Finite Group Databasebeta

← #49168923

Subgroups — #49168923

Order 37504.

450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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, complemented
2#34036459C211yesmaximal, characteristic, complemented
3#34036442C211yesmaximal, characteristic, complemented
4#34036429C212yesmaximal, complemented
5#34036344C212yesmaximal, complemented
6#34036280C211yesmaximal, characteristic, complemented
7#34036263C211yesmaximal, characteristic
8#34036239C212yesmaximal, complemented
9#34036229C212yesmaximal, complemented
10#34036186C211yesmaximal, characteristic, complemented
11C2×C4×D4×C293C211yesmaximal, characteristic, complemented
12C2×#17989790C2212yes—
13C2×#17989787C2212yes—
14#22627618—21no—
15#22627616C2211yescharacteristic, complemented
16#22627612C2211yescharacteristic, complemented
17#22627607—21no—
18#22627603C2211yescharacteristic
19#22627598C2211yescharacteristic
20C4×Dic586C2211yescharacteristic, complemented
21C4×D1172C2211yescharacteristic, complemented
22C4×C22⋊D293—21no—
23#22627581—21no—
24#22627557C2212yescomplemented
25#22627555C2212yescomplemented
26C4⋊#14556873C2212yescomplemented
27#22627547C2212yescomplemented
28#22627545C2212yes—
29#22627545C2212yes—
30#22627544C2212yescomplemented
31C22⋊#14556873C2211yescharacteristic
32C22⋊#14556873C2211yescharacteristic
33#22627535C2212yescomplemented
34C22×D4×C293C2211yescharacteristic
35C23×C4×C293—21no—
36C4×D4×C293—21no—
37C4×D4×C293—21no—
38C4×D4×C293C2212yes—
39C4×D4×C293C2212yes—
40C2×C4⋊C4×C293C2211yescharacteristic
41C2×C22⋊C4×C293—21no—
42C2×C42×C293C2211yescharacteristic
43C2×Dic586C2311yescharacteristic
44C2×D1172C2311yescharacteristic
45C2×C22⋊D293—21no—
46C2×C4×D293—21no—
47#17989790—24no—
48#17989787—24no—
49C2×#14556873C2312yes—
50C2×#14556873C2312yes—
51C4⋊Dic293C2311yescharacteristic
52C4⋊Dic293C2311yescharacteristic
53#17989781—21no—
54#17989781—21no—
55#17989781—21no—
56#17989781—21no—
57C22⋊Dic293—21no—
58#17989779—21no—
59#17989779—21no—
60#17989779—21no—
61#17989779—21no—
62C4×Dic293—21no—
63C24×C293—21no—
64C2×D4×C293—24no—
65C2×D4×C293—21no—
66C2×D4×C293C2312yes—
67C22×C4×C293—21no—
68C22×C4×C293—22no—
69C22×C4×C293—22no—
70C22×C4×C293—44no—
71C22×C4×C293D411yescharacteristic
72C22×C4×C293D411yescharacteristic
73C22×C4×C293C2311yescharacteristic
74C4⋊C4×C293—21no—
75C4⋊C4×C293C2312yes—
76C22⋊C4×C293—22no—
77C22⋊C4×C293—22no—
78C42×C293D411yescharacteristic
79C42×C293D411yescharacteristic
80C42×C293C2311yescharacteristic
81C42×C293C2311yescharacteristic
82C22×D293—21no—
83Dic586—22no—
84D1172—22no—
85C22⋊D293—42no—
86C2×Dic293—21no—
87C2×Dic293—21no—
88C2×Dic293—21no—
89C4×D293—42no—
90#14556873—22no—
91#14556873—22no—
92C23×C293—24no—
93C23×C293—22no—
94C23×C293—42no—
95C23×C293—42no—
96C23×C293C2×D411yescharacteristic
97D4×C293—24no—
98D4×C293—22no—
99D4×C293#4114yes—
100C2×C4×C293—22no—
101C2×C4×C293—22no—
102C2×C4×C293—22no—
103C2×C4×C293—41no—
104C2×C4×C293—44no—
105C2×C4×C293—44no—
106C2×C4×C293—42no—
107C2×C4×C293C2×D411yescharacteristic
108C2×C4×C293C2×D411yescharacteristic
109C2×C4×C293C2×D411yescharacteristic
110C2×C4×C293C2×D411yescharacteristic
111C2×C4×C293C2×D411yescharacteristic
112C2×C4×C293C2411yescharacteristic
113C22×C293—21no—
114C22×C293—21no—
115C22×C293—24no—
116C22×C293—48no—
117C22×C293—42no—
118C22×C293—42no—
119C22×C293AGL(1,ℤ/8)12yes—
120C22×C293C22×D411yescharacteristic
121C2×D293—41no—
122C2×D293—41no—
123C2×D293—41no—
124C4×C293—21no—
125C4×C293—21no—
126C4×C293—21no—
127C4×C293—21no—
128C4×C293—21no—
129C4×C293—42no—
130C4×C293C2×#4112yes—
131Dic293—41no—
132Dic293—41no—
133Dic293—41no—
134C2×C293—22no—
135C2×C293—44no—
136C2×C293#52511yescharacteristic
