Finite Group Databasebeta

← #2003×C151 #34065335

Subgroups — #2003×C151 #34065335

Order 19328.

382 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 92 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×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic
2#536×C151C211yesmaximal, characteristic, complemented
3C2×#124×C151C211yesmaximal, characteristic, complemented
4C2×#104×C151C211yesmaximal, characteristic, complemented
5#418×C151C211yesmaximal, characteristic, complemented
6C2×#101×C151C211yesmaximal, characteristic, complemented
7#339×C151C211yesmaximal, characteristic, complemented
8C2×#41×C151C2211yescharacteristic
9C22×Q8×C151C2211yescharacteristic
10C22×D4×C151C2211yescharacteristic
11AGL(1,ℤ/8)×C151—22no—
12AGL(1,ℤ/8)×C151—22no—
13C2×SD16×C151—21no—
14C2×D8×C151—21no—
15C2×M16×C151C2211yescharacteristic
16C2×M16×C151C2211yescharacteristic
17C4⋊Q8×C151—21no—
18#124×C151—22no—
19#124×C151—21no—
20#124×C151—22no—
21#123×C151—22no—
22C22⋊Q8×C151—22no—
23#117×C151C2211yescharacteristic
24C2×C22⋊C4×C151—22no—
25C2×C42×C151C2211yescharacteristic
26#104×C151—22no—
27#102×C151—22no—
28#101×C151—22no—
29C24×C151—21no—
30#41×C151—21no—
31#41×C151—21no—
32#41×C151—21no—
33#41×C151—21no—
34C2×Q8×C151—21no—
35C2×Q8×C151—21no—
36C2×Q8×C151—21no—
37C2×Q8×C151—21no—
38C2×Q8×C151—21no—
39C2×Q8×C151—21no—
40C2×Q8×C151D411yescharacteristic
41C2×D4×C151—21no—
42C2×D4×C151—21no—
43C2×D4×C151—21no—
44C2×D4×C151—21no—
45C2×D4×C151—21no—
46C2×D4×C151—21no—
47C2×D4×C151D411yescharacteristic
48C2×D4×C151D412yes—
49C22×C4×C151—21no—
50C22×C4×C151—21no—
51C22×C4×C151D412yes—
52C22×C4×C151C2311yescharacteristic
53SD16×C151—24no—
54D8×C151—24no—
55M16×C151—21no—
56M16×C151—21no—
57M16×C151—21no—
58M16×C151D412yes—
59C2×C8×C151—21no—
60C2×C8×C151—21no—
61C4⋊C4×C151—24no—
62C4⋊C4×C151D412yes—
63C22⋊C4×C151—28no—
64C22⋊C4×C151—24no—
65C22⋊C4×C151—21no—
66C42×C151—21no—
67C42×C151—21no—
68C42×C151D412yes—
69C23×C151—22no—
70C23×C151—21no—
71C23×C151—44no—
72C23×C151—41no—
73C23×C151—41no—
74C23×C151C2×D411yescharacteristic
75Q8×C151—21no—
76Q8×C151—21no—
77Q8×C151—41no—
78Q8×C151—41no—
79Q8×C151—41no—
80Q8×C151—41no—
81D4×C151—21no—
82D4×C151—22no—
83D4×C151—21no—
84D4×C151—22no—
85D4×C151—41no—
86D4×C151—41no—
87D4×C151—41no—
88D4×C151—41no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—21no—
93C2×C4×C151—22no—
94C2×C4×C151—22no—
95C2×C4×C151—42no—
96C2×C4×C151—41no—
97C2×C4×C151—41no—
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151C2×D411yescharacteristic
100C2×C4×C151C2×D411yescharacteristic
101C2×C4×C151C2×D411yescharacteristic
102C2×C4×C151C2×D411yescharacteristic
103C2×C4×C151#4111yescharacteristic
104C8×C151—22no—
105C8×C151—41no—
106C22×C151—22no—
107C22×C151—44no—
108C22×C151—41no—
109C22×C151—42no—
110C22×C151—42no—
111C22×C151—82no—
112C22×C151—82no—
113C22×C151#12011yescharacteristic
114C22×C151#12011yescharacteristic
115C22×C151#12111yescharacteristic
116C4×C151—42no—
117C4×C151—42no—
118C4×C151—41no—
119C4×C151—42no—
120C4×C151#12011yescharacteristic
121C4×C151#12111yescharacteristic
122C4×C151#12111yescharacteristic
123C4×C151#12711yescharacteristic
124C2×C151—21no—
125C2×C151—21no—
126C2×C151—81no—
127C2×C151—82no—
128C2×C151#39211yescharacteristic
129C2×C151#45412yes—
