Finite Group Databasebeta

← C151×#12974 #50317899

Subgroups — C151×#12974 #50317899

Order 38656.

408 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 114 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#2980×C151C211yesmaximal, characteristic
2#2132×C151C211yesmaximal, characteristic
3#1884×C151C211yesmaximal, characteristic
4#1858×C151C212yesmaximal, complemented
5#1395×C151C212yesmaximal, complemented
6#568×C151C2211yescharacteristic
7#532×C151C2211yescharacteristic
8#435×C151—22no—
9#435×C151—22no—
10#432×C151—21no—
11#430×C151—22no—
12#421×C151—21no—
13#413×C151C2212yes—
14#410×C151C2211yescharacteristic
15#408×C151—21no—
16#408×C151C2212yes—
17#356×C151C412yescomplemented
18#355×C151C412yescomplemented
19#341×C151—22no—
20#339×C151—21no—
21C2×#41×C151D411yescharacteristic
22C2×#41×C151C2311yescharacteristic
23#131×C151—42no—
24C2×M16×C151—21no—
25C2×M16×C151—21no—
26C2×M16×C151—22no—
27C2×M16×C151—22no—
28C2×M16×C151D412yes—
29C22×C8×C151—21no—
30C22×C8×C151D412yes—
31C4⋊Q8×C151C2×C411yescharacteristic
32#127×C151Q811yescharacteristic
33#124×C151C2×C411yescharacteristic
34#124×C151Q811yescharacteristic
35#121×C151—22no—
36C4×D4×C151—22no—
37#117×C151—21no—
38C2×C42×C151D411yescharacteristic
39#108×C151—44no—
40C4⋊C8×C151—21no—
41C4⋊C8×C151—21no—
42#104×C151—42no—
43#101×C151C2×C414yes—
44#100×C151—22no—
45#99×C151—22no—
46C22⋊C8×C151—22no—
47C22⋊C8×C151—22no—
48C22⋊C8×C151—22no—
49#97×C151—22no—
50#41×C151—41no—
51#41×C151—41no—
52#41×C151—41no—
53#41×C151—41no—
54C2×Q8×C151C4⋊C411yescharacteristic
55C2×Q8×C151C22×C411yescharacteristic
56C2×D4×C151—22no—
57C2×D4×C151—21no—
58C2×D4×C151C4⋊C411yescharacteristic
59C2×D4×C151C2×Q811yescharacteristic
60C2×D4×C151#4112yes—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151C2×D411yescharacteristic
64C22×C4×C151C2×D412yes—
65M16×C151—22no—
66M16×C151—24no—
67M16×C151—24no—
68M16×C151—42no—
69M16×C151—41no—
70M16×C151—42no—
71M16×C151—81no—
72C2×C8×C151—22no—
73C2×C8×C151—22no—
74C2×C8×C151—42no—
75C2×C8×C151—41no—
76C2×C8×C151—42no—
77C2×C8×C151—42no—
78C2×C8×C151—81no—
79C4⋊C4×C151—22no—
80C4⋊C4×C151—41no—
81C22⋊C4×C151—22no—
82C22⋊C4×C151—22no—
83C22⋊C4×C151—41no—
84C42×C151—21no—
85C42×C151—41no—
86C42×C151C4⋊C411yescharacteristic
87C42×C151C4⋊C411yescharacteristic
88C23×C151—21no—
89C23×C151C22⋊Q812yes—
90C23×C151#12311yescharacteristic
91Q8×C151—41no—
92Q8×C151—41no—
93D4×C151—41no—
94D4×C151—42no—
95D4×C151—41no—
96D4×C151—81no—
97D4×C151—82no—
98C2×C4×C151—21no—
99C2×C4×C151—22no—
100C2×C4×C151—21no—
101C2×C4×C151—22no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—41no—
106C2×C4×C151—41no—
107C2×C4×C151—81no—
108C2×C4×C151—81no—
109C2×C4×C151C2×C4⋊C411yescharacteristic
110C2×C4×C151C4×D412yes—
111C2×C4×C151#12011yescharacteristic
112C8×C151—44no—
113C8×C151—42no—
114C8×C151—42no—
115C8×C151—42no—
116C22×C151—21no—
117C22×C151—22no—
118C22×C151—41no—
119C22×C151—42no—
120C22×C151—42no—
121C22×C151—41no—
122C22×C151#38511yescharacteristic
123C4×C151—22no—
124C4×C151—21no—
125C4×C151—41no—
126C4×C151—41no—
127C4×C151—41no—
128C4×C151—161no—
129C4×C151B(4,𝔽2)11yescharacteristic
130C4×C151#45811yescharacteristic
131C2×C151—21no—
132C2×C151—41no—
133C2×C151—42no—
134C2×C151—81no—
135C2×C151#186711yescharacteristic
136#12974C15111yesmaximal, characteristic, direct product factor, Sylow