137C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C293#57511yescharacteristic
139D293—81no—
140C293#311411yescharacteristic, complemented, Sylow
141#3114—2931nomaximal, Sylow
142#529—2931no—
143C2×C4×D4D29311yescharacteristic, complemented
144#483—2931no—
145#480—2931no—
146#478—2932no—
147#463—2932no—
148#450—2931no—
149#447—2931no—
150#442—2932no—
151#440—2932no—
152#432—2931no—
153C22×D4C2×D29311yescharacteristic
154C23×C4—21no—
155C2×SD16—2932no—
156C2×D8—2932no—
157#126—5861no—
158#125—2931no—
159#124—2931no—
160#123—5861no—
161C22⋊Q8—2931no—
162#121—2931no—
163C4×Q8—2931no—
164C4×D4—21no—
165C4×D4—21no—
166C4×D4—2931no—
167C4×D4—5861no—
168C4×D4C2×D29312yes—
169C4×D4C2×D29312yes—
170#117—5861no—
171C2×C4⋊C4C2×D29311yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C2×D29311yescharacteristic
174#107—2932no—
175#106—2932no—
176C4⋊C8—2932no—
177#103—2932no—
178#102—2932no—
179#102—2932no—
180#102—2932no—
181C22⋊C8—2931no—
182C22⋊C8—2931no—
183#97—2932no—
184C24—21no—
185C2×Q8—2931no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—2931no—
189C2×D4—5861no—
190C2×D4C22×D29312yes—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—5861no—
196C22×C4C22⋊D29311yescharacteristic
197C22×C4C22⋊D29311yescharacteristic
198C22×C4C22×D29311yescharacteristic
199SD16—5864no—
200D8—5864no—
201C2×C8—2932no—
202C2×C8—2932no—
203C4⋊C4—21no—
204C4⋊C4—2931no—
205C4⋊C4—2931no—
206C4⋊C4—5861no—
207C4⋊C4—5861no—
208C4⋊C4—5861no—
209C4⋊C4—5861no—
210C4⋊C4C22×D29312yes—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—5861no—
214C22⋊C4—5861no—
215C22⋊C4—5861no—
216C22⋊C4—5861no—
217C22⋊C4—5861no—
218C42—5861no—
219C42C22⋊D29311yescharacteristic
220C42C22⋊D29311yescharacteristic
221C42C22×D29311yescharacteristic
222C42C22×D29311yescharacteristic
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—5861no—
228C23C2×C22⋊D29311yescharacteristic
229Q8—5862no—
230D4—24no—
231D4—22no—
232D4—5862no—
233D4—11722no—
234D4#1798980214yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—5861no—
243C2×C4—5861no—
244C2×C4—5861no—
245C2×C4—11722no—
246C2×C4C2×C22⋊D29311yescharacteristic
247C2×C4C2×C22⋊D29311yescharacteristic
248C2×C4C2×C22⋊D29311yescharacteristic
249C2×C4C2×C22⋊D29311yescharacteristic
250C2×C4C2×C22⋊D29311yescharacteristic
251C2×C4C23×D29311yescharacteristic
252C8—5862no—
253C8—5862no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—11721no—
261C22—11721no—
262C22—11721no—
263C22#2262765012yes—
264C22C22×C22⋊D29311yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—11721no—
272C4—11721no—
273C4—11721no—
274C4C2×#1798980212yes—
275C2—22no—
276C2—44no—
277C2—23441no—
278C2#3403664011yescharacteristic
279C2C2×#2262765011yescharacteristic
280C2#3403692711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×C4×D4×C293C2
socleC22×C293C22×D4
prime radical#34036263C2
hypercenterC2×C4×D4D293
hypocenterC293#3114
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #34036663C2semidirect
2. #34036459C2semidirect
3. #34036442C2semidirect
4. #34036429C2semidirect
5. #34036344C2semidirect
6. #34036280C2semidirect
8. #34036239C2semidirect
9. #34036229C2semidirect
10. #34036186C2semidirect
11. C2×C4×D4×C293C2semidirect
15. #22627616C22semidirect
16. #22627612C22semidirect
20. C4×Dic586C22semidirect
21. C4×D1172C22semidirect
24. #22627557C22semidirect
25. #22627555C22semidirect
26. C4⋊#14556873C22semidirect
27. #22627547C22semidirect
30. #22627544C22semidirect
33. #22627535C22semidirect
140. C293#3114semidirect
143. C2×C4×D4D293semidirect

Maximal subgroups

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

subgroupindex
#340366632
#340364592
#340364422
#340364292
#340363442
#340362802
#340362632
#340362392
#340362292
#340361862
C2×C4×D4×C2932
#3114293