130C151#200311yescharacteristic, direct product factor, Sylow
131#2003C15111yesmaximal, characteristic, direct product factor, Sylow
132C2×AGL(1,ℤ/8)C2×C15111yescharacteristic
133#536C2×C15111yescharacteristic, complemented
134C2×#124C2×C15111yescharacteristic, complemented
135C2×#104C2×C15111yescharacteristic, complemented
136#418C2×C15111yescharacteristic, complemented
137C2×#101C2×C15111yescharacteristic, complemented
138#339C2×C15111yescharacteristic, complemented
139C2×#41C22×C15111yescharacteristic
140C22×Q8C22×C15111yescharacteristic
141C22×D4C22×C15111yescharacteristic
142AGL(1,ℤ/8)—22no—
143AGL(1,ℤ/8)—22no—
144C2×SD16—21no—
145C2×D8—21no—
146C2×M16C22×C15111yescharacteristic
147C2×M16C22×C15111yescharacteristic
148C4⋊Q8—21no—
149#124—22no—
150#124—21no—
151#124—22no—
152#123—22no—
153C22⋊Q8—22no—
154#117C22×C15111yescharacteristic
155C2×C22⋊C4—22no—
156C2×C42C22×C15111yescharacteristic
157#104—22no—
158#102—22no—
159#101—22no—
160C24—21no—
161#41—21no—
162#41—21no—
163#41—21no—
164#41—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8D4×C15111yescharacteristic
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4D4×C15111yescharacteristic
179C2×D4D4×C15112yes—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4D4×C15112yes—
183C22×C4C23×C15111yescharacteristic
184SD16—24no—
185D8—24no—
186M16—21no—
187M16—21no—
188M16—21no—
189M16D4×C15112yes—
190C2×C8—21no—
191C2×C8—21no—
192C4⋊C4—24no—
193C4⋊C4D4×C15112yes—
194C22⋊C4—28no—
195C22⋊C4—24no—
196C22⋊C4—21no—
197C42—21no—
198C42—21no—
199C42D4×C15112yes—
200C23—21no—
201C23—22no—
202C23—44no—
203C23—41no—
204C23—41no—
205C23C2×D4×C15111yescharacteristic
206Q8—21no—
207Q8—21no—
208Q8—41no—
209Q8—41no—
210Q8—41no—
211Q8—41no—
212D4—21no—
213D4—22no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—41no—
219D4—41no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4C2×D4×C15111yescharacteristic
230C2×C4C2×D4×C15111yescharacteristic
231C2×C4C2×D4×C15111yescharacteristic
232C2×C4C2×D4×C15111yescharacteristic
233C2×C4C2×D4×C15111yescharacteristic
234C2×C4#41×C15111yescharacteristic
235C8—22no—
236C8—41no—
237C22—22no—
238C22—44no—
239C22—41no—
240C22—42no—
241C22—42no—
242C22—82no—
243C22—82no—
244C22#120×C15111yescharacteristic
245C22#120×C15111yescharacteristic
246C22#121×C15111yescharacteristic
247C4—42no—
248C4—42no—
249C4—41no—
250C4—42no—
251C4#120×C15111yescharacteristic
252C4#121×C15111yescharacteristic
253C4#121×C15111yescharacteristic
254C4#127×C15111yescharacteristic
255C2—21no—
256C2—21no—
257C2—82no—
258C2—81no—
259C2#392×C15111yescharacteristic
260C2#454×C15112yes—
subgroupG/H
center, socleC22×C151#120
commutator, Frattini, cosocleC22×C4C23×C151
prime radicalC2×AGL(1,ℤ/8)×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #536×C151C2semidirect
3. C2×#124×C151C2semidirect
4. C2×#104×C151C2semidirect
5. #418×C151C2semidirect
6. C2×#101×C151C2semidirect
7. #339×C151C2semidirect
130. C151#2003direct (N × H)
131. #2003C151direct (N × H)
133. #536C2×C151semidirect
134. C2×#124C2×C151semidirect
135. C2×#104C2×C151semidirect
136. #418C2×C151semidirect
137. C2×#101C2×C151semidirect
138. #339C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×AGL(1,ℤ/8)×C1512
#536×C1512
C2×#124×C1512
C2×#104×C1512
#418×C1512
C2×#101×C1512
#339×C1512
#2003151