137C151#1297411yescharacteristic, direct product factor, Sylow
138#2980C2×C15111yescharacteristic
139#2132C2×C15111yescharacteristic
140#1884C2×C15111yescharacteristic
141#1858C2×C15112yescomplemented
142#1395C2×C15112yescomplemented
143#568C22×C15111yescharacteristic
144#532C22×C15111yescharacteristic
145#435—22no—
146#435—22no—
147#432—21no—
148#430—22no—
149#421—21no—
150#413C22×C15112yes—
151#410C22×C15111yescharacteristic
152#408—21no—
153#408C22×C15112yes—
154#356C4×C15112yescomplemented
155#355C4×C15112yescomplemented
156#341—22no—
157#339—21no—
158C2×#41D4×C15111yescharacteristic
159C2×#41C23×C15111yescharacteristic
160#131—42no—
161C2×M16—21no—
162C2×M16—21no—
163C2×M16—22no—
164C2×M16—22no—
165C2×M16D4×C15112yes—
166C22×C8—21no—
167C22×C8D4×C15112yes—
168C4⋊Q8C2×C4×C15111yescharacteristic
169#127Q8×C15111yescharacteristic
170#124C2×C4×C15111yescharacteristic
171#124Q8×C15111yescharacteristic
172#121—22no—
173C4×D4—22no—
174#117—21no—
175C2×C42D4×C15111yescharacteristic
176#108—44no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179#104—42no—
180#101C2×C4×C15114yes—
181#100—22no—
182#99—22no—
183C22⋊C8—22no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186#97—22no—
187#41—41no—
188#41—41no—
189#41—41no—
190#41—41no—
191C2×Q8C4⋊C4×C15111yescharacteristic
192C2×Q8C22×C4×C15111yescharacteristic
193C2×D4—22no—
194C2×D4—21no—
195C2×D4C4⋊C4×C15111yescharacteristic
196C2×D4C2×Q8×C15111yescharacteristic
197C2×D4#41×C15112yes—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4C2×D4×C15111yescharacteristic
201C22×C4C2×D4×C15112yes—
202M16—22no—
203M16—24no—
204M16—24no—
205M16—42no—
206M16—41no—
207M16—42no—
208M16—81no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—42no—
212C2×C8—41no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—81no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C22⋊C4—22no—
219C22⋊C4—22no—
220C22⋊C4—41no—
221C42—21no—
222C42—41no—
223C42C4⋊C4×C15111yescharacteristic
224C42C4⋊C4×C15111yescharacteristic
225C23—21no—
226C23C22⋊Q8×C15112yes—
227C23#123×C15111yescharacteristic
228Q8—41no—
229Q8—41no—
230D4—41no—
231D4—42no—
232D4—41no—
233D4—81no—
234D4—82no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C2×C4⋊C4×C15111yescharacteristic
247C2×C4C4×D4×C15112yes—
248C2×C4#120×C15111yescharacteristic
249C8—44no—
250C8—42no—
251C8—42no—
252C8—42no—
253C22—21no—
254C22—22no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22#385×C15111yescharacteristic
260C4—22no—
261C4—21no—
262C4—41no—
263C4—41no—
264C4—41no—
265C4—161no—
266C4B(4,𝔽2)×C15111yescharacteristic
267C4#458×C15111yescharacteristic
268C2—21no—
269C2—41no—
270C2—42no—
271C2—81no—
272C2#1867×C15111yescharacteristic
subgroupG/H
centerC4×C151B(4,𝔽2)
commutatorC2×Q8C22×C4×C151
Frattini, cosocleC2×#41C23×C151
socleC2×C151#1867
prime radical#532×C151C22
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C2×C4×C151 ◁ C2×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1858×C151C2semidirect
5. #1395×C151C2semidirect
17. #356×C151C4semidirect
18. #355×C151C4semidirect
136. #12974C151direct (N × H)
137. C151#12974direct (N × H)
141. #1858C2×C151semidirect
142. #1395C2×C151semidirect
154. #356C4×C151semidirect
155. #355C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2980×C1512
#2132×C1512
#1884×C1512
#1858×C1512
#1395×C1512
#12974151