
81C4×D293—41no—
82C4×D293—41no—
83C4×D293—42no—
84C4×D293—48no—
85#14556873—41no—
86C23×C293C2×D411yescharacteristic
87Q8×C293—41no—
88C2×C4×C293—22no—
89C2×C4×C293—21no—
90C2×C4×C293—21no—
91C2×C4×C293—41no—
92C2×C4×C293—41no—
93C2×C4×C293—41no—
94C2×C4×C293C22×C411yescharacteristic
95C2×C4×C293C2×D411yescharacteristic
96C8×C293—41no—
97C22×C293—21no—
98C22×C293—21no—
99C22×C293C2×C22⋊C411yescharacteristic
100C22×C293AGL(1,ℤ/8)11yescharacteristic
101C22×C293#13711yescharacteristic
102C2×D293—24no—
103C2×D293—24no—
104C2×D293—21no—
105C2×D293—21no—
106C2×D293—21no—
107C2×D293—21no—
108C2×D293—41no—
109C2×D293—41no—
110C2×D293—41no—
111C2×D293#9912yes—
112C2×D293#10412yes—
113C4×C293—21no—
114C4×C293—21no—
115C4×C293—42no—
116C4×C293—41no—
117C4×C293—41no—
118Dic293—21no—
119Dic293—21no—
120Dic293—42no—
121Dic293—41no—
122C2×C293—21no—
123C2×C293—21no—
124C2×C293C2×#9911yescharacteristic
125C2×C293#41711yescharacteristic
126C2×C293C2×#10411yescharacteristic
127D293—22no—
128D293—22no—
129D293—81no—
130C293#150411yescharacteristic, complemented, Sylow
131#1504—2931nomaximal, Sylow
132#525—2931no—
133#407—2931no—
134C2×#95—2931no—
135#328—2931no—
136#328D29311yescharacteristic, complemented
137#327—2931no—
138#327—2931no—
139C2×#41—2931no—
140C23×C4—2931no—
141C23×C4—5861no—
142C2×M16—5861no—
143#123—5861no—
144C22⋊Q8—2931no—
145C22⋊Q8C2×D29311yescharacteristic
146#121—2931no—
147#121—2931no—
148#120—5861no—
149C4×D4—5861no—
150C4×D4—5861no—
151#117—2931no—
152C22⋊C8—2931no—
153C22⋊C8—5861no—
154C22⋊C8C2×D29311yescharacteristic
155#95—2931no—
156#95—5861no—
157#95C2×D29311yescharacteristic
158C24—2931no—
159#41—11722no—
160C2×Q8C4×D29311yescharacteristic, complemented
161C2×D4—2931no—
162C2×D4—5861no—
163C2×D4—5861no—
164C2×D4—5861no—
165C22×C4—21no—
166C22×C4—2931no—
167C22×C4—2931no—
168C22×C4—2931no—
169C22×C4—2931no—
170C22×C4—2931no—
171C22×C4—5861no—
172C22×C4—5864no—
173C22×C4—5861no—
174C22×C4—11722no—
175C22×C4—11722no—
176C22×C4—11722no—
177C22×C4C22×D29311yescharacteristic
178M16—11722no—
179C2×C8—21no—
180C2×C8—5861no—
181C4⋊C4—21no—
182C4⋊C4—2931no—
183C4⋊C4—5861no—
184C4⋊C4C4×D29311yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—5861no—
187C22⋊C4—5861no—
188C22⋊C4—5861no—
189C22⋊C4—5861no—
190C42—5861no—
191C23—2931no—
192C23—2931no—
193C23—5862no—
194C23—5862no—
195C23—5861no—
196C23—5861no—
197C23—5861no—
198C23D4×D29311yescharacteristic
199Q8—41no—
200D4—11721no—
201D4—11722no—
202D4—11722no—
203D4—11721no—
204D4—11721no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2931no—
212C2×C4—2931no—
213C2×C4—5862no—
214C2×C4—5862no—
215C2×C4—5862no—
216C2×C4—5861no—
217C2×C4—11721no—
218C2×C4—11721no—
219C2×C4—11722no—
220C2×C4—11728no—
221C2×C4—11721no—
222C2×C4—11721no—
223C2×C4—11721no—
224C2×C4C2×C4×D29311yescharacteristic
225C2×C4D4×D29311yescharacteristic
226C8—41no—
227C8—11721no—
228C22—21no—
229C22—21no—
230C22—2932no—
231C22—2932no—
232C22—5864no—
233C22—5864no—
234C22—5861no—
235C22—5861no—
236C22—5861no—
237C22—5861no—
238C22—11721no—
239C22—11721no—
240C22—11721no—
241C22C22⋊C4×D29311yescharacteristic
242C22#2262765111yescharacteristic
243C22#2262765611yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—5861no—
250C4—5861no—
251C4—11722no—
252C4—11721no—
253C2—21no—
254C2—21no—
255C2—23441no—
256C2—5862no—
257C2—5862no—
258C2#99×D29311yescharacteristic
259C2#3403612911yescharacteristic
260C2#104×D29311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D293
commutatorC2×C4×C293C22×C4
FrattiniC22×C4C22×D293
Fitting#328×C293C2
socleC22×C293C2×C22⋊C4
prime radical#34036642C2
cosocleC22×C4×C293C23
hypercenter#328D293
hypocenterC293#1504
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #34036091C2semidirect
3. #95×D293C2semidirect
4. #34035866C2semidirect
5. #34035864C2semidirect
6. #34035862C2semidirect
7. #328×C293C2semidirect
8. C2×#17989803C4semidirect
13. #22627600C4semidirect
14. #22627599C4semidirect
19. #22627582C4semidirect
31. C2×D1172C2×C4semidirect
46. C4⋊Dic293C2×C4semidirect
53. C2×Q8×C293C2×C4semidirect
58. C4⋊C4×C293C2×C4semidirect
130. C293#1504semidirect
136. #328D293semidirect
160. C2×Q8C4×D293semidirect
184. C4⋊C4C4×D293semidirect

Maximal subgroups

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

subgroupindex
#340366422
#340360912
#95×D2932
#340358662
#340358642
#340358622
#328×C2932
#1504293